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+Draft version February 1, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+A Pilot Study of Nulling in 22 Pulsars Using Mixture Modeling
+Akash Anumarlapudi
+,1 Joseph K. Swiggum
+,1, 2 David L. Kaplan
+,1 and Travis D. J. Fichtenbauer1
+1Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee, PO Box 413,
+Milwaukee, WI, 53201, USA
+2Dept. of Physics, 730 High St., Lafayette College, Easton, PA 18042, USA
+ABSTRACT
+The phenomenon of pulsar nulling, observed as the temporary inactivity of a pulsar, remains poorly
+understood both observationally and theoretically. Most observational studies that quantify nulling
+employ a variant of Ritchings (1976)’s algorithm which can suffer significant biases for pulsars where
+the emission is weak. Using a more robust mixture model method, we study pulsar nulling in a sample
+of 22 recently discovered pulsars, for which we publish the nulling fractions for the first time. These
+data clearly demonstrate biases of the former approach and show how an otherwise non-nulling pulsar
+can be classified as having significant nulls. We show that the population-wide studies that find a
+positive correlation of nulling with pulsar period/characteristic age can similarly be biased because
+of the bias in estimating the nulling fraction. We use our probabilistic approach to find the evidence
+for periodicity in the nulls in a subset of three pulsars in our sample. In addition, we also provide
+improved timing parameters for 17 of the 22 pulsars that had no prior follow-up.
+Keywords: Pulsar Nulling — Neutron Stars — Radio Astronomy
+1. INTRODUCTION
+Pulsar nulling, initially observed by Backer (1970a),
+is the absence of observed emission from a pulsar for
+one or more pulse periods.
+Observationally, the phe-
+nomenon of pulsar nulling remains poorly understood.
+It is clear that nulling is a broadband phenomenon, ob-
+served from 102 MHz (Davies et al. 1984) to 8.35 GHz
+(Honnappa et al. 2012).
+However, it is not firmly
+established whether nulling is simultaneous over this
+frequency range using a large sample of nulling pul-
+sars.
+Prior studies found contradictory conclusions.
+For example, observing over two frequency ranges, 50-
+140 MHz and 275-430 MHz, Taylor et al. (1975) found
+that nulls are simultaneous in two different pulsars (PSR
+B0031−07, PSR B0809+74), while Davies et al. (1984)
+found the evidence for excessive nulls in single pulses at
+102 MHz compared to 406 MHz in PSR B0809+74. A
+more recent study by Gajjar et al. (2014a) found that the
+nulls are highly coherent in three pulsars at four different
+frequencies — 313, 607, 1380, and 4850 MHz. In addi-
+Corresponding author: Akash Anumarlapudi
+aakash@uwm.edu
+tion, it is also not clear whether pulsars null randomly.
+Redman & Rankin (2009) and Gajjar et al. (2012) found
+that nulls might not occur randomly but might be clus-
+tered, where nulls and bursts tend to occur in groups,
+but the latter found that the null durations can be ran-
+dom. However, for many of these results the dependency
+of the nulling inferences on signal-to-noise ratio makes
+it hard to robustly interpret their findings.
+Although the formation of a pair cascade and the radi-
+ation from these accelerated pairs in the pulsar magne-
+tosphere is often invoked to explain the observed emis-
+sion from a pulsar (Ruderman & Sutherland 1975), a
+full theory of pulsar magnetospheres and its emission to
+explain the diverse morphology in pulse profiles and phe-
+nomenology is yet to be developed. As such, the theory
+of pulsar nulling remains largely speculative, though it is
+often attributed to one of two classes: i) inherent to the
+magnetosphere itself such as loss of coherence condition
+required for radio emission, e.g., Filippenko & Radhakr-
+ishnan (1982), or the depletion of pairs in the magneto-
+sphere themselves, e.g., Kramer et al. (2006) or ii) geo-
+metrical factors external to the magnetosphere such as
+the line of sight traversing through the ‘empty’ region
+between rotating emission carousels, e.g., Herfindal &
+Rankin (2007, 2009). Further progress may require ad-
+arXiv:2301.13258v1  [astro-ph.HE]  30 Jan 2023
+
+ID2
+Anumarlapudi et al.
+ditional observational data to understand how the prop-
+erties of nulling relate to the properties of the pulsars
+themselves.
+Nulling as a phenomenon may be related to other more
+extreme forms of intensity modulation, where the pulses
+can disappear for hours to months in the cases of rotat-
+ing radio transients (RRATs; McLaughlin et al. 2006)
+or intermittent pulsars (Kramer et al. 2006; Lyne 2009).
+However, the connection between these populations is
+not clear. Furthermore, pulsar nulling is often discussed
+in tandem with two other forms of single pulse vari-
+ations: mode changing – a phenomenon in which an
+otherwise stable pulse profile switches between multiple
+shapes (or modes) (Backer 1970b) and sub-pulse drift-
+ing – a phenomenon in which the single pulse phase
+shows a uniform periodic drift (Drake & Craft 1968).
+Regardless, in all of these cases the appearance of these
+phenomena can be limited by instrumental sensitivity:
+without enough sensitivity to probe single pulses at high
+significance, one cannot be certain whether the pulsar
+emission is truly missing during the nulls or the pulsar
+switches to an alternate mode with lower intensity. To-
+gether all three are often thought of as different represen-
+tatives of a larger underlying phenomenon of sub-pulse
+intensity variations (Lorimer & Kramer 2004).
+Nulling is usually quantified by the fraction of pulses
+where there is no discernible emission, called the Nulling
+Fraction (NF). NF can vary from 0 – in the case of stan-
+dard emission picture that shows no nulls – to 1, in the
+extreme case where the pulsar emission is visible only
+between long nulls (intermittent pulsars and RRATs).
+NF has been measured in roughly 8% of pulsars, but
+this has more to do with the lack of single pulse studies
+as opposed to nulling being restricted to a small subset
+of pulsars. This smaller data set of nulling pulsars is en-
+tirely restricted to normal (not recycled) pulsars, owing
+to the high sensitivity demands that would be needed
+to observe single pulses of millisecond pulsars (MSPs),
+although some recent studies (Rajwade et al. 2014) have
+been conducted in a sample of bright MSPs which did
+not find a signature of nulling with high confidence. In
+addition, there can be a bias against discovering normal
+pulsars which tend to have a high NF, or are intermit-
+tent. Hence the fraction (8%), can only be considered
+as a conservative lower limit.
+Such a small data set restricts our ability to infer
+population-wide properties, which might give clues to
+the origin of the phenomenon, and hence studies done
+thus far have not reached a consensus. An initial study
+done by Ritchings (1976) claimed a correlation between
+NF and pulsar period (with longer period pulsars expe-
+riencing higher NF) and also a stronger correlation with
+the characteristic age. Wang et al. (2007) also suggested
+a correlation with spin-down age, albeit qualitatively,
+with older pulsars experiencing higher NF, before even-
+tually crossing the death line.
+Konar & Deka (2019)
+found that there may be two different populations of
+pulsars separated by a NF of ∼ 40% but did not find
+correlations with any intrinsic pulsar properties, while
+Sheikh & MacDonald (2021) claimed that there is no
+strong evidence for the existence of two sub-populations.
+All of these studies may be significantly biased since the
+samples used are restricted to the pulsars that explicitly
+showed nulling.
+In general, most studies (Wang et al. 2007; Gajjar
+et al. 2012, 2014b,a; Herfindal & Rankin 2009) estimate
+NF using the methodology (or a variant) proposed by
+Ritchings (1976). But as Kaplan et al. (2018) demon-
+strated, this method can suffer strong biases in the case
+of weaker pulsars which can lead to overestimating the
+NF and classifying an otherwise standard weak pulsar
+as a nulling pulsar. This can also lead to systematic bi-
+ases in population inferences. In addition, Kaplan et al.
+(2018) proposed an alternate method in which they use
+Gaussian Mixtures to model the single pulse intensities
+and estimate the NF , and demonstrate the reliability of
+this method in accurately measuring the NF in weaker
+pulsars. In this study, we expand on the Gaussian Mix-
+ture Model (GMM) of Kaplan et al. (2018)1 to general-
+ize their method and apply it to a larger sample of 22
+pulsars2.
+Pulsars selected for this study were discovered as a
+part of the Green Bank North Celestial Cap (GBNCC)
+pulsar survey (Stovall et al. 2014) in 2-min drift scans
+at 350 MHz with a 100 MHz bandwidth and with data
+sampled every 81.92 µs. At 350 MHz the beam size is
+36′ (Full Width at Half Maximum; FWHM) and hence
+the astrometric precision prior to a coherent timing so-
+lution is limited by the beam size depending on the
+Signal-to-noise ratio (SNR) of the discovery candidate.
+These were later followed up at the Green Bank Tele-
+scope (GBT) and Arecibo Observatory (AO) to improve
+their timing solutions and establish their nulling char-
+acteristics.
+The structure of this paper is as follows: In Section 2,
+we detail our data acquisition and reduction methods,
+and provide updated timing solutions for the pulsars in
+this study. We then describe the mixture model and pro-
+vide our basic results in Section 3. Finally, we present
+1 As noted in Kaplan et al. (2018), a similar method may have
+been used in Arjunwadkar et al. (2014).
+2 All of our code is available at https://github.com/AkashA98/
+pulsar nulling
+
+Pulsar Nulling with Mixture Models
+3
+the implications of the results in Section 4 and conclude
+in Section 5.
+2. DATA ANALYSIS
+2.1. Observations and Data Reduction
+A sample of 22 recently discovered pulsars was selected
+for this pilot study if they showed any signs of intermit-
+tency in their discovery plots3. Data for 15 out of 22
+pulsars were collected using the 100-m Robert C. Byrd
+Green Bank Telescope (GBT) (hereafter referred to as
+the GBT sample), operating at 820 MHz with a band-
+width of 200 MHz, in 2 hr contiguous scans, with the
+primary aim of determining the pulsars’ nulling charac-
+teristics (project code 18A−436; PI: J. Swiggum). Data
+for another nine pulsars were collected at the 300-m
+William E. Gordon Arecibo Observatory (AO) operat-
+ing at 430 MHz over a bandwidth of 24 MHz, with the
+goals to both establish coherent timing solutions and de-
+termine nulling characteristics (project code P3436; PI:
+J. Swiggum) (hereafter referred to as the AO sample).
+Two pulsars in our sample, PSR J0414+31, and PSR
+J1829+25, were observed at both observatories.
+Six of the 15 pulsars in the GBT sample already had
+coherent timing solutions (Lynch et al. 2018) and the
+data for these were collected in coherent search mode us-
+ing the Green Bank Ultimate Pulsar Processing Instru-
+ment (GUPPI; Ransom et al. 2009) with 128 frequency
+channels sampled at 10.24 µs and retaining full polar-
+ization information. The remaining nine pulsars had no
+prior follow-up campaigns and so we first improved their
+positions using gridding observations and then observed
+them in incoherent search mode with 2048 frequency
+channels sampled at 40.96 µs. Data for the AO sample
+were collected in coherent search mode using the Puerto
+Rico Ultimate Pulsar Processing Instrument4 (PUPPI),
+with 64 channels sampled at 40.96 µs, over a span of ∼
+six months to establish coherent timing solutions in ad-
+dition to studying the nulling properties. A summary of
+observations for each pulsar is provided in Tables 1 and
+2.
+Starting with the raw search mode data, we used
+dspsr (van Straten & Bailes 2011) to fold the data.
+We then used pazi, the interactive zapping routine in
+psrchive (van Straten et al. 2011) to remove radio fre-
+quency interference (RFI)-affected frequency channels
+and single pulses. For GBT data, we also made use of
+RFI scans taken at the observatory5, when available, to
+3 See the GBNCC discovery page:
+http://astro.phys.wvu.edu/
+GBNCC.
+4 http://www.naic.edu/puppi-observing/
+5 https://greenbankobservatory.org/rfi-gui-user-guide/
+Table 1. Times and durations of GBT ob-
+servations
+Pulsar
+Observations
+Total Time
+MJD (hr)
+(hr)
+J0054+6946
+58163 (2.00)
+2.00
+J0111+6624
+58163 (2.24)
+2.24
+J0325+6744
+58163 (1.52)
+2.00
+58164 (0.48)
+· · ·
+J0414+31a
+58164 (1.50)
+1.50
+J0614+83
+58164 (1.90)
+1.90
+J0738+6904
+58209 (2.00)
+2.00
+J1529−26
+58209 (1.50)
+1.50
+J1536−30
+58209 (1.50)
+1.50
+J1629+33
+58209 (1.50)
+1.50
+J1821+4147
+58209 (1.69)
+1.69
+J1829+25a
+58246 (1.50)
+1.50
+J1901−04
+58246 (1.50)
+1.50
+J2040−21
+58246 (1.50)
+1.50
+J2131−31
+58246 (0.33)
+0.33
+J2310+6706
+58246 (1.75)
+1.75
+Note—For each pulsar we give the individual
+Modified Julian Date (MJD) and duration of
+each session, as well as the total observing
+time.
+aThis pulsar was observed at both AO and
+GBT
+identify the frequency bands that are affected by RFI,
+which are otherwise not obvious visually. In some cases,
+we found that one of the polarization channels was per-
+sistently affected by RFI, and in such cases we excluded
+data from that polarization channel at the cost of SNR.
+Fortunately, this did not have a significant impact on
+the determination of the nulling fractions. Some of the
+AO data had periodic “drop-outs” in the data with sub-
+millisecond periodicity at zero dispersion measure (DM),
+caused by data rate overflow during the observations.
+We cleaned these “drop-outs” by replacing the data with
+NaN values and being careful to exclude those when fold-
+ing/averaging.
+After cleaning the RFI, both for tim-
+ing and estimating nulling, we averaged polarizations to
+measure the total intensity.
+2.2. Timing
+For the 16 pulsars in our sample that had no prior
+follow-up, we first tried to improve the timing parame-
+ters. We used paas from psrchive (van Straten et al.
+2011) to make a standard template and then used pat
+
+4
+Anumarlapudi et al.
+Table 2. Times and durations of Arecibo observations
+Pulsar
+Observations
+Total Time
+MJD (hr)
+(hr)
+J0355+28
+58890 (0.25), 58922 (0.33)
+2.95
+58924 (0.42), 58928 (0.39)
+· · ·
+58936 (0.39), 58951 (0.39)
+· · ·
+58982 (0.39), 59013 (0.39)
+· · ·
+J0414+31a
+58890 (0.50), 58922 (0.38)
+3.46
+58924 (0.50), 58928 (0.35)
+· · ·
+58936 (0.30), 58951 (0.40)
+· · ·
+58982 (0.63), 59013 (0.40)
+· · ·
+J1822+02
+58941 (0.22), 58968 (0.17)
+1.55
+58970 (0.17), 58974 (0.17)
+· · ·
+58981 (0.17), 59000 (0.33)
+· · ·
+59029 (0.17), 59063 (0.17)
+· · ·
+J1829+25a
+58852 (0.17), 58941 (0.17)
+1.03
+58968 (0.14), 58970 (0.11)
+· · ·
+58974 (0.11), 58981 (0.11)
+· · ·
+59029 (0.11), 59063 (0.11)
+· · ·
+J1904+33
+58852 (0.17), 58882 (0.17)
+1.34
+58941 (0.17), 58968 (0.14)
+· · ·
+58970 (0.14), 58974 (0.14)
+· · ·
+58981 (0.14), 59029 (0.14)
+· · ·
+59063 (0.14)
+· · ·
+J1928+28
+58852 (0.17), 58882 (0.17)
+1.98
+58941 (0.17), 58968 (0.14)
+· · ·
+58970 (0.17), 58974 (0.17)
+· · ·
+58981 (0.17), 59000 (0.50)
+· · ·
+59029 (0.17), 59063 (0.17)
+· · ·
+J1941+02
+58852 (0.17), 58882 (0.17)
+1.5
+58912 (0.14), 58941 (0.17)
+· · ·
+58968 (0.14), 58970 (0.14)
+· · ·
+58974 (0.14), 58981 (0.10)
+· · ·
+59029 (0.17), 59063 (0.17)
+· · ·
+J2000+29
+58852 (0.39), 58882 (0.17)
+1.83
+58941 (0.10), 58968 (0.14)
+· · ·
+58970 (0.14), 58974 (0.14)
+· · ·
+58981 (0.14), 59000 (0.33)
+· · ·
+59029 (0.14), 59063 (0.14)
+· · ·
+J2044+28
+58852 (0.17), 58882 (0.17)
+1.18
+58968 (0.07), 58970 (0.14)
+· · ·
+58974 (0.14), 58981 (0.14)
+· · ·
+59000 (0.07), 59029 (0.14)
+· · ·
+59063 (0.14)
+· · ·
+aThis pulsar was observed at both AO and GBT
+to extract the Times of Arrival (TOAs) from the data.
+For the GBT data, our goal was to improve the spin fre-
+quency (F0) and DM measurements since we had only
+2 hour scan at a single epoch for each source. For the
+AO data, the data spanned ∼3–6 months depending on
+the pulsar and hence we can generate a phase-connected
+solution. However, the relatively narrow bandwidth of
+the observations (24 MHz) restricted our ability to fit
+for DM using sub-banded TOAs and hence we used the
+DM of the discovery candidate found on the GBNCC
+discovery page.
+The timing solutions for all the pulsars in this study
+are given in Table 3. For pulsars observed at GBT we
+improved the positions through gridding, and F0 and
+DM estimates through timing.
+For pulsars observed
+at AO, we improved the gridded positions, F0 and the
+frequency derivative F1 = ˙F0 through coherent timing.
+For the two overlapping pulsars observed at both GBT
+and AO, a timing solution was obtained by combining
+the TOAs from both observatories. In the case of pul-
+sars observed at AO for only ∼3 months (J0355+28,
+J0414+31, J1822+02), and pulsars where a combina-
+tion of low SNR and nulling resulted in few TOAs with
+SNR > 8 (J1928+28), it is difficult to estimate both po-
+sition and F1 precisely (they are highly covariant). In
+such cases, we rely on the
+F-statistic, given by
+F = (χ2
+0 − χ2)/(p − p0)
+χ2/p
+where χ2
+0 and χ2 are the chi-squared values of the timing
+residuals, and p0 and the p are the degrees of freedom
+before and after the addition of F1 (or any additional
+parameter(s), in general). This F-statistic follows an F-
+distribution (Lomax 2007) and hence we include F1 in
+the fit if the improvement in the goodness of fit (χ2) due
+to F1 is <1% by chance. The resulting timing residuals
+are shown in Figure 1.
+2.3. ON/OFF histograms
+Once we had improved the timing solution, we used
+dspsr in single pulse mode to generate single pulses for
+all scans and used psradd, from psrchive, to phase
+align pulses from different scans after cleaning the data
+for RFI. We then averaged the data along the polariza-
+tion and frequency axes to obtain the pulse intensity of
+the single pulses as a function of the rotational phase
+and generated single pulse stacks such as that shown in
+Figure 2.
+The most important aspect in estimating the nulling
+fraction is determining the “ON”-pulse and “OFF”-
+
+Pulsar Nulling with Mixture Models
+5
+Table 3. Timing Parameters for the GBNCC pulsars used to study nulling
+Pulsar
+Position (J2000)
+Period
+Period derivative
+DM
+RA
+RA error
+DEC
+DEC error
+(′′)
+(′′)
+(s)
+(10−15 s/s)
+(pc/cm3)
+GBT sample
+J0054+6946a
+00h 54m 59.s1
+00.1
++69◦ 46′ 16.′′8
+00.0(3)
+0.832911328744(4)
+−0.7194(8)
+116.52(5)
+J0111+6624a
+01h 11m 21.s9
+01.7
++66◦ 24′ 10.′′9
+00.6
+4.3018721007(3)
+−8.4(2)
+111.20(3)
+J0325+6744a
+03h 25m 05.s1
+00.3
++67◦ 44′ 59.′′4
+00.1
+1.36467876728(1)
+−1.553(9)
+65.28(5)
+J0414+31b
+04h 14m 35.s6
+02.6
++31◦ 38′ 35.′′4
+25.3
+1.0805116(1)
+−3.6(5)
+64.64(3)
+J0614+83c
+06h 14m 03.s4
+34.6
++83◦ 13′ 46.′′2
+34.6
+1.03918794(5)
+· · ·
+44.2(1)
+J0738+6904a
+07h 38m 22.s6
+00.5
++69◦ 04′ 20.′′0
+00.3
+6.8276928023(5)
+−26.97(4)
+17.22(2)
+J1529−26c
+15h 29m 07.s2
+38.9
+−26◦ 26′ 35.′′5
+38.9
+0.79857094(5)
+· · ·
+44.7(1)
+J1536−30c
+15h 36m 33.s4
+17.3
+−30◦ 06′ 14.′′4
+17.3
+0.190084143(9)
+· · ·
+63.40(7)
+J1629+33c
+16h 29m 22.s6
+99.2
++33◦ 23′ 35.′′9
+99.2
+1.5247311(3)
+· · ·
+34.8(5)
+J1821+4147a
+18h 21m 52.s3
+00.1
++41◦ 47′ 02.′′6
+00.0(4)
+1.26185719(3)
+−1.7292(9)
+40.63(5)
+J1829+25b
+18h 30m 31.s8
+01.8
++25◦ 08′ 00.′′4
+01.4
+2.85769207(9)
+−1.9(4)
+73.64(9)
+J1901−04c
+19h 01m 37.s1
+62.0
+−04◦ 54′ 44.′′9
+62.0
+1.8255459(8)
+· · ·
+105.4(9)
+J2040−21c
+20h 40m 40.s6
+09.7
++21◦ 52′ 51.′′6
+09.7
+0.562564125(4)
+· · ·
+23.77(1)
+J2131−31c
+21h 31m 30.s9
+65.9
+−31◦ 32′ 53.′′4
+65.9
+3.32537(3)
+· · ·
+31.753
+J2310+6706a
+23h 10m 42.s1
+02.9
++67◦ 06′ 52.′′1
+00.9
+1.944788973(1)
+−0.06(5)
+97.7(2)
+AO sample
+J0355+28
+03h 55m 22.s8
+00.4
++28◦ 38′ 50.′′1
+00.8
+0.36492919909(3)
+· · ·
+48.788
+J0414+31b
+04h 14m 35.s6
+02.6
++31◦ 38′ 35.′′4
+25.3
+1.0805116(1)
+−3.6(5)
+64.64(3)
+J1822+02
+18h 22m 43.s6
+01.4
++02◦ 28′ 53.′′8
+01.2
+1.5081132778(9)
+· · ·
+103.22
+J1829+25b
+18h 30m 31.s8
+01.8
++25◦ 08′ 00.′′4
+01.4
+2.85769207(9)
+−1.9(4)
+73.64(9)
+J1904+33
+19h 04m 40.s2
+00.2
++33◦ 58′ 25.′′9
+00.1
+0.417032327(1)
+−0.247(5)
+81.139
+J1928+28
+19h 27m 58.s4
+01.1
++28◦ 59′ 12.′′4
+01.0
+1.0630373062(5)
+· · ·
+79.34
+J1941+02
+19h 40m 34.s1
+00.8
++02◦ 39′ 21.′′7
+01.0
+1.23229077(1)
+−0.18(9)
+87.478
+J2000+29
+20h 00m 16.s5
+00.4
++29◦ 20′ 07.′′6
+00.1
+3.07377646(2)
+−37.37(8)
+132.62
+J2044+28
+20h 43m 36.s9
+00.4
++28◦ 28′ 37.′′3
+00.2
+1.61816650(1)
+−3.99(4)
+90.169
+Note—Quantities in parentheses are 1σ uncertainties on the last digit.
+aCoherent timing solutions are given in Lynch et al. (2018)
+b Timing solution is obtained by combining AO and GBT data.
+c Astrometric positions are estimated from gridding and the positional uncertainties are estimated from the beam size (15′)
+and the Signal to Noise Ratio (SNR)
+
+6
+Anumarlapudi et al.
+-1.0
+0
+1.0
+PSR J0355+28
+-3.0
+0
+3.0
+PSR J0414+31
+-11.0
+0
+11.0
+PSR J1822+02
+-3.0
+0
+3.0
+PSR J1829+25
+-1.0
+0
+1.0
+Residuals (ms)
+PSR J1904+33
+-2.0
+0
+2.0
+PSR J1928+28
+-2.0
+0
+2.0
+PSR J1941+02
+-2.0
+0
+2.0
+PSR J2000+29
+58800
+58850
+58900
+58950
+59000
+59050
+59100
+Modified Julian Date (MJD)
+-2.0
+0
+2.0
+PSR J2044+28
+-0.002
+0
+0.002
+-0.002
+0
+0.002
+-0.007
+0
+0.007
+-0.001
+0
+0.001
+-0.002
+0
+0.002
+Residuals (cycles)
+-0.001
+0
+0.001
+-0.001
+0
+0.001
+-0.0006
+0
+0.0006
+-0.001
+0
+0.001
+Figure 1. Timing residuals for the pulsars observed in the timing/nulling campaign at the AO. The red dots are the residuals
+(in milliseconds) from the timing model with the error bars representing the 1-σ error on the TOAs. The timing model solutions
+are presented in Table 3.
+
+Pulsar Nulling with Mixture Models
+7
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+200
+400
+Single pulses
+ON
+OFF
+−0.1
+0.0
+0.1
+0
+2
+0
+0.5
+1
+NP
+NP= 0.5
+Intensity
+(a) Single pulse stack of PSR J0325+6744
+−1
+0
+1
+2
+3
+4
+5
+Normalized Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Density
+OFF window
+ON window
+(b) Pulse intensity histogram for PSR J0325+6744
+Figure 2. (a)The bottom left panel shows the single pulse
+stack with the ON and OFF windows marked with black
+dashed lines. Null probabilities (NP) for every single pulse
+are calculated using the method described in §3.2 and are
+shown in the bottom right plot. The distribution of NP is
+shown in the top right panel where we can clearly see the
+evidence for two classes of pulses. The summed profile of
+all the single pulses with null probability < 0.5 is shown in
+the top left panel, while the summed profile for pulses with
+null probability > 0.5 is shown in the middle panel. (b) The
+pulse intensities in the OFF and ON windows are shown
+in blue and orange histograms.
+The presence of excessive
+counts in the ON histogram (the null component) at the
+background noise level separated from a second component
+at higher intensities (the emission component) is evidence for
+the nulling behavior.
+pulse phase windows. The single pulse intensities in the
+“OFF”-pulse window should be entirely due to radiome-
+ter noise, while the intensities in the “ON”-pulse window
+should be the sum of the radiometer noise component
+(same as the “OFF”-pulse window) and the pulsar emis-
+sion component. We first generated the average pulse
+profile to visually select on and off windows of the same
+widths. We then fit a sixth-order polynomial as a func-
+tion of pulse phase to each single pulse (similar to Rosen
+et al. 2013; Lynch et al. 2013; Kaplan et al. 2018) after
+masking the ON/OFF windows to remove any trends
+and construct a flat baseline. We recorded the ON/OFF
+intensities as the sum of the baseline-subtracted inten-
+sities across the windows. Finally, we constructed his-
+tograms of the ON/OFF intensities which we used to
+determine the nulling properties.
+Figure 2 shows the
+single pulse intensity distribution in the ON/OFF win-
+dow. The OFF histogram can be accurately described
+by a single component (Gaussian noise), but the ON
+histogram can have multiple components — “null” and
+“emission” components. The presence of nulling man-
+ifests in the ON histogram as an excess of samples at
+levels consistent with the OFF component, which we
+refer to as the null component. The residual distribu-
+tion, after removing the null component, is supposed to
+be a realization of pulsar’s emission distribution (here-
+after referred to as ‘emission’ component). The emission
+component can be a single distribution or a combination
+of multiple distributions. The ON distribution can be
+thought of as the sum of the null and the emission com-
+ponents.
+3. METHODS & RESULTS
+3.1. Determining Nulling Frations
+As demonstrated by Kaplan et al. (2018), Ritchings’
+method can give biased estimates for NF (hereafter re-
+ferred as NFr) in pulsars where the emission compo-
+nent is close to the noise level. Therefore, following Ka-
+plan et al. (2018) we adopt a method which models the
+ON/OFF histograms using a mixture model (MM). This
+means that the intensities x can be considered as ran-
+dom draws from the probability density function (PDF)
+p(x|¯θ) =
+m
+�
+n=1
+cn Fn(x|{θn}),
+(1)
+where the Fn functions are the individual probability
+density functions parameterized by the set {θn}, cn are
+the weights. In the case where all the Fn functions are
+the same and are normal distributions
+Fn(x; µn, σn) = N(x; µn, σn) =
+1
+√
+2πσn
+e− 1
+2(
+x−µn
+σn )
+2
+,
+where {µn} and {σn} are the means and standard devia-
+tions of component n, this reduces to a Gaussian mixture
+model (GMM), but more general models are considered.
+
+8
+Anumarlapudi et al.
+There is an additional constraint that the weights cn add
+to one:
+m
+�
+n=1
+cn = 1,
+which comes from the normalization of the PDF, which
+leaves the total number of free parameters to be deter-
+mined as �m
+n=1 dim({θn}) model parameters, and m−1
+latent parameters.
+In general, the OFF histogram can be well-described
+by a Gaussian as expected of radiometer noise (assum-
+ing that RFI has been sufficiently removed), and this is
+what we observe in our data. The emission component
+usually can be described by a single Gaussian as well.
+However, there are cases when it deviates from a single
+Gaussian component. More than one component is a
+possibility considered in Kaplan et al. (2018), which can
+be tested against the single-component model through a
+model comparison test. However, we also consider non-
+Gaussian models here. Specifically, multi-path propaga-
+tion of the pulses through the interstellar medium (ISM)
+(Smith 1973; Bhat et al. 2003; Lorimer & Kramer 2004),
+can result in the emission distribution having long tails
+towards higher intensities. This effect can be reasonably
+well described by the intensity distribution
+F(x; µ, σ, τ) = 1
+2τ exp
+� σ2
+2τ 2
+�
+exp
+�
+−x − µ
+τ
+�
+erfc
+�
+−x − (µ + σ2/τ)
+√
+2σ
+�
+(2)
+which is a convolution of a Gaussian N(x; µ, σ) and a
+one-sided exponential 1
+τ exp(−x/τ)U(x), where U(x) is
+the Heaviside or step function, erfc(x) is the complemen-
+tary error function, and τ is the decay time of the ex-
+ponential (McKinnon 2014). Hence we try to model the
+emission component using multi-component Gaussians
+and Gaussians with exponential tails and rank them us-
+ing their Bayesian Information Criterion (BIC) values
+to choose the best-fit model.
+We employ the scikit-learn Gaussian mixture
+model (Pedregosa et al. 2011) to derive an initial fit for
+the ON and OFF histograms. This is based on the ex-
+pectation–maximization (EM) algorithm, in which pa-
+rameters are estimated by maximizing the likelihood
+function L(data | ¯θ) (see Ivezi´c et al. 2020, for details).
+This produces a very good fit for the OFF histogram.
+However, in the case of weaker pulsars where the emis-
+sion can be confused with the background, Kaplan et al.
+(2018) showed that this method can still fail in produc-
+ing a reliable fit for the null and emission components
+of the ON histogram simultaneously, although this bias
+can be small compared to the Ritchings’ algorithm. As
+such, a refined fit for the null and emission components
+can be obtained by performing a Markov-Chain Monte
+Carlo (MCMC) analysis.
+For MCMC analysis, the likelihood function is given
+by
+L(¯x|¯θ) =
+�
+i
+p(xi|¯θ)
+(3)
+following p(xi|¯θ) from Equation 1.
+The priors chosen are:
+• Initial Gaussian fit from the EM algorithm for the
+off-pulse mean and standard deviation
+• Uniform between the bounds dictated by the on-
+pulse intensities for the parameters governing the
+pulsar emission component
+• Dirichlet distribution for the m coefficients cm
+(Wilks 2008)
+We use the emcee (Foreman-Mackey et al. 2013) en-
+semble sampler to sample the posterior. We initialize
+32 walkers within a ±5σ range of the initial fit values
+of the parameters. To account for the finite correlation
+length of the chains and produce independent samples,
+we first let the walkers “burn-in” to erase their start-
+ing conditions, and we then let the walkers explore the
+parameter space until we have at least 100 independent
+samples for each walker.
+Figure (3, left column) shows the pulse intensity his-
+tograms for PSR J0325+6744: a pulsar in which the
+emission component is easily discernible from the noise;
+and PSR J1529−26: a pulsar where these two start to
+blend into each other. Looking at the null component in
+the ON histogram for the two pulsars, the evidence for
+nulling is clear in J0325+6744 while J1529−26 behaves
+like a non-nulling pulsar whose emission is weak. The
+blue, green and orange-filled regions show the fit for the
+OFF, null, and emission components respectively, and
+the black dotted line shows the overall fit for the ON
+component.
+The posteriors for the model parameters
+are presented in Figure (3, right column) with the point
+estimates (median6) of the NF from MM given in Ta-
+ble 4.
+For PSR J0325+6744, where the null and emission
+components are well separated (bright pulsars), our
+method yields a NF = 53.92 ± 0.81% while Ritchings’
+6 In the case of non-nulling pulsars where the distribution of NF
+is one-sided, the median will be over-estimated compared to the
+true value. Even so, the uncertainty on NF is larger than the
+difference between the median and mode and hence NF is still
+consistent with 0.
+
+Pulsar Nulling with Mixture Models
+9
+Table 4. Nulling properties of the GBNCC pulsars
+Pulsar
+Model
+NF
+NFr
+Null period
+Lengths
+Null
+Em.
+(%)
+(%)
+(pulse periods)
+GBT sample
+J0054+6946
+G3
+27.5±5.1
+36.8
+· · ·
+2
+3
+J0111+6624
+G2
+10.2±1.7
+17.9
+· · ·
+2
+7
+J0325+6744
+G2
+53.9±0.8
+55.1
+· · ·
+3
+4
+J0414+31
+G2
+27.5±1.9
+40.7
+28.4c
+2
+4
+J0614+83
+G2
+06.7±3.1
+52.3
+· · ·
+1-2a
+· · ·
+J0738+6904
+Eg2
+66.6±1.5
+64.9
+42.7c
+9
+4
+J1529−26
+G2
+05.4±4.3
+48.5
+· · ·
+1-2a
+· · ·
+J1536−30
+G2
+43.1±2.2
+57.5
+· · ·
+4
+J1629+33
+G2
+83.8±1.9
+83.9
+· · ·
+12
+1-2a
+J1821+4147
+G2
+00.0±0.6
+20.9
+· · ·
+1-2a
+· · ·
+J1829+25
+G2
+00.0±0.6
+07.8
+· · ·
+0b
+· · ·
+J1901−04
+G2
+13.9±4.1
+50.4
+1a
+· · ·
+J2040−21
+G2
+25.4±1.8
+42.4
+23.3c
+2
+5
+J2131−31
+G2
+49.8±8.6
+54.2
+· · ·
+3
+3
+J2310+6706
+Eg2
+54.1±2.7
+52.7
+3
+3
+AO sample
+J0355+28
+G2
+01.6±1.1
+30.3
+· · ·
+1-2a
+· · ·
+J0414+31
+G2
+33.0±0.7
+37.1
+28.4c
+2
+4
+J1822+02
+G2
+00.1±0.7
+09.3
+· · ·
+1a
+· · ·
+J1829+25
+G2
+00.0±0.6
+05.5
+· · ·
+0b
+· · ·
+J1904+33
+G2
+00.0±0.1
+09.4
+· · ·
+1a
+· · ·
+J1928+28
+G2
+47.6±2.4
+71.9
+· · ·
+3
+3
+J1941+02
+G2
+00.2±1.7
+31.1
+· · ·
+1-3a
+· · ·
+J2000+29
+G2
+19.3±1.1
+23.4
+· · ·
+1-2a
+3
+J2044+28
+G2
+15.2±0.9
+17.4
+· · ·
+1-2a
+6
+Note—Naming convention for the model represents the model used
+to describe the emission histogram (G=Gaussian, Eg=Exponentially
+modified Gaussian) followed by the number of components in the ON
+histogram.
+aWe find that in extreme cases (non-nulling/highly-nulling), one of the
+distributions is confined to very few bins and so we quote this range
+rather than fitting for it.
+b We find that there are no single pulses with NP>0.5.
+c We observe quasi-periodicity in these cases.
+method (see Ritchings 1976; Wang et al. 2007; Kaplan
+et al. 2018, for implementation) gives a comparable esti-
+mate of 55.01%. However in the case of a weaker pulsar,
+PSR J1529−26, where the emission component is closer
+to the background noise, our method gives a best-fit
+value of NF = 5.55 ± 4.4% compared to 48.1% given
+by the Ritchings’ method.
+The latter is significantly
+overestimated and can easily lead to (mis)classifying the
+source as a nulling pulsar, further illuminating the bias
+of Ritchings’ method in weaker pulsars.
+Full results for all the 23 pulsars, including the single
+pulse stacks, posteriors from the MCMC run and the
+resultant ON/OFF histogram model fits are shown in
+Appendix A.
+3.2. Nulling Correlations
+After determining the nulling properties we wish to
+know whether the locations and durations of nulls are
+completely random, or if there is any correlation be-
+tween different nulling and emission episodes in a pulsar.
+Specifically, given a single pulse that shows emission (or
+that nulls), how likely are we to see emission for the next
+pulse, and are there any patterns of longer duration?
+We test this using the probability of a null (the nulling
+“responsibility”) evaluated for each individual pulse,
+given by
+NPI =
+c0F0(I|{θ0})
+�m
+n=1 cn Fn(I|{θn}).
+(4)
+We divided the data into stacks of 256 pulses (similar to
+Ritchings 1976; Herfindal & Rankin 2009) to calculate
+more robust estimates and to be less sensitive to long-
+term variations like scintillation and system temperature
+changes, and use equation 4 to calculate the probabil-
+ity of a given single pulse being a null. We then looked
+for periodic signature by taking the Fourier transform
+(FT) within each stack and co-adding the power from all
+stacks incoherently. Figure 4 shows the resultant spec-
+trum for PSR J0414+31, in which a certain pattern of
+combination of emission and nulls seems to be periodic
+over ∼28 pulse periods. We estimate the significance of
+peaks in the stacked power spectra assuming that the
+null distribution from n stacks follows a χ2 distribution
+with 2n degrees of freedom (this assumes white noise).
+We see significant periodic or quasi-periodic (a signifi-
+cant broad peak in the power spectrum) signatures in a
+few other pulsars, and tabulate their periods in Table 4.
+In the case of precise period measurements, we estimate
+the uncertainty as described in Ransom et al. (2002).
+However, this only points to the periodic nature of
+a certain pattern of emission and nulls.
+To find how
+emissions and nulls are ‘bunched’, we look for the dis-
+tribution of continuous emissions and nulls, where we
+use NPI=0.5 to be the boundary between an emission
+and a null. Figure 5 shows the emission and null length
+
+10
+Anumarlapudi et al.
+−1
+0
+1
+2
+3
+4
+5
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+(a1) PSR J0325+6744 – NF = 53.92 ± 0.81% vs NFr =
+55.01%
+µ0
+µ0=-0.001
+2.10
+2.16
+2.22
+µ1
+µ1=2.183
+0.345
+0.360
+σ0
+σ0=0.355
+0.80
+0.85
+0.90
+σ1
+σ1=0.853
+−0.015
+0.000
+0.015
+µ0
+0.52
+0.54
+0.56
+NF
+2.10
+2.16
+2.22
+µ1
+0.345
+0.360
+σ0
+0.80
+0.85
+0.90
+σ1
+0.52
+0.54
+0.56
+NF
+NF=0.54
+(a2) Model parameter posteriors for PSR J0325+6744
+−5.0
+−2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+Raw Intensity
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+(b1) PSR J1529−26 – NF = 5.4 ± 4.4% vs NFr =48.5%
+µ0
+µ0=0.011
+1.05
+1.20
+µ1
+µ1=1.082
+1.3
+1.4
+σ0
+σ0=1.35
+1.30
+1.35
+1.40
+σ1
+σ1=1.389
+−0.06
+0.00
+0.06
+µ0
+0.08
+0.16
+NF
+1.05
+1.20
+µ1
+1.3
+1.4
+σ0
+1.30
+1.35
+1.40
+σ1
+0.08
+0.16
+NF
+NF=0.054
+(b2) Model parameter posteriors for PSR J1529−26
+Figure 3. Left (a1, b1) Two-component Gaussian model fits for the ON and OFF histograms. Individual ON/OFF histograms
+are shown in solid black lines. The blue, green and orange-filled regions shows the OFF, the null (NF × OFF) and the emission
+(ON − NF × OFF) components respectively, where this estimate of NF is obtained using the mixture model. The black dotted
+line shows the overall fit for the ON pulse distribution. Right (a2, b2) Corner plots for 2-component Gaussian fit to the ON/OFF
+histograms parameterized by the means {µ1, µ2}, standard deviations {σ1, σ2} and the nulling fraction NF. The dashed vertical
+lines are the quoted median point estimates of the parameters
+
+Pulsar Nulling with Mixture Models
+11
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Fourier frequency (in 1/P)
+0
+20
+40
+60
+80
+100
+120
+140
+160
+Power (arbitrary units)
+NP FFT (ON)
+NP FFT (OFF)
+analytical limit
+(a) PSR J0414+31 (GBT)
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Fourier frequency (in 1/P)
+0
+100
+200
+300
+400
+500
+Power (arbitrary units)
+NP FFT (ON)
+NP FFT (OFF)
+analytical limit
+(b) PSR J0414+31 (AO)
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Fourier frequency (in 1/P)
+0
+50
+100
+150
+200
+250
+Power (arbitrary units)
+NP FFT (ON)
+NP FFT (OFF)
+analytical limit
+(e) PSR J2040−21
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Fourier frequency (in 1/P)
+0
+20
+40
+60
+80
+Power (arbitrary units)
+NP FFT (ON)
+NP FFT (OFF)
+analytical limit
+(f) PSR J0738+6904
+Figure 4. Fourier transform of the null probability for the pulsars in our sample that show periodicity.
+Power combined
+incoherently from multiple stacks of 256 pulses is shown at 129 discrete frequencies (in the units of 1/pulse period) in the
+blue line. The orange curve shows the same for the OFF component (background noise) which can be used to eliminate any
+instrumental variations/artifacts and/or RFI. The black dotted line shows the upper limit that allows for 1 false positive in 1000
+trails, corresponding to a 99.9% confidence limit. The gray curves are the normalized power from the individual stacks (not to
+scale) that are used to look for quasi-periodicity. The value of the periodicities are given in Table 4
+
+12
+Anumarlapudi et al.
+0
+5
+10
+15
+20
+Pulse periods
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Normalized counts
+null lengths
+em. lengths
+null fit τem=0.49
+null fit τem=0.3
+Figure 5. Distribution of emission lengths and null lengths
+for J0414+31. The gray-filled and the black-open histograms
+show the distribution of null and emission episodes respec-
+tively.
+The orange curve shows an exponential fit for the
+emission length distribution with decay constant τem=0.3,
+whereas the blue curve shoes the same for the null length
+distribution with τnull=0.49.
+distributions for the single pulses of PSR J0414+31. We
+find that these distributions can be well described by an
+exponential distribution (p(x) = τ −1 exp(−x/λ)), where
+x is the null or emission length and the mean duration
+of the episode is λ. We find that for PSR J0414+31, the
+emission episodes have a characteristic period of four
+periods, whereas the nulls are two periods long, which
+is consistent with the observed nulling fraction of ∼ 33%
+(see Table 4). We repeat this for all the pulsars and the
+results are tabulated in Table 4.
+3.3. Sub-pulse Drifting
+Beyond nulling, we also look for any correlations be-
+tween nulling and sub-pulse drifting. Drifting is usually
+characterized by two periods: the drifting period P3,
+defined as the period for which the pulse is seen at the
+same longitude (phase), and P2, the spacing between
+two sub-pluses within the same single pulse (see Figure
+6). To estimate both, we prepared the data by selecting
+only the on-pulse window of data (np phase bins) for all
+the single pulses (ns single pulses). We then calculated
+Longitude Resolved Fluctuation Spectra (LRFS, Backer
+1970c), where we take a 1-D Fourier transform of the
+(ns × np) data along the ns axis. Figure 6 shows one
+of the two pulsars in our sample, J1822+02, that shows
+clear signs of drifting. A period P3 of ∼ 28 pulse periods
+and P2 of ∼ 35/1024 pulse periods can be clearly seen.
+We also find the evidence for drifting in PSR J1829+25
+(see figure 7), with a P3 of ∼ three pulse periods and a
+P2 of 1/128 pulse periods, with similar inferences in the
+data from both AO and GBT.
+4. DISCUSSION
+4.1. Biases in Nulling Models
+Kaplan et al. (2018) demonstrated the bias of Ritch-
+ings’ method for weaker pulsars through simulated data,
+where the mixture model was able to recover the true in-
+jected nulling fraction. They also showed that for Gaus-
+sian mixtures, an analytical correction can correct the
+biased estimate of Ritchings’ method to find the true
+value. We extend the same technique using our sam-
+ple of 22 pulsars. Figure 8 shows the comparison of the
+NF estimates derived using both methods.
+The blue
+points show the NF estimate derived using Ritchings’
+algorithm (NFr), the orange points show NFr estimate
+corrected for the bias (as in Kaplan et al. 2018), and the
+green points show the NF derived using mixture model-
+ing. In the case of highly nulling pulsars, the contamina-
+tion of the null component from the emission component
+can be small, and both methods perform comparably.
+However, in the case of pulsars with small NF a system-
+atic bias can be seen as the pulsar emission component
+becomes blended with the background noise, and the
+fact that the green and orange points agree quite well
+demonstrates our confidence in estimating the bias in
+the Ritchings method and the utility of mixture models.
+4.2. Is the Nulling Fraction Correlated with Pulsar
+Properties?
+Comparing the nulling estimates from the mixture
+modelling and Ritchings’ method in Table 4, it can be
+seen that there can be significant differences between
+these estimates. Such a scenario can lead to significant
+biases in population-wide studies that look for corre-
+lation between nulling fraction and pulsar properties.
+Figure 9 shows the most complete list of nulling pulsars,
+extended from Konar & Deka (2019), on the P − ˙P dia-
+gram. We do not find any clear visual trends of NF with
+respect to period (P), spin-down rate ( ˙P), characteris-
+tic age (τc), or surface magnetic field (Bsurf), although
+we emphasize that most of the pulsars here (142/164)
+have their NF estimates derived using some variant of
+the Ritchings method.
+Our sample size of 22 pulsars is too small to derive
+reliable correlations. However, we can test the similar-
+ity/disparity in the correlations obtained using nulling
+estimates derived with mixture models versus the Ritch-
+ings algorihtm. We use the Spearman correlation test, a
+non-parametric correlation test to quantify any correla-
+tions between the relevant parameters (P/ ˙P/Bsurf/τc)
+and NF. Table 5 shows the correlation coefficients of
+nulling fraction with parameters of interest (P, ˙P, Bsurf,
+τc). In no case do we see an evidence for strong cor-
+relations but we can see large differences between these
+coefficients obtained using the NF derived using the two
+
+Pulsar Nulling with Mixture Models
+13
+0.1
+0.16
+0.21
+0.27
+0.33
+0.39
+Phase
+0
+50
+100
+150
+200
+250
+Singlepulse number
+P2
+P3
+0.21
+0.23
+0.25
+0.27
+0.29
+Pulse phase
+0.6
+0.8
+1.0
+Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Frequency (in units of 1/Period)
+0.25
+0.50
+0.75
+1.00
+Power
+Figure 6. Left: A stack of 300 single pulses of PSR J1822+02 clearly showing the sub-pulse drifting phenomenon. The drifting
+periods P2 and P3 are shown. Right: LFRS of the single pulse stack of J1822+02. The 2D spectrogram shows the Fourier
+transform of data along the axis of single pulses. The evidence of a single drifting frequency across the phase bins is evident
+from the spectrogram. The bottom panel shows the 2D spectrogram scrunched along the phase axis and the right-hand plot
+shows the same scrunched along the frequency axis.
+methods. We emphasize that the values of these have to
+be taken with a high degree of caution, given the relative
+sample size under study and the presence of outliers. In
+particular we find that PSR J2310+6706 turns out to be
+a strong outlier, especially in the τc and Bsurf space and
+this significantly affects the results (see Table 5), further
+illustrating the limitations of a small sample size.
+Previously, using a sample size (23) comparable to
+ours, Wang et al. (2007) qualitatively found that NF is
+related to age with older population experiencing larger
+nulling fractions. Ritchings (1976) found a positive cor-
+relation both with the pulsar period and age in a sample
+(32) slightly larger than the one in this study. However,
+as mentioned above those and most other nulling esti-
+mates in the literature are derived using some variant
+of Ritchings’ algorithm. Computing the Spearman coef-
+ficient for all of the archival sources we cannot confirm
+either correlation and suggest caution in interpreting re-
+sults using Ritchings’ algorithm.
+However, we also note that the source of this dispar-
+ity does not seem to be straightforward: For a sam-
+ple of pulsars with a given SNR, the energy per sin-
+gle pulse will be lower for pulsars with shorter peri-
+ods, which means that the NF estimates for the short-
+period pulsars should experience larger biases and have
+higher nulling fractions measured with the Richtings’
+method.
+Under the (overly simplistic) assumption of
+a uniform distribution of luminosity with period (cf.
+Faucher-Gigu`ere & Kaspi 2006; Bates et al. 2014), the
+correlation of inferred nulling fraction with period will
+then be negative which is contrary to the previous stud-
+ies.
+This suggests that the source of this bias is not
+simple and needs careful understanding of the under-
+Table 5. Spearman rank correlation coefficients for our sam-
+ple data set and archival data set.
+Parameter
+MM
+Ritchings
+Catalog
+P
+0.356
+0.008
+0.311
+0.314
+−0.064
+· · ·
+| ˙P|
+0.274
+0.035
+−0.013
+0.457
+0.057
+· · ·
+τc
+−0.353
+−0.088
+0.149
+−0.557
+−0.207
+· · ·
+Bsurf
+0.291
+−0.006
+0.110
+0.450
+0.071
+· · ·
+Note—Not all the pulsars in the sample have
+˙P measurements. Hence the sample size used
+for period is larger. The two rows for each pa-
+rameter correspond to the rank coefficients
+including and excluding PSR J2310+6706
+(see Figure 10).
+lying distribution of NF with pulsar properties and a
+larger sample of pulsars with more robust and unbiased
+NF estimates.
+4.3. Is Nulling Periodic?
+As shown in Section 3.2, we find that nulling appears
+periodic/quasi-periodic in a subset of pulsars, with their
+periods noted in Table 4. Herfindal & Rankin (2007,
+2009) also find evidence for such signatures and at-
+tributd this to the line of sight passing through a struc-
+tured rotating carousel. In addition we also find that
+
+14
+Anumarlapudi et al.
+0.36
+0.41
+0.45
+0.5
+0.55
+0.6
+0.65
+0.7
+0.75
+Pulse phase
+0
+20
+40
+60
+80
+100
+120
+140
+160
+Single pulses
+(a) AO data single pulse stack
+0.556
+0.56
+0.565
+0.57
+0.574
+Pulse phase
+0.25
+0.50
+0.75
+1.00
+Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Frequency (in units of (1/P))
+0.0
+0.5
+1.0
+Power
+(b) LRFS (AO data)
+0.36
+0.41
+0.45
+0.5
+0.55
+0.6
+0.65
+0.7
+0.75
+Pulse phase
+0
+25
+50
+75
+100
+125
+150
+175
+Single pulses
+(a) GBT data single pulse stack
+0.487
+0.492
+0.496
+0.5
+0.505
+Pulse phase
+0.4
+0.6
+0.8
+1.0
+Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Frequency (in units of (1/P))
+0.25
+0.50
+0.75
+1.00
+Power
+(b) LRFS (GBT data)
+Figure 7. Sub-pulse drifting in PSR J1829+25: The left panels shows the stack of single pulses, in the data taken at AO and
+GBT, which shows the signature of drifting phenomenon. The right panels shows the LRFS (see §3.3) of the single pulse stacks.
+Data from AO (top right) shows a strong feature with a periodicity ∼ 3 pulse periods. Data from GBT (bottom right) shows a
+quasi-periodic (broad) peak consistent with the period from AO data.
+in PSR J0414+31, which was observed at two differ-
+ent frequencies with different instruments, this period is
+the same. It should be noted that the frequency reso-
+lution here is ∼ 0.004 pulse period−1 (from the stacks of
+256 pulses) and so we will be insensitive to any changes
+that are finer than this. Although significant correla-
+tions can not be drawn from these periodicities given
+our sample size and the number of pulsars that show
+periodic nulling, the occurrence of such a phenomenon
+in modest set of pulsars in our sample suggests that this
+might not be uncommon and should be searched for in
+future data.
+5. CONCLUSIONS
+In this study, we have extended the Gaussian mixture
+model of Kaplan et al. (2018) to study nulling behav-
+ior in 22 pulsars, spanning a wider range of properties
+than in the initial paper but still not selected indepen-
+dent of nulling behavior. We find that all pulsars can
+be well-represented by mixture model, but we find that
+a single Gaussian is not sufficient to describe the emis-
+
+Pulsar Nulling with Mixture Models
+15
+0.2
+1.0
+1.3
+2.6
+6.5
+Emission component SNR
+0.0
+0.2
+0.4
+0.6
+0.8
+NF
+Uncorrected NFr
+Corrected NFr
+NF
+Figure 8. Comparison of NF estimates from Ritchings’ al-
+gorithm and mixture model as a function of pulsar emission
+component (significance; in units of σOFF). The blue error
+bars show the estimates from Ritchings’ algorithm while the
+orange error bars are from mixture model.
+The green er-
+ror bars are derived by estimating the systematic bias from
+the Ritchings’ method and clearly depict the bias in the cases
+where the emission component is weak compared to the back-
+ground.
+10−1
+100
+Period (s)
+10−18
+10−17
+10−16
+10−15
+10−14
+10−13
+10−12
+10−11
+Period derivative (s/s)
+109 yr
+107 yr
+105 yr
+1013 G
+1012 G
+1011 G
+ATNF catalog
+Archival NF
+This work
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Nulling Fraction
+Figure 9. Period-period derivative (P − ˙P) diagram high-
+lighting nulling pulsars.
+Shown in grey circles are all the
+pulsar from the ATNF catalog (Manchester et al. 2005), in
+colored circles are the archival nulling pulsars from Konar
+& Deka (2019) and in diamonds are the pulsars from this
+study. The contours represent lines of constant character-
+istic age τc and dipolar surface magnetic field (Bsurf). The
+color bar shows the nulling fraction which ranges from 0 to 1.
+No clear discernible trend of NF with any of P/ ˙P/Bsurf/τc
+is visible.
+sion component in some pulsars7.
+Similar to Kaplan
+et al. (2018), we find that previous methods used to
+estimate NF can suffer significant biases when the pul-
+sar emission is weak compared to the background noise.
+Such biases may lead to misinterpreting weak pulsars
+as nulling pulsars. We also show that these biases may
+lead to spurious correlations between the NF and pulsar
+properties in population-wide studies.
+Drawing on the more robust statistics that we calcu-
+late, we find that nulling can appear periodic, with three
+pulsars in our sample showing this behavior. Two pul-
+sars in our sample, PSR J1822+02 and PSR J1829+25,
+shows clear signs of sub-pulse drifting, and they have an
+inferred nulling fraction consistent with 0. In contrast,
+studies like Gajjar et al. (2014a); Davies et al. (1984)
+find sub-pulse drifting in pulsars that exhibit moderate
+nulling, indicating that sub-pulse drifting and nulling
+might be two independent manifestations of sub-pulse
+intensity variations. In all cases we look forward to us-
+ing larger, less-biased samples to more robustly explore
+the nulling population and seeing if it is related to other
+phenomenology.
+Two pulsars in our sample, PSR J0414+31 and PSR
+J1829+25, were observed at two different frequencies
+(430 MHz and 820 MHz), albeit not simultaneously.
+PSR J1829+25 has nulling estimates that agree at both
+frequencies, consistent with 0, but we find that PSR
+J0414+31, has NF estimates in tension at the ∼ 2σ
+level, with the NF higher at lower frequencies.
+Al-
+though it is hard to draw definite conclusions from these
+two pulsars since the observations are not simultane-
+ous, it emphasizes the need for simultaneous observa-
+tions at multiple frequencies (or across a larger band-
+width). Observing at 4 different frequencies (325, 610,
+1400, 4850 MHz), Gajjar et al. (2014a) find coherent
+nulling in three different pulsars whereas Bhat et al.
+(2007) find the evidence for null excess at lower frequen-
+cies in PSR B1133+16 further emphasizing the need for
+multi-frequency observations in a larger sample to find
+whether nulling is universally broadband.
+One of the pulsars in our sample (PSR J2310+6706)
+has a two-component profile with a faint leading peak in
+addition to the primary peak. The very low SNR of the
+leading component limits our ability to find a stringent
+estimate of the NF independent of the primary com-
+ponent, but we find that the NF values obtained from
+each component is consistent. Analyzing nulling charac-
+teristics in pulsars with multi-component pulse profiles
+7 PSR J0054+6946 is better described by 2 different emission com-
+ponents, one at lower amplitude and the other at higher ampli-
+tude, as seen in Figure 11.
+
+16
+Anumarlapudi et al.
+0
+2
+4
+6
+Period (s)
+0.0
+0.2
+0.4
+0.6
+0.8
+NF
+10−16
+10−15
+10−14
+Period derivative (s/s)
+107
+108
+109
+Characteristic Age (yr)
+J2310+6706
+1012
+1013
+Surface Magnetic field (G)
+J2310+6706
+Figure 10. Scatter plot showing the NF of the pulsars in this study vs their properties. It can be seen that the pulsars appear
+scattered in the P/ ˙P space. However, with the exclusion of PSR J2310+6706 which appears as an outlier in the τc/Bsurf space,
+a rough trend can be seen that of NF decreasing with the age τc and increasing with the surface magnetic field Bsurf. The
+correlation coefficients are given in Table 5.
+with a robust method like mixture modeling can provide
+insights into the simultaneous nulling in the different re-
+gions of the pulsar’s magnetosphere.
+So far we have only analyzed normal, non-recycled
+pulsars. Current sensitivity limitations restrict the sam-
+ple of nulling pulsars to normal pulsars (as is evident
+from Figure 9), while MSPs are largely unexplored. Ini-
+tial single pulse studies done by Rajwade et al. (2014)
+do not find any compelling evidence for nulling in MSPs.
+Using the mixture model technique, which does not suf-
+fer from the same biases at low signal-to-noise, for MSPs,
+together with newer higher-sensitivity facilities may help
+explore whether the nulling phenomenon affects all pul-
+sars, or is limited to a sub-population.
+We thank an anonymous referee for helpful suggestions
+that clarified this work. AA, JS, and DK receive sup-
+port from National Science Foundation (NSF) Physics
+Frontiers Center award numbers 1430284 and 2020265.
+AA thanks Alex McEwen for helpful discussions dur-
+ing the data reduction stage.
+The Arecibo Observa-
+tory is a facility of the NSF operated under cooperative
+agreement (#AST-1744119) by the University of Cen-
+tral Florida (UCF) in alliance with Universidad Ana G.
+M´endez (UAGM) and Yang Enterprises (YEI), Inc. The
+Green Bank Observatory is a facility of the NSF oper-
+ated under cooperative agreement by Associated Uni-
+versities, Inc.
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+Facilities: GBT (GUPPI), Arecibo (PUPPI)
+Software:
+PINT (Luo et al. 2019), PSRCHIVE (van
+Straten et al. 2011), dspsr (van Straten & Bailes 2011),
+NumPy (Harris et al. 2020), Matplotlib (Hunter 2007),
+AstroPy (Astropy Collaboration et al. 2013, 2018),
+emcee (Foreman-Mackey et al. 2013)
+APPENDIX
+A. NULLING RESULTS FOR ALL PULSARS
+We show pulse profiles, MCMC corner plot results,
+and nulling histograms for all of the pulsars in our sam-
+ple.
+
+Pulsar Nulling with Mixture Models
+17
+REFERENCES
+Arjunwadkar, M., Rajwade, K., & Gupta, Y. 2014, in
+Astronomical Society of India Conference Series, Vol. 13,
+Astronomical Society of India Conference Series, 79–81
+Astropy Collaboration, Robitaille, T. P., Tollerud, E. J.,
+et al. 2013, A&A, 558, A33,
+doi: 10.1051/0004-6361/201322068
+Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M.,
+et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
+Backer, D. C. 1970a, Nature, 228, 42, doi: 10.1038/228042a0
+—. 1970b, Nature, 228, 1297, doi: 10.1038/2281297a0
+—. 1970c, Nature, 228, 752, doi: 10.1038/228752a0
+Bates, S. D., Lorimer, D. R., Rane, A., & Swiggum, J.
+2014, MNRAS, 439, 2893, doi: 10.1093/mnras/stu157
+Bhat, N. D. R., Cordes, J. M., & Chatterjee, S. 2003, ApJ,
+584, 782, doi: 10.1086/345775
+Bhat, N. D. R., Gupta, Y., Kramer, M., et al. 2007, A&A,
+462, 257, doi: 10.1051/0004-6361:20053157
+Davies, J. G., Lyne, A. G., Smith, F. G., et al. 1984,
+MNRAS, 211, 57, doi: 10.1093/mnras/211.1.57
+Drake, F. D., & Craft, H. D. 1968, Nature, 220, 231,
+doi: 10.1038/220231a0
+Faucher-Gigu`ere, C.-A., & Kaspi, V. M. 2006, ApJ, 643,
+332, doi: 10.1086/501516
+Filippenko, A. V., & Radhakrishnan, V. 1982, ApJ, 263,
+828, doi: 10.1086/160553
+Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman,
+J. 2013, PASP, 125, 306, doi: 10.1086/670067
+Gajjar, V., Joshi, B. C., & Kramer, M. 2012, MNRAS, 424,
+1197, doi: 10.1111/j.1365-2966.2012.21296.x
+Gajjar, V., Joshi, B. C., Kramer, M., Karuppusamy, R., &
+Smits, R. 2014a, ApJ, 797, 18,
+doi: 10.1088/0004-637X/797/1/18
+Gajjar, V., Joshi, B. C., & Wright, G. 2014b, MNRAS, 439,
+221, doi: 10.1093/mnras/stt2389
+Harris, C. R., Millman, K. J., van der Walt, S. J., et al.
+2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
+Herfindal, J. L., & Rankin, J. M. 2007, MNRAS, 380, 430,
+doi: 10.1111/j.1365-2966.2007.12089.x
+—. 2009, MNRAS, 393, 1391,
+doi: 10.1111/j.1365-2966.2008.14119.x
+Honnappa, S., Lewandowski, W., Kijak, J., et al. 2012,
+MNRAS, 421, 1996,
+doi: 10.1111/j.1365-2966.2012.20424.x
+Hunter, J. D. 2007, Computing in Science & Engineering, 9,
+90, doi: 10.1109/MCSE.2007.55
+Ivezi´c, ˇZ., Connolly, A. J., VanderPlas, J. T., & Gray, A.
+2020, Statistics, Data Mining, and Machine Learning in
+Astronomy. A Practical Python Guide for the Analysis of
+Survey Data, Updated Edition
+Kaplan, D. L., Swiggum, J. K., Fichtenbauer, T. D. J., &
+Vallisneri, M. 2018, ApJ, 855, 14,
+doi: 10.3847/1538-4357/aaab62
+Konar, S., & Deka, U. 2019, Journal of Astrophysics and
+Astronomy, 40, 42, doi: 10.1007/s12036-019-9608-z
+Kramer, M., Lyne, A. G., O’Brien, J. T., Jordan, C. A., &
+Lorimer, D. R. 2006, Science, 312, 549,
+doi: 10.1126/science.1124060
+Lomax, R. 2007, Statistical Concepts: A Second Course
+(Lawrence Erlbaum Associates).
+https://books.google.com/books?id=p17rT373FNAC
+Lorimer, D. R., & Kramer, M. 2004, Handbook of Pulsar
+Astronomy, Vol. 4
+Luo, J., Ransom, S., Demorest, P., et al. 2019, PINT:
+High-precision pulsar timing analysis package,
+Astrophysics Source Code Library, record ascl:1902.007.
+http://ascl.net/1902.007
+Lynch, R. S., Boyles, J., Ransom, S. M., et al. 2013, ApJ,
+763, 81, doi: 10.1088/0004-637X/763/2/81
+Lynch, R. S., Swiggum, J. K., Kondratiev, V. I., et al.
+2018, ApJ, 859, 93, doi: 10.3847/1538-4357/aabf8a
+Lyne, A. G. 2009, in Astrophysics and Space Science
+Library, Vol. 357, Astrophysics and Space Science
+Library, ed. W. Becker, 67,
+doi: 10.1007/978-3-540-76965-1 4
+Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M.
+2005, AJ, 129, 1993, doi: 10.1086/428488
+McKinnon, M. M. 2014, PASP, 126, 476,
+doi: 10.1086/676975
+McLaughlin, M. A., Lyne, A. G., Lorimer, D. R., et al.
+2006, Nature, 439, 817, doi: 10.1038/nature04440
+Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011,
+Journal of Machine Learning Research, 12, 2825.
+http://jmlr.org/papers/v12/pedregosa11a.html
+Rajwade, K., Gupta, Y., Kumar, U., & Arjunwadkar, M.
+2014, in Astronomical Society of India Conference Series,
+Vol. 13, Astronomical Society of India Conference Series,
+73–77
+Ransom, S. M., Demorest, P., Ford, J., et al. 2009, in
+American Astronomical Society Meeting Abstracts, Vol.
+214, American Astronomical Society Meeting Abstracts
+#214, 605.08
+Ransom, S. M., Eikenberry, S. S., & Middleditch, J. 2002,
+AJ, 124, 1788, doi: 10.1086/342285
+Redman, S. L., & Rankin, J. M. 2009, MNRAS, 395, 1529,
+doi: 10.1111/j.1365-2966.2009.14632.x
+Ritchings, R. T. 1976, MNRAS, 176, 249,
+doi: 10.1093/mnras/176.2.249
+
+18
+Anumarlapudi et al.
+Rosen, R., Swiggum, J., McLaughlin, M. A., et al. 2013,
+ApJ, 768, 85, doi: 10.1088/0004-637X/768/1/85
+Ruderman, M. A., & Sutherland, P. G. 1975, ApJ, 196, 51,
+doi: 10.1086/153393
+Sheikh, S. Z., & MacDonald, M. G. 2021, MNRAS, 502,
+4669, doi: 10.1093/mnras/stab282
+Smith, F. G. 1973, MNRAS, 161, 9P,
+doi: 10.1093/mnras/161.1.9P
+Stovall, K., Lynch, R. S., Ransom, S. M., et al. 2014, ApJ,
+791, 67, doi: 10.1088/0004-637X/791/1/67
+Taylor, J. H., Manchester, R. N., & Huguenin, G. R. 1975,
+ApJ, 195, 513, doi: 10.1086/153351
+van Straten, W., & Bailes, M. 2011, PASA, 28, 1,
+doi: 10.1071/AS10021
+van Straten, W., Demorest, P., Khoo, J., et al. 2011,
+PSRCHIVE: Development Library for the Analysis of
+Pulsar Astronomical Data, Astrophysics Source Code
+Library, record ascl:1105.014. http://ascl.net/1105.014
+Wang, N., Manchester, R. N., & Johnston, S. 2007,
+MNRAS, 377, 1383,
+doi: 10.1111/j.1365-2966.2007.11703.x
+Wilks, S. 2008, Mathematical Statistics (Read Books).
+https://books.google.com/books?id=iMDWgCcqswkC
+
+Pulsar Nulling with Mixture Models
+19
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.001
+0.25
+0.50
+0.75
+µ1
+µ1=0.498
+1.6
+1.8
+2.0
+µ2
+µ2=1.821
+0.425
+0.450
+0.475
+σ0
+σ0=0.442
+0.45
+0.60
+σ1
+σ1=0.509
+0.80
+0.88
+0.96
+σ2
+σ2=0.91
+0.15
+0.30
+c0 (NF)
+NF=0.273
+−0.02
+0.00
+0.02
+µ0
+0.15
+0.30
+0.45
+c1
+0.25
+0.50
+0.75
+µ1
+1.6
+1.8
+2.0
+µ2
+0.425
+0.450
+0.475
+σ0
+0.45
+0.60
+σ1
+0.80
+0.88
+0.96
+σ2
+0.15
+0.30
+c0 (NF)
+0.15
+0.30
+0.45
+c1
+c1=0.257
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission comps.
+MM null fit
+Figure 11. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0054+6946. In this case the best fit model is a 3-component Gaussian mixture
+
+20
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.016
+1.08
+1.14
+1.20
+µ1
+µ1=1.141
+0.24
+0.28
+σ0
+σ0=0.268
+0.64
+0.68
+0.72
+σ1
+σ1=0.667
+0.000
+0.025
+µ0
+0.08
+0.12
+0.16
+NF
+1.08
+1.14
+1.20
+µ1
+0.24
+0.28
+σ0
+0.64
+0.68
+0.72
+σ1
+0.08
+0.12
+0.16
+NF
+NF=0.108
+−2
+−1
+0
+1
+2
+3
+4
+Raw Intensity
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 12. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0111+6624. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+21
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.001
+2.10
+2.16
+2.22
+µ1
+µ1=2.183
+0.345
+0.360
+σ0
+σ0=0.355
+0.80
+0.85
+0.90
+σ1
+σ1=0.853
+−0.015
+0.000
+0.015
+µ0
+0.52
+0.54
+0.56
+NF
+2.10
+2.16
+2.22
+µ1
+0.345
+0.360
+σ0
+0.80
+0.85
+0.90
+σ1
+0.52
+0.54
+0.56
+NF
+NF=0.54
+−1
+0
+1
+2
+3
+4
+5
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 13. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0325+6744. In this case the best fit model is a 2-component Gaussian mixture
+
+22
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.0
+1.000
+1.025
+1.050
+µ1
+µ1=1.014
+0.66
+0.68
+0.70
+σ0
+σ0=0.672
+0.960
+0.975
+σ1
+σ1=0.972
+−0.015
+0.000
+0.015
+µ0
+0.02
+0.04
+NF
+1.000
+1.025
+1.050
+µ1
+0.66
+0.68
+0.70
+σ0
+0.960
+0.975
+σ1
+0.02
+0.04
+NF
+NF=0.018
+−4
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 14. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0355+28. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+23
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.042
+1.35
+1.50
+µ1
+µ1=1.351
+0.60
+0.65
+σ0
+σ0=0.618
+1.10
+1.15
+1.20
+σ1
+σ1=1.136
+0.00
+0.04
+0.08
+µ0
+0.24
+0.32
+NF
+1.35
+1.50
+µ1
+0.60
+0.65
+σ0
+1.10
+1.15
+1.20
+σ1
+0.24
+0.32
+NF
+NF=0.275
+−4
+−2
+0
+2
+4
+6
+8
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 15. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0414+31 (GBT). In this case the best fit model is a 2-component Gaussian mixture
+
+24
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.024
+1.44
+1.50
+µ1
+µ1=1.476
+0.285
+0.300
+σ0
+σ0=0.296
+0.99
+1.02
+σ1
+σ1=1.011
+0.015
+0.030
+µ0
+0.300
+0.325
+0.350
+NF
+1.44
+1.50
+µ1
+0.285
+0.300
+σ0
+0.99
+1.02
+σ1
+0.300
+0.325
+0.350
+NF
+NF=0.329
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 16. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0414+31 (arecibo). In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+25
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.015
+1.05
+1.20
+µ1
+µ1=1.09
+1.7
+1.8
+1.9
+σ0
+σ0=1.795
+1.50
+1.56
+1.62
+σ1
+σ1=1.568
+−0.08
+0.00
+µ0
+0.08
+0.16
+NF
+1.05
+1.20
+µ1
+1.7
+1.8
+1.9
+σ0
+1.50
+1.56
+1.62
+σ1
+0.08
+0.16
+NF
+NF=0.074
+−7.5
+−5.0
+−2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+Raw Intensity
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 17. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0614+83. In this case the best fit model is a 2-component Gaussian mixture
+
+26
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.003
+0.50
+0.75
+1.00
+µ1
+µ1=0.857
+0.020
+0.022
+σ0
+σ0=0.021
+0.4
+0.6
+σ1
+σ1=0.462
+0.4
+0.5
+0.6
+λ
+λ=0.47
+0.002
+0.004
+µ0
+0.60
+0.65
+0.70
+NF
+0.50
+0.75
+1.00
+µ1
+0.020
+0.022
+σ0
+0.4
+0.6
+σ1
+0.4
+0.5
+0.6
+λ
+0.60
+0.65
+0.70
+NF
+NF=0.666
+0
+100
+101
+Raw Intensity
+0
+100
+101
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 18. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J0738+6904. In this case the best fit model is a 2-component Exponential convolved Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+27
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.011
+1.05
+1.20
+µ1
+µ1=1.082
+1.3
+1.4
+σ0
+σ0=1.35
+1.30
+1.35
+1.40
+σ1
+σ1=1.389
+−0.06
+0.00
+0.06
+µ0
+0.08
+0.16
+NF
+1.05
+1.20
+µ1
+1.3
+1.4
+σ0
+1.30
+1.35
+1.40
+σ1
+0.08
+0.16
+NF
+NF=0.054
+−5.0
+−2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+Raw Intensity
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 19. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1529-26. In this case the best fit model is a 2-component Gaussian mixture
+
+28
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.018
+1.50
+1.75
+2.00
+µ1
+µ1=1.786
+0.55
+0.60
+0.65
+σ0
+σ0=0.607
+1.20
+1.35
+σ1
+σ1=1.33
+−0.05
+0.00
+µ0
+0.40
+0.48
+NF
+1.50
+1.75
+2.00
+µ1
+0.55
+0.60
+0.65
+σ0
+1.20
+1.35
+σ1
+0.40
+0.48
+NF
+NF=0.429
+−4
+−2
+0
+2
+4
+6
+8
+10
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 20. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1536-30. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+29
+0
+1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.153
+4.5
+6.0
+7.5
+µ1
+µ1=5.61
+2.55
+2.70
+σ0
+σ0=2.655
+4.8
+5.6
+σ1
+σ1=4.952
+0.00
+0.15
+0.30
+µ0
+0.78
+0.84
+0.90
+NF
+4.5
+6.0
+7.5
+µ1
+2.55
+2.70
+σ0
+4.8
+5.6
+σ1
+0.78
+0.84
+0.90
+NF
+NF=0.84
+−10
+0
+10
+20
+30
+Raw Intensity
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+0.12
+0.14
+0.16
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 21. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1629+33. In this case the best fit model is a 2-component Gaussian mixture
+
+30
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.0
+1.00
+1.04
+1.08
+µ1
+µ1=1.028
+0.60
+0.65
+0.70
+σ0
+σ0=0.646
+0.850
+0.875
+σ1
+σ1=0.861
+−0.04
+0.00
+0.04
+µ0
+0.015
+0.030
+NF
+1.00
+1.04
+1.08
+µ1
+0.60
+0.65
+0.70
+σ0
+0.850
+0.875
+σ1
+0.015
+0.030
+NF
+NF=0.004
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 22. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1821+4147. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+31
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.002
+0.99
+1.02
+1.05
+µ1
+µ1=1.003
+0.30
+0.33
+0.36
+σ0
+σ0=0.334
+0.58
+0.60
+0.62
+σ1
+σ1=0.596
+−0.02
+0.00
+0.02
+µ0
+0.02
+0.04
+NF
+0.99
+1.02
+1.05
+µ1
+0.30
+0.33
+0.36
+σ0
+0.58
+0.60
+0.62
+σ1
+0.02
+0.04
+NF
+NF=0.007
+−3
+−2
+−1
+0
+1
+2
+3
+4
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 23. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1822+02. In this case the best fit model is a 2-component Gaussian mixture
+
+32
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.014
+1.00
+1.05
+1.10
+µ1
+µ1=1.04
+0.36
+0.42
+σ0
+σ0=0.389
+0.57
+0.60
+0.63
+σ1
+σ1=0.584
+−0.04
+0.00
+0.04
+µ0
+0.02
+0.04
+NF
+1.00
+1.05
+1.10
+µ1
+0.36
+0.42
+σ0
+0.57
+0.60
+0.63
+σ1
+0.02
+0.04
+NF
+NF=0.004
+−1
+0
+1
+2
+3
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 24. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1829+25 (GBT). In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+33
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+50
+100
+150
+200
+250
+300
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.014
+1.00
+1.05
+1.10
+µ1
+µ1=1.04
+0.36
+0.42
+σ0
+σ0=0.389
+0.57
+0.60
+0.63
+σ1
+σ1=0.584
+−0.04
+0.00
+0.04
+µ0
+0.02
+0.04
+NF
+1.00
+1.05
+1.10
+µ1
+0.36
+0.42
+σ0
+0.57
+0.60
+0.63
+σ1
+0.02
+0.04
+NF
+NF=0.004
+−1
+0
+1
+2
+3
+Raw Intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 25. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1829+25 (AO). In this case the best fit model is a 2-component Gaussian mixture
+
+34
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.015
+1.0
+1.2
+1.4
+µ1
+µ1=1.17
+1.4
+1.6
+1.8
+σ0
+σ0=1.646
+1.3
+1.4
+1.5
+σ1
+σ1=1.384
+−0.15
+0.00
+0.15
+µ0
+0.15
+0.30
+NF
+1.0
+1.2
+1.4
+µ1
+1.4
+1.6
+1.8
+σ0
+1.3
+1.4
+1.5
+σ1
+0.15
+0.30
+NF
+NF=0.147
+−7.5
+−5.0
+−2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+Raw Intensity
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 26. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1901-04. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+35
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.002
+0.990
+1.005
+µ1
+µ1=0.997
+0.475
+0.500
+0.525
+σ0
+σ0=0.503
+0.59
+0.60
+σ1
+σ1=0.593
+−0.015
+0.000
+0.015
+µ0
+0.003
+0.006
+NF
+0.990
+1.005
+µ1
+0.475
+0.500
+0.525
+σ0
+0.59
+0.60
+σ1
+0.003
+0.006
+NF
+NF=0.001
+−2
+−1
+0
+1
+2
+3
+4
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 27. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1904+33. In this case the best fit model is a 2-component Gaussian mixture
+
+36
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0=-0.015
+1.8
+2.1
+µ1=1.836
+1.4
+1.5
+1.6
+σ0=1.467
+2.40
+2.55
+σ1=2.517
+−0.08
+0.00
+0.08
+0.40
+0.48
+0.56
+1.8
+2.1
+1.4
+1.5
+1.6
+2.40
+2.55
+0.40
+0.48
+0.56
+NF=0.476
+−10
+−5
+0
+5
+10
+15
+Raw Intensity
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 28. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1928+28. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+37
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.006
+1.04
+1.12
+µ1
+µ1=1.027
+0.78
+0.84
+0.90
+σ0
+σ0=0.831
+0.92
+0.96
+1.00
+σ1
+σ1=0.979
+−0.05
+0.00
+0.05
+µ0
+0.04
+0.08
+NF
+1.04
+1.12
+µ1
+0.78
+0.84
+0.90
+σ0
+0.92
+0.96
+1.00
+σ1
+0.04
+0.08
+NF
+NF=0.013
+−4
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 29. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J1941+02. In this case the best fit model is a 2-component Gaussian mixture
+
+38
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.001
+1.20
+1.25
+1.30
+µ1
+µ1=1.246
+0.120
+0.135
+0.150
+σ0
+σ0=0.137
+0.64
+0.68
+0.72
+σ1
+σ1=0.686
+0.000
+0.015
+µ0
+0.18
+0.21
+NF
+1.20
+1.25
+1.30
+µ1
+0.120
+0.135
+0.150
+σ0
+0.64
+0.68
+0.72
+σ1
+0.18
+0.21
+NF
+NF=0.197
+−1
+0
+1
+2
+3
+4
+5
+Raw Intensity
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 30. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J2000+29. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+39
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.016
+1.2
+1.3
+1.4
+µ1
+µ1=1.328
+0.68
+0.72
+σ0
+σ0=0.697
+1.05
+1.10
+1.15
+σ1
+σ1=1.119
+0.00
+0.04
+µ0
+0.20
+0.25
+0.30
+NF
+1.2
+1.3
+1.4
+µ1
+0.68
+0.72
+σ0
+1.05
+1.10
+1.15
+σ1
+0.20
+0.25
+0.30
+NF
+NF=0.254
+−4
+−2
+0
+2
+4
+6
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 31. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J2040-21. In this case the best fit model is a 2-component Gaussian mixture
+
+40
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=-0.001
+1.16
+1.20
+µ1
+µ1=1.188
+0.180
+0.195
+0.210
+σ0
+σ0=0.198
+0.475
+0.500
+0.525
+σ1
+σ1=0.499
+−0.015
+0.000
+0.015
+µ0
+0.14
+0.16
+NF
+1.16
+1.20
+µ1
+0.180
+0.195
+0.210
+σ0
+0.475
+0.500
+0.525
+σ1
+0.14
+0.16
+NF
+NF=0.152
+0
+1
+2
+3
+4
+Raw Intensity
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 32. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J2044+28. In this case the best fit model is a 2-component Gaussian mixture
+
+Pulsar Nulling with Mixture Models
+41
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+50
+100
+150
+200
+250
+300
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.02
+1.6
+2.4
+µ1
+µ1=2.032
+0.75
+1.00
+1.25
+σ0
+σ0=0.998
+0.8
+1.2
+1.6
+σ1
+σ1=1.026
+−0.25
+0.00
+0.25
+µ0
+0.25
+0.50
+NF
+1.6
+2.4
+µ1
+0.75
+1.00
+1.25
+σ0
+0.8
+1.2
+1.6
+σ1
+0.25
+0.50
+NF
+NF=0.485
+−2
+0
+2
+4
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 33. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J2131-31. In this case the best fit model is a 2-component Gaussian mixture
+
+42
+Anumarlapudi et al.
+0.0
+0.5
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Pulse phase
+0
+100
+200
+300
+400
+Single pulses
+ON
+OFF
+Intensity
+µ0
+µ0=0.03
+0.0
+0.3
+0.6
+µ1
+µ1=0.371
+0.70
+0.75
+0.80
+σ0
+σ0=0.727
+0.2
+0.4
+0.6
+σ1
+σ1=0.349
+0.54
+0.60
+0.66
+λ
+λ=0.589
+0.00
+0.05
+0.10
+µ0
+0.30
+0.45
+0.60
+NF
+0.0
+0.3
+0.6
+µ1
+0.70
+0.75
+0.80
+σ0
+0.2
+0.4
+0.6
+σ1
+0.54
+0.60
+0.66
+λ
+0.30
+0.45
+0.60
+NF
+NF=0.533
+−2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+Raw Intensity
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Probability Density
+MM On fit
+ON/OFF histograms
+MM Off fit
+MM emission fit
+MM null fit
+Figure 34. Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR
+J2310+6706. In this case the best fit model is a 2-component Exponential convolved Gaussian mixture
+
diff --git a/-NFQT4oBgHgl3EQfKDVk/content/tmp_files/load_file.txt b/-NFQT4oBgHgl3EQfKDVk/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..283272899dab0996f8c12986e0bbf030162b555b
--- /dev/null
+++ b/-NFQT4oBgHgl3EQfKDVk/content/tmp_files/load_file.txt
@@ -0,0 +1,2574 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf,len=2573
+page_content='Draft version February 1, 2023  Typeset using LATEX twocolumn style in AASTeX631  A Pilot Study of Nulling in 22 Pulsars Using Mixture Modeling  Akash Anumarlapudi  ,1 Joseph K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Swiggum  ,1, 2 David L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Kaplan  ,1 and Travis D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Fichtenbauer1  1Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee, PO Box 413,  Milwaukee, WI, 53201, USA  2Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' of Physics, 730 High St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lafayette College, Easton, PA 18042, USA  ABSTRACT  The phenomenon of pulsar nulling, observed as the temporary inactivity of a pulsar, remains poorly  understood both observationally and theoretically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Most observational studies that quantify nulling  employ a variant of Ritchings (1976)’s algorithm which can suffer significant biases for pulsars where  the emission is weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Using a more robust mixture model method, we study pulsar nulling in a sample  of 22 recently discovered pulsars, for which we publish the nulling fractions for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' These  data clearly demonstrate biases of the former approach and show how an otherwise non-nulling pulsar  can be classified as having significant nulls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We show that the population-wide studies that find a  positive correlation of nulling with pulsar period/characteristic age can similarly be biased because  of the bias in estimating the nulling fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We use our probabilistic approach to find the evidence  for periodicity in the nulls in a subset of three pulsars in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In addition, we also provide  improved timing parameters for 17 of the 22 pulsars that had no prior follow-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Keywords: Pulsar Nulling — Neutron Stars — Radio Astronomy  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' INTRODUCTION  Pulsar nulling, initially observed by Backer (1970a),  is the absence of observed emission from a pulsar for  one or more pulse periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Observationally, the phe-  nomenon of pulsar nulling remains poorly understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  It is clear that nulling is a broadband phenomenon, ob-  served from 102 MHz (Davies et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1984) to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35 GHz  (Honnappa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, it is not firmly  established whether nulling is simultaneous over this  frequency range using a large sample of nulling pul-  sars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Prior studies found contradictory conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For example, observing over two frequency ranges, 50-  140 MHz and 275-430 MHz, Taylor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (1975) found  that nulls are simultaneous in two different pulsars (PSR  B0031−07, PSR B0809+74), while Davies et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (1984)  found the evidence for excessive nulls in single pulses at  102 MHz compared to 406 MHz in PSR B0809+74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A  more recent study by Gajjar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2014a) found that the  nulls are highly coherent in three pulsars at four different  frequencies — 313, 607, 1380, and 4850 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In addi-  Corresponding author: Akash Anumarlapudi  aakash@uwm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='edu  tion, it is also not clear whether pulsars null randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Redman & Rankin (2009) and Gajjar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2012) found  that nulls might not occur randomly but might be clus-  tered, where nulls and bursts tend to occur in groups,  but the latter found that the null durations can be ran-  dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However, for many of these results the dependency  of the nulling inferences on signal-to-noise ratio makes  it hard to robustly interpret their findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Although the formation of a pair cascade and the radi-  ation from these accelerated pairs in the pulsar magne-  tosphere is often invoked to explain the observed emis-  sion from a pulsar (Ruderman & Sutherland 1975), a  full theory of pulsar magnetospheres and its emission to  explain the diverse morphology in pulse profiles and phe-  nomenology is yet to be developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' As such, the theory  of pulsar nulling remains largely speculative, though it is  often attributed to one of two classes: i) inherent to the  magnetosphere itself such as loss of coherence condition  required for radio emission, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Filippenko & Radhakr-  ishnan (1982), or the depletion of pairs in the magneto-  sphere themselves, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2006) or ii) geo-  metrical factors external to the magnetosphere such as  the line of sight traversing through the ‘empty’ region  between rotating emission carousels, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Herfindal &  Rankin (2007, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Further progress may require ad-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='13258v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='HE]  30 Jan 2023  ID2  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  ditional observational data to understand how the prop-  erties of nulling relate to the properties of the pulsars  themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Nulling as a phenomenon may be related to other more  extreme forms of intensity modulation, where the pulses  can disappear for hours to months in the cases of rotat-  ing radio transients (RRATs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' McLaughlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2006)  or intermittent pulsars (Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Lyne 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, the connection between these populations is  not clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Furthermore, pulsar nulling is often discussed  in tandem with two other forms of single pulse vari-  ations: mode changing – a phenomenon in which an  otherwise stable pulse profile switches between multiple  shapes (or modes) (Backer 1970b) and sub-pulse drift-  ing – a phenomenon in which the single pulse phase  shows a uniform periodic drift (Drake & Craft 1968).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Regardless, in all of these cases the appearance of these  phenomena can be limited by instrumental sensitivity:  without enough sensitivity to probe single pulses at high  significance, one cannot be certain whether the pulsar  emission is truly missing during the nulls or the pulsar  switches to an alternate mode with lower intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' To-  gether all three are often thought of as different represen-  tatives of a larger underlying phenomenon of sub-pulse  intensity variations (Lorimer & Kramer 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Nulling is usually quantified by the fraction of pulses  where there is no discernible emission, called the Nulling  Fraction (NF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' NF can vary from 0 – in the case of stan-  dard emission picture that shows no nulls – to 1, in the  extreme case where the pulsar emission is visible only  between long nulls (intermittent pulsars and RRATs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  NF has been measured in roughly 8% of pulsars, but  this has more to do with the lack of single pulse studies  as opposed to nulling being restricted to a small subset  of pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This smaller data set of nulling pulsars is en-  tirely restricted to normal (not recycled) pulsars, owing  to the high sensitivity demands that would be needed  to observe single pulses of millisecond pulsars (MSPs),  although some recent studies (Rajwade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014) have  been conducted in a sample of bright MSPs which did  not find a signature of nulling with high confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In  addition, there can be a bias against discovering normal  pulsars which tend to have a high NF, or are intermit-  tent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Hence the fraction (8%), can only be considered  as a conservative lower limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Such a small data set restricts our ability to infer  population-wide properties, which might give clues to  the origin of the phenomenon, and hence studies done  thus far have not reached a consensus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' An initial study  done by Ritchings (1976) claimed a correlation between  NF and pulsar period (with longer period pulsars expe-  riencing higher NF) and also a stronger correlation with  the characteristic age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2007) also suggested  a correlation with spin-down age, albeit qualitatively,  with older pulsars experiencing higher NF, before even-  tually crossing the death line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Konar & Deka (2019)  found that there may be two different populations of  pulsars separated by a NF of ∼ 40% but did not find  correlations with any intrinsic pulsar properties, while  Sheikh & MacDonald (2021) claimed that there is no  strong evidence for the existence of two sub-populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  All of these studies may be significantly biased since the  samples used are restricted to the pulsars that explicitly  showed nulling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  In general, most studies (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Gajjar  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2012, 2014b,a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Herfindal & Rankin 2009) estimate  NF using the methodology (or a variant) proposed by  Ritchings (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' But as Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018) demon-  strated, this method can suffer strong biases in the case  of weaker pulsars which can lead to overestimating the  NF and classifying an otherwise standard weak pulsar  as a nulling pulsar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This can also lead to systematic bi-  ases in population inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In addition, Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  (2018) proposed an alternate method in which they use  Gaussian Mixtures to model the single pulse intensities  and estimate the NF , and demonstrate the reliability of  this method in accurately measuring the NF in weaker  pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this study, we expand on the Gaussian Mix-  ture Model (GMM) of Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018)1 to general-  ize their method and apply it to a larger sample of 22  pulsars2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Pulsars selected for this study were discovered as a  part of the Green Bank North Celestial Cap (GBNCC)  pulsar survey (Stovall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014) in 2-min drift scans  at 350 MHz with a 100 MHz bandwidth and with data  sampled every 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='92 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' At 350 MHz the beam size is  36′ (Full Width at Half Maximum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' FWHM) and hence  the astrometric precision prior to a coherent timing so-  lution is limited by the beam size depending on the  Signal-to-noise ratio (SNR) of the discovery candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  These were later followed up at the Green Bank Tele-  scope (GBT) and Arecibo Observatory (AO) to improve  their timing solutions and establish their nulling char-  acteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The structure of this paper is as follows: In Section 2,  we detail our data acquisition and reduction methods,  and provide updated timing solutions for the pulsars in  this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We then describe the mixture model and pro-  vide our basic results in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Finally, we present  1 As noted in Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018), a similar method may have  been used in Arjunwadkar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2 All of our code is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='com/AkashA98/  pulsar nulling  Pulsar Nulling with Mixture Models  3  the implications of the results in Section 4 and conclude  in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' DATA ANALYSIS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Observations and Data Reduction  A sample of 22 recently discovered pulsars was selected  for this pilot study if they showed any signs of intermit-  tency in their discovery plots3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Data for 15 out of 22  pulsars were collected using the 100-m Robert C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Byrd  Green Bank Telescope (GBT) (hereafter referred to as  the GBT sample), operating at 820 MHz with a band-  width of 200 MHz, in 2 hr contiguous scans, with the  primary aim of determining the pulsars’ nulling charac-  teristics (project code 18A−436;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' PI: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Swiggum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Data  for another nine pulsars were collected at the 300-m  William E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Gordon Arecibo Observatory (AO) operat-  ing at 430 MHz over a bandwidth of 24 MHz, with the  goals to both establish coherent timing solutions and de-  termine nulling characteristics (project code P3436;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' PI:  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Swiggum) (hereafter referred to as the AO sample).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Two pulsars in our sample, PSR J0414+31, and PSR  J1829+25, were observed at both observatories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Six of the 15 pulsars in the GBT sample already had  coherent timing solutions (Lynch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018) and the  data for these were collected in coherent search mode us-  ing the Green Bank Ultimate Pulsar Processing Instru-  ment (GUPPI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Ransom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2009) with 128 frequency  channels sampled at 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='24 µs and retaining full polar-  ization information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The remaining nine pulsars had no  prior follow-up campaigns and so we first improved their  positions using gridding observations and then observed  them in incoherent search mode with 2048 frequency  channels sampled at 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='96 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Data for the AO sample  were collected in coherent search mode using the Puerto  Rico Ultimate Pulsar Processing Instrument4 (PUPPI),  with 64 channels sampled at 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='96 µs, over a span of ∼  six months to establish coherent timing solutions in ad-  dition to studying the nulling properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A summary of  observations for each pulsar is provided in Tables 1 and  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Starting with the raw search mode data, we used  dspsr (van Straten & Bailes 2011) to fold the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We then used pazi, the interactive zapping routine in  psrchive (van Straten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011) to remove radio fre-  quency interference (RFI)-affected frequency channels  and single pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' For GBT data, we also made use of  RFI scans taken at the observatory5, when available, to  3 See the GBNCC discovery page:  http://astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='wvu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='edu/  GBNCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  4 http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='naic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='edu/puppi-observing/  5 https://greenbankobservatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='org/rfi-gui-user-guide/  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Times and durations of GBT ob-  servations  Pulsar  Observations  Total Time  MJD (hr)  (hr)  J0054+6946  58163 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  J0111+6624  58163 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='24)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='24  J0325+6744  58163 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='52)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  58164 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='48)  · ·  J0414+31a  58164 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  J0614+83  58164 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='90)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='90  J0738+6904  58209 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  J1529−26  58209 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  J1536−30  58209 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  J1629+33  58209 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='33)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='33  J2310+6706  58246 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='75)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='75  Note—For each pulsar we give the individual  Modified Julian Date (MJD) and duration of  each session, as well as the total observing  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  aThis pulsar was observed at both AO and  GBT  identify the frequency bands that are affected by RFI,  which are otherwise not obvious visually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In some cases,  we found that one of the polarization channels was per-  sistently affected by RFI, and in such cases we excluded  data from that polarization channel at the cost of SNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Fortunately, this did not have a significant impact on  the determination of the nulling fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Some of the  AO data had periodic “drop-outs” in the data with sub-  millisecond periodicity at zero dispersion measure (DM),  caused by data rate overflow during the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We cleaned these “drop-outs” by replacing the data with  NaN values and being careful to exclude those when fold-  ing/averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  After cleaning the RFI, both for tim-  ing and estimating nulling, we averaged polarizations to  measure the total intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Timing  For the 16 pulsars in our sample that had no prior  follow-up, we first tried to improve the timing parame-  ters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We used paas from psrchive (van Straten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2011) to make a standard template and then used pat  4  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Times and durations of Arecibo observations  Pulsar  Observations  Total Time  MJD (hr)  (hr)  J0355+28  58890 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='14)  · ·  59063 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='14)  · ·  aThis pulsar was observed at both AO and GBT  to extract the Times of Arrival (TOAs) from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For the GBT data, our goal was to improve the spin fre-  quency (F0) and DM measurements since we had only  2 hour scan at a single epoch for each source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' For the  AO data, the data spanned ∼3–6 months depending on  the pulsar and hence we can generate a phase-connected  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However, the relatively narrow bandwidth of  the observations (24 MHz) restricted our ability to fit  for DM using sub-banded TOAs and hence we used the  DM of the discovery candidate found on the GBNCC  discovery page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The timing solutions for all the pulsars in this study  are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' For pulsars observed at GBT we  improved the positions through gridding, and F0 and  DM estimates through timing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For pulsars observed  at AO, we improved the gridded positions, F0 and the  frequency derivative F1 = ˙F0 through coherent timing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For the two overlapping pulsars observed at both GBT  and AO, a timing solution was obtained by combining  the TOAs from both observatories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In the case of pul-  sars observed at AO for only ∼3 months (J0355+28,  J0414+31, J1822+02), and pulsars where a combina-  tion of low SNR and nulling resulted in few TOAs with  SNR > 8 (J1928+28), it is difficult to estimate both po-  sition and F1 precisely (they are highly covariant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In  such cases, we rely on the  F-statistic, given by  F = (χ2  0 − χ2)/(p − p0)  χ2/p  where χ2  0 and χ2 are the chi-squared values of the timing  residuals, and p0 and the p are the degrees of freedom  before and after the addition of F1 (or any additional  parameter(s), in general).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This F-statistic follows an F-  distribution (Lomax 2007) and hence we include F1 in  the fit if the improvement in the goodness of fit (χ2) due  to F1 is <1% by chance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The resulting timing residuals  are shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' ON/OFF histograms  Once we had improved the timing solution, we used  dspsr in single pulse mode to generate single pulses for  all scans and used psradd, from psrchive, to phase  align pulses from different scans after cleaning the data  for RFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We then averaged the data along the polariza-  tion and frequency axes to obtain the pulse intensity of  the single pulses as a function of the rotational phase  and generated single pulse stacks such as that shown in  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The most important aspect in estimating the nulling  fraction is determining the “ON”-pulse and “OFF”-  Pulsar Nulling with Mixture Models  5  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Timing Parameters for the GBNCC pulsars used to study nulling  Pulsar  Position (J2000)  Period  Period derivative  DM  RA  RA error  DEC  DEC error  (′′)  (′′)  (s)  (10−15 s/s)  (pc/cm3)  GBT sample  J0054+6946a  00h 54m 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='  c Astrometric positions are estimated from gridding and the positional uncertainties are estimated from the beam size (15′)  and the Signal to Noise Ratio (SNR)  6  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Timing residuals for the pulsars observed in the timing/nulling campaign at the AO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The red dots are the residuals  (in milliseconds) from the timing model with the error bars representing the 1-σ error on the TOAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The timing model solutions  are presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='5  1  NP  NP= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Intensity  (a) Single pulse stack of PSR J0325+6744  −1  0  1  2  3  4  5  Normalized Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  Density  OFF window  ON window  (b) Pulse intensity histogram for PSR J0325+6744  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (a)The bottom left panel shows the single pulse  stack with the ON and OFF windows marked with black  dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Null probabilities (NP) for every single pulse  are calculated using the method described in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2 and are  shown in the bottom right plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The distribution of NP is  shown in the top right panel where we can clearly see the  evidence for two classes of pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The summed profile of  all the single pulses with null probability < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5 is shown in  the top left panel, while the summed profile for pulses with  null probability > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5 is shown in the middle panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (b) The  pulse intensities in the OFF and ON windows are shown  in blue and orange histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The presence of excessive  counts in the ON histogram (the null component) at the  background noise level separated from a second component  at higher intensities (the emission component) is evidence for  the nulling behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  pulse phase windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The single pulse intensities in the  “OFF”-pulse window should be entirely due to radiome-  ter noise, while the intensities in the “ON”-pulse window  should be the sum of the radiometer noise component  (same as the “OFF”-pulse window) and the pulsar emis-  sion component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We first generated the average pulse  profile to visually select on and off windows of the same  widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We then fit a sixth-order polynomial as a func-  tion of pulse phase to each single pulse (similar to Rosen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Lynch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018) after  masking the ON/OFF windows to remove any trends  and construct a flat baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We recorded the ON/OFF  intensities as the sum of the baseline-subtracted inten-  sities across the windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Finally, we constructed his-  tograms of the ON/OFF intensities which we used to  determine the nulling properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Figure 2 shows the  single pulse intensity distribution in the ON/OFF win-  dow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The OFF histogram can be accurately described  by a single component (Gaussian noise), but the ON  histogram can have multiple components — “null” and  “emission” components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The presence of nulling man-  ifests in the ON histogram as an excess of samples at  levels consistent with the OFF component, which we  refer to as the null component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The residual distribu-  tion, after removing the null component, is supposed to  be a realization of pulsar’s emission distribution (here-  after referred to as ‘emission’ component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The emission  component can be a single distribution or a combination  of multiple distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The ON distribution can be  thought of as the sum of the null and the emission com-  ponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' METHODS & RESULTS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Determining Nulling Frations  As demonstrated by Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018), Ritchings’  method can give biased estimates for NF (hereafter re-  ferred as NFr) in pulsars where the emission compo-  nent is close to the noise level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Therefore, following Ka-  plan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018) we adopt a method which models the  ON/OFF histograms using a mixture model (MM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This  means that the intensities x can be considered as ran-  dom draws from the probability density function (PDF)  p(x|¯θ) =  m  �  n=1  cn Fn(x|{θn}),  (1)  where the Fn functions are the individual probability  density functions parameterized by the set {θn}, cn are  the weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In the case where all the Fn functions are  the same and are normal distributions  Fn(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' µn, σn) = N(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' µn, σn) =  1  √  2πσn  e− 1  2(  x−µn  σn )  2  ,  where {µn} and {σn} are the means and standard devia-  tions of component n, this reduces to a Gaussian mixture  model (GMM), but more general models are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  8  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  There is an additional constraint that the weights cn add  to one:  m  �  n=1  cn = 1,  which comes from the normalization of the PDF, which  leaves the total number of free parameters to be deter-  mined as �m  n=1 dim({θn}) model parameters, and m−1  latent parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  In general, the OFF histogram can be well-described  by a Gaussian as expected of radiometer noise (assum-  ing that RFI has been sufficiently removed), and this is  what we observe in our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The emission component  usually can be described by a single Gaussian as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, there are cases when it deviates from a single  Gaussian component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' More than one component is a  possibility considered in Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018), which can  be tested against the single-component model through a  model comparison test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However, we also consider non-  Gaussian models here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Specifically, multi-path propaga-  tion of the pulses through the interstellar medium (ISM)  (Smith 1973;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Bhat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Lorimer & Kramer 2004),  can result in the emission distribution having long tails  towards higher intensities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This effect can be reasonably  well described by the intensity distribution  F(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' µ, σ, τ) = 1  2τ exp  � σ2  2τ 2  �  exp  �  −x − µ  τ  �  erfc  �  −x − (µ + σ2/τ)  √  2σ  �  (2)  which is a convolution of a Gaussian N(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' µ, σ) and a  one-sided exponential 1  τ exp(−x/τ)U(x), where U(x) is  the Heaviside or step function, erfc(x) is the complemen-  tary error function, and τ is the decay time of the ex-  ponential (McKinnon 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Hence we try to model the  emission component using multi-component Gaussians  and Gaussians with exponential tails and rank them us-  ing their Bayesian Information Criterion (BIC) values  to choose the best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We employ the scikit-learn Gaussian mixture  model (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011) to derive an initial fit for  the ON and OFF histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' This is based on the ex-  pectation–maximization (EM) algorithm, in which pa-  rameters are estimated by maximizing the likelihood  function L(data | ¯θ) (see Ivezi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2020, for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  This produces a very good fit for the OFF histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, in the case of weaker pulsars where the emis-  sion can be confused with the background, Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  (2018) showed that this method can still fail in produc-  ing a reliable fit for the null and emission components  of the ON histogram simultaneously, although this bias  can be small compared to the Ritchings’ algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' As  such, a refined fit for the null and emission components  can be obtained by performing a Markov-Chain Monte  Carlo (MCMC) analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For MCMC analysis, the likelihood function is given  by  L(¯x|¯θ) =  �  i  p(xi|¯θ)  (3)  following p(xi|¯θ) from Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The priors chosen are:  Initial Gaussian fit from the EM algorithm for the  off-pulse mean and standard deviation  Uniform between the bounds dictated by the on-  pulse intensities for the parameters governing the  pulsar emission component  Dirichlet distribution for the m coefficients cm  (Wilks 2008)  We use the emcee (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013) en-  semble sampler to sample the posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We initialize  32 walkers within a ±5σ range of the initial fit values  of the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' To account for the finite correlation  length of the chains and produce independent samples,  we first let the walkers “burn-in” to erase their start-  ing conditions, and we then let the walkers explore the  parameter space until we have at least 100 independent  samples for each walker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Figure (3, left column) shows the pulse intensity his-  tograms for PSR J0325+6744: a pulsar in which the  emission component is easily discernible from the noise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  and PSR J1529−26: a pulsar where these two start to  blend into each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Looking at the null component in  the ON histogram for the two pulsars, the evidence for  nulling is clear in J0325+6744 while J1529−26 behaves  like a non-nulling pulsar whose emission is weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The  blue, green and orange-filled regions show the fit for the  OFF, null, and emission components respectively, and  the black dotted line shows the overall fit for the ON  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The posteriors for the model parameters  are presented in Figure (3, right column) with the point  estimates (median6) of the NF from MM given in Ta-  ble 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  For PSR J0325+6744, where the null and emission  components are well separated (bright pulsars), our  method yields a NF = 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='81% while Ritchings’  6 In the case of non-nulling pulsars where the distribution of NF  is one-sided, the median will be over-estimated compared to the  true value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Even so, the uncertainty on NF is larger than the  difference between the median and mode and hence NF is still  consistent with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Pulsar Nulling with Mixture Models  9  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Nulling properties of the GBNCC pulsars  Pulsar  Model  NF  NFr  Null period  Lengths  Null  Em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  (%)  (%)  (pulse periods)  GBT sample  J0054+6946  G3  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  · ·  2  3  J0111+6624  G2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9  · ·  2  7  J0325+6744  G2  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  · ·  3  4  J0414+31  G2  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='7  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='4  · ·  1a  · ·  J1928+28  G2  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9  · ·  3  3  J1941+02  G2  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='7  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  · ·  1-3a  · ·  J2000+29  G2  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  · ·  1-2a  3  J2044+28  G2  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  · ·  1-2a  6  Note—Naming convention for the model represents the model used  to describe the emission histogram (G=Gaussian, Eg=Exponentially  modified Gaussian) followed by the number of components in the ON  histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  aWe find that in extreme cases (non-nulling/highly-nulling), one of the  distributions is confined to very few bins and so we quote this range  rather than fitting for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  b We find that there are no single pulses with NP>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  c We observe quasi-periodicity in these cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  method (see Ritchings 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Kaplan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018, for implementation) gives a comparable esti-  mate of 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='01%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However in the case of a weaker pulsar,  PSR J1529−26, where the emission component is closer  to the background noise, our method gives a best-fit  value of NF = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='55 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4% compared to 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1% given  by the Ritchings’ method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The latter is significantly  overestimated and can easily lead to (mis)classifying the  source as a nulling pulsar, further illuminating the bias  of Ritchings’ method in weaker pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Full results for all the 23 pulsars, including the single  pulse stacks, posteriors from the MCMC run and the  resultant ON/OFF histogram model fits are shown in  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Nulling Correlations  After determining the nulling properties we wish to  know whether the locations and durations of nulls are  completely random, or if there is any correlation be-  tween different nulling and emission episodes in a pulsar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Specifically, given a single pulse that shows emission (or  that nulls), how likely are we to see emission for the next  pulse, and are there any patterns of longer duration?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We test this using the probability of a null (the nulling  “responsibility”) evaluated for each individual pulse,  given by  NPI =  c0F0(I|{θ0})  �m  n=1 cn Fn(I|{θn}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  (4)  We divided the data into stacks of 256 pulses (similar to  Ritchings 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Herfindal & Rankin 2009) to calculate  more robust estimates and to be less sensitive to long-  term variations like scintillation and system temperature  changes, and use equation 4 to calculate the probabil-  ity of a given single pulse being a null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We then looked  for periodic signature by taking the Fourier transform  (FT) within each stack and co-adding the power from all  stacks incoherently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Figure 4 shows the resultant spec-  trum for PSR J0414+31, in which a certain pattern of  combination of emission and nulls seems to be periodic  over ∼28 pulse periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We estimate the significance of  peaks in the stacked power spectra assuming that the  null distribution from n stacks follows a χ2 distribution  with 2n degrees of freedom (this assumes white noise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We see significant periodic or quasi-periodic (a signifi-  cant broad peak in the power spectrum) signatures in a  few other pulsars, and tabulate their periods in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  In the case of precise period measurements, we estimate  the uncertainty as described in Ransom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, this only points to the periodic nature of  a certain pattern of emission and nulls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  To find how  emissions and nulls are ‘bunched’, we look for the dis-  tribution of continuous emissions and nulls, where we  use NPI=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5 to be the boundary between an emission  and a null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Figure 5 shows the emission and null length  10  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  −1  0  1  2  3  4  5  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  (a1) PSR J0325+6744 – NF = 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='81% vs NFr =  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='01%  µ0  µ0=-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='001  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='22  µ1  µ1=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='183  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='345  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='360  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='355  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='90  σ1  σ1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='853  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='015  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='56  NF  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='22  µ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='345  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='360  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='90  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='56  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='54  (a2) Model parameter posteriors for PSR J0325+6744  −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='30  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  (b1) PSR J1529−26 – NF = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4% vs NFr =48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5%  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='20  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='082  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  σ0  σ0=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='40  σ1  σ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='389  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='06  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='16  NF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='20  µ1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  σ0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='40  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='16  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='054  (b2) Model parameter posteriors for PSR J1529−26  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Left (a1, b1) Two-component Gaussian model fits for the ON and OFF histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Individual ON/OFF histograms  are shown in solid black lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The blue, green and orange-filled regions shows the OFF, the null (NF × OFF) and the emission  (ON − NF × OFF) components respectively, where this estimate of NF is obtained using the mixture model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The black dotted  line shows the overall fit for the ON pulse distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Right (a2, b2) Corner plots for 2-component Gaussian fit to the ON/OFF  histograms parameterized by the means {µ1, µ2}, standard deviations {σ1, σ2} and the nulling fraction NF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The dashed vertical  lines are the quoted median point estimates of the parameters  Pulsar Nulling with Mixture Models  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Fourier frequency (in 1/P)  0  20  40  60  80  100  120  140  160  Power (arbitrary units)  NP FFT (ON)  NP FFT (OFF)  analytical limit  (a) PSR J0414+31 (GBT)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Fourier frequency (in 1/P)  0  100  200  300  400  500  Power (arbitrary units)  NP FFT (ON)  NP FFT (OFF)  analytical limit  (b) PSR J0414+31 (AO)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Fourier frequency (in 1/P)  0  50  100  150  200  250  Power (arbitrary units)  NP FFT (ON)  NP FFT (OFF)  analytical limit  (e) PSR J2040−21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Fourier frequency (in 1/P)  0  20  40  60  80  Power (arbitrary units)  NP FFT (ON)  NP FFT (OFF)  analytical limit  (f) PSR J0738+6904  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Fourier transform of the null probability for the pulsars in our sample that show periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Power combined  incoherently from multiple stacks of 256 pulses is shown at 129 discrete frequencies (in the units of 1/pulse period) in the  blue line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The orange curve shows the same for the OFF component (background noise) which can be used to eliminate any  instrumental variations/artifacts and/or RFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The black dotted line shows the upper limit that allows for 1 false positive in 1000  trails, corresponding to a 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9% confidence limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The gray curves are the normalized power from the individual stacks (not to  scale) that are used to look for quasi-periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The value of the periodicities are given in Table 4  12  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  0  5  10  15  20  Pulse periods  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Normalized counts  null lengths  em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' lengths  null fit τem=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='49  null fit τem=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Distribution of emission lengths and null lengths  for J0414+31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The gray-filled and the black-open histograms  show the distribution of null and emission episodes respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The orange curve shows an exponential fit for the  emission length distribution with decay constant τem=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3,  whereas the blue curve shoes the same for the null length  distribution with τnull=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  distributions for the single pulses of PSR J0414+31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We  find that these distributions can be well described by an  exponential distribution (p(x) = τ −1 exp(−x/λ)), where  x is the null or emission length and the mean duration  of the episode is λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We find that for PSR J0414+31, the  emission episodes have a characteristic period of four  periods, whereas the nulls are two periods long, which  is consistent with the observed nulling fraction of ∼ 33%  (see Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We repeat this for all the pulsars and the  results are tabulated in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Sub-pulse Drifting  Beyond nulling, we also look for any correlations be-  tween nulling and sub-pulse drifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Drifting is usually  characterized by two periods: the drifting period P3,  defined as the period for which the pulse is seen at the  same longitude (phase), and P2, the spacing between  two sub-pluses within the same single pulse (see Figure  6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' To estimate both, we prepared the data by selecting  only the on-pulse window of data (np phase bins) for all  the single pulses (ns single pulses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We then calculated  Longitude Resolved Fluctuation Spectra (LRFS, Backer  1970c), where we take a 1-D Fourier transform of the  (ns × np) data along the ns axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Figure 6 shows one  of the two pulsars in our sample, J1822+02, that shows  clear signs of drifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A period P3 of ∼ 28 pulse periods  and P2 of ∼ 35/1024 pulse periods can be clearly seen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We also find the evidence for drifting in PSR J1829+25  (see figure 7), with a P3 of ∼ three pulse periods and a  P2 of 1/128 pulse periods, with similar inferences in the  data from both AO and GBT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' DISCUSSION  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Biases in Nulling Models  Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018) demonstrated the bias of Ritch-  ings’ method for weaker pulsars through simulated data,  where the mixture model was able to recover the true in-  jected nulling fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' They also showed that for Gaus-  sian mixtures, an analytical correction can correct the  biased estimate of Ritchings’ method to find the true  value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We extend the same technique using our sam-  ple of 22 pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Figure 8 shows the comparison of the  NF estimates derived using both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The blue  points show the NF estimate derived using Ritchings’  algorithm (NFr), the orange points show NFr estimate  corrected for the bias (as in Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018), and the  green points show the NF derived using mixture model-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In the case of highly nulling pulsars, the contamina-  tion of the null component from the emission component  can be small, and both methods perform comparably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, in the case of pulsars with small NF a system-  atic bias can be seen as the pulsar emission component  becomes blended with the background noise, and the  fact that the green and orange points agree quite well  demonstrates our confidence in estimating the bias in  the Ritchings method and the utility of mixture models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Is the Nulling Fraction Correlated with Pulsar  Properties?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Comparing the nulling estimates from the mixture  modelling and Ritchings’ method in Table 4, it can be  seen that there can be significant differences between  these estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Such a scenario can lead to significant  biases in population-wide studies that look for corre-  lation between nulling fraction and pulsar properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Figure 9 shows the most complete list of nulling pulsars,  extended from Konar & Deka (2019), on the P − ˙P dia-  gram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We do not find any clear visual trends of NF with  respect to period (P), spin-down rate ( ˙P), characteris-  tic age (τc), or surface magnetic field (Bsurf), although  we emphasize that most of the pulsars here (142/164)  have their NF estimates derived using some variant of  the Ritchings method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Our sample size of 22 pulsars is too small to derive  reliable correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However, we can test the similar-  ity/disparity in the correlations obtained using nulling  estimates derived with mixture models versus the Ritch-  ings algorihtm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We use the Spearman correlation test, a  non-parametric correlation test to quantify any correla-  tions between the relevant parameters (P/ ˙P/Bsurf/τc)  and NF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Table 5 shows the correlation coefficients of  nulling fraction with parameters of interest (P, ˙P, Bsurf,  τc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In no case do we see an evidence for strong cor-  relations but we can see large differences between these  coefficients obtained using the NF derived using the two  Pulsar Nulling with Mixture Models  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='39  Phase  0  50  100  150  200  250  Singlepulse number  P2  P3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='29  Pulse phase  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Frequency (in units of 1/Period)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  Power  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Left: A stack of 300 single pulses of PSR J1822+02 clearly showing the sub-pulse drifting phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The drifting  periods P2 and P3 are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Right: LFRS of the single pulse stack of J1822+02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The 2D spectrogram shows the Fourier  transform of data along the axis of single pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The evidence of a single drifting frequency across the phase bins is evident  from the spectrogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The bottom panel shows the 2D spectrogram scrunched along the phase axis and the right-hand plot  shows the same scrunched along the frequency axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We emphasize that the values of these have to  be taken with a high degree of caution, given the relative  sample size under study and the presence of outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In  particular we find that PSR J2310+6706 turns out to be  a strong outlier, especially in the τc and Bsurf space and  this significantly affects the results (see Table 5), further  illustrating the limitations of a small sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Previously, using a sample size (23) comparable to  ours, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2007) qualitatively found that NF is  related to age with older population experiencing larger  nulling fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Ritchings (1976) found a positive cor-  relation both with the pulsar period and age in a sample  (32) slightly larger than the one in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However,  as mentioned above those and most other nulling esti-  mates in the literature are derived using some variant  of Ritchings’ algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Computing the Spearman coef-  ficient for all of the archival sources we cannot confirm  either correlation and suggest caution in interpreting re-  sults using Ritchings’ algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  However, we also note that the source of this dispar-  ity does not seem to be straightforward: For a sam-  ple of pulsars with a given SNR, the energy per sin-  gle pulse will be lower for pulsars with shorter peri-  ods, which means that the NF estimates for the short-  period pulsars should experience larger biases and have  higher nulling fractions measured with the Richtings’  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Under the (overly simplistic) assumption of  a uniform distribution of luminosity with period (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Faucher-Gigu`ere & Kaspi 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Bates et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014), the  correlation of inferred nulling fraction with period will  then be negative which is contrary to the previous stud-  ies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  This suggests that the source of this bias is not  simple and needs careful understanding of the under-  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Spearman rank correlation coefficients for our sam-  ple data set and archival data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Parameter  MM  Ritchings  Catalog  P  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='356  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='311  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='314  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='064  · ·  | ˙P|  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='274  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='035  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='457  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='057  · ·  τc  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='353  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='088  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='149  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='557  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='207  · ·  Bsurf  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='291  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='071  · ·  Note—Not all the pulsars in the sample have  ˙P measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Hence the sample size used  for period is larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The two rows for each pa-  rameter correspond to the rank coefficients  including and excluding PSR J2310+6706  (see Figure 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  lying distribution of NF with pulsar properties and a  larger sample of pulsars with more robust and unbiased  NF estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Is Nulling Periodic?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  As shown in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2, we find that nulling appears  periodic/quasi-periodic in a subset of pulsars, with their  periods noted in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Herfindal & Rankin (2007,  2009) also find evidence for such signatures and at-  tributd this to the line of sight passing through a struc-  tured rotating carousel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In addition we also find that  14  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='75  Pulse phase  0  20  40  60  80  100  120  140  160  Single pulses  (a) AO data single pulse stack  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='574  Pulse phase  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='00  Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='5  Frequency (in units of (1/P))  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Power  (b) LRFS (AO data)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='75  Pulse phase  0  25  50  75  100  125  150  175  Single pulses  (a) GBT data single pulse stack  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='487  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='492  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='505  Pulse phase  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Frequency (in units of (1/P))  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  Power  (b) LRFS (GBT data)  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Sub-pulse drifting in PSR J1829+25: The left panels shows the stack of single pulses, in the data taken at AO and  GBT, which shows the signature of drifting phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The right panels shows the LRFS (see §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3) of the single pulse stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Data from AO (top right) shows a strong feature with a periodicity ∼ 3 pulse periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Data from GBT (bottom right) shows a  quasi-periodic (broad) peak consistent with the period from AO data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  in PSR J0414+31, which was observed at two differ-  ent frequencies with different instruments, this period is  the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' It should be noted that the frequency reso-  lution here is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='004 pulse period−1 (from the stacks of  256 pulses) and so we will be insensitive to any changes  that are finer than this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Although significant correla-  tions can not be drawn from these periodicities given  our sample size and the number of pulsars that show  periodic nulling, the occurrence of such a phenomenon  in modest set of pulsars in our sample suggests that this  might not be uncommon and should be searched for in  future data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' CONCLUSIONS  In this study, we have extended the Gaussian mixture  model of Kaplan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018) to study nulling behav-  ior in 22 pulsars, spanning a wider range of properties  than in the initial paper but still not selected indepen-  dent of nulling behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We find that all pulsars can  be well-represented by mixture model, but we find that  a single Gaussian is not sufficient to describe the emis-  Pulsar Nulling with Mixture Models  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  Emission component SNR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  NF  Uncorrected NFr  Corrected NFr  NF  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Comparison of NF estimates from Ritchings’ al-  gorithm and mixture model as a function of pulsar emission  component (significance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' in units of σOFF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The blue error  bars show the estimates from Ritchings’ algorithm while the  orange error bars are from mixture model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The green er-  ror bars are derived by estimating the systematic bias from  the Ritchings’ method and clearly depict the bias in the cases  where the emission component is weak compared to the back-  ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  10−1  100  Period (s)  10−18  10−17  10−16  10−15  10−14  10−13  10−12  10−11  Period derivative (s/s)  109 yr  107 yr  105 yr  1013 G  1012 G  1011 G  ATNF catalog  Archival NF  This work  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  Nulling Fraction  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Period-period derivative (P − ˙P) diagram high-  lighting nulling pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Shown in grey circles are all the  pulsar from the ATNF catalog (Manchester et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2005), in  colored circles are the archival nulling pulsars from Konar  & Deka (2019) and in diamonds are the pulsars from this  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The contours represent lines of constant character-  istic age τc and dipolar surface magnetic field (Bsurf).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The  color bar shows the nulling fraction which ranges from 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  No clear discernible trend of NF with any of P/ ˙P/Bsurf/τc  is visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  sion component in some pulsars7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Similar to Kaplan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2018), we find that previous methods used to  estimate NF can suffer significant biases when the pul-  sar emission is weak compared to the background noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Such biases may lead to misinterpreting weak pulsars  as nulling pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' We also show that these biases may  lead to spurious correlations between the NF and pulsar  properties in population-wide studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Drawing on the more robust statistics that we calcu-  late, we find that nulling can appear periodic, with three  pulsars in our sample showing this behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Two pul-  sars in our sample, PSR J1822+02 and PSR J1829+25,  shows clear signs of sub-pulse drifting, and they have an  inferred nulling fraction consistent with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In contrast,  studies like Gajjar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2014a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Davies et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (1984)  find sub-pulse drifting in pulsars that exhibit moderate  nulling, indicating that sub-pulse drifting and nulling  might be two independent manifestations of sub-pulse  intensity variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In all cases we look forward to us-  ing larger, less-biased samples to more robustly explore  the nulling population and seeing if it is related to other  phenomenology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Two pulsars in our sample, PSR J0414+31 and PSR  J1829+25, were observed at two different frequencies  (430 MHz and 820 MHz), albeit not simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  PSR J1829+25 has nulling estimates that agree at both  frequencies, consistent with 0, but we find that PSR  J0414+31, has NF estimates in tension at the ∼ 2σ  level, with the NF higher at lower frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Al-  though it is hard to draw definite conclusions from these  two pulsars since the observations are not simultane-  ous, it emphasizes the need for simultaneous observa-  tions at multiple frequencies (or across a larger band-  width).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Observing at 4 different frequencies (325, 610,  1400, 4850 MHz), Gajjar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2014a) find coherent  nulling in three different pulsars whereas Bhat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  (2007) find the evidence for null excess at lower frequen-  cies in PSR B1133+16 further emphasizing the need for  multi-frequency observations in a larger sample to find  whether nulling is universally broadband.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  One of the pulsars in our sample (PSR J2310+6706)  has a two-component profile with a faint leading peak in  addition to the primary peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The very low SNR of the  leading component limits our ability to find a stringent  estimate of the NF independent of the primary com-  ponent, but we find that the NF values obtained from  each component is consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Analyzing nulling charac-  teristics in pulsars with multi-component pulse profiles  7 PSR J0054+6946 is better described by 2 different emission com-  ponents, one at lower amplitude and the other at higher ampli-  tude, as seen in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  16  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  0  2  4  6  Period (s)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  NF  10−16  10−15  10−14  Period derivative (s/s)  107  108  109  Characteristic Age (yr)  J2310+6706  1012  1013  Surface Magnetic field (G)  J2310+6706  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Scatter plot showing the NF of the pulsars in this study vs their properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' It can be seen that the pulsars appear  scattered in the P/ ˙P space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' However, with the exclusion of PSR J2310+6706 which appears as an outlier in the τc/Bsurf space,  a rough trend can be seen that of NF decreasing with the age τc and increasing with the surface magnetic field Bsurf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The  correlation coefficients are given in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  with a robust method like mixture modeling can provide  insights into the simultaneous nulling in the different re-  gions of the pulsar’s magnetosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  So far we have only analyzed normal, non-recycled  pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Current sensitivity limitations restrict the sam-  ple of nulling pulsars to normal pulsars (as is evident  from Figure 9), while MSPs are largely unexplored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Ini-  tial single pulse studies done by Rajwade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' (2014)  do not find any compelling evidence for nulling in MSPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Using the mixture model technique, which does not suf-  fer from the same biases at low signal-to-noise, for MSPs,  together with newer higher-sensitivity facilities may help  explore whether the nulling phenomenon affects all pul-  sars, or is limited to a sub-population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  We thank an anonymous referee for helpful suggestions  that clarified this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' AA, JS, and DK receive sup-  port from National Science Foundation (NSF) Physics  Frontiers Center award numbers 1430284 and 2020265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  AA thanks Alex McEwen for helpful discussions dur-  ing the data reduction stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  The Arecibo Observa-  tory is a facility of the NSF operated under cooperative  agreement (#AST-1744119) by the University of Cen-  tral Florida (UCF) in alliance with Universidad Ana G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  M´endez (UAGM) and Yang Enterprises (YEI), Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' The  Green Bank Observatory is a facility of the NSF oper-  ated under cooperative agreement by Associated Uni-  versities, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  1  2  3  4  5  6  7  8  9  10  11  12  13  Facilities: GBT (GUPPI), Arecibo (PUPPI)  Software:  PINT (Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2019), PSRCHIVE (van  Straten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011), dspsr (van Straten & Bailes 2011),  NumPy (Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2020), Matplotlib (Hunter 2007),  AstroPy (Astropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013, 2018),  emcee (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013)  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' NULLING RESULTS FOR ALL PULSARS  We show pulse profiles, MCMC corner plot results,  and nulling histograms for all of the pulsars in our sam-  ple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Pulsar Nulling with Mixture Models  17  REFERENCES  Arjunwadkar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Rajwade, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Gupta, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014, in  Astronomical Society of India Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 13,  Astronomical Society of India Conference Series, 79–81  Astropy Collaboration, Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Tollerud, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013, A&A, 558, A33,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1051/0004-6361/201322068  Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018, AJ, 156, 123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3847/1538-3881/aabc4f  Backer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1970a, Nature, 228, 42, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/228042a0  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1970b, Nature, 228, 1297, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/2281297a0  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1970c, Nature, 228, 752, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/228752a0  Bates, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Rane, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Swiggum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2014, MNRAS, 439, 2893, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/stu157  Bhat, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Cordes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Chatterjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2003, ApJ,  584, 782, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/345775  Bhat, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Gupta, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007, A&A,  462, 257, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1051/0004-6361:20053157  Davies, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lyne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Smith, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1984,  MNRAS, 211, 57, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='57  Drake, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Craft, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1968, Nature, 220, 231,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/220231a0  Faucher-Gigu`ere, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Kaspi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2006, ApJ, 643,  332, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/501516  Filippenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Radhakrishnan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1982, ApJ, 263,  828, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/160553  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Hogg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Goodman,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013, PASP, 125, 306, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/670067  Gajjar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Joshi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2012, MNRAS, 424,  1197, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='21296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='x  Gajjar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Joshi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Karuppusamy, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', &  Smits, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014a, ApJ, 797, 18,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1088/0004-637X/797/1/18  Gajjar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Joshi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Wright, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014b, MNRAS, 439,  221, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/stt2389  Harris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Millman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2020, Nature, 585, 357, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/s41586-020-2649-2  Herfindal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Rankin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007, MNRAS, 380, 430,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='12089.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='x  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2009, MNRAS, 393, 1391,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='14119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='x  Honnappa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lewandowski, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kijak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2012,  MNRAS, 421, 1996,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='20424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='x  Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007, Computing in Science & Engineering, 9,  90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='55  Ivezi´c, ˇZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Connolly, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', VanderPlas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Gray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2020, Statistics, Data Mining, and Machine Learning in  Astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A Practical Python Guide for the Analysis of  Survey Data, Updated Edition  Kaplan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Swiggum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Fichtenbauer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', &  Vallisneri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2018, ApJ, 855, 14,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3847/1538-4357/aaab62  Konar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Deka, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2019, Journal of Astrophysics and  Astronomy, 40, 42, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1007/s12036-019-9608-z  Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lyne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', O’Brien, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Jordan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', &  Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2006, Science, 312, 549,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1124060  Lomax, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2007, Statistical Concepts: A Second Course  (Lawrence Erlbaum Associates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  https://books.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='com/books?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='id=p17rT373FNAC  Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2004, Handbook of Pulsar  Astronomy, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 4  Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Demorest, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2019, PINT:  High-precision pulsar timing analysis package,  Astrophysics Source Code Library, record ascl:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  http://ascl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='net/1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='007  Lynch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Boyles, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013, ApJ,  763, 81, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1088/0004-637X/763/2/81  Lynch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Swiggum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kondratiev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2018, ApJ, 859, 93, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='3847/1538-4357/aabf8a  Lyne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2009, in Astrophysics and Space Science  Library, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 357, Astrophysics and Space Science  Library, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Becker, 67,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1007/978-3-540-76965-1 4  Manchester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Hobbs, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Teoh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Hobbs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2005, AJ, 129, 1993, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/428488  McKinnon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014, PASP, 126, 476,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/676975  McLaughlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lyne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2006, Nature, 439, 817, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1038/nature04440  Pedregosa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Varoquaux, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Gramfort, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011,  Journal of Machine Learning Research, 12, 2825.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  http://jmlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='org/papers/v12/pedregosa11a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='html  Rajwade, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Gupta, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Kumar, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Arjunwadkar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  2014, in Astronomical Society of India Conference Series,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 13, Astronomical Society of India Conference Series,  73–77  Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Demorest, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Ford, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2009, in  American Astronomical Society Meeting Abstracts, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  214, American Astronomical Society Meeting Abstracts  #214, 605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='08  Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Eikenberry, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Middleditch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2002,  AJ, 124, 1788, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/342285  Redman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Rankin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2009, MNRAS, 395, 1529,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='14632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='x  Ritchings, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1976, MNRAS, 176, 249,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='249  18  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  Rosen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Swiggum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', McLaughlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2013,  ApJ, 768, 85, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1088/0004-637X/768/1/85  Ruderman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Sutherland, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1975, ApJ, 196, 51,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/153393  Sheikh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & MacDonald, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2021, MNRAS, 502,  4669, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/stab282  Smith, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1973, MNRAS, 161, 9P,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1093/mnras/161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9P  Stovall, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Lynch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2014, ApJ,  791, 67, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1088/0004-637X/791/1/67  Taylor, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Manchester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Huguenin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 1975,  ApJ, 195, 513, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1086/153351  van Straten, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', & Bailes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011, PASA, 28, 1,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='1071/AS10021  van Straten, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Demorest, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', Khoo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' 2011,  PSRCHIVE: Development Library for the Analysis of  Pulsar Astronomical Data, Astrophysics Source Code  Library, record ascl:1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0111+6624.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' In this case the best fit model is a 2-component Gaussian mixture  22  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0355+28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='08  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='32  NF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='50  µ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='65  σ0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='32  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='6  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0414+31 (GBT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  24  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='024  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='50  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='476  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='300  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='02  σ1  σ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='030  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='300  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='02  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='300  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='350  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='4  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0414+31 (arecibo).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='015  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='20  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='9  σ0  σ0=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='795  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='62  σ1  σ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='568  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='9  σ0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='62  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='16  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='074  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='25  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0614+83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  26  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='022  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='021  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J0738+6904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Exponential convolved Gaussian mixture  Pulsar Nulling with Mixture Models  27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='20  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='40  σ1  σ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='389  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='054  −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1529-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  28  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='00  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='65  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='35  σ1  σ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='33  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='65  σ0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='35  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='48  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='429  −4  −2  0  2  4  6  8  10  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='6  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1536-30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  29  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='153  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  µ1  µ1=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='61  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='55  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='70  σ0  σ0=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='655  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  σ1  σ1=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='90  NF  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='55  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='70  σ0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='6  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='84  −10  0  10  20  30  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='16  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1629+33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  30  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='08  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='70  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='646  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='850  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='875  σ1  σ1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='030  NF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='70  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='850  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='875  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='030  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='004  −2  0  2  4  6  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='6  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1821+4147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='05  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='36  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='334  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='62  σ1  σ1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='596  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='02  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  NF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='99  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='05  µ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='36  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='62  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='007  −3  −2  −1  0  1  2  3  4  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='2  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1822+02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  32  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='0  Pulse phase  0  100  200  300  400  Single pulses  ON  OFF  Intensity  µ0  µ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='014  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='10  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='42  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='389  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='63  σ1  σ1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='584  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='04  µ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  NF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='10  µ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='42  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='63  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='004  −1  0  1  2  3  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='2  Probability Density  MM On fit  ON/OFF histograms  MM Off fit  MM emission fit  MM null fit  Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1829+25 (GBT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='014  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='10  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='42  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='389  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='63  σ1  σ1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='584  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='42  σ0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='63  σ1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='04  NF  NF=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='004  −1  0  1  2  3  Raw Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1829+25 (AO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  34  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J1901-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' In this case the best fit model is a 2-component Gaussian mixture  36  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J2000+29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='4  µ1  µ1=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content='328  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content='72  σ0  σ0=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J2040-21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  40  Anumarlapudi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+page_content=' Single pulse stack (upper left), MCMC corner plot (bottom), and pulse intensity histogram (upper right) for PSR  J2044+28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
+page_content=' In this case the best fit model is a 2-component Gaussian mixture  Pulsar Nulling with Mixture Models  41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-NFQT4oBgHgl3EQfKDVk/content/2301.13258v1.pdf'}
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+Fairness-aware Vision Transformer via Debiased Self-Attention
+Yao Qiang
+Chengyin Li
+Prashant Khanduri
+Dongxiao Zhu
+Department of Computer Science, Wayne State University
+{yao,cyli,khanduri.prashant,dzhu}@wayne.edu
+Abstract
+Vision Transformer (ViT) has recently gained significant
+interest in solving computer vision (CV) problems due to
+its capability of extracting informative features and mod-
+eling long-range dependencies through the self-attention
+mechanism. To fully realize the advantages of ViT in real-
+world applications, recent works have explored the trust-
+worthiness of ViT, including its robustness and explainabil-
+ity. However, another desiderata, fairness has not yet been
+adequately addressed in the literature. We establish that
+the existing fairness-aware algorithms (primarily designed
+for CNNs) do not perform well on ViT. This necessitates
+the need for developing our novel framework via Debiased
+Self-Attention (DSA). DSA is a fairness-through-blindness
+approach that enforces ViT to eliminate spurious features
+correlated with the sensitive attributes for bias mitigation.
+Notably, adversarial examples are leveraged to locate and
+mask the spurious features in the input image patches. In
+addition, DSA utilizes an attention weights alignment reg-
+ularizer in the training objective to encourage learning in-
+formative features for target prediction. Importantly, our
+DSA framework leads to improved fairness guarantees over
+prior works on multiple prediction tasks without compro-
+mising target prediction performance.
+1. Introduction
+Recently, Visual Transformer (ViT) [11, 30] has emerged
+as an architectural paradigm and a viable alternative to the
+standard Convolutional Neural Network (CNN) [19,27,42]
+for computer vision (CV) tasks. Unlike CNN, ViT is ca-
+pable of extracting global relationships via self-attention
+mechanism as well as informative features from the input
+images, leading to impressive feature representation capa-
+bilities. Consequently, ViT has demonstrated improved per-
+formance in a variety of CV tasks, including image classi-
+fication [11, 30], object detection [3, 9], semantic segmen-
+tation [55, 67], and image generation [21], to name a few.
+Due to its promising performance, it is anticipated that ViT
+will form the architectural backbone of CV algorithms in
+the near-future for real-world applications. This has led the
+(a) Original Image
+(b) Vanilla 
+(c) DSA 
+Figure 1. An illustration example. The prediction target is hair
+color and the sensitive attribute is gender. The heatmap of atten-
+tion weights show that Vanilla ViT (b) uses gender-sensitive fea-
+tures, e.g., ‘red lip’ and ‘eye shadow’, whereas our fairness-aware
+ViT DSA (c) uses informative features, e.g., ‘hair’, for predictions.
+researchers to analyze the trustworthiness of ViT for solving
+CV tasks.
+Studying the robustness of ViT has recently attracted a
+growing interest [2, 13, 38, 50, 68]. It is critical to improve
+ViT’s robustness in order to deploy them safely in the real-
+world. On the other hand, investigating ViT’s vulnerability
+to attacks can give us a deeper understanding of its underly-
+ing working mechanism. In the past, researchers have dis-
+sected the self-attention mechanism [1,47] and the gradient-
+based attribution [4] to offer a faithful explanation of the
+inner workings of ViT or Transformer at large.
+Besides robustness and explainability, fairness also
+stands as a core trustworthy desiderata for both industry
+[20] and academia [7].
+Several studies show that many
+deep-learning-based CV models simply make predictions
+by exploiting spurious correlations with the input features
+[23, 58]. These spurious features are statistically informa-
+tive features that work for a majority of training examples
+but do not capture the underlying relationship between the
+input features and the target labels.
+For illustration, let
+us consider the example in Figure 1 (taken from CelebA
+dataset). Since the target label, hair color, is spuriously cor-
+related with the gender-related sensitive attributes, e.g., ‘eye
+shadow’ or ‘red lips’ in Figure 1(b), a vanilla ViT model
+would simply learn these spurious features as a shortcut to
+predict the hair color whereas our fairness-aware ViT model
+learns the informative features, e.g., ‘hair’ in Figure 1(c), to
+make prediction.
+arXiv:2301.13803v1  [cs.CV]  31 Jan 2023
+
+Such spurious correlations can cause ViT to behave in
+a biased manner, e.g., a lower performance on some pop-
+ulation subgroups [54, 61]. Although an array of debias-
+ing algorithms have been proposed for image classification
+tasks [23, 36, 46, 60, 65, 66], most are designed for learn-
+ing with the CNN models. Whether these algorithms are
+compatible or even transferable to the ViT architecture is
+unclear. Regardless of the neural network architecture, lim-
+iting the spurious correlation between the input features and
+the target labels for bias mitigation is still a challenging
+problem. The difficulty arises from the fact that automat-
+ically locating the spurious features in the input images is
+computationally intractable. For example, one simple solu-
+tion is to have domain experts and/or crowd workers curate
+the entire training set, which neither works well with un-
+known bias [29] nor is scalable to large-scale datasets [39].
+Moreover, even if one can identify the spurious features,
+the major challenge is how to make the classifier blind to
+such features? Image in-painting [35, 59] appears to be a
+promising approach to remove the undesired features; nev-
+ertheless, significant challenges remain regarding what old
+features to cut out for debiasing and what new features to
+fill up to repair the corrupted images.
+To address the above challenges, we propose a novel
+framework for ensuring bias mitigation training of ViT via
+Debiasing Self-Attention (DSA) to decouple the target pre-
+diction from the spurious features.
+DSA takes a hierar-
+chical approach, where, in the first stage, we first localize
+the spurious features from the input imaging patches. This
+is achieved by training a bias-only model which exploits
+the spurious features to explicitly predict the sensitive at-
+tributes (e.g., gender and race). We then use adversarial
+attacks against the bias-only model to identify and perturb
+(or mask) the top patches that are responsible for the de-
+creased accuracy in predicting the sensitive attributes. No-
+tably, our approach for the fair ViTs is a novel addition to
+the growing body of work on “adversarial examples for fair-
+ness” [62,66].
+DSA relies on the intuitive hypothesis that the adversar-
+ial attacks initially designed to evaluate and understand the
+robustness of ViT can also be a viable approach for identi-
+fying and removing the spurious features towards training
+the fair ViT models. Meanwhile, whether the approaches
+that generate adversarial examples for CNN are transferable
+to ViT remains a matter of contention [17, 41, 44, 45, 53],
+the work in [13] propose Patch-Fool as one of the first ap-
+proaches to fool the self-attention mechanism by attack-
+ing image patches (as opposed to pixels) during ViT’s self-
+attention computations. In this work, we apply Patch-Fool
+to attack the bias-only model with the goal of capturing the
+most important patches for learning the sensitive attributes.
+As a result, the effect of sensitive features can be miti-
+gated with adversarial examples, which are constructed by
+directly perturbing (attacking) the sensitive patches.
+In the second stage, in addition to augmenting the
+original training set with these adversarial examples as the
+debiased training set, we also align the biased examples
+and their corresponding (unbiased) adversarial examples
+via an attention weights aligning regularizer tailor-made
+for self-attention mechanism in ViT. This leads to a novel
+training objective that encourages learning informative
+features while ensuring fairness of the trained ViT models.
+Major contributions: We summarize our major contribu-
+tions as follows: (1) We tackle the under-addressed fair-
+ness problem in ViT from a novel perspective of leveraging
+adversarial examples to eliminate spurious features while
+utilizing attention weights alignment to retain informative
+features. (2) We design a novel DSA framework for ViT
+to mitigate bias in both training set and learning algorithm
+via identifying and decorrelating the sensitive features from
+the target label. (3) DSA presents a flexible and modular
+debiasing approach that can be used either standalone or
+with other fairness-aware training algorithms to ensure ViT
+fairness. (4) Experimental results show that DSA improves
+group fairness with respect to demographic parity (DP) and
+equality of odds (EO) metrics while achieving a competitive
+or even better prediction accuracy compared to the base-
+lines. The qualitative analysis further indicates that DSA
+has reduced attention on sensitive features.
+2. Related Work
+ViT based Classification.
+The earlier exploration of ViT
+either used a hybrid architecture combining convolution and
+self-attention [3] or a pure self-attention architecture with-
+out convolution [48]. The work in [11] proposed a ViT
+that achieves impressive results on image classification us-
+ing ImageNet data set. This success has motivated a se-
+ries of subsequent works to further exploit ViT’s expressive
+power from various perspectives, such as incorporating lo-
+cality into ViT [28,30,63], and finding well-performing ViT
+using neural architecture search (NAS) [6].
+Fairness and Debiased Learning.
+The field of fairness in
+deep learning has grown significantly over the past several
+years as a result of bias in training data and algorithms [36,
+46]. The existing techniques for debiased learning can be
+roughly categorized into pre-, in-, and post-processing.
+– Pre-processing methods attempt to debias and increase
+the quality of the training set with the assumption that fair
+training sets would result in fair models [8, 25, 66]. The
+work in [66] proposed to balance the data distribution over
+different protected attributes by generating adversarial ex-
+amples to supplement the training dataset. Similarly, [25]
+generated the bias-swapped image augmentations to bal-
+ance protected attributes, which would remove spurious
+
+correlation between the target label and protected attributes.
+In [8], the authors presented fair mixup as a new data aug-
+mentation method to generate interpolated samples to find
+middle-ground representation for different sensitive groups.
+The work [46] described a novel generative data augmen-
+tation approach to create counterfactual samples that d-
+separates the sensitive attributes and the targets ensuring
+fairness and attribution-based explainability.
+– In-processing approaches aim to mitigate bias during the
+training process by directly modifying the learning algo-
+rithm and model weights with specifically designed fair-
+ness penalties/constraints or adversarial mechanism [24,36,
+40, 49, 65]. To enforce the fairness constraints, one line
+of works either disentangles the association between model
+predictions and the sensitive attributes via an auxiliary reg-
+ularization term [40] or minimize the performance differ-
+ence between protected groups with a novel objective func-
+tion [49]. However, the issue is that the trained models may
+behave differently at the inference stage even though such
+fairness constraints are satisfied during the training. An-
+other line of works [24, 36, 60, 65] enforce the model to
+generate fair outputs with adversarial training techniques
+through the min-max objective: maximizing accuracy while
+minimizing the ability of a discriminator to predict the pro-
+tected (sensitive) attribute. Nevertheless, this process can
+compromise the model performance on the main prediction
+task. Additional line of works impose either orthogonal-
+ity [51], disentanglement [32], or feature alignment [23]
+constraints on the feature representation and force the repre-
+sentation to be agnostic to the sensitive attributes. We note
+that most of these approaches are exclusively designed for
+CNN architectures, and whether these approaches are trans-
+ferable to the ViT has not yet been demonstrated.
+– Post-processing techniques directly calibrate or modify
+the classifier’s decisions to certain fairness criteria at infer-
+ence time [26, 33]. These methods require access to the
+sensitive attribute for fair inference, which may not be fea-
+sible in real-world applications due to the salient security
+and privacy concerns.
+Fairness in ViT.
+Recently, [16] explored how the spuri-
+ous correlations are manifested in ViT and performed exten-
+sive experiments to understand the role of the self-attention
+mechanism in debiased learning of ViT. Despite the new
+insights, the authors did not provide any debiasing tech-
+niques for ViT. The authors in [56] proposed a new method,
+named TADeT, for debiasing ViT that aims to discover and
+remove bias primarily from query matrix features. To our
+knowledge, this is the only published work along the line
+of fairness ViT. Nevertheless, this pioneering work TADeT
+has two weaknesses: first, it requires parameter sharing
+across the key and value weights in self-attention mecha-
+nism, which may conflict with most ViT architectures; sec-
+ond, the complex alignment strategy on the query matrix
+is not straightforward and well investigated. Thus, TADeT
+does not even outperform the compared baselines that pri-
+marily designed for CNNs.
+In contrast to the above works, this work tackles the de-
+biasing problem through a novel perspective of fairness-
+through-adversarial-attack. The proposed DSA framework
+combines the strengths of both pre- and in-processing ap-
+proaches via leveraging data augmentation (for ensuring
+fairness in the training set) and feature alignment for bias
+mitigation. The adversarial examples are used to both dis-
+entangle spurious features from informative features and to
+align attention weights, specifically, tailor-made for the self-
+attention mechanism in ViT.
+3. Preliminaries
+3.1. Overview of Vision Transformer
+Similar to the Transformer architecture [57], the ViT model
+expects the input to be a linear sequence of token/patch
+embeddings. An input image is first partitioned into non-
+overlapping fixed-size square patches with resolution p×p,
+resulting in a sequence of flattened 2D patches. For ex-
+ample, given an image of size 384 × 384 and patch size
+p = 16, the image is divided into patches of resolution
+16 × 16, resulting in 576 image patches. These patches are
+then mapped to constant-size embeddings using a trainable
+linear projection. In this example, the projection layer will
+produce 576 embedding vectors of fixed dimensions. Next,
+position embeddings are added to the patch embeddings to
+imbibe relative positional information of the patches. Fi-
+nally. the ViT model prepends a learnable embedding (class
+token) to the sequence of embedded patches following [10],
+which is used as image representation at the model’s output.
+The core architecture of ViT mainly consists of mul-
+tiple stacked encoder blocks, where each block primarily
+consists of a Multi-head Self Attention (MSA) layer and
+a Feed-Forward Network (FFN) layer.
+Within the MSA
+layer, multiple self-attention heads learn relationships be-
+tween each pair of input patches. Using three different lin-
+ear transformations, the input patch xi is first projected to
+a query qi, a key ki, and a value vi in each self-attention
+head, i here is the index of the patches. The query qi then
+computes the dot products with all the keys k, which are
+further scaled and normalized by the softmax layer to obtain
+the attention weights. After this, it outputs hi by weighted
+sum up all the values v with the obtained attention weights.
+Finally, the outputs from all heads are concatenated and
+re-projected by a linear layer into an output patch. FFN
+consists of two linear layers, which are connected by the
+GeLU activation function and process each hi ∈ Rd from
+the precedent MSA layer individually. Both MSA and FFN
+layers function as the residual connection.
+
+3.2. Fairness Metrics
+Many different notions of fairness have been proposed in
+the literature [12, 18]. In this work, we mainly focus on
+the two most widely used definitions: demographic par-
+ity [12] and equalized odds [18] as the metrics to assess
+group fairness of the model. Demographic Parity (DP) mea-
+sures whether the true positive rates across all groups (de-
+fined by a sensitive attribute s, e.g., gender) are equal, par-
+ticularly between the vulnerable minority group (s = 0)
+and others (s = 1), formally: DP = TPRs=1 − TPRs=0.
+Equalized Odds (EO) is used to understand the dispari-
+ties in both the true positive rates and the false positive
+rates in the vulnerable group compared to others: EO =
+1
+2[TPRs=1 − TPRs=0] + 1
+2[FPRs=1 − FPRs=0]. In ad-
+dition, we also use Accuracy (ACC) and Balanced Accu-
+racy (BA) [43], where BA =
+1
+4[TPRs=0 + TNRs=0 +
+TPRs=1 + TNRs=1], to evaluate the utility of the model.
+However, when a dataset is class imbalanced, BA will have
+an implicit bias against the minority class. Therefore, we
+introduce Difference of Balanced Accuracy (DBA) as a
+way to measure the difference in a model’s performance
+across groups defined by a sensitive attribute while account-
+ing for class imbalance, formally: DBA = 1
+2[TPRs=1 +
+TNRs=1] − 1
+2[TPRs=0 + TNRs=0].
+4. The Proposed Framework
+4.1. Problem Formulation
+We consider a supervised classification task with training
+samples {x, y, s} ∼ pdata, where x ∈ X is the input fea-
+ture, y ∈ Y is the target label, and s ∈ S is an annotated
+sensitive categorical attribute that we wish to protect. Some
+examples of s include gender, race, age or other attributes
+that can identify a certain protected group. We assume that
+the sensitive attributes S can only be used during training
+phase, and are not accessible during the inference (post-
+training phase). Moreover, we suppose that each input fea-
+ture x can be split into two parts, one with sensitive features
+xs that are highly relevant to the sensitive attribute s, and
+the rest xt that are relevant to the prediction of the target
+label y, i.e., we have x = (xs, xt) ∈ X.
+We develop a two-step hierarchical approach for bias
+mitigation, wherein, in the first stage, we localize and mask
+the sensitive attributes xs from the input x in order to
+disentangle xs from xt.
+This is accomplished by trans-
+forming the model prediction from p(x) = p(y|xs, xt) to
+p(x) ∝ p(x′) = p(y|x′
+t), where x′ is the sample constructed
+after masking the sensitive attributes xs from x via adver-
+sarial attacks. In the second stage, we utilize the original
+x and the augmented data x′ to train a ViT model f(·) for
+generating the prediction, as ˆy = f(x), while at the same
+time satisfying certain fairness requirements (i.e., DP, EO,
+and DBA) with respect to the sensitive attributes s.
+4.2. Bias in Training Set and ViT Model
+The tendency of neural networks (including ViT) to learn
+spurious correlations makes them particularly vulnerable
+to utilizing sensitive features to make predictions, thereby,
+propagating biases towards a particular group [15]. This
+issue is particularly salient with the current deep learning
+models that follow the data-driven learning paradigm and
+are trained with imbalanced data set where some sensitive
+features could have a high correlation with certain class la-
+bels. Our work is motivated by the empirical observation
+that the bias in learning is mainly caused by the model’s
+reliance on sensitive features for prediction. Note that the
+sensitive features xs are parts of the input features x, that
+are highly predictive of the sensitive attribute s. In Figure
+1, we visualize the attention weights from the ViT model to
+analyze the importance of different features. In this exam-
+ple, gender is the sensitive attribute that is highly correlated
+with the prediction task of hair color. The Vanilla model
+may pay more attention on the gender related features, in-
+dicating that it has associated gender with the hair color.
+This association might lead the ViT model to discriminate
+against the female group. We have thus established that, for
+the image classification task using CelebA dataset, the ViT
+model is heavily biased as it relies on the sensitive features
+for prediction. This observation naturally leads to our DSA
+framework for bias mitigation discussed next.
+4.3. Debiased Self-Attention (DSA) Framework
+The discussion in Section 4.2 demonstrates that the reliance
+of ViT on the sensitive features for prediction can lead to
+bias. Therefore, to mitigate the bias originating from the
+sensitive features, we propose to achieve fairness by miti-
+gating the influence of sensitive features on the prediction
+task. However, note that it is a challenging task to locate the
+sensitive features in the input. To address this challenge, we
+propose a hierarchical framework as discussed in Section
+4.1. Specifically, our DSA framework follows a two-step
+procedure (Figure 2):
+Step 1: Firstly, we train a bias-only model that deliberately
+maximizes the usage of sensitive features for prediction,
+followed by adversarial attack on the bias-only model to lo-
+calize and mask the sensitive attributes.
+Step 2: Second, we train a debiased model with augmented
+adversarial examples and attention weights alignment.
+4.3.1
+Training the Bias-only Model
+Recall that the input feature x = (xs, xt) ∈ X where xs are
+the sensitive features while xt are the target related features.
+The goal of Step 1 (see Section 4.2) is to learn only the sen-
+sitive features xs, during training the bias-only model. To
+achieve this, we first build a bias-only ViT model which
+maximally utilizes the sensitive features for prediction. We
+
+Debiased Self-Attention 
+Sensitive Label (s) Prediction 
+11
+15
+16
+6
+7
+Bias-Only 
+0
+2
+1
+11
+Target Label (y) Prediction 
+0
+2
+1
+15
+16
+6
+7
+Adversarial Attack 
+16
+15
+0
+2
+1
+6
+7
+11
+16
+15
+0
+2
+1
+6
+7
+11
+cls
+low
+attention 
+pos
+Attention Weights
+Alignment
+adversarial attack
+train bias-only model
+train debiased model
+attention weights
+alignment
+Figure 2. The DSA framework. The bias-only model is first trained to learn the spurious features (the green patches) for predicting sensitive
+attribute (s ∈ S) (see Section 4.3.1). Adversarial attack is then applied against the bias-only model to generate the adversarial examples,
+(x′), by perturbing the sensitive patches (the grid shadow patches) of the original inputs (x ∈ X) (see Section 4.3.2). Finally, both x
+and x′ are used to train a fairness-aware ViT with an attention weights alignment objective (see Eq. (10)) and learn the target (y)-related
+informative features (the red patches) (see Sections 4.3.3 and 4.3.4). Best viewed in color.
+denote the bias-only model by fB(x, s) = c(h(x), s),
+where h(x) is the intermediate representation of the input
+x, and c(·) maps the intermediate representation to the final
+prediction. Note that h(x) contains only m elements from
+the categories in S, e.g., m = 2 in most of our experimental
+settings. The key motivation of using the m elements for
+input representation h(x) is to force the bias-only model
+to only utilize sensitive attributes to obtain the prediction
+fB(x, s).
+Given N samples of the input, xi, and the sensitive at-
+tribute, si, pairs {xi, si}N
+i=1, the bias-only model minimizes
+the following loss.
+LB(x) = − 1
+N
+N
+�
+i=1
+si log(fB(xi, si))
++ (1 − si) log(1 − fB(xi, si)).
+(1)
+We illustrate the idea using the example in Figure 2. We
+consider the hair color classification tasks with gender bias.
+Input representation h(x) is denoted using two elements,
+indicating the sensitive attributes male and female, respec-
+tively. The bias-only model fB(x, s) mainly relies on the
+sensitive features, like ‘eye shadow’ and/or ‘red lips’, to
+predict the label as female, while at the same time pay-
+ing nearly no attention to the hair color related features like
+‘hair’ themselves.
+4.3.2
+Adversarial Attack Against the Bias-only Model
+After obtaining the bias-only model, the following proce-
+dure in Step 2 of the DSA framework localizes and masks
+the spurious (sensitive) features via adversarial attacks that
+are generated using the Patch-Fool construction proposed
+in [13].
+Specifically, Patch-Fool is designed to fool the
+self-attention mechanism in ViTs by attacking their basic
+component (i.e., a single patch) with a series of attention-
+aware optimization techniques, demonstrating that the ViTs
+are more vulnerable to adversarial attacks than the CNNs.
+However, in contrast to [13], instead of applying Patch-Fool
+as an adversarial attack method to evaluate the robustness of
+ViT, we utilize it to efficiently localize and mask the sensi-
+tive features in the inputs. To this end, we adapt the objec-
+tive function of Patch-Fool in order to attack the bias-only
+model on the sensitive labels instead of the target labels.
+Specifically, given the objective function LB(x) and a se-
+ries of input image patches X = [x1, · · · , xp, · · · , xn]T ∈
+Rn×d with its associated sensitive label s, the objective of
+the adversarial algorithm is
+arg max
+1≤p≤n,E∈Rn×dLB(X + 1 ⊙ E, s),
+(2)
+where E denotes the adversarial perturbation; 1 ∈ Rn is the
+identifying one-hot vector demonstrating whether current p-
+th patch is selected or not; ⊙ represents the penetrating face
+product [13]. Thus, the Patch-Fool needs to (1) select the
+adversarial patch p, and (2) optimize the corresponding ad-
+versarial attack, E.
+Selection of p: For encoder blocks in the ViT, we define:
+t(l)
+j
+= �
+h,i a(l,h,i)
+j
+to measure the importance of the j-th
+patch in the l-th block based on its contributions to other
+patches in the self-attention calculation, where a(l,h,i) =
+[a(l,h,i)
+1
+, · · · , a(l,h,i)
+n
+] denotes the attention distribution for
+
+the ith patch of the hth head in the lth block. The moti-
+vation behind applying Patch-Fool is to localize the most
+influence patch p according to the predicted sensitive at-
+tribute s. Here, we derive the top k (which is a tunable
+hyper-parameter) important patches from arg max t(l)
+j .
+Optimize E: Given the selected adversarial patch index p
+from the previous step, an attention-aware loss is applied for
+the lth block as: LAttn = �
+h,i a(l,h,i)
+p
+. This loss is expected
+to be maximized so that the adversarial patch p, serving as
+the target adversarial patch, can attract more attention from
+other patches for effectively fooling ViTs. The perturbation
+E is then updated based on both the final sensitive classifi-
+cation loss and a layer-wise attention-aware loss:
+L(X′, s, p) = LB(X′, s) + α
+�
+l
+LAttn(X′, p),
+(3)
+where X′ ≜ X + 1 ⊙ E and α is a weight hyper-parameter
+set to 0.5 in the experiments. Moreover, PCGrad [64] is
+adopted to avoid the gradient conflict of the two losses and
+E is updated using:
+δE = ∇EL(X′, s, p) − α
+�
+l
+βl∇ELB(X′, s),
+(4)
+where
+βl =
+�
+�
+�
+0,
+⟨∇ELB(X′, s), ∇ELAttn(X′, p)⟩ > 0
+⟨∇ELB(X′, s), ∇ELAttn(X′, p)⟩
+∥∇ELB(X′, s)∥2
+,
+otherwise.
+(5)
+Following PGD [37], we iteratively update E using an
+Adam optimizer: Et+1 = Et + η · Adam(δEt), where η
+is the step-size for each update.
+4.3.3
+Attention Weights Alignment
+After Step 1, the DSA framework generates the adversarial
+example x′, whose top k patches containing sensitive at-
+tributes are perturbed through the adversarial attack. Here,
+besides using these adversarial examples as augmentation
+during training of the debiased ViT models, we also lever-
+age them via attention weights alignment to further guide
+the model to pay more attention to the target-related fea-
+tures. This also allows more sensitive features to be dis-
+covered and ignored by self-attention mechanism in the
+ViT models as shown in Figure 2. In particular, we ap-
+ply three different feature discrepancy metrics D(·, ·), i.e.,
+Mean Squared Error (MSE), Kullback-Leibler Divergence
+(KL-Div), and Attention Transfer (AT), to evaluate the dis-
+crepancy between the attention weights Ax and Ax′ from
+the original sample x and the adversarial example x′, re-
+spectively. We define the three metrics as:
+LA = D⋆(Ax, Ax′),
+(6)
+where D⋆ is either
+DMSE(Ax, Ax′) = 1
+2
+�
+j∈I
+∥Ax
+j − Ax′
+j ∥2
+(7)
+DKL−Div(Ax∥Ax′) =
+�
+j∈I
+Ax
+j log Ax
+j
+Ax′
+j
+(8)
+DAT(Ax, Ax′) = 1
+2
+�
+j∈I
+����
+Ax
+j
+∥Ax
+j ∥2
+−
+Ax′
+j
+∥Ax′∥2
+����
+2
+,
+(9)
+where I denotes the indices of all the adversarial examples
+and the original example attention weights pairs for which
+we perform alignment. Finally, to incorporate the attention
+distributions of Ax and Ax′ in the objective, we add LA as
+a regularizer in the overall objective.
+4.3.4
+Overall Loss Function
+Putting the above Steps 1 and 2 together, the overall objec-
+tive for training the proposed debiased model is:
+L = λ1LCE(x, y) + λ2LCE(x′, y) + λ3LA,
+(10)
+where LCE denotes the standard cross entropy (CE) loss;
+λ1, λ2, and λ3 are three weighted coefficients for control-
+ling the three losses. These parameters are designed for
+controlling the fairness-utility trade-off. We provide further
+ablation study on these terms in the experiments.
+5. Experimental Settings
+5.1. Datasets
+We evaluate the DSA framework on two popular CV
+datasets, namely, Waterbirds [49] and CelebA [31]. Wa-
+terbirds dataset contains spurious correlation between the
+background features S = {water, land} and target label Y =
+{waterbird, landbird}. The spurious correlation is injected
+by pairing waterbirds with the water background and land-
+birds with the land background more frequently, as com-
+pared to other combinations. CelebA dataset, which has
+been widely used in the fairness literature, contains 200k
+celebrity face images with annotations for 40 binary at-
+tributes. We present the results on three settings follow-
+ing [16,56], each with a corresponding binary task (Y) that
+the model is trained to predict, and a binary sensitive at-
+tribute (S) over which we wish the model to be unbiased.
+The three settings described as a tuple (Y, S) are as follows:
+(Gray Hair, Gender), (Wavy Hair, Gender), and (Smiling,
+High Cheekbones). We provide more details of these set-
+tings in the Supplementary Materials.
+5.2. Implementation Details
+We train the ViT-S/16 models from scratch for each pre-
+diction task. The ViT-S/16 model consists of 196 patches
+
+ACC
+DP
+BA
+DBA
+EO
+82.4 84.8 87.2 89.6 92.0
+Vanila
+TADeT
+MMD
+MFD
+DANN
+LAFTRE
+AM
+DSA (Ours)
+0.25
+0.28
+0.3
+0.33
+0.35
+79.0
+80.0
+81.0
+82.0
+83.0
+0.01
+0.02
+0.03
+0.04
+0.05
+0.26
+0.28
+0.31
+0.33
+0.35
+(a) Y: Gray hair S: Gender
+ACC
+DP
+BA
+DBA
+EO
+68.0 71.0 74.0 77.0 80.0
+Vanila
+TADeT
+MMD
+MFD
+DANN
+LAFTRE
+AM
+DSA (Ours)
+0.23
+0.29
+0.34
+0.4
+0.45
+59.0
+63.0
+67.0
+71.0
+75.0
+1.4
+2.8
+4.2
+5.6
+7.0
+0.2
+0.25
+0.3
+0.35
+0.4
+(b) Y: Wavy hair S: Gender
+ACC
+DP
+BA
+DBA
+EO
+85.2 86.4 87.6 88.8 90.0
+Vanila
+TADeT
+MMD
+MFD
+DANN
+LAFTRE
+AM
+DSA (Ours)
+0.31
+0.34
+0.36
+0.39
+0.42
+72.4
+74.8
+77.2
+79.6
+82.0
+0.0
+0.01
+0.01
+0.02
+0.02
+0.32
+0.35
+0.37
+0.4
+0.42
+(c) Y: Smiling S: High Cheeckbones
+Figure 3. Fairness and accuracy evaluation for all methods over different combinations of target (y) and sensitive (s) on CelebA dataset. For
+DSA, we use LA = DAT . The test accuracies of the bias-only model used in AM and DSA for predicting gender and high cheekbones are
+82.62% and 80.71%, respectively. The success rates of adversarial attacks are reported in Supplementary Material. The ↙ signs indicate
+the lower value of the corresponding metric is better, while ↗ denotes the higher value is better. Best viewed in color.
+(each representing a 16x16 sub-image), 1 class token patch,
+12 transformer encoder layers, and 8 attention heads. We
+flatten and project each patch into a 64-dimensional vec-
+tor and add positional embeddings. The embedded patches
+are fed into the ViT encoder. After the ViT encoder pro-
+cesses the patch embeddings, the class token patch is fed
+into 2 fully-connected layers (with hidden state size as 256)
+and a sigmoid layer to produce a single normalized output
+score (since we deal with binary classification). We train the
+ViT models using momentum Stochastic Gradient Descent
+(SGD) with a momentum parameter of 0.9 and an initial
+learning rate of 3e-2 for 20 epochs. We use a fixed batch
+size of 32, gradient clipping at global norm 1, and a cosine
+decay learning rate schedule with a linear warmup follow-
+ing [16]. We select the model with the best accuracy on the
+validation sets.
+5.3. Baselines
+We select the following debiasing algorithms as baselines
+for performance evaluation, for which we select the best
+model that yields the highest validation performance. To
+our knowledge, besides the proposed DSA and AM as a
+home run method, TADeT is the only third-party fairness-
+aware algorithm tailor-made for ViT while all the others are
+designed for CNN. We consider the following baselines:
+Vanilla [11]: The ViT models are only trained with CE
+loss for target prediction. Attention Masking (AM): The
+self-attention mechanism is critical in ViT as it provides
+important weights for extracting visual features. We pro-
+pose the AM method as a home run that directly masks
+the top-k patches with highest attention scores for the bias-
+only model. Mitigating Bias in ViT via Target Alignment
+(TADeT) [56] uses a targeted alignment strategy for debi-
+asing ViT that aims to identify and remove bias primarily
+from query matrix features. Maximum Mean Discrepancy
+(MMD) [34] calculates the mean of penultimate layer fea-
+ture activation values for each sensitive attribute setting and
+then minimizes their L2 distance. MMD-based Fair Dis-
+tillation (MFD) [23] adds a MMD-based regularizer that
+utilizes the group-indistinguishable predictive features from
+the teacher model while discouraging the student model
+from discriminating against any protected group. Domain
+Adversarial Neural Network (DANN) [14] employs a sen-
+sitive attribute adversary learned on top of the penultimate
+layer activation. The adversarial head consists of two linear
+layers in the same dimension as the class token, followed by
+a sigmoid function. Learning Adversarially Fair and Trans-
+ferable Representation (LAFTR) [36] trains a model with
+a modified adversarial objective that attempts to meet the
+EO fairness criterion. This objective is implemented by
+minimizing the average absolute difference on each task.
+6. Main Results and Discussion
+In this Section, we report the results of fairness and accu-
+racy evaluations, the ablation study, and the effects of model
+size and patch size.
+In Supplementary Materials, many
+more experimental results are reported, including the im-
+pact of several tunable hyper-parameters, results with dif-
+ferent D⋆ in the regularizer LA, and some qualitative eval-
+uations.
+6.1. Fairness and Accuracy Evaluations
+We report the fairness and accuracy performance on the
+three aforementioned settings (see Section 5.1) on CelebA
+dataset in Figure 3. We make the following observations.
+First, DSA outperforms all the baselines, demonstrated with
+the largest area (enclosed by the red lines) in the radar
+charts, significantly improving the ViT fairness with lower
+EO, DP, and DBA while maintaining higher accuracy in
+terms of BA and ACC. Second, several baseline methods
+
+0.02
+0.03
+0.04
+0.05
+0.06
+0.07
+0.08
+EO
+0.010
+0.015
+0.020
+0.025
+0.030
+0.035
+0.040
+DP
+Vanilla(62.36)
+TADeT(69.05)
+MMD(67.81)
+MFD(67.36)
+DANN(60.04)
+LAFTRE(64.80)
+AM(61.70)
+DSA(69.58)
+Figure 4. Fairness and accuracy evaluation on Waterbirds dataset.
+The ACCs are shown in the legends. All tunable hyper- parameters
+and other settings are same as in Figure 3.
+(e.g., MMD, MFD, and DANN) that have shown strong per-
+formance with CNN models, do not even outperform the
+vanilla model on some fairness metrics (e.g., EO), partic-
+ularly under the (Wavy Hair, Gender) setting. This may
+happen because ViT primarily learns global image fea-
+tures by modeling long-range dependencies using the self-
+attention mechanism, which is fundamentally different form
+convolution-based local feature leaning with CNN. As such,
+these baseline methods (designed for the CNNs) are not
+transferable for bias mitigation with the ViT models. Third,
+we note the home run method AM is also designed by blind-
+ing the sensitive attributes in the input based on only the
+attention weights of the bias-only model. However, sev-
+eral works [1, 22, 52] have questioned whether highly at-
+tentive inputs would significantly impact the model outputs.
+Since self-attention mechanism involves the computation of
+queries, keys, and values, reducing it only to the derived
+attention weights (inner products of queries and keys) can
+be insufficient to capture the importance of the features.
+Hence, the home run AM method fails to achieve a com-
+parable performance with the proposed DSA method.
+Similarly, we observe the same patterns on the results of
+Waterbirds dataset as shown in Figure 4. DSA outperforms
+all other baselines in terms of fairness evaluations, i.e., DP
+and EO, as well as accuracy performance.
+6.2. Ablating DSA
+The training objective of DSA contains three essential com-
+ponents for bias mitigation. We conduct ablation study us-
+ing the (Gray Hair, Gender) setting to analyze their indi-
+vidual contributions and report the results in Table 1 (the
+other two settings are reported in the Supplementary Ma-
+terials). We summarize our major findings. First, all of
+the components contribute towards the improved fairness
+performance across all three fairness metrics (i.e., EO, DP
+and DBA). Second, both the target (task) related CE losses
+in Eq.(10) are critical in preventing DSA from compro-
+mising the prediction performance (otherwise, the accu-
+racy drops from 90.95 to 88.32 and 88.54, respectively).
+Third, the training objective LA in Eq.(10) contributes the
+most to the higher fairness measures, as is clearly shown
+by: EO (0.2934→0.2558), DP (0.2865→0.2337), and DBA
+(0.0206→0.0031).
+Table 1. Ablation study of the three training objectives. Best re-
+sults are bold faced. ‘w/o’ represents without.
+Models
+Y : Gray Hair S: Gender
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+L(all)
+0.2558
+0.2337
+0.0031
+82.92
+90.95
+w/o LCE(x, y)
+0.2754
+0.2541
+0.0175
+81.21
+88.32
+w/o LCE(x′, y)
+0.2641
+0.2503
+0.0129
+80.65
+88.54
+w/o LA
+0.2934
+0.2865
+0.0206
+81.54
+89.91
+6.3. Effect of ViT Model Size and Patch Size
+We examine the effect of ViT model size and patch size
+on DSA in Table 2. The ViT-B model is much larger than
+the ViT-S model, which has 12 self-attention heads in each
+block and 256 hidden state size in the two fully-connected
+layers. Each patch is flattened and projected into a vector
+of 768 dimensions. We draw two conclusions from Table 2.
+First, the larger ViT-B models outperform the smaller ViT-S
+on most of the fairness and accuracy metrics, demonstrat-
+ing better feature learning capabilities with higher feature
+dimensions and more self-attention heads. Second, smaller
+patch size (16) achieves a better performance on both fair-
+ness and accuracy measurements because small patches en-
+ables extracting more fine-grained features [5].
+Table 2. Evaluations with different ViT models (i.e., ViT-B (B)
+and ViT-S (S)) and patch sizes (i.e., 16 and 32). All tunable hyper-
+parameters are set same as Figure 3. VA is short for Vanilla.
+Model
+Y : Gray Hair S: Gender
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+B/16
+VA
+0.2984
+0.2841
+0.0142
+81.95
+91.05
+DSA
+0.2424
+0.2205
+0.0081
+83.42
+91.24
+S/16
+VA
+0.2763
+0.3185
+0.0422
+81.84
+90.25
+DSA
+0.2558
+0.2337
+0.0031
+82.92
+90.95
+B/32
+VA
+0.2982
+0.2976
+0.0205
+81.11
+90.16
+DSA
+0.2629
+0.2520
+0.0109
+82.73
+91.03
+S/32
+VA
+0.3014
+0.3213
+0.0198
+80.64
+89.18
+DSA
+0.2935
+0.3165
+0.0086
+80.86
+89.45
+7. Conclusion
+In this work, we proposed a novel hierarchical fairness-
+aware ViT training framework named DSA for bias mitiga-
+tion in both the training set and the learning algorithm. The
+DSA framework eliminates the spurious features through
+adversarial attacks on the bias-only model while retaining
+the informative features through an attention weights align-
+ment regularizer. The experimental results demonstrate the
+effectiveness of DSA for bias mitigation without compro-
+mising prediction performance.
+
+References
+[1] Samira Abnar and Willem Zuidema.
+Quantifying atten-
+tion flow in transformers. arXiv preprint arXiv:2005.00928,
+2020. 1, 8
+[2] Srinadh Bhojanapalli, Ayan Chakrabarti, Daniel Glasner,
+Daliang Li, Thomas Unterthiner, and Andreas Veit. Under-
+standing robustness of transformers for image classification.
+In Proceedings of the IEEE/CVF International Conference
+on Computer Vision, pages 10231–10241, 2021. 1
+[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas
+Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-
+end object detection with transformers. In European confer-
+ence on computer vision, pages 213–229. Springer, 2020. 1,
+2
+[4] Hila Chefer, Shir Gur, and Lior Wolf. Transformer inter-
+pretability beyond attention visualization. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pages 782–791, 2021. 1
+[5] Chun-Fu Richard Chen, Quanfu Fan, and Rameswar Panda.
+Crossvit: Cross-attention multi-scale vision transformer for
+image classification. In Proceedings of the IEEE/CVF in-
+ternational conference on computer vision, pages 357–366,
+2021. 8
+[6] Minghao Chen, Houwen Peng, Jianlong Fu, and Haibin
+Ling. Autoformer: Searching transformers for visual recog-
+nition. In Proceedings of the IEEE/CVF International Con-
+ference on Computer Vision, pages 12270–12280, 2021. 2
+[7] Alexandra Chouldechova and Aaron Roth.
+The fron-
+tiers of fairness in machine learning.
+arXiv preprint
+arXiv:1810.08810, 2018. 1
+[8] Ching-Yao Chuang and Youssef Mroueh. Fair mixup: Fair-
+ness via interpolation.
+arXiv preprint arXiv:2103.06503,
+2021. 2, 3
+[9] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen.
+Up-detr: Unsupervised pre-training for object detection with
+transformers. In Proceedings of the IEEE/CVF conference
+on computer vision and pattern recognition, pages 1601–
+1610, 2021. 1
+[10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina
+Toutanova.
+Bert:
+Pre-training of deep bidirectional
+transformers for language understanding.
+arXiv preprint
+arXiv:1810.04805, 2018. 3
+[11] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov,
+Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner,
+Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl-
+vain Gelly, et al. An image is worth 16x16 words: Trans-
+formers for image recognition at scale.
+arXiv preprint
+arXiv:2010.11929, 2020. 1, 2, 7
+[12] Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Rein-
+gold, and Richard Zemel. Fairness through awareness. In
+Proceedings of the 3rd innovations in theoretical computer
+science conference, pages 214–226, 2012. 4
+[13] Yonggan Fu, Shunyao Zhang, Shang Wu, Cheng Wan, and
+Yingyan Lin. Patch-fool: Are vision transformers always
+robust against adversarial perturbations?
+arXiv preprint
+arXiv:2203.08392, 2022. 1, 2, 5
+[14] Yaroslav Ganin and Victor Lempitsky. Unsupervised domain
+adaptation by backpropagation. In International conference
+on machine learning, pages 1180–1189. PMLR, 2015. 7
+[15] Robert Geirhos, J¨orn-Henrik Jacobsen, Claudio Michaelis,
+Richard Zemel, Wieland Brendel, Matthias Bethge, and Fe-
+lix A Wichmann. Shortcut learning in deep neural networks.
+Nature Machine Intelligence, 2(11):665–673, 2020. 4
+[16] Soumya Suvra Ghosal, Yifei Ming, and Yixuan Li. Are vi-
+sion transformers robust to spurious correlations?
+arXiv
+preprint arXiv:2203.09125, 2022. 3, 6, 7
+[17] Jindong Gu, Volker Tresp, and Yao Qin. Are vision trans-
+formers robust to patch perturbations?
+In European Con-
+ference on Computer Vision, pages 404–421. Springer, 2022.
+2
+[18] Moritz Hardt, Eric Price, and Nati Srebro. Equality of op-
+portunity in supervised learning. Advances in neural infor-
+mation processing systems, 29, 2016. 4
+[19] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
+Deep residual learning for image recognition. In Proceed-
+ings of the IEEE conference on computer vision and pattern
+recognition, pages 770–778, 2016. 1
+[20] Kenneth
+Holstein,
+Jennifer
+Wortman
+Vaughan,
+Hal
+Daum´e III, Miro Dudik, and Hanna Wallach.
+Improving
+fairness in machine learning systems: What do industry
+practitioners need?
+In Proceedings of the 2019 CHI
+conference on human factors in computing systems, pages
+1–16, 2019. 1
+[21] Drew A Hudson and Larry Zitnick. Generative adversarial
+transformers. In International conference on machine learn-
+ing, pages 4487–4499. PMLR, 2021. 1
+[22] Sarthak Jain and Byron C Wallace. Attention is not explana-
+tion. arXiv preprint arXiv:1902.10186, 2019. 8
+[23] Sangwon Jung, Donggyu Lee, Taeeon Park, and Taesup
+Moon.
+Fair feature distillation for visual recognition.
+In
+Proceedings of the IEEE/CVF conference on computer vi-
+sion and pattern recognition, pages 12115–12124, 2021. 1,
+2, 3, 7
+[24] Byungju Kim, Hyunwoo Kim, Kyungsu Kim, Sungjin Kim,
+and Junmo Kim. Learning not to learn: Training deep neural
+networks with biased data. In Proceedings of the IEEE/CVF
+Conference on Computer Vision and Pattern Recognition,
+pages 9012–9020, 2019. 3
+[25] Eungyeup Kim, Jihyeon Lee, and Jaegul Choo. Biaswap:
+Removing dataset bias with bias-tailored swapping augmen-
+tation. In Proceedings of the IEEE/CVF International Con-
+ference on Computer Vision, pages 14992–15001, 2021. 2
+[26] Michael P Kim, Amirata Ghorbani, and James Zou. Multi-
+accuracy: Black-box post-processing for fairness in classifi-
+cation. In Proceedings of the 2019 AAAI/ACM Conference
+on AI, Ethics, and Society, pages 247–254, 2019. 3
+[27] Xin Li, Xiangrui Li, Deng Pan, and Dongxiao Zhu. Improv-
+ing adversarial robustness via probabilistically compact loss
+with logit constraints. In Proceedings of the AAAI Confer-
+ence on Artificial Intelligence, volume 35, pages 8482–8490,
+2021. 1
+[28] Yawei Li, Kai Zhang, Jiezhang Cao, Radu Timofte, and Luc
+Van Gool. Localvit: Bringing locality to vision transformers.
+arXiv preprint arXiv:2104.05707, 2021. 2
+
+[29] Zhiheng Li, Anthony Hoogs, and Chenliang Xu. Discover
+and mitigate unknown biases with debiasing alternate net-
+works. In European Conference on Computer Vision, pages
+270–288. Springer, 2022. 2
+[30] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng
+Zhang, Stephen Lin, and Baining Guo. Swin transformer:
+Hierarchical vision transformer using shifted windows. In
+Proceedings of the IEEE/CVF International Conference on
+Computer Vision, pages 10012–10022, 2021. 1, 2
+[31] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang.
+Deep learning face attributes in the wild. In Proceedings of
+the IEEE international conference on computer vision, pages
+3730–3738, 2015. 6
+[32] Francesco Locatello, Gabriele Abbati, Thomas Rainforth,
+Stefan Bauer, Bernhard Sch¨olkopf, and Olivier Bachem. On
+the fairness of disentangled representations.
+Advances in
+Neural Information Processing Systems, 32, 2019. 3
+[33] Pranay K Lohia, Karthikeyan Natesan Ramamurthy, Man-
+ish Bhide, Diptikalyan Saha, Kush R Varshney, and Ruchir
+Puri.
+Bias mitigation post-processing for individual and
+group fairness. In Icassp 2019-2019 ieee international con-
+ference on acoustics, speech and signal processing (icassp),
+pages 2847–2851. IEEE, 2019. 3
+[34] Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jor-
+dan. Learning transferable features with deep adaptation net-
+works.
+In International conference on machine learning,
+pages 97–105. PMLR, 2015. 7
+[35] Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher
+Yu, Radu Timofte, and Luc Van Gool.
+Repaint: Inpaint-
+ing using denoising diffusion probabilistic models. In Pro-
+ceedings of the IEEE/CVF Conference on Computer Vision
+and Pattern Recognition (CVPR), pages 11461–11471, June
+2022. 2
+[36] David Madras, Elliot Creager, Toniann Pitassi, and Richard
+Zemel. Learning adversarially fair and transferable represen-
+tations. In International Conference on Machine Learning,
+pages 3384–3393. PMLR, 2018. 2, 3, 7
+[37] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt,
+Dimitris Tsipras, and Adrian Vladu. Towards deep learn-
+ing models resistant to adversarial attacks. arXiv preprint
+arXiv:1706.06083, 2017. 6
+[38] Xiaofeng Mao, Gege Qi, Yuefeng Chen, Xiaodan Li, Ranjie
+Duan, Shaokai Ye, Yuan He, and Hui Xue. Towards robust
+vision transformer. In Proceedings of the IEEE/CVF Con-
+ference on Computer Vision and Pattern Recognition, pages
+12042–12051, 2022. 1
+[39] Tyler McDonnell, Matthew Lease, Mucahid Kutlu, and
+Tamer Elsayed.
+Why is that relevant? collecting annota-
+tor rationales for relevance judgments. In Proceedings of the
+AAAI Conference on Human Computation and Crowdsourc-
+ing, volume 4, pages 139–148, 2016. 2
+[40] Junhyun Nam, Hyuntak Cha, Sungsoo Ahn, Jaeho Lee, and
+Jinwoo Shin. Learning from failure: De-biasing classifier
+from biased classifier. Advances in Neural Information Pro-
+cessing Systems, 33:20673–20684, 2020. 3
+[41] Muzammal Naseer, Kanchana Ranasinghe, Salman Khan,
+Fahad Shahbaz Khan, and Fatih Porikli.
+On improving
+adversarial transferability of vision transformers.
+arXiv
+preprint arXiv:2106.04169, 2021. 2
+[42] Deng Pan, Xin Li, and Dongxiao Zhu. Explaining deep neu-
+ral network models with adversarial gradient integration. In
+IJCAI, pages 2876–2883, 2021. 1
+[43] Sungho Park, Dohyung Kim, Sunhee Hwang, and Hyeran
+Byun. Readme: Representation learning by fairness-aware
+disentangling method.
+arXiv preprint arXiv:2007.03775,
+2020. 4
+[44] Sayak Paul and Pin-Yu Chen. Vision transformers are robust
+learners. In Proceedings of the AAAI Conference on Artificial
+Intelligence, volume 36, pages 2071–2081, 2022. 2
+[45] Francesco Pinto, Philip Torr, and Puneet K Dokania. Are
+vision transformers always more robust than convolutional
+neural networks? 2021. 2
+[46] Yao Qiang, Chengyin Li, Marco Brocanelli, and Dongxiao
+Zhu. Counterfactual interpolation augmentation (cia): A uni-
+fied approach to enhance fairness and explainability of dnn.
+In Proceedings of the Thirty-First International Joint Con-
+ference on Artificial Intelligence, IJCAI-22, LD Raedt, Ed.
+International Joint Conferences on Artificial Intelligence Or-
+ganization, volume 7, pages 732–739, 2022. 2, 3
+[47] Yao Qiang, Deng Pan, Chengyin Li, Xin Li, Rhongho Jang,
+and Dongxiao Zhu. AttCAT: Explaining transformers via at-
+tentive class activation tokens. In Alice H. Oh, Alekh Agar-
+wal, Danielle Belgrave, and Kyunghyun Cho, editors, Ad-
+vances in Neural Information Processing Systems, 2022. 1
+[48] Prajit Ramachandran, Niki Parmar, Ashish Vaswani, Irwan
+Bello, Anselm Levskaya, and Jon Shlens. Stand-alone self-
+attention in vision models. Advances in Neural Information
+Processing Systems, 32, 2019. 2
+[49] Shiori Sagawa, Pang Wei Koh, Tatsunori B Hashimoto, and
+Percy Liang.
+Distributionally robust neural networks for
+group shifts: On the importance of regularization for worst-
+case generalization. arXiv preprint arXiv:1911.08731, 2019.
+3, 6
+[50] Hadi Salman, Saachi Jain, Eric Wong, and Aleksander
+Madry. Certified patch robustness via smoothed vision trans-
+formers. In Proceedings of the IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, pages 15137–
+15147, 2022. 1
+[51] Mhd Hasan Sarhan, Nassir Navab, Abouzar Eslami, and
+Shadi Albarqouni. Fairness by learning orthogonal disentan-
+gled representations. In European Conference on Computer
+Vision, pages 746–761. Springer, 2020. 3
+[52] Sofia Serrano and Noah A Smith. Is attention interpretable?
+arXiv preprint arXiv:1906.03731, 2019. 8
+[53] Rulin Shao, Zhouxing Shi, Jinfeng Yi, Pin-Yu Chen, and
+Cho-Jui Hsieh. On the adversarial robustness of vision trans-
+formers. arXiv preprint arXiv:2103.15670, 2021. 2
+[54] Krishna Kumar Singh, Dhruv Mahajan, Kristen Grauman,
+Yong Jae Lee, Matt Feiszli, and Deepti Ghadiyaram. Don’t
+judge an object by its context: learning to overcome con-
+textual bias. In Proceedings of the IEEE/CVF Conference
+on Computer Vision and Pattern Recognition, pages 11070–
+11078, 2020. 2
+
+[55] Robin Strudel, Ricardo Garcia, Ivan Laptev, and Cordelia
+Schmid. Segmenter: Transformer for semantic segmenta-
+tion. In Proceedings of the IEEE/CVF International Confer-
+ence on Computer Vision, pages 7262–7272, 2021. 1
+[56] Sruthi Sudhakar, Viraj Prabhu, Arvindkumar Krishnakumar,
+and Judy Hoffman. Mitigating bias in visual transformers
+via targeted alignment. 2021. 3, 6, 7
+[57] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko-
+reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia
+Polosukhin. Attention is all you need. Advances in neural
+information processing systems, 30, 2017. 3
+[58] Mei Wang and Weihong Deng. Mitigating bias in face recog-
+nition using skewness-aware reinforcement learning. In Pro-
+ceedings of the IEEE/CVF conference on computer vision
+and pattern recognition, pages 9322–9331, 2020. 1
+[59] Wentao Wang, Li Niu, Jianfu Zhang, Xue Yang, and Liqing
+Zhang. Dual-path image inpainting with auxiliary gan inver-
+sion. In Proceedings of the IEEE/CVF Conference on Com-
+puter Vision and Pattern Recognition, pages 11421–11430,
+2022. 2
+[60] Zhibo Wang, Xiaowei Dong, Henry Xue, Zhifei Zhang,
+Weifeng Chiu, Tao Wei, and Kui Ren. Fairness-aware ad-
+versarial perturbation towards bias mitigation for deployed
+deep models. In Proceedings of the IEEE/CVF Conference
+on Computer Vision and Pattern Recognition, pages 10379–
+10388, 2022. 2, 3
+[61] Benjamin Wilson, Judy Hoffman, and Jamie Morgenstern.
+Predictive inequity in object detection.
+arXiv preprint
+arXiv:1902.11097, 2019. 2
+[62] Han Xu, Xiaorui Liu, Yaxin Li, Anil Jain, and Jiliang Tang.
+To be robust or to be fair: Towards fairness in adversarial
+training. In International Conference on Machine Learning,
+pages 11492–11501. PMLR, 2021. 2
+[63] Jianwei Yang, Chunyuan Li, Pengchuan Zhang, Xiyang Dai,
+Bin Xiao, Lu Yuan, and Jianfeng Gao. Focal self-attention
+for local-global interactions in vision transformers.
+arXiv
+preprint arXiv:2107.00641, 2021. 2
+[64] Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine,
+Karol Hausman, and Chelsea Finn.
+Gradient surgery for
+multi-task learning. Advances in Neural Information Pro-
+cessing Systems, 33:5824–5836, 2020. 6
+[65] Brian Hu Zhang, Blake Lemoine, and Margaret Mitchell.
+Mitigating unwanted biases with adversarial learning.
+In
+Proceedings of the 2018 AAAI/ACM Conference on AI,
+Ethics, and Society, pages 335–340, 2018. 2, 3
+[66] Yi Zhang and Jitao Sang. Towards accuracy-fairness para-
+dox: Adversarial example-based data augmentation for vi-
+sual debiasing.
+In Proceedings of the 28th ACM Interna-
+tional Conference on Multimedia, pages 4346–4354, 2020.
+2
+[67] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu,
+Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao
+Xiang, Philip HS Torr, et al. Rethinking semantic segmen-
+tation from a sequence-to-sequence perspective with trans-
+formers.
+In Proceedings of the IEEE/CVF conference on
+computer vision and pattern recognition, pages 6881–6890,
+2021. 1
+[68] Daquan Zhou, Zhiding Yu, Enze Xie, Chaowei Xiao, An-
+imashree Anandkumar, Jiashi Feng, and Jose M Alvarez.
+Understanding the robustness in vision transformers. In In-
+ternational Conference on Machine Learning, pages 27378–
+27394. PMLR, 2022. 1
+
+8. Supplementary Materials
+In this Section, we provide additional experiments for per-
+formance evaluation of the proposed DSA framework on
+CelebA and Waterbird datasets.
+8.1. Dataset Statistics
+Recall from Section 5.1 that we choose three settings from
+the CelebA dataset and one setting from the Waterbird
+dataset to evaluate the baselines against the proposed DSA
+framework. We describe these four settings using the tuples
+(Y, S) as follows: a) (Smiling, High Cheekbones), b) (Wavy
+Hair, Gender), c) (Gray Hair, Gender), and d) (Waterbird,
+Place). Note that the first three settings are considered for
+the CelebA dataset while the last setting is considered for
+the Waterbird dataset. We first provide the data statistics
+for all these settings in Figure 5. We note that significant
+biases exist in all these settings. For example, a majority
+of “Smiling” faces are correlated with “High Cheekbones”
+whereas the majority of “Not Smiling” faces are correlated
+with “Not High Cheekbones”. Similar spurious correlations
+are also observed in other settings as well, which can lead to
+biased models. We establish this by further analyzing and
+reporting the True Positive Rate (TPR) of the vanilla ViT
+models trained on these biased datasets in Table 3. Clearly,
+the biased ViT models perform significantly worse on the
+minority groups, e.g., predicting “Smiling” when the indi-
+vidual does not have “High Cheekbones” (S = 0: 63.93%)
+compared to the ones that have “High Cheekbones” (S = 1:
+96.50%). Next, we analyze the effect of the tunable hyper-
+parameters on the performance of DSA.
+Table 3. Disparities of true positive rate (TPR) among different
+task and sensitive attribute tuples.
+Y
+S
+TPR%↑
+∆TPR%
+Smiling
+Not High Cheekbones (0)
+63.93
+32.57
+High Cheekbones (1)
+96.50
+Wavy Hair
+Female (0)
+77.62
+20.04
+Male (1)
+57.58
+Gray Hair
+Female (0)
+63.31
+31.85
+Male (1)
+95.16
+Waterbird
+Land (0)
+55.75
+14.14
+Water (1)
+69.89
+8.2. Effect of Discrepancy Metrics
+Since We apply three different feature discrepancy metrics
+D(·, ·), i.e., MSE, KL-Div, and AT, to evaluate the discrep-
+ancy between the attention weights Ax and Ax′ in (6), we
+report the effect of these discrepancy metrics in Table 4.
+Although the differences between these discrepancy met-
+rics are relatively small, AT clearly achieves the best per-
+formance, especially on the fairness metrics. Since AT can
+capture the most significant differences between Ax and
+Ax′ as shown in (9), the regularizer LA is more efficient
+to minimize their differences.
+Table 4. Evaluations with different discrepancy metrics in the reg-
+ularizer (6).
+D⋆
+Y : Gray Hair S: Gender
+EO↓
+DP↓
+DBA↓
+BA↑
+Acc%↑
+MSE
+0.2706
+0.2488
+0.0136
+82.07
+90.13
+KL-Div
+0.2608
+0.2467
+0.0106
+83.26
+89.48
+AT
+0.2558
+0.2337
+0.0031
+82.92
+90.95
+8.3. Effect of Tunable Hyper-parameters
+There are several tunable hyper-parameters in the proposed
+DSA framework, including the various coefficient weights
+in the objective function and the number of masked patches
+learned during the adversarial attack.
+We tune the three coefficient weights in the objective
+function (10) to identify the best-performing model as
+shown in Table 5. To improve model performance, we be-
+lieve that these coefficient weights should be carefully tuned
+and selected under different settings and datasets.
+The effect of the number of masked patches learned dur-
+ing the adversarial attack is shown in Table 6. In our ex-
+periments, the ViT model with k = 3 patches achieves the
+best performance among all compared metrics in most set-
+tings. Looking into more details of the adversarial examples
+shown in Figure 6, if we perturb only one patch out of all
+the input patches, some sensitive attributes may not be lo-
+calized and masked. On the contrary, perturbing excessive
+patches (e.g., 5 patches) would increase the risk of masking
+the related attributes to the target task, resulting in a worse
+prediction performance. For example, the ACC drops from
+90.95 to 88.55 in the setting of (Gray Hair, Gender) with 5
+perturbed patches, as shown in Table 6.
+Table 5. Evaluations with different tunable coefficient weights in
+the objective function (10).
+λ1, λ2, λ3
+Y : Gray Hair S: Gender
+EO↓
+DP↓
+DBA↓
+BA↑
+Acc%↑
+1.0, 0.5, 0.5
+0.2843
+0.2675
+0.0125
+81.45
+91.12
+0.5, 1.0, 0.5
+0.2633
+0.2578
+0.0106
+81.32
+89.26
+1.0, 1.0, 0.5
+0.2558
+0.2337
+0.0031
+82.92
+90.95
+8.4. Ablation Studies and Effect of Patch Size
+We report the adversarial success rates of DSA on the sen-
+sitive attributes as target with different number of masked
+patches in Table 7. Note that we only generate adversarial
+examples for the training sets.
+In Table 8, we report additional ablation study results for
+the DSA framework on the other two settings from CelebA
+dataset. It is straightforward to make a similar conclusion
+
+Smiling
+Not Smiling
+0
+20000
+40000
+60000
+80000
+78899
+13290
+18770
+91640
+High CheekBones
+Not High CheekBones
+(a) Y: Smiling S: High Cheeckbones
+Wavy Hair
+Not Wavy Hair
+0
+10000
+20000
+30000
+40000
+50000
+60000
+70000
+11892
+72542
+52852
+65313
+Male
+Female
+(b) Y: Wavy hair S: Gender
+Gray Hair
+Not Gray Hair
+0
+1000
+2000
+3000
+4000
+5000
+6000
+6136
+1262
+1262
+6136
+Male
+Female
+(c) Y: Gray hair S: Gender
+Waterbird
+Landbird
+0
+1000
+2000
+3000
+4000
+5000
+6000
+6220
+831
+2905
+1832
+Water
+Land
+(d) Y: Waterbird S: Place
+Figure 5. Spurious correlation between tasks (Y ) and sensitive attributes (S) tuples (Y, S). Note that Figures 5a, 5b and 5c represent the
+data statistics for the CelebA dataset while Figure 5d represents the data statistics of the Waterbird dataset.
+Table 6. Performance of DSA with different number of masked or perturbed patches.
+k
+Y : Smiling
+S: High Cheekbones
+Y : Wavy Hair
+S: Gender
+Y : Gray Hair
+S: Gender
+EO↓
+DP↓
+DBA↓
+BA(%)↑
+Acc(%)↑
+EO↓
+DP↓
+DBA↓
+BA(%)↑
+Acc(%)↑
+EO↓
+DP↓
+DBA↓
+BA(%)↑
+Acc(%)↑
+1
+0.3502
+0.3341
+0.0046
+77.84
+87.18
+0.1822
+0.2036
+0.0098
+72.79
+77.26
+0.2946
+0.3075
+0.0110
+81.77
+90.61
+3
+0.3012
+0.2864
+0.0034
+80.10
+89.23
+0.1618
+0.1844
+0.0056
+73.34
+79.34
+0.2558
+0.2337
+0.0031
+82.92
+90.95
+5
+0.3218
+0.3179
+0.0040
+79.88
+88.12
+0.1604
+0.1776
+0.0087
+72.13
+78.16
+0.2776
+0.2560
+0.0216
+81.91
+88.55
+Table 7. Adversarial attack success rates of DSA on the sensitive
+attributes target with different number of masked patches, k.
+S
+k
+Success Rate%↑
+Gender
+1
+88.52
+3
+91.47
+5
+93.69
+High Cheekbones
+1
+85.41
+3
+88.64
+5
+91.58
+as in Section 6.2. We note that all the terms in the objec-
+tive function in (10) contribute towards better fairness and
+accuracy performance.
+Additional evaluations capturing the effect of different
+patch sizes on the performance of DSA are reported in Ta-
+ble 9. Similar to our conclusion in Section 6.3, the ViT
+models with smaller patch sizes, i.e., 16, achieve the best
+performance on two other settings from the CelebA dataset.
+Figure 6. Adversarial examples with different number of masked
+patches in the (Gray Hair, Gender) setting.
+8.5. Qualitative Evaluations
+In Figures 7, 8, and 9, we demonstrate some more qualita-
+tive evaluations to further demonstrate the effectiveness of
+the DSA approach. We note that the distribution of the at-
+tention weights for the ViT models trained with the vanilla
+method simply focuses on the sensitive attributes, e.g., “eye
+shadow”. This demonstrates that the vanilla ViT models are
+biased and simply leverage the sensitive features to predict
+the target labels. On the contrary, DSA reduces the atten-
+tion on these sensitive features but pays more attention on
+the target-related features, e.g., the hair, which actually de-
+termines the target label Gray and Wavy hair.
+8.6. Summary
+We summarize the major findings of our experimental study
+here. First, DSA reduces the attention on the sensitive fea-
+tures while focusing on the target-related features as an ef-
+fective approach to bias mitigation. Second, the additional
+ablation studies demonstrate that each term in the objec-
+tive function (10) contributes towards the improved fairness
+and accuracy performance of DSA. Third, we noted that the
+smaller patch size results in better performance of DSA due
+to their capability of efficiently extracting fine-grained fea-
+tures.
+(a) Original Image
+(b) Vanilla 
+(c) DSA 
+Figure 7.
+Qualitative evaluation of DSA. Y: Smiling S: High
+Cheeckbones.
+
+VANN
+.(a) Original Image
+(b) Vanilla 
+(c) DSA 
+Figure 8. Qualitative evaluation. Y: Gray hair S: Gender.
+(a) Original Image
+(b) Vanilla 
+(c) DSA 
+Figure 9. Qualitative evaluation. Y: Wavy hair S: Gender.
+Table 8. Ablation study of DSA for the three training objectives on two other settings from the CelebA data set. Best results are bold faced.
+‘w/o’ represents without.
+Models
+Y : Wavy Hair S: Gender
+Y : Smiling S: High Cheekbones
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+L(all)
+0.1618
+0.1844
+0.0056
+73.34
+79.34
+0.3012
+0.2864
+0.0034
+80.10
+89.23
+w/o LCE(x, y)
+0.2114
+0.22.03
+0.0288
+72.42
+77.56
+0.3105
+0.3014
+0.0231
+79.54
+88.06
+w/o LCE(x′, y)
+0.2004
+0.2154
+0.0275
+72.45
+77.98
+0.3198
+0.2987
+0.0129
+78.39
+88.54
+w/o LA
+0.1942
+0.2012
+0.0312
+72.33
+77.45
+0.3125
+0.2955
+0.0198
+79.21
+87.95
+Table 9. Performance evaluation of DSA with different patch sizes (i.e., 16 and 32). All tunable hyper-parameters are set same as Figure
+3. VA is short for Vanilla.
+Model
+Y : Wavy Hair S: Gender
+Y : Smiling S: High Cheekbones
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+EO↓
+DP↓
+DBA↓
+BA↑
+ACC↑
+S/16
+VA
+0.2193
+0.2204
+0.0310
+72.69
+78.78
+0.3382
+0.3256
+0.0125
+77.80
+88.04
+DSA
+0.1618
+0.1844
+0.0056
+73.34
+79.34
+0.3012
+0.2864
+0.0034
+80.10
+89.23
+S/32
+VA
+0.2236
+0.2319
+0.0450
+72.05
+78.68
+0.3398
+0.3315
+0.0213
+78.12
+87.54
+DSA
+0.1805
+0.2196
+0.0254
+72.58
+79.02
+0.3209
+0.3177
+0.0156
+79.27
+88.15
+
diff --git a/-tFST4oBgHgl3EQfcjgx/content/tmp_files/load_file.txt b/-tFST4oBgHgl3EQfcjgx/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf,len=1098
+page_content='Fairness-aware Vision Transformer via Debiased Self-Attention  Yao Qiang  Chengyin Li  Prashant Khanduri  Dongxiao Zhu  Department of Computer Science, Wayne State University  {yao,cyli,khanduri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='prashant,dzhu}@wayne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='edu  Abstract  Vision Transformer (ViT) has recently gained significant  interest in solving computer vision (CV) problems due to  its capability of extracting informative features and mod-  eling long-range dependencies through the self-attention  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To fully realize the advantages of ViT in real-  world applications, recent works have explored the trust-  worthiness of ViT, including its robustness and explainabil-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' However, another desiderata, fairness has not yet been  adequately addressed in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We establish that  the existing fairness-aware algorithms (primarily designed  for CNNs) do not perform well on ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This necessitates  the need for developing our novel framework via Debiased  Self-Attention (DSA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' DSA is a fairness-through-blindness  approach that enforces ViT to eliminate spurious features  correlated with the sensitive attributes for bias mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Notably, adversarial examples are leveraged to locate and  mask the spurious features in the input image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In  addition, DSA utilizes an attention weights alignment reg-  ularizer in the training objective to encourage learning in-  formative features for target prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Importantly, our  DSA framework leads to improved fairness guarantees over  prior works on multiple prediction tasks without compro-  mising target prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Introduction  Recently, Visual Transformer (ViT) [11, 30] has emerged  as an architectural paradigm and a viable alternative to the  standard Convolutional Neural Network (CNN) [19,27,42]  for computer vision (CV) tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Unlike CNN, ViT is ca-  pable of extracting global relationships via self-attention  mechanism as well as informative features from the input  images, leading to impressive feature representation capa-  bilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Consequently, ViT has demonstrated improved per-  formance in a variety of CV tasks, including image classi-  fication [11, 30], object detection [3, 9], semantic segmen-  tation [55, 67], and image generation [21], to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Due to its promising performance, it is anticipated that ViT  will form the architectural backbone of CV algorithms in  the near-future for real-world applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This has led the  (a) Original Image  (b) Vanilla  (c) DSA  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' An illustration example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The prediction target is hair  color and the sensitive attribute is gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The heatmap of atten-  tion weights show that Vanilla ViT (b) uses gender-sensitive fea-  tures, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', ‘red lip’ and ‘eye shadow’, whereas our fairness-aware  ViT DSA (c) uses informative features, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', ‘hair’, for predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  researchers to analyze the trustworthiness of ViT for solving  CV tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Studying the robustness of ViT has recently attracted a  growing interest [2, 13, 38, 50, 68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' It is critical to improve  ViT’s robustness in order to deploy them safely in the real-  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' On the other hand, investigating ViT’s vulnerability  to attacks can give us a deeper understanding of its underly-  ing working mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In the past, researchers have dis-  sected the self-attention mechanism [1,47] and the gradient-  based attribution [4] to offer a faithful explanation of the  inner workings of ViT or Transformer at large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Besides robustness and explainability, fairness also  stands as a core trustworthy desiderata for both industry  [20] and academia [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Several studies show that many  deep-learning-based CV models simply make predictions  by exploiting spurious correlations with the input features  [23, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' These spurious features are statistically informa-  tive features that work for a majority of training examples  but do not capture the underlying relationship between the  input features and the target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  For illustration, let  us consider the example in Figure 1 (taken from CelebA  dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Since the target label, hair color, is spuriously cor-  related with the gender-related sensitive attributes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', ‘eye  shadow’ or ‘red lips’ in Figure 1(b), a vanilla ViT model  would simply learn these spurious features as a shortcut to  predict the hair color whereas our fairness-aware ViT model  learns the informative features, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', ‘hair’ in Figure 1(c), to  make prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='13803v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='CV]  31 Jan 2023  Such spurious correlations can cause ViT to behave in  a biased manner, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', a lower performance on some pop-  ulation subgroups [54, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Although an array of debias-  ing algorithms have been proposed for image classification  tasks [23, 36, 46, 60, 65, 66], most are designed for learn-  ing with the CNN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Whether these algorithms are  compatible or even transferable to the ViT architecture is  unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Regardless of the neural network architecture, lim-  iting the spurious correlation between the input features and  the target labels for bias mitigation is still a challenging  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The difficulty arises from the fact that automat-  ically locating the spurious features in the input images is  computationally intractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' For example, one simple solu-  tion is to have domain experts and/or crowd workers curate  the entire training set, which neither works well with un-  known bias [29] nor is scalable to large-scale datasets [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Moreover, even if one can identify the spurious features,  the major challenge is how to make the classifier blind to  such features?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Image in-painting [35, 59] appears to be a  promising approach to remove the undesired features;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' nev-  ertheless, significant challenges remain regarding what old  features to cut out for debiasing and what new features to  fill up to repair the corrupted images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  To address the above challenges, we propose a novel  framework for ensuring bias mitigation training of ViT via  Debiasing Self-Attention (DSA) to decouple the target pre-  diction from the spurious features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  DSA takes a hierar-  chical approach, where, in the first stage, we first localize  the spurious features from the input imaging patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This  is achieved by training a bias-only model which exploits  the spurious features to explicitly predict the sensitive at-  tributes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', gender and race).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We then use adversarial  attacks against the bias-only model to identify and perturb  (or mask) the top patches that are responsible for the de-  creased accuracy in predicting the sensitive attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' No-  tably, our approach for the fair ViTs is a novel addition to  the growing body of work on “adversarial examples for fair-  ness” [62,66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  DSA relies on the intuitive hypothesis that the adversar-  ial attacks initially designed to evaluate and understand the  robustness of ViT can also be a viable approach for identi-  fying and removing the spurious features towards training  the fair ViT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Meanwhile, whether the approaches  that generate adversarial examples for CNN are transferable  to ViT remains a matter of contention [17, 41, 44, 45, 53],  the work in [13] propose Patch-Fool as one of the first ap-  proaches to fool the self-attention mechanism by attack-  ing image patches (as opposed to pixels) during ViT’s self-  attention computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In this work, we apply Patch-Fool  to attack the bias-only model with the goal of capturing the  most important patches for learning the sensitive attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  As a result, the effect of sensitive features can be miti-  gated with adversarial examples, which are constructed by  directly perturbing (attacking) the sensitive patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In the second stage, in addition to augmenting the  original training set with these adversarial examples as the  debiased training set, we also align the biased examples  and their corresponding (unbiased) adversarial examples  via an attention weights aligning regularizer tailor-made  for self-attention mechanism in ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This leads to a novel  training objective that encourages learning informative  features while ensuring fairness of the trained ViT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Major contributions: We summarize our major contribu-  tions as follows: (1) We tackle the under-addressed fair-  ness problem in ViT from a novel perspective of leveraging  adversarial examples to eliminate spurious features while  utilizing attention weights alignment to retain informative  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (2) We design a novel DSA framework for ViT  to mitigate bias in both training set and learning algorithm  via identifying and decorrelating the sensitive features from  the target label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (3) DSA presents a flexible and modular  debiasing approach that can be used either standalone or  with other fairness-aware training algorithms to ensure ViT  fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (4) Experimental results show that DSA improves  group fairness with respect to demographic parity (DP) and  equality of odds (EO) metrics while achieving a competitive  or even better prediction accuracy compared to the base-  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The qualitative analysis further indicates that DSA  has reduced attention on sensitive features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Related Work  ViT based Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The earlier exploration of ViT  either used a hybrid architecture combining convolution and  self-attention [3] or a pure self-attention architecture with-  out convolution [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The work in [11] proposed a ViT  that achieves impressive results on image classification us-  ing ImageNet data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This success has motivated a se-  ries of subsequent works to further exploit ViT’s expressive  power from various perspectives, such as incorporating lo-  cality into ViT [28,30,63], and finding well-performing ViT  using neural architecture search (NAS) [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Fairness and Debiased Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The field of fairness in  deep learning has grown significantly over the past several  years as a result of bias in training data and algorithms [36,  46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The existing techniques for debiased learning can be  roughly categorized into pre-, in-, and post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  – Pre-processing methods attempt to debias and increase  the quality of the training set with the assumption that fair  training sets would result in fair models [8, 25, 66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The  work in [66] proposed to balance the data distribution over  different protected attributes by generating adversarial ex-  amples to supplement the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Similarly, [25]  generated the bias-swapped image augmentations to bal-  ance protected attributes, which would remove spurious  correlation between the target label and protected attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In [8], the authors presented fair mixup as a new data aug-  mentation method to generate interpolated samples to find  middle-ground representation for different sensitive groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The work [46] described a novel generative data augmen-  tation approach to create counterfactual samples that d-  separates the sensitive attributes and the targets ensuring  fairness and attribution-based explainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  – In-processing approaches aim to mitigate bias during the  training process by directly modifying the learning algo-  rithm and model weights with specifically designed fair-  ness penalties/constraints or adversarial mechanism [24,36,  40, 49, 65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To enforce the fairness constraints, one line  of works either disentangles the association between model  predictions and the sensitive attributes via an auxiliary reg-  ularization term [40] or minimize the performance differ-  ence between protected groups with a novel objective func-  tion [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' However, the issue is that the trained models may  behave differently at the inference stage even though such  fairness constraints are satisfied during the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' An-  other line of works [24, 36, 60, 65] enforce the model to  generate fair outputs with adversarial training techniques  through the min-max objective: maximizing accuracy while  minimizing the ability of a discriminator to predict the pro-  tected (sensitive) attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Nevertheless, this process can  compromise the model performance on the main prediction  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Additional line of works impose either orthogonal-  ity [51], disentanglement [32], or feature alignment [23]  constraints on the feature representation and force the repre-  sentation to be agnostic to the sensitive attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We note  that most of these approaches are exclusively designed for  CNN architectures, and whether these approaches are trans-  ferable to the ViT has not yet been demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  – Post-processing techniques directly calibrate or modify  the classifier’s decisions to certain fairness criteria at infer-  ence time [26, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' These methods require access to the  sensitive attribute for fair inference, which may not be fea-  sible in real-world applications due to the salient security  and privacy concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Fairness in ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Recently, [16] explored how the spuri-  ous correlations are manifested in ViT and performed exten-  sive experiments to understand the role of the self-attention  mechanism in debiased learning of ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Despite the new  insights, the authors did not provide any debiasing tech-  niques for ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The authors in [56] proposed a new method,  named TADeT, for debiasing ViT that aims to discover and  remove bias primarily from query matrix features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To our  knowledge, this is the only published work along the line  of fairness ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Nevertheless, this pioneering work TADeT  has two weaknesses: first, it requires parameter sharing  across the key and value weights in self-attention mecha-  nism, which may conflict with most ViT architectures;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' sec-  ond, the complex alignment strategy on the query matrix  is not straightforward and well investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Thus, TADeT  does not even outperform the compared baselines that pri-  marily designed for CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In contrast to the above works, this work tackles the de-  biasing problem through a novel perspective of fairness-  through-adversarial-attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The proposed DSA framework  combines the strengths of both pre- and in-processing ap-  proaches via leveraging data augmentation (for ensuring  fairness in the training set) and feature alignment for bias  mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The adversarial examples are used to both dis-  entangle spurious features from informative features and to  align attention weights, specifically, tailor-made for the self-  attention mechanism in ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Preliminaries  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Overview of Vision Transformer  Similar to the Transformer architecture [57], the ViT model  expects the input to be a linear sequence of token/patch  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' An input image is first partitioned into non-  overlapping fixed-size square patches with resolution p×p,  resulting in a sequence of flattened 2D patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' For ex-  ample, given an image of size 384 × 384 and patch size  p = 16, the image is divided into patches of resolution  16 × 16, resulting in 576 image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' These patches are  then mapped to constant-size embeddings using a trainable  linear projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In this example, the projection layer will  produce 576 embedding vectors of fixed dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Next,  position embeddings are added to the patch embeddings to  imbibe relative positional information of the patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fi-  nally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' the ViT model prepends a learnable embedding (class  token) to the sequence of embedded patches following [10],  which is used as image representation at the model’s output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The core architecture of ViT mainly consists of mul-  tiple stacked encoder blocks, where each block primarily  consists of a Multi-head Self Attention (MSA) layer and  a Feed-Forward Network (FFN) layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Within the MSA  layer, multiple self-attention heads learn relationships be-  tween each pair of input patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Using three different lin-  ear transformations, the input patch xi is first projected to  a query qi, a key ki, and a value vi in each self-attention  head, i here is the index of the patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The query qi then  computes the dot products with all the keys k, which are  further scaled and normalized by the softmax layer to obtain  the attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' After this, it outputs hi by weighted  sum up all the values v with the obtained attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Finally, the outputs from all heads are concatenated and  re-projected by a linear layer into an output patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' FFN  consists of two linear layers, which are connected by the  GeLU activation function and process each hi ∈ Rd from  the precedent MSA layer individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Both MSA and FFN  layers function as the residual connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness Metrics  Many different notions of fairness have been proposed in  the literature [12, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In this work, we mainly focus on  the two most widely used definitions: demographic par-  ity [12] and equalized odds [18] as the metrics to assess  group fairness of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Demographic Parity (DP) mea-  sures whether the true positive rates across all groups (de-  fined by a sensitive attribute s, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', gender) are equal, par-  ticularly between the vulnerable minority group (s = 0)  and others (s = 1), formally: DP = TPRs=1 − TPRs=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Equalized Odds (EO) is used to understand the dispari-  ties in both the true positive rates and the false positive  rates in the vulnerable group compared to others: EO =  1  2[TPRs=1 − TPRs=0] + 1  2[FPRs=1 − FPRs=0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In ad-  dition, we also use Accuracy (ACC) and Balanced Accu-  racy (BA) [43], where BA =  1  4[TPRs=0 + TNRs=0 +  TPRs=1 + TNRs=1], to evaluate the utility of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  However, when a dataset is class imbalanced, BA will have  an implicit bias against the minority class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Therefore, we  introduce Difference of Balanced Accuracy (DBA) as a  way to measure the difference in a model’s performance  across groups defined by a sensitive attribute while account-  ing for class imbalance, formally: DBA = 1  2[TPRs=1 +  TNRs=1] − 1  2[TPRs=0 + TNRs=0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The Proposed Framework  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Problem Formulation  We consider a supervised classification task with training  samples {x, y, s} ∼ pdata, where x ∈ X is the input fea-  ture, y ∈ Y is the target label, and s ∈ S is an annotated  sensitive categorical attribute that we wish to protect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Some  examples of s include gender, race, age or other attributes  that can identify a certain protected group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We assume that  the sensitive attributes S can only be used during training  phase, and are not accessible during the inference (post-  training phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Moreover, we suppose that each input fea-  ture x can be split into two parts, one with sensitive features  xs that are highly relevant to the sensitive attribute s, and  the rest xt that are relevant to the prediction of the target  label y, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', we have x = (xs, xt) ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  We develop a two-step hierarchical approach for bias  mitigation, wherein, in the first stage, we localize and mask  the sensitive attributes xs from the input x in order to  disentangle xs from xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  This is accomplished by trans-  forming the model prediction from p(x) = p(y|xs, xt) to  p(x) ∝ p(x′) = p(y|x′  t), where x′ is the sample constructed  after masking the sensitive attributes xs from x via adver-  sarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In the second stage, we utilize the original  x and the augmented data x′ to train a ViT model f(·) for  generating the prediction, as ˆy = f(x), while at the same  time satisfying certain fairness requirements (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', DP, EO,  and DBA) with respect to the sensitive attributes s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Bias in Training Set and ViT Model  The tendency of neural networks (including ViT) to learn  spurious correlations makes them particularly vulnerable  to utilizing sensitive features to make predictions, thereby,  propagating biases towards a particular group [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This  issue is particularly salient with the current deep learning  models that follow the data-driven learning paradigm and  are trained with imbalanced data set where some sensitive  features could have a high correlation with certain class la-  bels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Our work is motivated by the empirical observation  that the bias in learning is mainly caused by the model’s  reliance on sensitive features for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Note that the  sensitive features xs are parts of the input features x, that  are highly predictive of the sensitive attribute s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Figure  1, we visualize the attention weights from the ViT model to  analyze the importance of different features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In this exam-  ple, gender is the sensitive attribute that is highly correlated  with the prediction task of hair color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The Vanilla model  may pay more attention on the gender related features, in-  dicating that it has associated gender with the hair color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  This association might lead the ViT model to discriminate  against the female group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We have thus established that, for  the image classification task using CelebA dataset, the ViT  model is heavily biased as it relies on the sensitive features  for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This observation naturally leads to our DSA  framework for bias mitigation discussed next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Debiased Self-Attention (DSA) Framework  The discussion in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2 demonstrates that the reliance  of ViT on the sensitive features for prediction can lead to  bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Therefore, to mitigate the bias originating from the  sensitive features, we propose to achieve fairness by miti-  gating the influence of sensitive features on the prediction  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' However, note that it is a challenging task to locate the  sensitive features in the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To address this challenge, we  propose a hierarchical framework as discussed in Section  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Specifically, our DSA framework follows a two-step  procedure (Figure 2):  Step 1: Firstly, we train a bias-only model that deliberately  maximizes the usage of sensitive features for prediction,  followed by adversarial attack on the bias-only model to lo-  calize and mask the sensitive attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Step 2: Second, we train a debiased model with augmented  adversarial examples and attention weights alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1  Training the Bias-only Model  Recall that the input feature x = (xs, xt) ∈ X where xs are  the sensitive features while xt are the target related features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The goal of Step 1 (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2) is to learn only the sen-  sitive features xs, during training the bias-only model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To  achieve this, we first build a bias-only ViT model which  maximally utilizes the sensitive features for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We  Debiased Self-Attention  Sensitive Label (s) Prediction  11  15  16  6  7  Bias-Only  0  2  1  11  Target Label (y) Prediction  0  2  1  15  16  6  7  Adversarial Attack  16  15  0  2  1  6  7  11  16  15  0  2  1  6  7  11  cls  low  attention  pos  Attention Weights  Alignment  adversarial attack  train bias-only model  train debiased model  attention weights  alignment  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The DSA framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The bias-only model is first trained to learn the spurious features (the green patches) for predicting sensitive  attribute (s ∈ S) (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Adversarial attack is then applied against the bias-only model to generate the adversarial examples,  (x′), by perturbing the sensitive patches (the grid shadow patches) of the original inputs (x ∈ X) (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Finally, both x  and x′ are used to train a fairness-aware ViT with an attention weights alignment objective (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (10)) and learn the target (y)-related  informative features (the red patches) (see Sections 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  denote the bias-only model by fB(x, s) = c(h(x), s),  where h(x) is the intermediate representation of the input  x, and c(·) maps the intermediate representation to the final  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Note that h(x) contains only m elements from  the categories in S, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', m = 2 in most of our experimental  settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The key motivation of using the m elements for  input representation h(x) is to force the bias-only model  to only utilize sensitive attributes to obtain the prediction  fB(x, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Given N samples of the input, xi, and the sensitive at-  tribute, si, pairs {xi, si}N  i=1, the bias-only model minimizes  the following loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  LB(x) = − 1  N  N  �  i=1  si log(fB(xi, si))  + (1 − si) log(1 − fB(xi, si)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (1)  We illustrate the idea using the example in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We  consider the hair color classification tasks with gender bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Input representation h(x) is denoted using two elements,  indicating the sensitive attributes male and female, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The bias-only model fB(x, s) mainly relies on the  sensitive features, like ‘eye shadow’ and/or ‘red lips’, to  predict the label as female, while at the same time pay-  ing nearly no attention to the hair color related features like  ‘hair’ themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2  Adversarial Attack Against the Bias-only Model  After obtaining the bias-only model, the following proce-  dure in Step 2 of the DSA framework localizes and masks  the spurious (sensitive) features via adversarial attacks that  are generated using the Patch-Fool construction proposed  in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Specifically, Patch-Fool is designed to fool the  self-attention mechanism in ViTs by attacking their basic  component (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', a single patch) with a series of attention-  aware optimization techniques, demonstrating that the ViTs  are more vulnerable to adversarial attacks than the CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  However, in contrast to [13], instead of applying Patch-Fool  as an adversarial attack method to evaluate the robustness of  ViT, we utilize it to efficiently localize and mask the sensi-  tive features in the inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To this end, we adapt the objec-  tive function of Patch-Fool in order to attack the bias-only  model on the sensitive labels instead of the target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Specifically, given the objective function LB(x) and a se-  ries of input image patches X = [x1, · · · , xp, · · · , xn]T ∈  Rn×d with its associated sensitive label s, the objective of  the adversarial algorithm is  arg max  1≤p≤n,E∈Rn×dLB(X + 1 ⊙ E, s),  (2)  where E denotes the adversarial perturbation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1 ∈ Rn is the  identifying one-hot vector demonstrating whether current p-  th patch is selected or not;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' ⊙ represents the penetrating face  product [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Thus, the Patch-Fool needs to (1) select the  adversarial patch p, and (2) optimize the corresponding ad-  versarial attack, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Selection of p: For encoder blocks in the ViT, we define:  t(l)  j  = �  h,i a(l,h,i)  j  to measure the importance of the j-th  patch in the l-th block based on its contributions to other  patches in the self-attention calculation, where a(l,h,i) =  [a(l,h,i)  1  , · · · , a(l,h,i)  n  ] denotes the attention distribution for  the ith patch of the hth head in the lth block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The moti-  vation behind applying Patch-Fool is to localize the most  influence patch p according to the predicted sensitive at-  tribute s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Here, we derive the top k (which is a tunable  hyper-parameter) important patches from arg max t(l)  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Optimize E: Given the selected adversarial patch index p  from the previous step, an attention-aware loss is applied for  the lth block as: LAttn = �  h,i a(l,h,i)  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This loss is expected  to be maximized so that the adversarial patch p, serving as  the target adversarial patch, can attract more attention from  other patches for effectively fooling ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The perturbation  E is then updated based on both the final sensitive classifi-  cation loss and a layer-wise attention-aware loss:  L(X′, s, p) = LB(X′, s) + α  �  l  LAttn(X′, p),  (3)  where X′ ≜ X + 1 ⊙ E and α is a weight hyper-parameter  set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5 in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Moreover, PCGrad [64] is  adopted to avoid the gradient conflict of the two losses and  E is updated using:  δE = ∇EL(X′, s, p) − α  �  l  βl∇ELB(X′, s),  (4)  where  βl =  �  �  �  0,  ⟨∇ELB(X′, s), ∇ELAttn(X′, p)⟩ > 0  ⟨∇ELB(X′, s), ∇ELAttn(X′, p)⟩  ∥∇ELB(X′, s)∥2  ,  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (5)  Following PGD [37], we iteratively update E using an  Adam optimizer: Et+1 = Et + η · Adam(δEt), where η  is the step-size for each update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3  Attention Weights Alignment  After Step 1, the DSA framework generates the adversarial  example x′, whose top k patches containing sensitive at-  tributes are perturbed through the adversarial attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Here,  besides using these adversarial examples as augmentation  during training of the debiased ViT models, we also lever-  age them via attention weights alignment to further guide  the model to pay more attention to the target-related fea-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This also allows more sensitive features to be dis-  covered and ignored by self-attention mechanism in the  ViT models as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In particular, we ap-  ply three different feature discrepancy metrics D(·, ·), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=',  Mean Squared Error (MSE), Kullback-Leibler Divergence  (KL-Div), and Attention Transfer (AT), to evaluate the dis-  crepancy between the attention weights Ax and Ax′ from  the original sample x and the adversarial example x′, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We define the three metrics as:  LA = D⋆(Ax, Ax′),  (6)  where D⋆ is either  DMSE(Ax, Ax′) = 1  2  �  j∈I  ∥Ax  j − Ax′  j ∥2  (7)  DKL−Div(Ax∥Ax′) =  �  j∈I  Ax  j log Ax  j  Ax′  j  (8)  DAT(Ax, Ax′) = 1  2  �  j∈I  ����  Ax  j  ∥Ax  j ∥2  −  Ax′  j  ∥Ax′∥2  ����  2  ,  (9)  where I denotes the indices of all the adversarial examples  and the original example attention weights pairs for which  we perform alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Finally, to incorporate the attention  distributions of Ax and Ax′ in the objective, we add LA as  a regularizer in the overall objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='4  Overall Loss Function  Putting the above Steps 1 and 2 together, the overall objec-  tive for training the proposed debiased model is:  L = λ1LCE(x, y) + λ2LCE(x′, y) + λ3LA,  (10)  where LCE denotes the standard cross entropy (CE) loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  λ1, λ2, and λ3 are three weighted coefficients for control-  ling the three losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' These parameters are designed for  controlling the fairness-utility trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We provide further  ablation study on these terms in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Experimental Settings  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Datasets  We evaluate the DSA framework on two popular CV  datasets, namely, Waterbirds [49] and CelebA [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Wa-  terbirds dataset contains spurious correlation between the  background features S = {water, land} and target label Y =  {waterbird, landbird}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The spurious correlation is injected  by pairing waterbirds with the water background and land-  birds with the land background more frequently, as com-  pared to other combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' CelebA dataset, which has  been widely used in the fairness literature, contains 200k  celebrity face images with annotations for 40 binary at-  tributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We present the results on three settings follow-  ing [16,56], each with a corresponding binary task (Y) that  the model is trained to predict, and a binary sensitive at-  tribute (S) over which we wish the model to be unbiased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The three settings described as a tuple (Y, S) are as follows:  (Gray Hair, Gender), (Wavy Hair, Gender), and (Smiling,  High Cheekbones).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We provide more details of these set-  tings in the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' Implementation Details  We train the ViT-S/16 models from scratch for each pre-  diction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The ViT-S/16 model consists of 196 patches  ACC  DP  BA  DBA  EO  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' Fairness and accuracy evaluation for all methods over different combinations of target (y) and sensitive (s) on CelebA dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' The success rates of adversarial attacks are reported in Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The ↙ signs indicate  the lower value of the corresponding metric is better, while ↗ denotes the higher value is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (each representing a 16x16 sub-image), 1 class token patch,  12 transformer encoder layers, and 8 attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We  flatten and project each patch into a 64-dimensional vec-  tor and add positional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The embedded patches  are fed into the ViT encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' After the ViT encoder pro-  cesses the patch embeddings, the class token patch is fed  into 2 fully-connected layers (with hidden state size as 256)  and a sigmoid layer to produce a single normalized output  score (since we deal with binary classification).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We train the  ViT models using momentum Stochastic Gradient Descent  (SGD) with a momentum parameter of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='9 and an initial  learning rate of 3e-2 for 20 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We use a fixed batch  size of 32, gradient clipping at global norm 1, and a cosine  decay learning rate schedule with a linear warmup follow-  ing [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We select the model with the best accuracy on the  validation sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Baselines  We select the following debiasing algorithms as baselines  for performance evaluation, for which we select the best  model that yields the highest validation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To  our knowledge, besides the proposed DSA and AM as a  home run method, TADeT is the only third-party fairness-  aware algorithm tailor-made for ViT while all the others are  designed for CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We consider the following baselines:  Vanilla [11]: The ViT models are only trained with CE  loss for target prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Attention Masking (AM): The  self-attention mechanism is critical in ViT as it provides  important weights for extracting visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We pro-  pose the AM method as a home run that directly masks  the top-k patches with highest attention scores for the bias-  only model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Mitigating Bias in ViT via Target Alignment  (TADeT) [56] uses a targeted alignment strategy for debi-  asing ViT that aims to identify and remove bias primarily  from query matrix features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Maximum Mean Discrepancy  (MMD) [34] calculates the mean of penultimate layer fea-  ture activation values for each sensitive attribute setting and  then minimizes their L2 distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' MMD-based Fair Dis-  tillation (MFD) [23] adds a MMD-based regularizer that  utilizes the group-indistinguishable predictive features from  the teacher model while discouraging the student model  from discriminating against any protected group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Domain  Adversarial Neural Network (DANN) [14] employs a sen-  sitive attribute adversary learned on top of the penultimate  layer activation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The adversarial head consists of two linear  layers in the same dimension as the class token, followed by  a sigmoid function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Learning Adversarially Fair and Trans-  ferable Representation (LAFTR) [36] trains a model with  a modified adversarial objective that attempts to meet the  EO fairness criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This objective is implemented by  minimizing the average absolute difference on each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Main Results and Discussion  In this Section, we report the results of fairness and accu-  racy evaluations, the ablation study, and the effects of model  size and patch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Supplementary Materials, many  more experimental results are reported, including the im-  pact of several tunable hyper-parameters, results with dif-  ferent D⋆ in the regularizer LA, and some qualitative eval-  uations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness and Accuracy Evaluations  We report the fairness and accuracy performance on the  three aforementioned settings (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1) on CelebA  dataset in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We make the following observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  First, DSA outperforms all the baselines, demonstrated with  the largest area (enclosed by the red lines) in the radar  charts, significantly improving the ViT fairness with lower  EO, DP, and DBA while maintaining higher accuracy in  terms of BA and ACC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Second, several baseline methods  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='08  EO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='040  DP  Vanilla(62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='36)  TADeT(69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='05)  MMD(67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='81)  MFD(67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='36)  DANN(60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='04)  LAFTRE(64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='80)  AM(61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='70)  DSA(69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='58)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness and accuracy evaluation on Waterbirds dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The ACCs are shown in the legends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' All tunable hyper- parameters  and other settings are same as in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', MMD, MFD, and DANN) that have shown strong per-  formance with CNN models, do not even outperform the  vanilla model on some fairness metrics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', EO), partic-  ularly under the (Wavy Hair, Gender) setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This may  happen because ViT primarily learns global image fea-  tures by modeling long-range dependencies using the self-  attention mechanism, which is fundamentally different form  convolution-based local feature leaning with CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' As such,  these baseline methods (designed for the CNNs) are not  transferable for bias mitigation with the ViT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Third,  we note the home run method AM is also designed by blind-  ing the sensitive attributes in the input based on only the  attention weights of the bias-only model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' However, sev-  eral works [1, 22, 52] have questioned whether highly at-  tentive inputs would significantly impact the model outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Since self-attention mechanism involves the computation of  queries, keys, and values, reducing it only to the derived  attention weights (inner products of queries and keys) can  be insufficient to capture the importance of the features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Hence, the home run AM method fails to achieve a com-  parable performance with the proposed DSA method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Similarly, we observe the same patterns on the results of  Waterbirds dataset as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' DSA outperforms  all other baselines in terms of fairness evaluations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', DP  and EO, as well as accuracy performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Ablating DSA  The training objective of DSA contains three essential com-  ponents for bias mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We conduct ablation study us-  ing the (Gray Hair, Gender) setting to analyze their indi-  vidual contributions and report the results in Table 1 (the  other two settings are reported in the Supplementary Ma-  terials).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We summarize our major findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' First, all of  the components contribute towards the improved fairness  performance across all three fairness metrics (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', EO, DP  and DBA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Second, both the target (task) related CE losses  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (10) are critical in preventing DSA from compro-  mising the prediction performance (otherwise, the accu-  racy drops from 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='95 to 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='32 and 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='54, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Third, the training objective LA in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (10) contributes the  most to the higher fairness measures, as is clearly shown  by: EO (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2934→0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2558), DP (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2865→0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2337), and DBA  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0206→0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0031).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Ablation study of the three training objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Best re-  sults are bold faced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' ‘w/o’ represents without.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Models  Y : Gray Hair S: Gender  EO↓  DP↓  DBA↓  BA↑  ACC↑  L(all)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2558  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2337  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0031  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='92  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='95  w/o LCE(x, y)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2754  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2541  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0175  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='21  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' Effect of ViT Model Size and Patch Size  We examine the effect of ViT model size and patch size  on DSA in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The ViT-B model is much larger than  the ViT-S model, which has 12 self-attention heads in each  block and 256 hidden state size in the two fully-connected  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Each patch is flattened and projected into a vector  of 768 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We draw two conclusions from Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  First, the larger ViT-B models outperform the smaller ViT-S  on most of the fairness and accuracy metrics, demonstrat-  ing better feature learning capabilities with higher feature  dimensions and more self-attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Second, smaller  patch size (16) achieves a better performance on both fair-  ness and accuracy measurements because small patches en-  ables extracting more fine-grained features [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Evaluations with different ViT models (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', ViT-B (B)  and ViT-S (S)) and patch sizes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=', 16 and 32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' All tunable hyper-  parameters are set same as Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' VA is short for Vanilla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Model  Y : Gray Hair S: Gender  EO↓  DP↓  DBA↓  BA↑  ACC↑  B/16  VA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='18  DSA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' Conclusion  In this work, we proposed a novel hierarchical fairness-  aware ViT training framework named DSA for bias mitiga-  tion in both the training set and the learning algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The  DSA framework eliminates the spurious features through  adversarial attacks on the bias-only model while retaining  the informative features through an attention weights align-  ment regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' The experimental results demonstrate the  effectiveness of DSA for bias mitigation without compro-  mising prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  References  [1] Samira Abnar and Willem Zuidema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Quantifying atten-  tion flow in transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' arXiv preprint arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='00928,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1, 8  [2] Srinadh Bhojanapalli, Ayan Chakrabarti, Daniel Glasner,  Daliang Li, Thomas Unterthiner, and Andreas Veit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Under-  standing robustness of transformers for image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF International Conference  on Computer Vision, pages 10231–10241, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas  Usunier, Alexander Kirillov, and Sergey Zagoruyko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' End-to-  end object detection with transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In European confer-  ence on computer vision, pages 213–229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1,  2  [4] Hila Chefer, Shir Gur, and Lior Wolf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Transformer inter-  pretability beyond attention visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pages 782–791, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [5] Chun-Fu Richard Chen, Quanfu Fan, and Rameswar Panda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Crossvit: Cross-attention multi-scale vision transformer for  image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF in-  ternational conference on computer vision, pages 357–366,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 8  [6] Minghao Chen, Houwen Peng, Jianlong Fu, and Haibin  Ling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Autoformer: Searching transformers for visual recog-  nition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF International Con-  ference on Computer Vision, pages 12270–12280, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [7] Alexandra Chouldechova and Aaron Roth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The fron-  tiers of fairness in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint  arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='08810, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [8] Ching-Yao Chuang and Youssef Mroueh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fair mixup: Fair-  ness via interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='06503,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2, 3  [9] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Up-detr: Unsupervised pre-training for object detection with  transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF conference  on computer vision and pattern recognition, pages 1601–  1610, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina  Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Bert:  Pre-training of deep bidirectional  transformers for language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint  arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='04805, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [11] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov,  Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner,  Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl-  vain Gelly, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' An image is worth 16x16 words: Trans-  formers for image recognition at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint  arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='11929, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1, 2, 7  [12] Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Rein-  gold, and Richard Zemel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness through awareness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In  Proceedings of the 3rd innovations in theoretical computer  science conference, pages 214–226, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 4  [13] Yonggan Fu, Shunyao Zhang, Shang Wu, Cheng Wan, and  Yingyan Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Patch-fool: Are vision transformers always  robust against adversarial perturbations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint  arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='08392, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1, 2, 5  [14] Yaroslav Ganin and Victor Lempitsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Unsupervised domain  adaptation by backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In International conference  on machine learning, pages 1180–1189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 7  [15] Robert Geirhos, J¨orn-Henrik Jacobsen, Claudio Michaelis,  Richard Zemel, Wieland Brendel, Matthias Bethge, and Fe-  lix A Wichmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Shortcut learning in deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Nature Machine Intelligence, 2(11):665–673, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 4  [16] Soumya Suvra Ghosal, Yifei Ming, and Yixuan Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Are vi-  sion transformers robust to spurious correlations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv  preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='09125, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3, 6, 7  [17] Jindong Gu, Volker Tresp, and Yao Qin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Are vision trans-  formers robust to patch perturbations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In European Con-  ference on Computer Vision, pages 404–421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  2  [18] Moritz Hardt, Eric Price, and Nati Srebro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Equality of op-  portunity in supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Advances in neural infor-  mation processing systems, 29, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 4  [19] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceed-  ings of the IEEE conference on computer vision and pattern  recognition, pages 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [20] Kenneth  Holstein,  Jennifer  Wortman  Vaughan,  Hal  Daum´e III, Miro Dudik, and Hanna Wallach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Improving  fairness in machine learning systems: What do industry  practitioners need?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Proceedings of the 2019 CHI  conference on human factors in computing systems, pages  1–16, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [21] Drew A Hudson and Larry Zitnick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Generative adversarial  transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In International conference on machine learn-  ing, pages 4487–4499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [22] Sarthak Jain and Byron C Wallace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Attention is not explana-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' arXiv preprint arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='10186, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 8  [23] Sangwon Jung, Donggyu Lee, Taeeon Park, and Taesup  Moon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Fair feature distillation for visual recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In  Proceedings of the IEEE/CVF conference on computer vi-  sion and pattern recognition, pages 12115–12124, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1,  2, 3, 7  [24] Byungju Kim, Hyunwoo Kim, Kyungsu Kim, Sungjin Kim,  and Junmo Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Learning not to learn: Training deep neural  networks with biased data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  Conference on Computer Vision and Pattern Recognition,  pages 9012–9020, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [25] Eungyeup Kim, Jihyeon Lee, and Jaegul Choo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Biaswap:  Removing dataset bias with bias-tailored swapping augmen-  tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF International Con-  ference on Computer Vision, pages 14992–15001, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [26] Michael P Kim, Amirata Ghorbani, and James Zou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Multi-  accuracy: Black-box post-processing for fairness in classifi-  cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the 2019 AAAI/ACM Conference  on AI, Ethics, and Society, pages 247–254, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [27] Xin Li, Xiangrui Li, Deng Pan, and Dongxiao Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Improv-  ing adversarial robustness via probabilistically compact loss  with logit constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the AAAI Confer-  ence on Artificial Intelligence, volume 35, pages 8482–8490,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [28] Yawei Li, Kai Zhang, Jiezhang Cao, Radu Timofte, and Luc  Van Gool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Localvit: Bringing locality to vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='05707, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [29] Zhiheng Li, Anthony Hoogs, and Chenliang Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Discover  and mitigate unknown biases with debiasing alternate net-  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In European Conference on Computer Vision, pages  270–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [30] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng  Zhang, Stephen Lin, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Swin transformer:  Hierarchical vision transformer using shifted windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In  Proceedings of the IEEE/CVF International Conference on  Computer Vision, pages 10012–10022, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1, 2  [31] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Deep learning face attributes in the wild.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of  the IEEE international conference on computer vision, pages  3730–3738, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 6  [32] Francesco Locatello, Gabriele Abbati, Thomas Rainforth,  Stefan Bauer, Bernhard Sch¨olkopf, and Olivier Bachem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' On  the fairness of disentangled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Advances in  Neural Information Processing Systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [33] Pranay K Lohia, Karthikeyan Natesan Ramamurthy, Man-  ish Bhide, Diptikalyan Saha, Kush R Varshney, and Ruchir  Puri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Bias mitigation post-processing for individual and  group fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Icassp 2019-2019 ieee international con-  ference on acoustics, speech and signal processing (icassp),  pages 2847–2851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [34] Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jor-  dan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Learning transferable features with deep adaptation net-  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In International conference on machine learning,  pages 97–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 7  [35] Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher  Yu, Radu Timofte, and Luc Van Gool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Repaint: Inpaint-  ing using denoising diffusion probabilistic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE/CVF Conference on Computer Vision  and Pattern Recognition (CVPR), pages 11461–11471, June  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [36] David Madras, Elliot Creager, Toniann Pitassi, and Richard  Zemel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Learning adversarially fair and transferable represen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In International Conference on Machine Learning,  pages 3384–3393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2, 3, 7  [37] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt,  Dimitris Tsipras, and Adrian Vladu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Towards deep learn-  ing models resistant to adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' arXiv preprint  arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='06083, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 6  [38] Xiaofeng Mao, Gege Qi, Yuefeng Chen, Xiaodan Li, Ranjie  Duan, Shaokai Ye, Yuan He, and Hui Xue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Towards robust  vision transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Con-  ference on Computer Vision and Pattern Recognition, pages  12042–12051, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [39] Tyler McDonnell, Matthew Lease, Mucahid Kutlu, and  Tamer Elsayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Why is that relevant?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' collecting annota-  tor rationales for relevance judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the  AAAI Conference on Human Computation and Crowdsourc-  ing, volume 4, pages 139–148, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [40] Junhyun Nam, Hyuntak Cha, Sungsoo Ahn, Jaeho Lee, and  Jinwoo Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Learning from failure: De-biasing classifier  from biased classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Advances in Neural Information Pro-  cessing Systems, 33:20673–20684, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [41] Muzammal Naseer, Kanchana Ranasinghe, Salman Khan,  Fahad Shahbaz Khan, and Fatih Porikli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  On improving  adversarial transferability of vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv  preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='04169, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [42] Deng Pan, Xin Li, and Dongxiao Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Explaining deep neu-  ral network models with adversarial gradient integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In  IJCAI, pages 2876–2883, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [43] Sungho Park, Dohyung Kim, Sunhee Hwang, and Hyeran  Byun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Readme: Representation learning by fairness-aware  disentangling method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='03775,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 4  [44] Sayak Paul and Pin-Yu Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Vision transformers are robust  learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Artificial  Intelligence, volume 36, pages 2071–2081, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [45] Francesco Pinto, Philip Torr, and Puneet K Dokania.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Are  vision transformers always more robust than convolutional  neural networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [46] Yao Qiang, Chengyin Li, Marco Brocanelli, and Dongxiao  Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Counterfactual interpolation augmentation (cia): A uni-  fied approach to enhance fairness and explainability of dnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Proceedings of the Thirty-First International Joint Con-  ference on Artificial Intelligence, IJCAI-22, LD Raedt, Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  International Joint Conferences on Artificial Intelligence Or-  ganization, volume 7, pages 732–739, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2, 3  [47] Yao Qiang, Deng Pan, Chengyin Li, Xin Li, Rhongho Jang,  and Dongxiao Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' AttCAT: Explaining transformers via at-  tentive class activation tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Alice H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Oh, Alekh Agar-  wal, Danielle Belgrave, and Kyunghyun Cho, editors, Ad-  vances in Neural Information Processing Systems, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [48] Prajit Ramachandran, Niki Parmar, Ashish Vaswani, Irwan  Bello, Anselm Levskaya, and Jon Shlens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Stand-alone self-  attention in vision models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [49] Shiori Sagawa, Pang Wei Koh, Tatsunori B Hashimoto, and  Percy Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Distributionally robust neural networks for  group shifts: On the importance of regularization for worst-  case generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='08731, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  3, 6  [50] Hadi Salman, Saachi Jain, Eric Wong, and Aleksander  Madry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Certified patch robustness via smoothed vision trans-  formers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on  Computer Vision and Pattern Recognition, pages 15137–  15147, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [51] Mhd Hasan Sarhan, Nassir Navab, Abouzar Eslami, and  Shadi Albarqouni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness by learning orthogonal disentan-  gled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In European Conference on Computer  Vision, pages 746–761.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [52] Sofia Serrano and Noah A Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Is attention interpretable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='03731, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 8  [53] Rulin Shao, Zhouxing Shi, Jinfeng Yi, Pin-Yu Chen, and  Cho-Jui Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' On the adversarial robustness of vision trans-  formers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='15670, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [54] Krishna Kumar Singh, Dhruv Mahajan, Kristen Grauman,  Yong Jae Lee, Matt Feiszli, and Deepti Ghadiyaram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Don’t  judge an object by its context: learning to overcome con-  textual bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference  on Computer Vision and Pattern Recognition, pages 11070–  11078, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [55] Robin Strudel, Ricardo Garcia, Ivan Laptev, and Cordelia  Schmid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Segmenter: Transformer for semantic segmenta-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF International Confer-  ence on Computer Vision, pages 7262–7272, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [56] Sruthi Sudhakar, Viraj Prabhu, Arvindkumar Krishnakumar,  and Judy Hoffman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Mitigating bias in visual transformers  via targeted alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3, 6, 7  [57] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko-  reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia  Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Advances in neural  information processing systems, 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 3  [58] Mei Wang and Weihong Deng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Mitigating bias in face recog-  nition using skewness-aware reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE/CVF conference on computer vision  and pattern recognition, pages 9322–9331, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [59] Wentao Wang, Li Niu, Jianfu Zhang, Xue Yang, and Liqing  Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Dual-path image inpainting with auxiliary gan inver-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on Com-  puter Vision and Pattern Recognition, pages 11421–11430,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [60] Zhibo Wang, Xiaowei Dong, Henry Xue, Zhifei Zhang,  Weifeng Chiu, Tao Wei, and Kui Ren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Fairness-aware ad-  versarial perturbation towards bias mitigation for deployed  deep models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference  on Computer Vision and Pattern Recognition, pages 10379–  10388, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2, 3  [61] Benjamin Wilson, Judy Hoffman, and Jamie Morgenstern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Predictive inequity in object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv preprint  arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='11097, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [62] Han Xu, Xiaorui Liu, Yaxin Li, Anil Jain, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  To be robust or to be fair: Towards fairness in adversarial  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In International Conference on Machine Learning,  pages 11492–11501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [63] Jianwei Yang, Chunyuan Li, Pengchuan Zhang, Xiyang Dai,  Bin Xiao, Lu Yuan, and Jianfeng Gao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Focal self-attention  for local-global interactions in vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  arXiv  preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='00641, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2  [64] Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine,  Karol Hausman, and Chelsea Finn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Gradient surgery for  multi-task learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Advances in Neural Information Pro-  cessing Systems, 33:5824–5836, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 6  [65] Brian Hu Zhang, Blake Lemoine, and Margaret Mitchell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Mitigating unwanted biases with adversarial learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In  Proceedings of the 2018 AAAI/ACM Conference on AI,  Ethics, and Society, pages 335–340, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 2, 3  [66] Yi Zhang and Jitao Sang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Towards accuracy-fairness para-  dox: Adversarial example-based data augmentation for vi-  sual debiasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Proceedings of the 28th ACM Interna-  tional Conference on Multimedia, pages 4346–4354, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  2  [67] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu,  Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao  Xiang, Philip HS Torr, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Rethinking semantic segmen-  tation from a sequence-to-sequence perspective with trans-  formers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF conference on  computer vision and pattern recognition, pages 6881–6890,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  [68] Daquan Zhou, Zhiding Yu, Enze Xie, Chaowei Xiao, An-  imashree Anandkumar, Jiashi Feng, and Jose M Alvarez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Understanding the robustness in vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In In-  ternational Conference on Machine Learning, pages 27378–  27394.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' 1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Supplementary Materials  In this Section, we provide additional experiments for per-  formance evaluation of the proposed DSA framework on  CelebA and Waterbird datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Dataset Statistics  Recall from Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='1 that we choose three settings from  the CelebA dataset and one setting from the Waterbird  dataset to evaluate the baselines against the proposed DSA  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We describe these four settings using the tuples  (Y, S) as follows: a) (Smiling, High Cheekbones), b) (Wavy  Hair, Gender), c) (Gray Hair, Gender), and d) (Waterbird,  Place).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Note that the first three settings are considered for  the CelebA dataset while the last setting is considered for  the Waterbird dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We first provide the data statistics  for all these settings in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We note that significant  biases exist in all these settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' For example, a majority  of “Smiling” faces are correlated with “High Cheekbones”  whereas the majority of “Not Smiling” faces are correlated  with “Not High Cheekbones”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Similar spurious correlations  are also observed in other settings as well, which can lead to  biased models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We establish this by further analyzing and  reporting the True Positive Rate (TPR) of the vanilla ViT  models trained on these biased datasets in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Clearly,  the biased ViT models perform significantly worse on the  minority groups, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', predicting “Smiling” when the indi-  vidual does not have “High Cheekbones” (S = 0: 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='93%)  compared to the ones that have “High Cheekbones” (S = 1:  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='50%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Next, we analyze the effect of the tunable hyper-  parameters on the performance of DSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Disparities of true positive rate (TPR) among different  task and sensitive attribute tuples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Y  S  TPR%↑  ∆TPR%  Smiling  Not High Cheekbones (0)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='93  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='57  High Cheekbones (1)  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='50  Wavy Hair  Female (0)  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='62  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='04  Male (1)  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='58  Gray Hair  Female (0)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='31  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='85  Male (1)  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='16  Waterbird  Land (0)  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='75  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='14  Water (1)  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='89  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Effect of Discrepancy Metrics  Since We apply three different feature discrepancy metrics  D(·, ·), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', MSE, KL-Div, and AT, to evaluate the discrep-  ancy between the attention weights Ax and Ax′ in (6), we  report the effect of these discrepancy metrics in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Although the differences between these discrepancy met-  rics are relatively small, AT clearly achieves the best per-  formance, especially on the fairness metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Since AT can  capture the most significant differences between Ax and  Ax′ as shown in (9), the regularizer LA is more efficient  to minimize their differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Evaluations with different discrepancy metrics in the reg-  ularizer (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  D⋆  Y : Gray Hair S: Gender  EO↓  DP↓  DBA↓  BA↑  Acc%↑  MSE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2706  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2488  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0136  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='07  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='13  KL-Div  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2467  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0106  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='26  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='48  AT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2558  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2337  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0031  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='92  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='95  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Effect of Tunable Hyper-parameters  There are several tunable hyper-parameters in the proposed  DSA framework, including the various coefficient weights  in the objective function and the number of masked patches  learned during the adversarial attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  We tune the three coefficient weights in the objective  function (10) to identify the best-performing model as  shown in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' To improve model performance, we be-  lieve that these coefficient weights should be carefully tuned  and selected under different settings and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  The effect of the number of masked patches learned dur-  ing the adversarial attack is shown in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' In our ex-  periments, the ViT model with k = 3 patches achieves the  best performance among all compared metrics in most set-  tings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Looking into more details of the adversarial examples  shown in Figure 6, if we perturb only one patch out of all  the input patches, some sensitive attributes may not be lo-  calized and masked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' On the contrary, perturbing excessive  patches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', 5 patches) would increase the risk of masking  the related attributes to the target task, resulting in a worse  prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' For example, the ACC drops from  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='95 to 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='55 in the setting of (Gray Hair, Gender) with 5  perturbed patches, as shown in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Evaluations with different tunable coefficient weights in  the objective function (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  λ1, λ2, λ3  Y : Gray Hair S: Gender  EO↓  DP↓  DBA↓  BA↑  Acc%↑  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2843  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2675  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0125  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='45  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2633  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2578  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0106  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='32  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='26  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2558  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2337  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0031  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='92  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='95  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Ablation Studies and Effect of Patch Size  We report the adversarial success rates of DSA on the sen-  sitive attributes as target with different number of masked  patches in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Note that we only generate adversarial  examples for the training sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  In Table 8, we report additional ablation study results for  the DSA framework on the other two settings from CelebA  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' It is straightforward to make a similar conclusion  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Smiling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Not Smiling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='20000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='40000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='60000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='80000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='78899  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='13290  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='18770  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='91640  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='High CheekBones  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Not High CheekBones  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='(a) Y: Smiling S: High Cheeckbones  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Wavy Hair  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Not Wavy Hair  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='10000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='(d) Y: Waterbird S: Place  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Spurious correlation between tasks (Y ) and sensitive attributes (S) tuples (Y, S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Note that Figures 5a, 5b and 5c represent the  data statistics for the CelebA dataset while Figure 5d represents the data statistics of the Waterbird dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Performance of DSA with different number of masked or perturbed patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  k  Y : Smiling  S: High Cheekbones  Y : Wavy Hair  S: Gender  Y : Gray Hair  S: Gender  EO↓  DP↓  DBA↓  BA(%)↑  Acc(%)↑  EO↓  DP↓  DBA↓  BA(%)↑  Acc(%)↑  EO↓  DP↓  DBA↓  BA(%)↑  Acc(%)↑  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='55  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Adversarial attack success rates of DSA on the sensitive  attributes target with different number of masked patches, k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  S  k  Success Rate%↑  Gender  1  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='52  3  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='69  High Cheekbones  1  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='58  as in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We note that all the terms in the objec-  tive function in (10) contribute towards better fairness and  accuracy performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Additional evaluations capturing the effect of different  patch sizes on the performance of DSA are reported in Ta-  ble 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Similar to our conclusion in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='3, the ViT  models with smaller patch sizes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', 16, achieve the best  performance on two other settings from the CelebA dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Adversarial examples with different number of masked  patches in the (Gray Hair, Gender) setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Qualitative Evaluations  In Figures 7, 8, and 9, we demonstrate some more qualita-  tive evaluations to further demonstrate the effectiveness of  the DSA approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' We note that the distribution of the at-  tention weights for the ViT models trained with the vanilla  method simply focuses on the sensitive attributes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', “eye  shadow”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' This demonstrates that the vanilla ViT models are  biased and simply leverage the sensitive features to predict  the target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' On the contrary, DSA reduces the atten-  tion on these sensitive features but pays more attention on  the target-related features, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=', the hair, which actually de-  termines the target label Gray and Wavy hair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Summary  We summarize the major findings of our experimental study  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' First, DSA reduces the attention on the sensitive fea-  tures while focusing on the target-related features as an ef-  fective approach to bias mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Second, the additional  ablation studies demonstrate that each term in the objec-  tive function (10) contributes towards the improved fairness  and accuracy performance of DSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Third, we noted that the  smaller patch size results in better performance of DSA due  to their capability of efficiently extracting fine-grained fea-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (a) Original Image  (b) Vanilla  (c) DSA  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Qualitative evaluation of DSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Y: Smiling S: High  Cheeckbones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  VANN  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' (a) Original Image  (b) Vanilla  (c) DSA  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Qualitative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Y: Gray hair S: Gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  (a) Original Image  (b) Vanilla  (c) DSA  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Qualitative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Y: Wavy hair S: Gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content='  Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Ablation study of DSA for the three training objectives on two other settings from the CelebA data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
+page_content=' Best results are bold faced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content='  Models  Y : Wavy Hair S: Gender  Y : Smiling S: High Cheekbones  EO↓  DP↓  DBA↓  BA↑  ACC↑  EO↓  DP↓  DBA↓  BA↑  ACC↑  L(all)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+page_content=' All tunable hyper-parameters are set same as Figure  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tFST4oBgHgl3EQfcjgx/content/2301.13803v1.pdf'}
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+arXiv:2301.03279v1  [cs.GT]  9 Jan 2023
+Revisiting the Distortion of Distributed Voting
+Aris Filos-Ratsikas1 and Alexandros A. Voudouris2
+1School of Informatics, University of Edinburgh, UK
+2School of Computer Science and Electronic Engineering, University of Essex, UK
+Abstract
+We consider a seting with agents that have preferences over alternatives and are partitioned
+into disjoint districts. Te goal is to choose one alternative as the winner using a mechanism
+which first decides a representative alternative for each district based on a local election with the
+agents therein as participants, and then chooses one of the district representatives as the winner.
+Previous work showed bounds on the distortion of a specific class of deterministic plurality-based
+mechanisms depending on the available information about the preferences of the agents in the
+districts. In this paper, we first consider the whole class of deterministic mechanisms and show
+asymptotically tight bounds on their distortion. We then initiate the study of the distortion of
+randomized mechanisms in distributed voting and show bounds based on several informational
+assumptions, which in many cases turn out to be tight. Finally, we also experimentally compare
+the distortion of many different mechanisms of interest using synthetic and real-world data.
+1
+Introduction
+Voting is a ubiquitous method for making decisions with a large number of applications, such as electing
+political representatives, deciding how to split a public budget between projects, or choosing which
+services (restaurants, hotels, etc) to recommend to new users based on past user experiences. As such, it
+has been at the epicenter of research within multiple disciplines including political sciences, economics
+and computer science [Brandt et al., 2016]. Te most prominent question in this research agenda is to
+identify the best voting rule to use to collectively aggregate the preferences of agents over alternative
+options into a single winning alternative, with most of the earlier literature focusing on axiomatic
+properties that good voting rules should have. An alternative way to tackle this question that has been
+proposed in computer science is through the distortion framework [Anshelevich et al., 2021] which
+allows to compare different voting rules based on how well they approximate the optimal choice as
+measured in terms of a social objective function like the utilitarian social welfare.
+Since its inception in 2006 by Procaccia and Rosenschein [2006], the distortion framework has been
+applied to several utilitarian social choice setings (e.g., [Boutilier et al., 2015, Anshelevich et al., 2018,
+Gkatzelis et al., 2020]). Te lion’s share of previous work has focused on centralized models with a
+single pool of agents whose preferences are directly given as input to a voting rule, which thus can
+utilize all the given information at once to make a decision. However, there are many applications
+with multiple pools of agents which make independent local decisions that can be thought of as rec-
+ommendations for the final decision. To give a concrete example, in most political election systems,
+the citizens are partitioned into districts based on geographic or other criteria, and vote within their
+districts to propose the candidate (party) they would like to be selected as the winner.
+Inspired by situations like the one described above, Filos-Ratsikas et al. [2020] initiated the study
+of the distortion of mechanisms in a distributed single-winner seting where a set of n agents with
+1
+
+Deterministic
+Randomized-of-Deterministic
+Randomized-of-Randomized
+Ordinal
+Θ(km2)
+Θ(km2)
+Ω(√m), O(√m log m)
+Cardinal
+Θ(km)
+Θ(k)
+Θ(k)
+Strategyproof
+Θ(nm)
+Θ(nm)
+Ω(√m), O(√m log m)
+Table 1: An overview of our results. Specific details can be found in the appropriate sections.
+cardinal preferences over a set of m alternatives are partitioned into k disjoint districts. Te authors
+focused on deterministic mechanisms of the form Plurality-of-f, which first choose a representative
+alternative for each district according to some rule f, by holding a local election with the agents of
+the district as the voters, and then picking the winner to be the alternative that is representative of
+the most districts (i.e., using the Plurality rule). Filos-Ratsikas et al. considered mechanisms for
+which the rule f can be cardinal or ordinal, i.e., it may use the actual numerical information about
+the preferences of the agents within the districts or just consistent rankings. Te authors showed
+that, when the districts are symmetric (that is, each of them contains the same number of agents), the
+distortion of a cardinal mechanism, namely Plurality-of-Range-Voting is O(km), and provided an
+asymptotically matching lower bound of Ω(km) on the distortion of any Plurality-of-f mechanism.
+For ordinal mechanisms, they showed that Plurality-of-Plurality achieves a distortion of O(km2),
+and that this is asymptotically best among all ordinal Plurality-of-f mechanisms.
+1.1
+Revisiting the distortion of distributed voting
+A first observation about the results of Filos-Ratsikas et al. [2020] is that there is a-priori no reason
+to restrict our atention to only mechanisms in the class Plurality-of-f, as using other over-districts
+rules could potentially lead to beter distortion. Indeed, follow-up work considered distributed social
+choice setings with metric preferences [Anshelevich et al., 2022, Filos-Ratsikas and Voudouris, 2021]
+without such restrictions on the over-districts rule. In addition, all of the previous work on these
+setings only considered deterministic mechanisms that use deterministic in-district and over-districts
+rules. Randomization has proven out to be a very useful tool in achieving beter (expected) distortion
+bounds in the centralized seting (see Boutilier et al. [2015], Ebadian et al. [2022]), so it is only natural
+to consider randomized mechanisms in the distributed seting as well. Finally, an important question
+is how the distortion bounds are affected in case the participants act selfishly, and whether there are
+strategyproof mechanisms with good distortion bounds. Tis question has been considered in the
+centralized seting [Filos-Ratsikas and Miltersen, 2014, Bhaskar and Ghosh, 2018, Bhaskar et al., 2018,
+Ebadian et al., 2022] and also in the distributed metric seting [Filos-Ratsikas and Voudouris, 2021]; we
+consider it in the context of the normalized seting of Filos-Ratsikas et al. [2020] as well.
+1.2
+Our Contributions
+We consider the class of all mechanisms for distributed voting in the seting of [Filos-Ratsikas et al.,
+2020]. In particular, we consider the fover-of-fin class of mechanisms, where fin is an in-district rule that
+takes as input the preferences of the agents within each district and outputs a representative alternative
+for the district, while fover is a rule that takes as input the representative alternatives of all districts and
+chooses one of them as the overall winner. We consider several different cases depending on the nature
+of fover and fin (deterministic or randomized), and the type of information they can utilize (cardinal or
+ordinal). We show the following results; see Table 1 for an overview.
+Deterministic Mechanisms. When fover and fin are both deterministic and the districts are symmet-
+ric, we show that the best possible distortion is Θ(km) when the valuation functions of the agents are
+2
+
+accessible (cardinal mechanisms), and is Θ(km2) when only ordinal information about the preferences
+of the agents is available (ordinal mechanisms). Te upper bounds were shown by Filos-Ratsikas et al.
+[2020] and here we provide asymptotically tight lower bounds. Tese results show that for general,
+unstructured (normalized) valuations, employing different over-district rules in fact does not result in
+improvements on the distortion. We present these results in Section 3.
+Randomized Mechanisms. In Section 4, we consider for the first time the distortion of randomized
+mechanisms in distributed voting. We first prove a simple composition theorem, which shows that
+using an in-district rule with known distortion δ in the centralizedseting and then selecting the winner
+uniformly at random from the set of representatives, defines a distributed mechanism with distortion
+O(kδ). Using this, complemented with new lower bounds, we show that the best possible distortion
+for cardinal unanimous mechanisms is Θ(k); in fact, this is true even when the districts are asymmetric
+and when fover is randomized but fin is deterministic.
+For ordinal mechanisms, we consider two cases: (a) mechanisms that use deterministic in-district
+rules fin, and (b) fully-randomized mechanisms, where both fover and fin are randomized rules. For
+(a), we show that the best possible distortion is Θ(km2). Te upper bound follows from the bound on
+Plurality-of-Plurality proven in [Filos-Ratsikas et al., 2020]; here, we provide an asymptotically
+matching lower bound assuming a natural universal tie-breaking rule. For (b), we prove a simple but
+very interesting result: For a well-studied class of randomized centralized voting rules called point-
+voting schemes (e.g., see Gibbard [1977], Barbera [1978]), there exists a distributed implementation so
+that there is no effect on the induced probability distribution, even for asymmetric districts. Simply put,
+using such rules it is possible to escape the ill effects of districts in terms of the distortion, even when
+the districts are asymmetric. From this result, it follows that there exists a distributed implementation
+of a well-known mechanism of Boutilier et al. [2015] that achieves distortion O(√m log m), almost
+matching the best possible lower bound of Ω(√m).
+Strategyproof Mechanisms. For strategyproof mechanisms, which are resilient to strategic manip-
+ulation, we show that a best-possible distortion of Θ(nm) for deterministic mechanisms (and more
+generally mechanisms with a deterministic in-district rule) is easy to achieve by a variation of a dic-
+tatorship rule. For randomized mechanisms, since point-voting schemes are strategyproof, the bound
+O(√m log m) carries over to this class as well. Results about deterministic strategyproof mechanisms
+are presented in Section 3, and about randomized strategyproof mechanisms in Section 4.
+Experiments. Finally, in Section 5, we perform experiments using real-world data and synthetic data
+to evaluate the effect of distributed decision making to the distortion in setings closer to practice. Te
+main conclusions of our experimental results mirror that of our theoretical results in Sections 3 and 4.
+1.3
+Further Related Work
+Te distortion literature is by now rather extensive, including topics such as single-winner voting
+[Boutilier et al., 2015, Anshelevich et al., 2018, Gkatzelis et al., 2020, Kizilkaya and Kempe, 2022],
+multi-winner voting [Caragiannis et al., 2017, 2022], matching problems [Filos-Ratsikas et al., 2014,
+Amanatidis et al., 2022a], and participatory budgeting [Benad`e et al., 2017]. Generally speaking, most
+works can be categorized as either studying a normalized utilitarian seting (e.g., [Procaccia and Rosen-
+schein, 2006, Boutilier et al., 2015, Filos-Ratsikas et al., 2014, Benad`e et al., 2017, Ebadian et al., 2022]) or
+a metric preference seting (e.g., [Anshelevich and Sekar, 2016, Anshelevich et al., 2018, Gkatzelis et al.,
+2020, Caragiannis et al., 2022, Kizilkaya and Kempe, 2022]). Some more recent works have also studied
+the interplay between information and distortion [Amanatidis et al., 2021, 2022a,b, Mandal et al., 2019,
+2020, Abramowitz et al., 2019], and there have also been several works on strategyproofness in the con-
+text of distortion [Filos-Ratsikas and Miltersen, 2014, Filos-Ratsikas et al., 2014, Bhaskar and Ghosh,
+3
+
+2018, Bhaskar et al., 2018, Ebadian et al., 2022]. We refer the reader to the survey of Anshelevich et al.
+[2021] for a detailed overview of the related literature.
+Besides the aforementioned works on distributed voting, Borodin et al. [2019] studied a related
+two-stage seting in which the voters participate in a central election, but the candidates themselves
+come from local elections within the political parties’ electorates. Beyond distortion, in the context of
+district-based elections, there have also been other works that have considered the degree of deviation
+from proportional representation (e.g., see [Bachrach et al., 2016] and references therein), and some
+works that have studied the complexity of manipulation (e.g., see [Elkind et al., 2021, Lewenberg et al.,
+2017, Lev and Lewenberg, 2019, Borodin et al., 2018]).
+2
+Preliminaries
+An instance I of our problem is given by a tuple I = (N, A, v, D). Tere is a set N of n agents (or
+voters) that have preferences over a set A of m alternatives (or candidates). Te preferences of each
+agent i ∈ N are captured by a valuation function vi : A → R≥0 that maps every alternative a ∈ A to a
+real non-negative value vi(a) = via. Following previous work, we assume that the valuation functions
+are normalized such that �
+a∈A via = 1 for every i ∈ N (unit-sum assumption). Let v = (vi)i∈N be
+the valuation profile consisting of the valuation functions of all agents. Te agents are also partitioned
+into a set D of k disjoint districts.
+For every district d ∈ D, let Nd be the set of agents it contains, such that �
+d∈D Nd = N. In the
+symmetric case, each district d contains exactly λ = n/k agents. In the asymmetric case, each district
+d contains a number nd of agents. All our lower bounds follow by instances consisting of symmetric
+districts, whereas our upper bounds in Section 4 hold for asymmetric districts.
+2.1
+Mechanisms
+Our goal is to choose an alternative to satisfy several criteria of interest. Tis choice must be done
+using a distributed mechanism that uses an in-district voting rule fin and an over-districts voting rule
+fover to implement the following two independent steps:
+• Step 1: For each district d, choose a representative alternative ad ∈ A by holding a local election
+based on fin.
+• Step 2: Choose a district representative as the winner based on fover by considering the districts
+as voters and their representatives as the candidates they approve.
+For simplicity we refer to such mechanisms as fover-of-fin. Different choices of fin and fover lead to
+different distributed mechanisms. Note that the in-district rule can in general use various types of
+information about the preferences of the agents. For instance, it may be able to use exact cardinal
+information about the valuation functions, or only ordinal information that is induced by the values
+(i.e., rankings of alternatives that are consistent to the values of the agents for them). In the later case,
+we will use σi to denote the preference ranking of agent i ∈ N so that σi(a) is the rank of alternative
+a ∈ A in the ranking of i, and σi(a) < σi(b) if vi(a) ≥ vi(b); let σ = (σi)i∈N be the ordinal
+profile consisting of the preference rankings of all agents. To be concise in the definitions below, let
+δ(I) be the information about the preferences of the agents in instance I = (N, A, v, D) that is used
+by a mechanism; that is, δ(I) = v in case of cardinal information, or δ(I) = σ in case of ordinal
+information.
+We will focus on different classes of distributed mechanisms depending on the available informa-
+tion about the preferences of the agents at the district level (cardinal or ordinal), and also on whether
+4
+
+their decision is deterministic or randomized (that is, they choose the district representatives or final
+winner based on probability distributions).
+2.2
+Social Welfare and Distortion
+Given an instance I, the social welfare of an alternative a ∈ A is the total value that the agents have for
+a, that is, SW(a|I) = �
+i∈N via. So, the expected social welfare achieved by a randomized distributed
+mechanism M that chooses alternative a ∈ A as the winner w with probability PrM[w = a] is
+E[SW(M(I))] =
+�
+a∈A
+Pr
+M [w = a] · SW(a|I).
+Te efficiency of a distributed mechanism is measured by the notion of distortion. Te distortion of a
+distributed mechanism M is the worst-case ratio (over all possible instances with n agents, m alterna-
+tives, and k districts) of the maximum social welfare achieved by any alternative over the (expected)
+social welfare of the alternative chosen by the mechanism as the winner w, that is,
+dist(M) = sup
+I
+maxa∈A SW(a|I)
+E[SW(M(δ(I))] .
+Clearly, dist(M) ≥ 1. When the denominator in the definition of the distortion tends to 0, we will
+say that the distortion is infinite or unbounded. Our goal is to identify the best possible distributed
+mechanisms in terms of distortion.
+2.3
+Strategyproofness
+Another important property that we would like our mechanisms to satisfy is that of strategyproof-
+ness. A strategyproof mechanism makes decisions such that providing false information never leads to
+the selection of an alternative that an agent prefers over the alternative chosen when the agent pro-
+vides truthful information. In particular, for any instance I, it must be the case that vi(M(δ(I))) ≥
+vi(M(δ(I′))) for any agent i ∈ N, where I′ is the instance obtained when only agent i reports infor-
+mation different than that in I.
+2.4
+Some useful observations and properties
+Before we present our technical results, let us briefly discuss some useful properties.
+Locality of distributed mechanisms: First, observe that any distributed mechanism fover-of-fin
+satisfies a locality property in the following sense. A district d (that is, the preferences of a number
+of agents) appears in different instances if in each of these instances there is a district with the same
+number of agents and the same information about theirs preferences as in d (depending on what is
+required by the mechanism). Since the information is the same, the in-district rule fin must decide the
+same alternative as the representative of the district in all these instances. Similarly, in all instances
+where the mechanism has decided the same set of district representatives, the over-districts rule fover
+must decide the same final winner.
+Distortion of distributed vs centralized: Another useful observation is that the distortion of a
+distributed mechanism fover-of-fin is at least as much as the distortion of the in-district centralized
+voting rule fin. Indeed, when k = 1, there is only one representative alternative chosen by fin, and
+thus this alternative must be chosen as the winner by fover; this is also true for instances with k ≥ 2
+districts which are all copies of one district. Consequently, the distortion of fin is a lower bound on
+the distortion of fover-of-fin.
+5
+
+Strategyproofness: Observe that for a distributed mechanism fover-of-fin to be strategyproof it is
+necessary that the in-district rule fin is strategyproof. Tis again follows by how the mechanism would
+work in instances with a single district, in which case the over-districts rule fover does not play any
+role in the selection of the final winner.
+Unanimity: A few of our results will require the in-district rules fin to be unanimous. Unanimity
+stipulates that if all of the agents have the same alternative as the top preference, that alternative
+must be selected (with probability 1). Unanimity is a very natural property of “reasonable” voting
+rules, especially deterministic ones. For randomized rules, there might be reasons to consider non-
+unanimous choices, e.g., see Gibbard [1977], Filos-Ratsikas and Miltersen [2014].
+3
+Deterministic mechanisms
+We start with deterministic distributed mechanisms and focus explicitly on the case of symmetric
+districts in this section (that is, the size of each district is λ). When full information about the valuations
+of the agents is known at the district level, Filos-Ratsikas et al. [2020] showed that the mechanism
+Plurality-of-Range-Voting, which chooses the representative of each district to be the alternative
+with maximum social welfare for the agents in the district, has distortion O(km). We show that this
+mechanism is asymptotically best possible over all possible deterministic distributed mechanisms that
+use unanimous in-district rules (but may not use Plurality as the over-districts rule).
+Teorem 3.1. Te distortion of any deterministic distributed mechanism with a unanimous in-district
+rule is Ω(km).
+Proof. Let M be some deterministic distributed mechanism with a unanimous in-district rule. Without
+loss of generality, whenever there are k distinct district representatives {a1, . . . , ak}, we assume that
+M chooses a1 as the overall winner. Let ε > 0 be some positive infinitesimal and consider the following
+instance with k districts {d1, . . . , dk} and m > k alternatives:
+• In district d1, all agents have value 1/m + ε for alternative a1, and value 1/m − ε/(m − 1) for
+any other alternative.
+• For any ℓ ∈ {2, . . . , k}, in district dℓ, all agents have value 1/2 + ε for alternative aℓ, value
+1/2 − ε for alternative x, and value 0 for any other alternative.
+Since the in-district rule is unanimous, the district representatives are alternatives {a1, . . . , ak}, and
+the overall winner is thus a1. Te social welfare of alternative a1 is approximately λ/m, whereas the
+social welfare of alternative x is approximately k · λ/2, leading to distortion Ω(km).
+When only ordinal information about the preferences of the agents is available, Filos-Ratsikas
+et al. [2020] showed that Plurality-of-Plurality, which chooses the favorite alternative of most of
+the agents in a district as its representative and then the alternative that represents the most districts
+as the winner, has distortion O(km2). We show that this mechanism is asymptotically best possible
+among all ordinal distributed mechanisms (without any restrictions), thus improving upon the result
+of Filos-Ratsikas et al. [2020] who showed that Plurality-of-Plurality is best possible only within
+the class of mechanisms they studied.
+We first prove an easy but important lemma showing that when only ordinal information is avail-
+able, to achieve finite distortion, it is necessary the representative of each district to be some alternative
+that is the favorite of at least one agent in the district.
+6
+
+Lemma 3.2. Te representative of any district must be some top-ranked alternative, otherwise the distor-
+tion is infinite.
+Proof. Let d be a district and let T be the set of top-ranked alternatives. Suppose that the representative
+of d is chosen to be some alternative x ̸∈ T. Ten, in any instance consisting of copies of d, the winner
+must be x. However, the valuation profile might be such that all agents have value 1 for their favorite
+alternative and 0 for any other alternative. Consequently, the social welfare of x might be 0, whereas
+the social welfare of any top-ranked alternative is positive, leading to infinite distortion.
+We say that a district is divided if its λ agents are partitioned into m/2 equal-sized sets such that all
+the 2λ/m agents in each set rank the same alternative first and different sets of agents have different
+top-ranked alternatives. By Lemma 3.2, the representative of such a district must be one of the top-
+ranked alternatives. Te following lemma shows that choosing the representative of a divided district
+as the winner is, under some circumstances, a bad choice.
+Lemma 3.3. Suppose that some alternative y1 is chosen as the winner by a deterministic ordinal dis-
+tributed mechanism when the set of representatives is {y1, . . . , yk}. If there exists a divided district that
+is represented by y1, then there are k − 1 districts with representatives y2, . . . , yk, and altogether these k
+districts define an instance such that the distortion of the mechanism is Ω(km2).
+Proof. Let M be a deterministic ordinal distributed mechanism that selects y1 as the winner when
+the set of representatives is {y1, . . . , yk}, and let d be the divided district that is represented by y1.
+Consider the following k districts:
+• Te first district is a copy of d.
+• For every ℓ ∈ {2, . . . , k}, the ℓ-th district is such that all agents therein rank yℓ first, x ̸∈
+{y1, . . . , yk} second, and then all other alternatives. By Lemma 3.2, M must choose yℓ as the
+representative of the ℓ-th district, as this is the only top-ranked alternative.
+So, indeed the set of representatives is {y1, . . . , yk} and M chooses y1 as the winner by assumption.
+One possible valuation profile is the following:
+• In the first, divided district, the 2λ/m agents that rank y1 first have value 1/m for all alternatives,
+and the remaining agents all have value 1 for their favorite alternative.
+• For every ℓ ∈ {2, . . . , k}, all agents in the ℓ-th district have value 1/2 for their two favorite
+alternatives (yℓ and x).
+Consequently, the social welfare of y1 is λ/m2 whereas the social welfare of x is approximately k·λ/2,
+and thus the distortion is Ω(km2).
+Lemma 3.3 shows that deterministic ordinal distributed mechanisms with distortion o(km2) must
+not output the representative of a divided district as the winner when it is given a set of districts with
+different representatives. However, as we show in the proof of the next theorem, there are instances
+where such a choice is inevitable, and thus the distortion is Ω(km2).
+Teorem 3.4. Te distortion of any deterministic ordinal distributed mechanism is Ω(km2).
+Proof. Let M be a deterministic ordinal distributed mechanism. We focus on instances with k districts
+and sets of alternatives A ∪ B ∪ C ∪ {x}, where A = {a1, . . . , ak}, B = {b1, . . . , bm/2+k−1}, and
+7
+
+C = {c1, . . . , cm−2k}. Without loss of generality, suppose that when the district representatives are
+{a1, . . . , ak}, M chooses a1 as the overall winner.
+Let d1 be a divided district with set of top-ranked alternatives {a1, b1, . . . , bm/2−1}. By Lemma 3.3,
+if a1 is the representative of d1, then there exists an instance such that the distortion of M is Ω(km2).
+So, suppose that the representative of d1 is some other top-ranked alternative, say b1. Again by
+Lemma 3.3, if b1 is chosen as the winner whenever she is part of a representative set consisting of
+k distinct alternatives, then the distortion of M would be Ω(km2). So, let us assume that when the
+district representatives are {b1, a2, . . . , ak}, the winner is an alternative different than b1, say a2.
+We can now repeat this argument step by step for each alternative aℓ, ℓ ∈ {2, . . . , k}. In particular,
+let dℓ be a divided district with top-ranked alternatives {aℓ, bℓ, . . . , bm/2+ℓ−2} (note that alternatives
+b1, . . . , bℓ−1 do not appear as top-ranked alternatives in dℓ). By Lemma 3.3, if aℓ is the representative
+of dℓ then the distortion of M is Ω(km2), so the representative is some other alternative from the set
+{bℓ, . . . , bm/2+ℓ−2}, say bℓ. Again by Lemma 3.3, if bℓ is chosen as the winner whenever she is part of
+a representative set consisting of k distinct alternatives, then the distortion of M would be Ω(km2).
+So, when the district representatives are {b1, . . . , bℓ, aℓ+1, . . . , ak}, the winner is an alternative not in
+{b1, . . . , bℓ}, say aℓ.
+Te last step of this repeated argument leads to the lower bound of Ω(km2): We have reached an
+instance with set of representatives {b1, . . . , bk} all of whom are representative of some divided district,
+and thus no mater who of them is chosen as the winner, by Lemma 3.3 there exists an instance that
+includes the corresponding divided district and k − 1 unanimous districts (like in the proof of the
+lemma) such that the distortion is Ω(km2).
+Finally, let us discuss the case of deterministic strategyproof distributed mechanisms. Bhaskar and
+Ghosh [2018] showed that the distortion of any deterministic centralized strategyproof voting rule
+(including those that have access to the valuation functions) is Θ(nm). From the discussion Section 2.4,
+we directly obtain a lower bound of Ω(nm) for the distributed seting as well. A tight upper bound is
+also not hard to derive by considering the straightforward First-of-First mechanism which works as
+follows:
+• For each district d, choose the favorite alternative of the first agent therein as the representative.
+• Choose the representative of the first district as the winner.
+Teorem 3.5. First-of-First is strategyproof and achieves an asymptotically best possible distortion of
+Θ(nm) within the class of deterministic strategyproof distributed mechanisms.
+Proof. Te mechanism is clearly strategyproof since the winner is the favorite alternative of the first
+agent of the first district who acts as a dictator. Since the winner is ranked first by an agent, the social
+welfare of the mechanism is at least 1/m. Te maximum possible social welfare is n, and thus the
+distortion is O(nm).
+4
+Randomized mechanisms
+We start our discussion on randomized distributed mechanisms by analyzing a general class of mech-
+anisms that we call Uniform-of-δ-Approximate. A mechanism M in this class works as follows:
+• For each district d, M chooses the representative ad according to some centralized voting rule
+fin that has distortion at most δ.
+• M chooses the winner uniformly at random from the set of representatives.
+8
+
+Picking the winner uniformly at random from the representatives that have been selected seems to be
+the most natural choice as there is not much information about the preferences of the agents in the
+districts, and essentially all we can do is assign higher proportional probability to an alternative that
+is representative of more districts. We have the following result.
+Teorem 4.1. Te distortion of any Uniform-of-δ-Approximate mechanism is O(kδ).
+Proof. Consider an arbitrary instance. Let o be the optimal alternative, ad the representative of district
+d, and w the final winner. Denote by SWd(x) the social welfare of alternative x only from the agents
+in d; clearly, SW(x) = �
+d∈D SWd(x). Te expected social welfare of the mechanism is
+E[SW(M)] =
+�
+a∈A
+Pr[w = a] · SW(a)
+= 1
+k
+�
+a∈A
+��
+d∈D
+Pr[ad = a]
+�
+SW(a)
+= 1
+k
+�
+d∈D
+�
+a∈A
+Pr[ad = a] · SW(a)
+= 1
+k
+�
+d∈D
+E[SW(ad)]
+≥ 1
+k
+�
+d∈D
+E[SWd(ad)]
+Since ad is chosen based on a voting rule with distortion at most δ, we have that E[SW(ad)] ≥ 1
+δ ·
+SWd(o). Combining this together with the fact that SW(o) = �
+d∈D SWd(o), and using the linearity
+of expectation, we obtain
+E[SW(M)] ≥ 1
+k
+�
+d∈D
+E[SWd(ad)]
+≥ 1
+k
+�
+d∈D
+1
+δ · SWd(o)
+= 1
+kδ · SW(o).
+Hence, the distortion of the mechanism is at most kδ.
+Teorem 4.1 is a simple composition theorem, analogous to the one presented by Anshelevich
+et al. [2022] for the metric seting. Based on it, we can define randomized distributed mechanisms
+with proven distortion guarantees by appropriately choosing the in-district rule. Before we continue,
+observe that the sizes of the districts do not appear in the proof of Teorem 4.1, and thus the distortion
+of any Uniform-of-δ-Approximate mechanism is O(kδ) even if the districts are asymmetric. So, the
+distortion of the mechanism depends on the number of agents only if the distortion δ of the in-district
+rule depends on the number of agents.
+If cardinal information is available at the district level, by using Range-Voting with δ = 1 as the
+in-district rule, we obtain the following.
+Corollary 4.2. Te distortion of Uniform-of-Range-Voting is O(k).
+If only ordinal information about the preferences of the agents is given at the district level, then we
+can use Plurality with δ = O(m2) and the randomized rule Stable-Lottery mechanism of Ebadian
+et al. [2022] with δ = O(√m) as the in-district rule to obtain the following results.
+9
+
+Corollary 4.3. Te distortion of Uniform-of-Plurality is O(km2).
+Corollary 4.4. Te distortion of Uniform-of-Stable-Lottery is O(k√m).
+An important question to ask next is under what circumstances the aforementioned upper bounds
+of Corollaries 4.2, 4.3 and 4.4 are tight. First, we show that Uniform-of-Range-Voting is the best
+among mechanisms with unanimous in-district rules which may even use cardinal information.
+Teorem 4.5. Te distortion of any randomized distributed mechanism with a unanimous in-district rule
+is Ω(k).
+Proof. Let ε > 0 be a positive infinitesimal. Consider an instance with the following k symmetric
+districts: For any ℓ ∈ [k], in district dℓ, all λ agents therein have value 1/2 + ε for alternative aℓ,
+1/2 − ε for alternative x, and 0 for any other alternative. Since, the in-district rule is unanimous, the
+representative of district dℓ must be aℓ with probability 1. Hence, no mater what the probability of
+choosing a district representative as the winner is, the expected social welfare of the mechanism is
+λ · (1/2 + ε). However, the social welfare of alternative x is k · λ · (1/2 − ε), and thus the distortion
+is Ω(k).
+If we consider non-unanimous in-district rules, but require the in-district rule to be deterministic,
+then we can show a weaker lower bound of Ω(
+√
+k); notice that the theorem also implies the same
+bound for fully deterministic distributed mechanisms without unanimous in-district rules.
+Teorem 4.6. Te distortion of any randomized distributed mechanism with a deterministic in-district
+rule is Ω(
+√
+k).
+Proof. Consider a district dℓ in which all agents have value 1/2 for alternative aℓ, value 1/(2
+√
+k) for
+each alternative in {b1, . . . , b√
+k}, and 0 for any other alternative. If the representative of this district is
+not aℓ, then in instances consisting of copies of this district, the distortion is at least
+√
+k; in particular, it
+is at least that much if some alternative in {b1, . . . , b√
+k} is chosen and infinite if any other alternative
+is chosen. So, suppose that the representative of dℓ is aℓ.
+Next, consider an instance with k symmetric districts d1, . . . , dk. By the above discussion, for any
+ℓ ∈ [k], the representative of dℓ is alternative aℓ with social welfare λ/2 (note that only the agents
+of dℓ have positive value, equal to 1/2, for aℓ). Hence, no mater which district representative is
+chosen as the winner (or the probability distribution over the representatives), the (expected) social
+welfare of the mechanism is λ/2. In contrast, the social welfare of any alternative in {b1, . . . , b√
+k} is
+k · λ/(2
+√
+k) =
+√
+k · λ/2, and thus the distortion is
+√
+k.
+Next, we show that Uniform-of-Plurality is the best possible among ordinal randomized dis-
+tributed mechanisms with deterministic in-district rules, assuming an arbitrary but fixed ordering of
+the alternatives. Tis is quite surprising, as it shows that randomization over the districts is not beter
+than just choosing an arbitrary alternative that is representative of the most districts (i.e., not beter
+than Plurality-of-Plurality).
+Teorem 4.7. Te distortion of any ordinal distributed mechanism with a deterministic in-district rule is
+Ω(km2), when there exists an arbitrary but fixed tie-breaking ordering of the alternatives.
+Proof. Without loss of generality, suppose that the tie-breaking ordering of the alternatives is a1 ≻
+. . . ≻ ak ≻ b1 ≻ . . . ≻ bm/2−1 ≻ x ≻ c1 ≻ . . . ≻ cm/2−k; the naming of the alternatives is arbitrary
+but is assumed to be known and can be exploited. For simplicity, for any set of alternatives X, denote
+by [X] an arbitrary ordering of the alternatives in X.
+10
+
+Consider an instance with k symmetric districts such that in district dℓ there is a set of 2λ/m
+agents with preference ordering aℓ ≻ x ≻ [A\{aℓ, x}], a set of 2λ/m agents with preference ordering
+b1 ≻ x ≻ [A \ {b1, x}], . . ., and a set of 2λ/m agents with preference ordering bm/2−1 ≻ x ≻
+[A \ {bm/2−1, x}]. By Lemma 3.2, the representative of dℓ must be one of the top-ranked alternatives
+(otherwise the distortion of the mechanism would be infinite). Since aℓ is ranked above the other
+alternatives in the tie-breaking ordering, she chosen as the representative of dℓ. Hence, the set of
+representatives is {a1, . . . , ak}, and the winner is chosen according to some probability distribution
+over this set.
+Te valuation profile may be such that the 2λ/m agents in district dℓ that rank aℓ first have value
+1/m for all alternatives, while all other agents in dℓ have value 1/2 for their two favorite alterna-
+tives. Consequently, the social welfare of alternative aℓ is 2λ/m2, and thus the social welfare of the
+mechanism is also this much, no mater the probability distribution over the district representatives.
+In contrast, the social welfare of x is approximately kλ/2, leading to a distortion of Ω(km2).
+When randomization at the district level can be leveraged by ordinal distributed mechanisms, then
+we achieve distortion much beter than what is implied by Corollary 4.4, while also achieving strat-
+egyproofness. In particular, there are several centralized voting rules that can be implemented as
+distributed mechanisms, in the sense that they define the same probability distribution over the alter-
+natives. One such important class of voting rules is that of point-voting schemes, which is part of a
+larger class of strategyproof mechanisms [Barbera, 1978, Hylland, 1980, Gibbard, 1977] and includes
+rules with almost best possible distortion guarantees [Boutilier et al., 2015, Ebadian et al., 2022].
+4.1
+Point-voting schemes
+A point-voting scheme chooses an agent uniformly at random and then outputs her t-th favorite al-
+ternative with probability pt, where p1 ≥ . . . ≥ pm ≥ 0 and �m
+t=1 pt = 1. Hence, the probability
+according to which the point-voting scheme using the probability vector p = (p1, . . . , pm) chooses
+alternative a ∈ A as the winner w is Pr[w = a] = 1
+n
+�
+i∈N pσi(a), where σi(a) is the position that i
+ranks a in her preference ranking σ.
+Tere are many point-voting schemes of interest. For every positional scoring rule using the scor-
+ing vector s = (s1, . . . , sm), we can define a point-voting scheme f(s) by normalizing the scoring
+vector, that is, define pt = st/
+��
+j∈[m] sj
+�
+for every t ∈ [m] so that the winning probability of
+alternative a is
+Pr[w = a] = 1
+n
+�
+i∈N
+sσi(a)
+�
+j∈[m] sj
+=
+�
+i∈N sσi(a)
+n · �
+j∈[m] sj
+.
+Another important point-voting scheme is the rule that chooses each alternative uniformly at random;
+in this case, we have pt = 1/m for every t ∈ [m] so that Pr[w = a] = 1
+n
+�
+i∈N
+1
+m = 1
+m.
+For any point-voting scheme f that uses a probability vector p, we consider the distributed mech-
+anism Proportional-of-f-Point-Voting, which works as follows:
+• For every district d, choose the representative ad to be alternative a ∈ A with probability
+1
+λ
+�
+i∈Nd pσi(a).
+• Choose the winner to be the representative of district d with probability nd/n.
+11
+
+Teorem 4.8. Proportional-of-f-Point-Voting defines the same probability distribution as the point-
+voting scheme f.
+Proof. Te probabilitythat alternativea is chosen as the winner by Proportional-of-f-Point-Voting
+is
+Pr[w = a] =
+�
+d∈D
+Pr[w = ad] · Pr[ad = a]
+=
+�
+d∈D
+nd
+n · 1
+nd
+�
+i∈Nd
+pσi(a)
+= 1
+n
+�
+i∈N
+pσi(a),
+that is, Proportional-of-f-Point-Voting chooses a with the same probability as f.
+Teorem 4.8 shows that Proportional-of-f-Point-Voting achieves the same distortion bound
+as the point-voting scheme f it uses as the in-district rule, and also that it inherits its strategyproofness
+property. Tis is extremely useful, as there are centralized voting rules that are based on point-voting
+schemes and achieve almost the best possible distortion.
+Boutilier et al. [2015] considered a voting rule that is a convex combination of two point-voting
+schemes: With probability 1/2 choose an alternative uniformly at random, and with probability 1/2
+run the point-voting scheme defined by normalizingthe harmonic scoring rule H = (1, 1/2, . . . , 1/m).
+We will refer to this mechanism as BCHLPS. Boutilier et al. [2015] showed that this voting rule has
+distortion O(√m log m). An important property of point-voting schemes is that any rule that is a
+convex combination of point-voting schemes is also a point-voting scheme. Te following lemma is
+similar to lemmas proved before in the literature (e.g., see Filos-Ratsikas and Miltersen [2014], Barbera
+[1978]); we provide a proof for completeness.
+Lemma 4.9. Let f1, . . . , fκ be point-voting schemes defined by the probability vectors p1, . . . , pκ. For
+any non-negative numbers q1, . . . , qκ such that �
+j∈[κ] qj = 1, the voting rule f that chooses the outcome
+of fj with probability qj is a point-voting scheme.
+Proof. Let σ be an arbitrary preference profile. For any j ∈ [κ], denote the t-th coordinate of pj as pj,t,
+and let Pj(a) = Pr[a = fj(σ)] be the probability of choosing a as the winner according to point-voting
+scheme fj. Ten, the voting rule f chooses alternative a as the winner w with probability
+Pr[w = a] =
+�
+j∈[κ]
+qj · Pj(a)
+=
+�
+j∈[κ]
+qj ·
+�
+1
+n
+�
+i∈N
+pj,σi(a)
+�
+= 1
+n
+�
+i∈N
+�
+j∈[κ]
+qj · pj,σi(a).
+Hence, f is a point-voting scheme defined by the probability vector p with pt = �
+j∈[κ] qj · pj,t.
+Consequently, by Teorem 4.8 and Lemma 4.9, we can construct a randomized ordinal distributed
+mechanism based on the point-voting scheme of Boutilier et al. [2015] that achieves the same distortion
+bound and is strategyproof.
+12
+
+Corollary 4.10. Tere exists a randomized ordinal strategyproof distributed mechanism with distortion
+O(√m log m).
+Tis distortion bound is almost best possible as the lower bound of Ω(√m) for randomized cen-
+tralized rules holds trivially for distributed mechanisms by considering single-district instances.
+5
+Experiments
+In this section, we perform experiments with real and synthetic datasets, aiming to identify paterns in
+the distortion of several well-known voting rules and examine whether these support our theoretical
+findings. It is well-documented in the literature (e.g., see [Boutilier et al., 2015, Filos-Ratsikas et al.,
+2020]) that when working with real or realistic preferences, it ofen is the case that the distortions
+bounds are small numbers quite close to 1. In this sense, our goal is not primarily to demonstrate the
+distortion bounds themselves, but rather the dependence of these bounds on the distributed decision-
+making process, in particular the number of districts, as well as the use of randomization. We perform
+two main experiments, one with real-world preferences and valuation data, and one with synthetic
+data. All our experiments are with symmetric districts.
+5.1
+Experiments with the Jester Dataset
+For our first experiment, we use the Jester Joke Dataset [Goldberg et al., 2001]. Te dataset contains
+ratings for 100 different jokes in the range [−10, 10], provided by 70000 users. We chose to work
+with this dataset as it has also been employed by Boutilier et al. [2015] in the context of centralized
+distortion bounds, and also by Filos-Ratsikas et al. [2020] for the distortion of deterministic distributed
+mechanisms that use plurality as the over-district rule.
+Following the methodology developed in these works, we construct inputs consisting of ratings
+for the 8 most-rated jokes. In particular, we perform 1000 random runs in which we sample 100 users
+from the set of all users that have provided rankings for all eight jokes, and then partition them into
+k equal-sized districts uniformly at random, for k ∈ {1, 2, 5, 10, 20, 25}. Clearly, the case of k = 1
+corresponds to the centralized seting and will be used as a reference point. We interpret the ratings
+of the jokes as cardinal valuations: to be consistent with our seting (and with the experiments of
+[Boutilier et al., 2015, Filos-Ratsikas et al., 2020]), we add 10 to each user’s rating vector, to ensure that
+the values are positive and then apply the unit-sum normalization. For these inputs, we compute the
+average distortion of a set of 20 voting rules over the 1000 runs of the experiment. In particular, we
+consider distributed mechanisms fover-of-fin, where for fover we use Plurality or Uniform, whereas
+for fin we have:
+Deterministic Rules: We use simple voting scoring rules, namely Plurality (PL), Veto, Borda and
+Harmonic, as well as Range-Voting (RV), which in the case of k = 1 finds the optimal alternative.
+Randomized Rules: Here we use several natural point-voting schemes with probability vectors that
+are proportional to the aforementioned scoring rules (recall the definition from Section 4), namely
+• Proportional to Plurality Score (PropPL);
+• Proportional to Borda Score (PropBorda);
+• Proportional to Veto Score (PropVeto);
+• Proportional to Harmonic Score (PropHarmonic).
+13
+
+k
+RV
+PL
+Veto
+Borda
+Harmonic
+PropPL
+PropVeto
+PropBorda
+PropHarmonic
+BCHLPS
+1
+1
+1.049
+1.035
+1.007
+1.017
+1.135
+1.166
+1.155
+1.156
+1.166
+2
+1.017
+1.070
+1.059
+1.018
+1.020
+1.137
+1.166
+1.155
+1.156
+1.165
+5
+1.018
+1.064
+1.070
+1.020
+1.036
+1.133
+1.162
+1.155
+1.156
+1.165
+10
+1.019
+1.066
+1.082
+1.021
+1.044
+1.133
+1.162
+1.153
+1.154
+1.163
+20
+1.024
+1.066
+1.107
+1.030
+1.050
+1.134
+1.165
+1.154
+1.155
+1.164
+25
+1.022
+1.067
+1.142
+1.031
+1.107
+1.133
+1.165
+1.153
+1.154
+1.164
+Table 2: Distortion bounds of various voting rules based on valuations defined by the provided scores of the Jester dataset and random district partitions.
+RV
+PL
+Veto
+Borda
+Harmonic
+PropPL
+PropVeto
+PropBorda
+PropHarmonic
+BCHLPS
+k = 1
+Uniform
+1
+1.038
+1.045
+1.006
+1.019
+1.079
+1.087
+1.085
+1.085
+1.087
+Beta
+1
+1.086
+1.105
+1.029
+1.050
+1.140
+1.152
+1.147
+1.147
+1.150
+Exponential
+1
+1.032
+1.096
+1.018
+1.013
+1.118
+1.137
+1.132
+1.131
+1.134
+k = 2
+Uniform
+1.026
+1.052
+1.056
+1.030
+1.039
+1.079
+1.087
+1.084
+1.084
+1.086
+Beta
+1.044
+1.111
+1.118
+1.064
+1.080
+1.140
+1.152
+1.147
+1.147
+1.150
+Exponential
+1.039
+1.062
+1.115
+1.055
+1.051
+1.118
+1.136
+1.132
+1.130
+1.135
+k = 5
+Uniform
+1.031
+1.050
+1.057
+1.029
+1.038
+1.076
+1.084
+1.081
+1.081
+1.084
+Beta
+1.052
+1.113
+1.125
+1.074
+1.094
+1.143
+1.155
+1.151
+1.150
+1.154
+Exponential
+1.039
+1.069
+1.110
+1.055
+1.056
+1.119
+1.137
+1.133
+1.131
+1.134
+k = 20
+Uniform
+1.031
+1.055
+1.077
+1.039
+1.042
+1.077
+1.085
+1.082
+1.082
+1.084
+Beta
+1.055
+1.105
+1.145
+1.073
+1.084
+1.141
+1.154
+1.149
+1.149
+1.152
+Exponential
+1.047
+1.069
+1.123
+1.060
+1.058
+1.115
+1.133
+1.128
+1.127
+1.129
+k = 25
+Uniform
+1.031
+1.056
+1.071
+1.036
+1.044
+1.077
+1.085
+1.082
+1.0824
+1.084
+Beta
+1.054
+1.124
+1.149
+1.084
+1.094
+1.148
+1.155
+1.150
+1.150
+1.151
+Exponential
+1.042
+1.069
+1.129
+1.060
+1.054
+1.116
+1.134
+1.129
+1.128
+1.131
+Table 3: Distortion bounds of various voting rules based on valuations defined according to several probability distributions and random district
+partitions. Results for deterministic mechanisms are presented at the lef of the bold vertical line, and results for randomized mechanisms are at the
+right of the bold vertical line.
+
+We also use the rule of Boutilier et al. [2015] (we refer to it as BCHLPS in the following); recall that this
+is a point-voting scheme that with probability 1/2 selects an alternative at random and with probability
+1/2 runs the PropHarmonic rule defined above. As established in Corollary 4.10 (and the discussion
+before the statement of the corollary), this is best possible in terms of the worst-case distortion.
+Te results of our experiments can be seen in Table 2. In the table we only present the results
+where as fover, we used Plurality for deterministic rules and Uniform for randomized rules. Tis
+is in accordance to our approach in the theoretical results in previous sections. Te bounds for the
+cases not shown are quite similar, and slightly larger in general. For each of the randomized rules,
+we perform 300 runs and calculate their expected social welfare, which we then use to calculate the
+distortion.
+From the results of Table 2 we observe that, as expected, the existence of multiple districts has an
+adverse effect on the distortion of deterministic mechanisms, which becomes worse compared to the
+centralized case k = 1. For these rules, we can also observe that the distortion generally increases as k
+increases. In contrast, the distortion of randomized rules remains virtually unchanged for any value of
+k. Tis is in complete accordance with our theoretical findings, where we established that these rules
+induce the same probability distribution. Te experiments showcase that this does not only hold in
+expectation, but also in practice (given sufficiently many runs).
+Another crucial observation is that, in terms of the absolute distortion numbers, randomization
+does not seem to help; if anything, it makesthe distortion bounds worse! Tis can be justified by the fact
+that real-world instances like those from the Jester dataset display a large degree of homogeneity, which
+results in the simple deterministic rules performing quite well. On the other hand, randomization ofen
+leads to suboptimal choices even on such “well-behaved” instances, demeaning the distortion bounds
+on average. Surprisingly, among ordinal voting rules, Borda seems to perform best across the board
+even though the theoretical distortion of Borda is in fact unbounded.
+5.2
+Experiments with Synthetic Datasets
+We also perform experiments with datasets that are generated from probability distributions. In par-
+ticular, and to be consistent with the Jester experiment presented above, we create instances with
+100 agents and 8 alternatives, by first drawing the values of the agents from a certain distribution,
+and then constructing the induced ordinal preference profile from those values. We use the following
+distributions:
+• Uniform distribution in [1, 100]. Tis is the simplest case, where all possible values are equally
+likely.
+• Beta distribution with α = 1/10 and β = 1/10. Tis distribution has a symmetric convex pdf
+function centered around a mean of 1/2, assigning higher probabilities to values very close to 1
+or 0.
+• Exponential distribution with exponent 4, i.e., the pdf is f(x) = 4e4 for x ≥ 0 and f(x) = 0
+otherwise. Tis distribution generates values close to 0 with high probability, and as the values
+increase, the probability of them being generated decreases exponentially.
+For the rest of the experiment, we perform similar steps as in the case of the Jester dataset: We nor-
+malize the values to sum up to 1, and run the set of mechanisms described above. For each ran-
+domized mechanism we now perform 150 individual runs and calculate its expected welfare. We
+calculate the average distortions over 500 runs of the experiment for k symmetric districts, where
+k ∈ {1, 2, 5, 20, 25}. Note that the number of runs and the number of district sizes is slightly smaller
+15
+
+in this experiment, because it is more computationally intensive (as we need to calculate bounds for 3
+different distributions). Again, we use Plurality as fover for deterministic and Uniform for random-
+ized mechanisms; the results for the other cases were similar and are not reported.
+Te results can be found in Table 3. Similarly to the Jester experiment, it is evident that the distor-
+tion of the deterministic mechanisms becomes worse for k ≥ 2, whereas it remains prety much the
+same for randomized mechanisms. Again, we observe that randomization results in worse distortion
+bounds overall, and that Borda performs best among deterministic mechanisms. Interestingly, con-
+trary to the Jester dataset, here we do not see a clear patern of the distortion increasing as k increases
+for deterministic mechanisms (other than the jump from k = 1 to k = 2). Tis is probably due to the
+fact that the synthetic instances are highly homogeneous, and with uniform random district partitions,
+the districts end up being quite uniform, regardless of their number and size.
+Te role of unit-sum. We remark here that normalizing the values to sum up to 1 effectively makes the
+Uniform and Exponential distributions prety similar, and this is reflected in the results. To get a sense
+of the effect of normalization, we also ran the experiments without it. We observe that the distortions
+for the exponential distribution are now larger than those of the uniform distribution. In general, the
+distortion bounds still lie in the range [1.03, 1.15] for all distributions, but their average values (over
+all documented distortion bounds) are larger for all distributions except Uniform. It is also the case
+that for the Beta distribution, the bounds of deterministic mechanisms are much closer to those of
+randomized ones. Te distortion of randomized mechanisms is still almost the same for any number
+of districts.
+6
+Open Problems
+From our results, an interesting technical challenge is to remove the requirement for a consistent tie-
+breaking ordering from the statement of Teorem 4.7. Similarly, we could atempt to remove unanimity
+from the lower bound of Teorem 3.1; although unanimity is usually prety natural, removing it would
+make the theorem stronger. More interestingly, our result about point-voting schemes in Teorem 4.8
+crucially does not depend on the normalization of the valuations, and hence also could be applied
+verbatim to the metric distributed social choice seting studied by Anshelevich et al. [2022], where
+randomized mechanisms have never been considered; this seems like a natural starting point for such
+an investigation.
+References
+Ben Abramowitz, Elliot Anshelevich, and Wennan Zhu. Awareness of voter passion greatly improves
+the distortion of metric social choice. In Proceedings of the Te 15th Conference on Web and Internet
+Economics (WINE), pages 3–16, 2019.
+Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A. Voudouris. Peeking
+behind the ordinal curtain: Improving distortion via cardinal queries. Artificial Intelligence, 296:
+103488, 2021.
+Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A. Voudouris. A few
+queries go a long way: Information-distortion tradeoffs in matching. Journal of Artificial Intelligence
+Research, 74, 2022a.
+Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A. Voudouris. Don’t roll
+the dice, ask twice: Te two-query distortion of matching problems and beyond. In Proceedings of
+the 36th Conference on Neural Information Processing Systems (NeurIPS), 2022b.
+16
+
+Elliot Anshelevich and Shreyas Sekar. Blind, greedy, and random: Algorithms for matching and clus-
+tering using only ordinal information. In Proceedings of the 30th AAAI Conference on Artificial Intel-
+ligence (AAAI), pages 390–396, 2016.
+Elliot Anshelevich, Onkar Bhardwaj, Edith Elkind, John Postl, and Piotr Skowron. Approximating
+optimal social choice under metric preferences. Artificial Intelligence, 264:27–51, 2018.
+Elliot Anshelevich, Aris Filos-Ratsikas, Nisarg Shah, and Alexandros A. Voudouris. Distortion in so-
+cial choice problems: Te first 15 years and beyond. In Proceedings of the 30th International Joint
+Conference on Artificial Intelligence (IJCAI), pages 4294–4301, 2021.
+Elliot Anshelevich, Aris Filos-Ratsikas, and Alexandros A Voudouris. Te distortion of distributed
+metric social choice. Artificial Intelligence, 308:103713, 2022.
+Yoram Bachrach, Omer Lev, Yoad Lewenberg, and Yair Zick. Misrepresentation in district voting. In
+IJCAI, pages 81–87, 2016.
+Salvador Barbera. Nice Decision Schemes. Springer Netherlands, 1978.
+Gerdus Benad`e, Swaprava Nath, Ariel D. Procaccia, and Nisarg Shah. Preference elicitation for partic-
+ipatory budgeting. In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI), pages
+376–382, 2017.
+Umang Bhaskar and Abheek Ghosh. On the welfare of cardinal voting mechanisms. In Proceedings of
+the 38th IARCS Annual Conference on Foundations of Sofware Technology and Teoretical Computer
+Science (FSTTCS), pages 27:1–27:22, 2018.
+Umang Bhaskar, Varsha Dani, and Abheek Ghosh. Truthful and near-optimal mechanisms for welfare
+maximization in multi-winner elections. In Proceedings of the 32nd AAAI Conference on Artificial
+Intelligence (AAAI), pages 925–932, 2018.
+Allan Borodin, Omer Lev, Nisarg Shah, and Tyrone Strangway. Big city vs. the great outdoors: Voter
+distribution and how it affects gerrymandering. In IJCAI, pages 98–104, 2018.
+Allan Borodin, Omer Lev, Nisarg Shah, and Tyrone Strangway. Primarily about primaries. In Proceed-
+ings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), pages 1804–1811, 2019.
+Craig Boutilier, Ioannis Caragiannis, Simi Haber, Tyler Lu, Ariel D. Procaccia, and Or Sheffet. Optimal
+social choice functions: A utilitarian view. Artificial Intelligence, 227:190–213, 2015.
+Felix Brandt, Vincent Conitzer, Ulle Endriss, J´erˆome Lang, and Ariel D. Procaccia, editors. Handbook
+of Computational Social Choice. Cambridge University Press, 2016.
+Ioannis Caragiannis, Swaprava Nath, Ariel D. Procaccia, and Nisarg Shah. Subset selection via implicit
+utilitarian voting. Journal of Artificial Intelligence Research, 58:123–152, 2017.
+Ioannis Caragiannis, Nisarg Shah, and Alexandros A. Voudouris. Te metric distortion of multiwinner
+voting. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI), pages 4900–4907,
+2022.
+Soroush Ebadian, Anson Kahng, Dominik Peters, and Nisarg Shah. Optimized distortion and propor-
+tional fairness in voting. In Proceedings of the 23rd ACM Conference on Economics and Computation
+(EC), pages 563–600, 2022.
+17
+
+Edith Elkind, Jiarui Gan, Svetlana Obraztsova, Zinovi Rabinovich, and Alexandros A. Voudouris. Pro-
+tecting elections by recounting ballots. Artificial Intelligence, 290:103401, 2021.
+Aris Filos-Ratsikas and Peter Bro Miltersen. Truthful approximations to range voting. In Proceedings
+of the 10th International Conference on Web and Internet Economics (WINE), pages 175–188, 2014.
+Aris Filos-Ratsikas and Alexandros A Voudouris. Approximate mechanism design for distributed facil-
+ity location. In International Symposium on Algorithmic Game Teory, pages 49–63. Springer, 2021.
+Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, and Jie Zhang. Social welfare in one-sided match-
+ings: Random priority and beyond. In Proceedings of the 7th Symposium of Algorithmic Game Teory
+(SAGT), pages 1–12, 2014.
+Aris Filos-Ratsikas, Evi Micha, and Alexandros A. Voudouris. Te distortion of distributed voting.
+Artificial Intelligence, 286:103343, 2020.
+Allan Gibbard. Manipulation of schemes that mix voting with chance. Econometrica: Journal of the
+Econometric Society, pages 665–681, 1977.
+Vasilis Gkatzelis, Daniel Halpern, and Nisarg Shah. Resolving the optimal metric distortion conjecture.
+In Proceedings of the 61st IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages
+1427–1438, 2020.
+Ken Goldberg, Teresa Roeder, Dhruv Gupta, and Chris Perkins. Eigentaste: A constant time collabo-
+rative filtering algorithm. information retrieval, 4(2):133–151, 2001.
+Aanund Hylland. Strategy proofness of voting procedures with loteries as outcomes and infinite sets
+of strategies. Technical report, 1980.
+Fatih Erdem Kizilkaya and David Kempe. Plurality veto: A simple voting rule achieving optimal metric
+distortion. In Proceedings of the 31st International Joint Conference on Artificial Intelligence (IJCAI),
+pages 349–355, 2022.
+Omer Lev and Yoad Lewenberg. “reverse gerrymandering”: Manipulation in multi-group decision
+making. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 2069–
+2076, 2019.
+Yoad Lewenberg, Omer Lev, and Jeffrey S Rosenschein. Divide and conquer: Using geographic manip-
+ulation to win district-based elections. In Proceedings of the 16th Conference on Autonomous Agents
+and MultiAgent Systems, pages 624–632, 2017.
+Debmalya Mandal, Ariel D. Procaccia, Nisarg Shah, and David P. Woodruff. Efficient and thrify vot-
+ing by any means necessary. In Proceedings of the 32nd Annual Conference on Neural Information
+Processing Systems (NeurIPS), pages 7178–7189, 2019.
+Debmalya Mandal, Nisarg Shah, and David P. Woodruff. Optimal communication-distortion tradeoff
+in voting. In Proceedings of the 21st ACM Conference on Economics and Computation (EC), pages
+795–813, 2020.
+Ariel D. Procaccia and Jeffrey S. Rosenschein. Te distortion of cardinal preferences in voting. In
+International Workshop on Cooperative Information Agents (CIA), pages 317–331, 2006.
+18
+
diff --git a/0tE1T4oBgHgl3EQflAQk/content/tmp_files/load_file.txt b/0tE1T4oBgHgl3EQflAQk/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf,len=945
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='03279v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='GT]  9 Jan 2023  Revisiting the Distortion of Distributed Voting  Aris Filos-Ratsikas1 and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris2  1School of Informatics, University of Edinburgh, UK  2School of Computer Science and Electronic Engineering, University of Essex, UK  Abstract  We consider a seting with agents that have preferences over alternatives and are partitioned  into disjoint districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te goal is to choose one alternative as the winner using a mechanism  which first decides a representative alternative for each district based on a local election with the  agents therein as participants, and then chooses one of the district representatives as the winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Previous work showed bounds on the distortion of a specific class of deterministic plurality-based  mechanisms depending on the available information about the preferences of the agents in the  districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In this paper, we first consider the whole class of deterministic mechanisms and show  asymptotically tight bounds on their distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We then initiate the study of the distortion of  randomized mechanisms in distributed voting and show bounds based on several informational  assumptions, which in many cases turn out to be tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Finally, we also experimentally compare  the distortion of many different mechanisms of interest using synthetic and real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  1  Introduction  Voting is a ubiquitous method for making decisions with a large number of applications, such as electing  political representatives, deciding how to split a public budget between projects, or choosing which  services (restaurants, hotels, etc) to recommend to new users based on past user experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' As such, it  has been at the epicenter of research within multiple disciplines including political sciences, economics  and computer science [Brandt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2016].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te most prominent question in this research agenda is to  identify the best voting rule to use to collectively aggregate the preferences of agents over alternative  options into a single winning alternative, with most of the earlier literature focusing on axiomatic  properties that good voting rules should have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' An alternative way to tackle this question that has been  proposed in computer science is through the distortion framework [Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2021] which  allows to compare different voting rules based on how well they approximate the optimal choice as  measured in terms of a social objective function like the utilitarian social welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Since its inception in 2006 by Procaccia and Rosenschein [2006], the distortion framework has been  applied to several utilitarian social choice setings (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', [Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018,  Gkatzelis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2020]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te lion’s share of previous work has focused on centralized models with a  single pool of agents whose preferences are directly given as input to a voting rule, which thus can  utilize all the given information at once to make a decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' However, there are many applications  with multiple pools of agents which make independent local decisions that can be thought of as rec-  ommendations for the final decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' To give a concrete example, in most political election systems,  the citizens are partitioned into districts based on geographic or other criteria, and vote within their  districts to propose the candidate (party) they would like to be selected as the winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Inspired by situations like the one described above, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] initiated the study  of the distortion of mechanisms in a distributed single-winner seting where a set of n agents with  1  Deterministic  Randomized-of-Deterministic  Randomized-of-Randomized  Ordinal  Θ(km2)  Θ(km2)  Ω(√m), O(√m log m)  Cardinal  Θ(km)  Θ(k)  Θ(k)  Strategyproof  Θ(nm)  Θ(nm)  Ω(√m), O(√m log m)  Table 1: An overview of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Specific details can be found in the appropriate sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  cardinal preferences over a set of m alternatives are partitioned into k disjoint districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te authors  focused on deterministic mechanisms of the form Plurality-of-f, which first choose a representative  alternative for each district according to some rule f, by holding a local election with the agents of  the district as the voters, and then picking the winner to be the alternative that is representative of  the most districts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', using the Plurality rule).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' considered mechanisms for  which the rule f can be cardinal or ordinal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', it may use the actual numerical information about  the preferences of the agents within the districts or just consistent rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te authors showed  that, when the districts are symmetric (that is, each of them contains the same number of agents), the  distortion of a cardinal mechanism, namely Plurality-of-Range-Voting is O(km), and provided an  asymptotically matching lower bound of Ω(km) on the distortion of any Plurality-of-f mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For ordinal mechanisms, they showed that Plurality-of-Plurality achieves a distortion of O(km2),  and that this is asymptotically best among all ordinal Plurality-of-f mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1  Revisiting the distortion of distributed voting  A first observation about the results of Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] is that there is a-priori no reason  to restrict our atention to only mechanisms in the class Plurality-of-f, as using other over-districts  rules could potentially lead to beter distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Indeed, follow-up work considered distributed social  choice setings with metric preferences [Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022, Filos-Ratsikas and Voudouris, 2021]  without such restrictions on the over-districts rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In addition, all of the previous work on these  setings only considered deterministic mechanisms that use deterministic in-district and over-districts  rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Randomization has proven out to be a very useful tool in achieving beter (expected) distortion  bounds in the centralized seting (see Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015], Ebadian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2022]), so it is only natural  to consider randomized mechanisms in the distributed seting as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Finally, an important question  is how the distortion bounds are affected in case the participants act selfishly, and whether there are  strategyproof mechanisms with good distortion bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis question has been considered in the  centralized seting [Filos-Ratsikas and Miltersen, 2014, Bhaskar and Ghosh, 2018, Bhaskar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018,  Ebadian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022] and also in the distributed metric seting [Filos-Ratsikas and Voudouris, 2021];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' we  consider it in the context of the normalized seting of Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2  Our Contributions  We consider the class of all mechanisms for distributed voting in the seting of [Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=',  2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular, we consider the fover-of-fin class of mechanisms, where fin is an in-district rule that  takes as input the preferences of the agents within each district and outputs a representative alternative  for the district, while fover is a rule that takes as input the representative alternatives of all districts and  chooses one of them as the overall winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We consider several different cases depending on the nature  of fover and fin (deterministic or randomized), and the type of information they can utilize (cardinal or  ordinal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We show the following results;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' see Table 1 for an overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Deterministic Mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' When fover and fin are both deterministic and the districts are symmet-  ric, we show that the best possible distortion is Θ(km) when the valuation functions of the agents are  2  accessible (cardinal mechanisms), and is Θ(km2) when only ordinal information about the preferences  of the agents is available (ordinal mechanisms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te upper bounds were shown by Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  [2020] and here we provide asymptotically tight lower bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tese results show that for general,  unstructured (normalized) valuations, employing different over-district rules in fact does not result in  improvements on the distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We present these results in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Randomized Mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Section 4, we consider for the first time the distortion of randomized  mechanisms in distributed voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We first prove a simple composition theorem, which shows that  using an in-district rule with known distortion δ in the centralizedseting and then selecting the winner  uniformly at random from the set of representatives, defines a distributed mechanism with distortion  O(kδ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Using this, complemented with new lower bounds, we show that the best possible distortion  for cardinal unanimous mechanisms is Θ(k);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' in fact, this is true even when the districts are asymmetric  and when fover is randomized but fin is deterministic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For ordinal mechanisms, we consider two cases: (a) mechanisms that use deterministic in-district  rules fin, and (b) fully-randomized mechanisms, where both fover and fin are randomized rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For  (a), we show that the best possible distortion is Θ(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te upper bound follows from the bound on  Plurality-of-Plurality proven in [Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2020];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' here, we provide an asymptotically  matching lower bound assuming a natural universal tie-breaking rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For (b), we prove a simple but  very interesting result: For a well-studied class of randomized centralized voting rules called point-  voting schemes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see Gibbard [1977], Barbera [1978]), there exists a distributed implementation so  that there is no effect on the induced probability distribution, even for asymmetric districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Simply put,  using such rules it is possible to escape the ill effects of districts in terms of the distortion, even when  the districts are asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' From this result, it follows that there exists a distributed implementation  of a well-known mechanism of Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] that achieves distortion O(√m log m), almost  matching the best possible lower bound of Ω(√m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Strategyproof Mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For strategyproof mechanisms, which are resilient to strategic manip-  ulation, we show that a best-possible distortion of Θ(nm) for deterministic mechanisms (and more  generally mechanisms with a deterministic in-district rule) is easy to achieve by a variation of a dic-  tatorship rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For randomized mechanisms, since point-voting schemes are strategyproof, the bound  O(√m log m) carries over to this class as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Results about deterministic strategyproof mechanisms  are presented in Section 3, and about randomized strategyproof mechanisms in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Finally, in Section 5, we perform experiments using real-world data and synthetic data  to evaluate the effect of distributed decision making to the distortion in setings closer to practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te  main conclusions of our experimental results mirror that of our theoretical results in Sections 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3  Further Related Work  Te distortion literature is by now rather extensive, including topics such as single-winner voting  [Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018, Gkatzelis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2020, Kizilkaya and Kempe, 2022],  multi-winner voting [Caragiannis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2017, 2022], matching problems [Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2014,  Amanatidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022a], and participatory budgeting [Benad`e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2017].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Generally speaking, most  works can be categorized as either studying a normalized utilitarian seting (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', [Procaccia and Rosen-  schein, 2006, Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2014, Benad`e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2017, Ebadian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022]) or  a metric preference seting (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', [Anshelevich and Sekar, 2016, Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018, Gkatzelis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=',  2020, Caragiannis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022, Kizilkaya and Kempe, 2022]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Some more recent works have also studied  the interplay between information and distortion [Amanatidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2021, 2022a,b, Mandal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2019,  2020, Abramowitz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2019], and there have also been several works on strategyproofness in the con-  text of distortion [Filos-Ratsikas and Miltersen, 2014, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2014, Bhaskar and Ghosh,  3  2018, Bhaskar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018, Ebadian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We refer the reader to the survey of Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  [2021] for a detailed overview of the related literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Besides the aforementioned works on distributed voting, Borodin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2019] studied a related  two-stage seting in which the voters participate in a central election, but the candidates themselves  come from local elections within the political parties’ electorates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Beyond distortion, in the context of  district-based elections, there have also been other works that have considered the degree of deviation  from proportional representation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see [Bachrach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2016] and references therein), and some  works that have studied the complexity of manipulation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see [Elkind et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2021, Lewenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=',  2017, Lev and Lewenberg, 2019, Borodin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2018]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  2  Preliminaries  An instance I of our problem is given by a tuple I = (N, A, v, D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tere is a set N of n agents (or  voters) that have preferences over a set A of m alternatives (or candidates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te preferences of each  agent i ∈ N are captured by a valuation function vi : A → R≥0 that maps every alternative a ∈ A to a  real non-negative value vi(a) = via.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Following previous work, we assume that the valuation functions  are normalized such that �  a∈A via = 1 for every i ∈ N (unit-sum assumption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let v = (vi)i∈N be  the valuation profile consisting of the valuation functions of all agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te agents are also partitioned  into a set D of k disjoint districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For every district d ∈ D, let Nd be the set of agents it contains, such that �  d∈D Nd = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In the  symmetric case, each district d contains exactly λ = n/k agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In the asymmetric case, each district  d contains a number nd of agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' All our lower bounds follow by instances consisting of symmetric  districts, whereas our upper bounds in Section 4 hold for asymmetric districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1  Mechanisms  Our goal is to choose an alternative to satisfy several criteria of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis choice must be done  using a distributed mechanism that uses an in-district voting rule fin and an over-districts voting rule  fover to implement the following two independent steps:  Step 1: For each district d, choose a representative alternative ad ∈ A by holding a local election  based on fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Step 2: Choose a district representative as the winner based on fover by considering the districts  as voters and their representatives as the candidates they approve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For simplicity we refer to such mechanisms as fover-of-fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Different choices of fin and fover lead to  different distributed mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Note that the in-district rule can in general use various types of  information about the preferences of the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For instance, it may be able to use exact cardinal  information about the valuation functions, or only ordinal information that is induced by the values  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', rankings of alternatives that are consistent to the values of the agents for them).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In the later case,  we will use σi to denote the preference ranking of agent i ∈ N so that σi(a) is the rank of alternative  a ∈ A in the ranking of i, and σi(a) < σi(b) if vi(a) ≥ vi(b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' let σ = (σi)i∈N be the ordinal  profile consisting of the preference rankings of all agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' To be concise in the definitions below, let  δ(I) be the information about the preferences of the agents in instance I = (N, A, v, D) that is used  by a mechanism;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' that is, δ(I) = v in case of cardinal information, or δ(I) = σ in case of ordinal  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We will focus on different classes of distributed mechanisms depending on the available informa-  tion about the preferences of the agents at the district level (cardinal or ordinal), and also on whether  4  their decision is deterministic or randomized (that is, they choose the district representatives or final  winner based on probability distributions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2  Social Welfare and Distortion  Given an instance I, the social welfare of an alternative a ∈ A is the total value that the agents have for  a, that is, SW(a|I) = �  i∈N via.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' So, the expected social welfare achieved by a randomized distributed  mechanism M that chooses alternative a ∈ A as the winner w with probability PrM[w = a] is  E[SW(M(I))] =  �  a∈A  Pr  M [w = a] · SW(a|I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te efficiency of a distributed mechanism is measured by the notion of distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of a  distributed mechanism M is the worst-case ratio (over all possible instances with n agents, m alterna-  tives, and k districts) of the maximum social welfare achieved by any alternative over the (expected)  social welfare of the alternative chosen by the mechanism as the winner w, that is,  dist(M) = sup  I  maxa∈A SW(a|I)  E[SW(M(δ(I))] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Clearly, dist(M) ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' When the denominator in the definition of the distortion tends to 0, we will  say that the distortion is infinite or unbounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Our goal is to identify the best possible distributed  mechanisms in terms of distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3  Strategyproofness  Another important property that we would like our mechanisms to satisfy is that of strategyproof-  ness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' A strategyproof mechanism makes decisions such that providing false information never leads to  the selection of an alternative that an agent prefers over the alternative chosen when the agent pro-  vides truthful information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular, for any instance I, it must be the case that vi(M(δ(I))) ≥  vi(M(δ(I′))) for any agent i ∈ N, where I′ is the instance obtained when only agent i reports infor-  mation different than that in I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4  Some useful observations and properties  Before we present our technical results, let us briefly discuss some useful properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Locality of distributed mechanisms: First, observe that any distributed mechanism fover-of-fin  satisfies a locality property in the following sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' A district d (that is, the preferences of a number  of agents) appears in different instances if in each of these instances there is a district with the same  number of agents and the same information about theirs preferences as in d (depending on what is  required by the mechanism).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Since the information is the same, the in-district rule fin must decide the  same alternative as the representative of the district in all these instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Similarly, in all instances  where the mechanism has decided the same set of district representatives, the over-districts rule fover  must decide the same final winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Distortion of distributed vs centralized: Another useful observation is that the distortion of a  distributed mechanism fover-of-fin is at least as much as the distortion of the in-district centralized  voting rule fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Indeed, when k = 1, there is only one representative alternative chosen by fin, and  thus this alternative must be chosen as the winner by fover;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' this is also true for instances with k ≥ 2  districts which are all copies of one district.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consequently, the distortion of fin is a lower bound on  the distortion of fover-of-fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  5  Strategyproofness: Observe that for a distributed mechanism fover-of-fin to be strategyproof it is  necessary that the in-district rule fin is strategyproof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis again follows by how the mechanism would  work in instances with a single district, in which case the over-districts rule fover does not play any  role in the selection of the final winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Unanimity: A few of our results will require the in-district rules fin to be unanimous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Unanimity  stipulates that if all of the agents have the same alternative as the top preference, that alternative  must be selected (with probability 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Unanimity is a very natural property of “reasonable” voting  rules, especially deterministic ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For randomized rules, there might be reasons to consider non-  unanimous choices, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see Gibbard [1977], Filos-Ratsikas and Miltersen [2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  3  Deterministic mechanisms  We start with deterministic distributed mechanisms and focus explicitly on the case of symmetric  districts in this section (that is, the size of each district is λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' When full information about the valuations  of the agents is known at the district level, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] showed that the mechanism  Plurality-of-Range-Voting, which chooses the representative of each district to be the alternative  with maximum social welfare for the agents in the district, has distortion O(km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We show that this  mechanism is asymptotically best possible over all possible deterministic distributed mechanisms that  use unanimous in-district rules (but may not use Plurality as the over-districts rule).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any deterministic distributed mechanism with a unanimous in-district  rule is Ω(km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let M be some deterministic distributed mechanism with a unanimous in-district rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Without  loss of generality, whenever there are k distinct district representatives {a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, we assume that  M chooses a1 as the overall winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let ε > 0 be some positive infinitesimal and consider the following  instance with k districts {d1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , dk} and m > k alternatives:  In district d1, all agents have value 1/m + ε for alternative a1, and value 1/m − ε/(m − 1) for  any other alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For any ℓ ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , k}, in district dℓ, all agents have value 1/2 + ε for alternative aℓ, value  1/2 − ε for alternative x, and value 0 for any other alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Since the in-district rule is unanimous, the district representatives are alternatives {a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, and  the overall winner is thus a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te social welfare of alternative a1 is approximately λ/m, whereas the  social welfare of alternative x is approximately k · λ/2, leading to distortion Ω(km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  When only ordinal information about the preferences of the agents is available, Filos-Ratsikas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] showed that Plurality-of-Plurality, which chooses the favorite alternative of most of  the agents in a district as its representative and then the alternative that represents the most districts  as the winner, has distortion O(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We show that this mechanism is asymptotically best possible  among all ordinal distributed mechanisms (without any restrictions), thus improving upon the result  of Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] who showed that Plurality-of-Plurality is best possible only within  the class of mechanisms they studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We first prove an easy but important lemma showing that when only ordinal information is avail-  able, to achieve finite distortion, it is necessary the representative of each district to be some alternative  that is the favorite of at least one agent in the district.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  6  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te representative of any district must be some top-ranked alternative, otherwise the distor-  tion is infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let d be a district and let T be the set of top-ranked alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Suppose that the representative  of d is chosen to be some alternative x ̸∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Ten, in any instance consisting of copies of d, the winner  must be x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' However, the valuation profile might be such that all agents have value 1 for their favorite  alternative and 0 for any other alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consequently, the social welfare of x might be 0, whereas  the social welfare of any top-ranked alternative is positive, leading to infinite distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We say that a district is divided if its λ agents are partitioned into m/2 equal-sized sets such that all  the 2λ/m agents in each set rank the same alternative first and different sets of agents have different  top-ranked alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2, the representative of such a district must be one of the top-  ranked alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te following lemma shows that choosing the representative of a divided district  as the winner is, under some circumstances, a bad choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Suppose that some alternative y1 is chosen as the winner by a deterministic ordinal dis-  tributed mechanism when the set of representatives is {y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , yk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' If there exists a divided district that  is represented by y1, then there are k − 1 districts with representatives y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , yk, and altogether these k  districts define an instance such that the distortion of the mechanism is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let M be a deterministic ordinal distributed mechanism that selects y1 as the winner when  the set of representatives is {y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , yk}, and let d be the divided district that is represented by y1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Consider the following k districts:  Te first district is a copy of d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For every ℓ ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , k}, the ℓ-th district is such that all agents therein rank yℓ first, x ̸∈  {y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , yk} second, and then all other alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2, M must choose yℓ as the  representative of the ℓ-th district, as this is the only top-ranked alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  So, indeed the set of representatives is {y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , yk} and M chooses y1 as the winner by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  One possible valuation profile is the following:  In the first, divided district, the 2λ/m agents that rank y1 first have value 1/m for all alternatives,  and the remaining agents all have value 1 for their favorite alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For every ℓ ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , k}, all agents in the ℓ-th district have value 1/2 for their two favorite  alternatives (yℓ and x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Consequently, the social welfare of y1 is λ/m2 whereas the social welfare of x is approximately k·λ/2,  and thus the distortion is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3 shows that deterministic ordinal distributed mechanisms with distortion o(km2) must  not output the representative of a divided district as the winner when it is given a set of districts with  different representatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' However, as we show in the proof of the next theorem, there are instances  where such a choice is inevitable, and thus the distortion is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any deterministic ordinal distributed mechanism is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let M be a deterministic ordinal distributed mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We focus on instances with k districts  and sets of alternatives A ∪ B ∪ C ∪ {x}, where A = {a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, B = {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bm/2+k−1}, and  7  C = {c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , cm−2k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Without loss of generality, suppose that when the district representatives are  {a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, M chooses a1 as the overall winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Let d1 be a divided district with set of top-ranked alternatives {a1, b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bm/2−1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3,  if a1 is the representative of d1, then there exists an instance such that the distortion of M is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  So, suppose that the representative of d1 is some other top-ranked alternative, say b1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Again by  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3, if b1 is chosen as the winner whenever she is part of a representative set consisting of  k distinct alternatives, then the distortion of M would be Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' So, let us assume that when the  district representatives are {b1, a2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, the winner is an alternative different than b1, say a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We can now repeat this argument step by step for each alternative aℓ, ℓ ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular,  let dℓ be a divided district with top-ranked alternatives {aℓ, bℓ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bm/2+ℓ−2} (note that alternatives  b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bℓ−1 do not appear as top-ranked alternatives in dℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3, if aℓ is the representative  of dℓ then the distortion of M is Ω(km2), so the representative is some other alternative from the set  {bℓ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bm/2+ℓ−2}, say bℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Again by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3, if bℓ is chosen as the winner whenever she is part of  a representative set consisting of k distinct alternatives, then the distortion of M would be Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  So, when the district representatives are {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bℓ, aℓ+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, the winner is an alternative not in  {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bℓ}, say aℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te last step of this repeated argument leads to the lower bound of Ω(km2): We have reached an  instance with set of representatives {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , bk} all of whom are representative of some divided district,  and thus no mater who of them is chosen as the winner, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3 there exists an instance that  includes the corresponding divided district and k − 1 unanimous districts (like in the proof of the  lemma) such that the distortion is Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Finally, let us discuss the case of deterministic strategyproof distributed mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Bhaskar and  Ghosh [2018] showed that the distortion of any deterministic centralized strategyproof voting rule  (including those that have access to the valuation functions) is Θ(nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' From the discussion Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4,  we directly obtain a lower bound of Ω(nm) for the distributed seting as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' A tight upper bound is  also not hard to derive by considering the straightforward First-of-First mechanism which works as  follows:  For each district d, choose the favorite alternative of the first agent therein as the representative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Choose the representative of the first district as the winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' First-of-First is strategyproof and achieves an asymptotically best possible distortion of  Θ(nm) within the class of deterministic strategyproof distributed mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te mechanism is clearly strategyproof since the winner is the favorite alternative of the first  agent of the first district who acts as a dictator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Since the winner is ranked first by an agent, the social  welfare of the mechanism is at least 1/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te maximum possible social welfare is n, and thus the  distortion is O(nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  4  Randomized mechanisms  We start our discussion on randomized distributed mechanisms by analyzing a general class of mech-  anisms that we call Uniform-of-δ-Approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' A mechanism M in this class works as follows:  For each district d, M chooses the representative ad according to some centralized voting rule  fin that has distortion at most δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  M chooses the winner uniformly at random from the set of representatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  8  Picking the winner uniformly at random from the representatives that have been selected seems to be  the most natural choice as there is not much information about the preferences of the agents in the  districts, and essentially all we can do is assign higher proportional probability to an alternative that  is representative of more districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We have the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any Uniform-of-δ-Approximate mechanism is O(kδ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consider an arbitrary instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let o be the optimal alternative, ad the representative of district  d, and w the final winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Denote by SWd(x) the social welfare of alternative x only from the agents  in d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' clearly, SW(x) = �  d∈D SWd(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te expected social welfare of the mechanism is  E[SW(M)] =  �  a∈A  Pr[w = a] · SW(a)  = 1  k  �  a∈A  ��  d∈D  Pr[ad = a]  �  SW(a)  = 1  k  �  d∈D  �  a∈A  Pr[ad = a] · SW(a)  = 1  k  �  d∈D  E[SW(ad)]  ≥ 1  k  �  d∈D  E[SWd(ad)]  Since ad is chosen based on a voting rule with distortion at most δ, we have that E[SW(ad)] ≥ 1  δ ·  SWd(o).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Combining this together with the fact that SW(o) = �  d∈D SWd(o), and using the linearity  of expectation, we obtain  E[SW(M)] ≥ 1  k  �  d∈D  E[SWd(ad)]  ≥ 1  k  �  d∈D  1  δ · SWd(o)  = 1  kδ · SW(o).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Hence, the distortion of the mechanism is at most kδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1 is a simple composition theorem, analogous to the one presented by Anshelevich  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2022] for the metric seting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Based on it, we can define randomized distributed mechanisms  with proven distortion guarantees by appropriately choosing the in-district rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Before we continue,  observe that the sizes of the districts do not appear in the proof of Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1, and thus the distortion  of any Uniform-of-δ-Approximate mechanism is O(kδ) even if the districts are asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' So, the  distortion of the mechanism depends on the number of agents only if the distortion δ of the in-district  rule depends on the number of agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  If cardinal information is available at the district level, by using Range-Voting with δ = 1 as the  in-district rule, we obtain the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of Uniform-of-Range-Voting is O(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  If only ordinal information about the preferences of the agents is given at the district level, then we  can use Plurality with δ = O(m2) and the randomized rule Stable-Lottery mechanism of Ebadian  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2022] with δ = O(√m) as the in-district rule to obtain the following results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  9  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of Uniform-of-Plurality is O(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of Uniform-of-Stable-Lottery is O(k√m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  An important question to ask next is under what circumstances the aforementioned upper bounds  of Corollaries 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4 are tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' First, we show that Uniform-of-Range-Voting is the best  among mechanisms with unanimous in-district rules which may even use cardinal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any randomized distributed mechanism with a unanimous in-district rule  is Ω(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let ε > 0 be a positive infinitesimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consider an instance with the following k symmetric  districts: For any ℓ ∈ [k], in district dℓ, all λ agents therein have value 1/2 + ε for alternative aℓ,  1/2 − ε for alternative x, and 0 for any other alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Since, the in-district rule is unanimous, the  representative of district dℓ must be aℓ with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Hence, no mater what the probability of  choosing a district representative as the winner is, the expected social welfare of the mechanism is  λ · (1/2 + ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' However, the social welfare of alternative x is k · λ · (1/2 − ε), and thus the distortion  is Ω(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  If we consider non-unanimous in-district rules, but require the in-district rule to be deterministic,  then we can show a weaker lower bound of Ω(  √  k);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' notice that the theorem also implies the same  bound for fully deterministic distributed mechanisms without unanimous in-district rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any randomized distributed mechanism with a deterministic in-district  rule is Ω(  √  k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consider a district dℓ in which all agents have value 1/2 for alternative aℓ, value 1/(2  √  k) for  each alternative in {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , b√  k}, and 0 for any other alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' If the representative of this district is  not aℓ, then in instances consisting of copies of this district, the distortion is at least  √  k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' in particular, it  is at least that much if some alternative in {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , b√  k} is chosen and infinite if any other alternative  is chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' So, suppose that the representative of dℓ is aℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Next, consider an instance with k symmetric districts d1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By the above discussion, for any  ℓ ∈ [k], the representative of dℓ is alternative aℓ with social welfare λ/2 (note that only the agents  of dℓ have positive value, equal to 1/2, for aℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Hence, no mater which district representative is  chosen as the winner (or the probability distribution over the representatives), the (expected) social  welfare of the mechanism is λ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In contrast, the social welfare of any alternative in {b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , b√  k} is  k · λ/(2  √  k) =  √  k · λ/2, and thus the distortion is  √  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Next, we show that Uniform-of-Plurality is the best possible among ordinal randomized dis-  tributed mechanisms with deterministic in-district rules, assuming an arbitrary but fixed ordering of  the alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis is quite surprising, as it shows that randomization over the districts is not beter  than just choosing an arbitrary alternative that is representative of the most districts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', not beter  than Plurality-of-Plurality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of any ordinal distributed mechanism with a deterministic in-district rule is  Ω(km2), when there exists an arbitrary but fixed tie-breaking ordering of the alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Without loss of generality, suppose that the tie-breaking ordering of the alternatives is a1 ≻  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' ≻ ak ≻ b1 ≻ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' ≻ bm/2−1 ≻ x ≻ c1 ≻ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' ≻ cm/2−k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' the naming of the alternatives is arbitrary  but is assumed to be known and can be exploited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For simplicity, for any set of alternatives X, denote  by [X] an arbitrary ordering of the alternatives in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  10  Consider an instance with k symmetric districts such that in district dℓ there is a set of 2λ/m  agents with preference ordering aℓ ≻ x ≻ [A\\{aℓ, x}], a set of 2λ/m agents with preference ordering  b1 ≻ x ≻ [A \\ {b1, x}], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', and a set of 2λ/m agents with preference ordering bm/2−1 ≻ x ≻  [A \\ {bm/2−1, x}].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2, the representative of dℓ must be one of the top-ranked alternatives  (otherwise the distortion of the mechanism would be infinite).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Since aℓ is ranked above the other  alternatives in the tie-breaking ordering, she chosen as the representative of dℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Hence, the set of  representatives is {a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , ak}, and the winner is chosen according to some probability distribution  over this set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te valuation profile may be such that the 2λ/m agents in district dℓ that rank aℓ first have value  1/m for all alternatives, while all other agents in dℓ have value 1/2 for their two favorite alterna-  tives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Consequently, the social welfare of alternative aℓ is 2λ/m2, and thus the social welfare of the  mechanism is also this much, no mater the probability distribution over the district representatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  In contrast, the social welfare of x is approximately kλ/2, leading to a distortion of Ω(km2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  When randomization at the district level can be leveraged by ordinal distributed mechanisms, then  we achieve distortion much beter than what is implied by Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='4, while also achieving strat-  egyproofness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular, there are several centralized voting rules that can be implemented as  distributed mechanisms, in the sense that they define the same probability distribution over the alter-  natives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' One such important class of voting rules is that of point-voting schemes, which is part of a  larger class of strategyproof mechanisms [Barbera, 1978, Hylland, 1980, Gibbard, 1977] and includes  rules with almost best possible distortion guarantees [Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Ebadian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1  Point-voting schemes  A point-voting scheme chooses an agent uniformly at random and then outputs her t-th favorite al-  ternative with probability pt, where p1 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' ≥ pm ≥ 0 and �m  t=1 pt = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Hence, the probability  according to which the point-voting scheme using the probability vector p = (p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , pm) chooses  alternative a ∈ A as the winner w is Pr[w = a] = 1  n  �  i∈N pσi(a), where σi(a) is the position that i  ranks a in her preference ranking σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Tere are many point-voting schemes of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For every positional scoring rule using the scor-  ing vector s = (s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , sm), we can define a point-voting scheme f(s) by normalizing the scoring  vector, that is, define pt = st/  ��  j∈[m] sj  �  for every t ∈ [m] so that the winning probability of  alternative a is  Pr[w = a] = 1  n  �  i∈N  sσi(a)  �  j∈[m] sj  =  �  i∈N sσi(a)  n · �  j∈[m] sj  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Another important point-voting scheme is the rule that chooses each alternative uniformly at random;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  in this case, we have pt = 1/m for every t ∈ [m] so that Pr[w = a] = 1  n  �  i∈N  1  m = 1  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For any point-voting scheme f that uses a probability vector p, we consider the distributed mech-  anism Proportional-of-f-Point-Voting, which works as follows:  For every district d, choose the representative ad to be alternative a ∈ A with probability  1  λ  �  i∈Nd pσi(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Choose the winner to be the representative of district d with probability nd/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  11  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Proportional-of-f-Point-Voting defines the same probability distribution as the point-  voting scheme f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te probabilitythat alternativea is chosen as the winner by Proportional-of-f-Point-Voting  is  Pr[w = a] =  �  d∈D  Pr[w = ad] · Pr[ad = a]  =  �  d∈D  nd  n · 1  nd  �  i∈Nd  pσi(a)  = 1  n  �  i∈N  pσi(a),  that is, Proportional-of-f-Point-Voting chooses a with the same probability as f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='8 shows that Proportional-of-f-Point-Voting achieves the same distortion bound  as the point-voting scheme f it uses as the in-district rule, and also that it inherits its strategyproofness  property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis is extremely useful, as there are centralized voting rules that are based on point-voting  schemes and achieve almost the best possible distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] considered a voting rule that is a convex combination of two point-voting  schemes: With probability 1/2 choose an alternative uniformly at random, and with probability 1/2  run the point-voting scheme defined by normalizingthe harmonic scoring rule H = (1, 1/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , 1/m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We will refer to this mechanism as BCHLPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] showed that this voting rule has  distortion O(√m log m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' An important property of point-voting schemes is that any rule that is a  convex combination of point-voting schemes is also a point-voting scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te following lemma is  similar to lemmas proved before in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see Filos-Ratsikas and Miltersen [2014], Barbera  [1978]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' we provide a proof for completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , fκ be point-voting schemes defined by the probability vectors p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , pκ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For  any non-negative numbers q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' , qκ such that �  j∈[κ] qj = 1, the voting rule f that chooses the outcome  of fj with probability qj is a point-voting scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Let σ be an arbitrary preference profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For any j ∈ [κ], denote the t-th coordinate of pj as pj,t,  and let Pj(a) = Pr[a = fj(σ)] be the probability of choosing a as the winner according to point-voting  scheme fj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Ten, the voting rule f chooses alternative a as the winner w with probability  Pr[w = a] =  �  j∈[κ]  qj · Pj(a)  =  �  j∈[κ]  qj ·  �  1  n  �  i∈N  pj,σi(a)  �  = 1  n  �  i∈N  �  j∈[κ]  qj · pj,σi(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Hence, f is a point-voting scheme defined by the probability vector p with pt = �  j∈[κ] qj · pj,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Consequently, by Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='8 and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='9, we can construct a randomized ordinal distributed  mechanism based on the point-voting scheme of Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] that achieves the same distortion  bound and is strategyproof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  12  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tere exists a randomized ordinal strategyproof distributed mechanism with distortion  O(√m log m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Tis distortion bound is almost best possible as the lower bound of Ω(√m) for randomized cen-  tralized rules holds trivially for distributed mechanisms by considering single-district instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  5  Experiments  In this section, we perform experiments with real and synthetic datasets, aiming to identify paterns in  the distortion of several well-known voting rules and examine whether these support our theoretical  findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' It is well-documented in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', see [Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=',  2020]) that when working with real or realistic preferences, it ofen is the case that the distortions  bounds are small numbers quite close to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In this sense, our goal is not primarily to demonstrate the  distortion bounds themselves, but rather the dependence of these bounds on the distributed decision-  making process, in particular the number of districts, as well as the use of randomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We perform  two main experiments, one with real-world preferences and valuation data, and one with synthetic  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' All our experiments are with symmetric districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1  Experiments with the Jester Dataset  For our first experiment, we use the Jester Joke Dataset [Goldberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2001].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te dataset contains  ratings for 100 different jokes in the range [−10, 10], provided by 70000 users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We chose to work  with this dataset as it has also been employed by Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] in the context of centralized  distortion bounds, and also by Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2020] for the distortion of deterministic distributed  mechanisms that use plurality as the over-district rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Following the methodology developed in these works, we construct inputs consisting of ratings  for the 8 most-rated jokes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular, we perform 1000 random runs in which we sample 100 users  from the set of all users that have provided rankings for all eight jokes, and then partition them into  k equal-sized districts uniformly at random, for k ∈ {1, 2, 5, 10, 20, 25}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Clearly, the case of k = 1  corresponds to the centralized seting and will be used as a reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We interpret the ratings  of the jokes as cardinal valuations: to be consistent with our seting (and with the experiments of  [Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2015, Filos-Ratsikas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', 2020]), we add 10 to each user’s rating vector, to ensure that  the values are positive and then apply the unit-sum normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For these inputs, we compute the  average distortion of a set of 20 voting rules over the 1000 runs of the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In particular, we  consider distributed mechanisms fover-of-fin, where for fover we use Plurality or Uniform, whereas  for fin we have:  Deterministic Rules: We use simple voting scoring rules, namely Plurality (PL), Veto, Borda and  Harmonic, as well as Range-Voting (RV), which in the case of k = 1 finds the optimal alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Randomized Rules: Here we use several natural point-voting schemes with probability vectors that  are proportional to the aforementioned scoring rules (recall the definition from Section 4), namely  Proportional to Plurality Score (PropPL);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proportional to Borda Score (PropBorda);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proportional to Veto Score (PropVeto);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Proportional to Harmonic Score (PropHarmonic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  13  k  RV  PL  Veto  Borda  Harmonic  PropPL  PropVeto  PropBorda  PropHarmonic  BCHLPS  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
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+page_content='164  Table 2: Distortion bounds of various voting rules based on valuations defined by the provided scores of the Jester dataset and random district partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  RV  PL  Veto  Borda  Harmonic  PropPL  PropVeto  PropBorda  PropHarmonic  BCHLPS  k = 1  Uniform  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
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+page_content='131  Table 3: Distortion bounds of various voting rules based on valuations defined according to several probability distributions and random district  partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Results for deterministic mechanisms are presented at the lef of the bold vertical line, and results for randomized mechanisms are at the  right of the bold vertical line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  We also use the rule of Boutilier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2015] (we refer to it as BCHLPS in the following);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' recall that this  is a point-voting scheme that with probability 1/2 selects an alternative at random and with probability  1/2 runs the PropHarmonic rule defined above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' As established in Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='10 (and the discussion  before the statement of the corollary), this is best possible in terms of the worst-case distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te results of our experiments can be seen in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In the table we only present the results  where as fover, we used Plurality for deterministic rules and Uniform for randomized rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis  is in accordance to our approach in the theoretical results in previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te bounds for the  cases not shown are quite similar, and slightly larger in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For each of the randomized rules,  we perform 300 runs and calculate their expected social welfare, which we then use to calculate the  distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  From the results of Table 2 we observe that, as expected, the existence of multiple districts has an  adverse effect on the distortion of deterministic mechanisms, which becomes worse compared to the  centralized case k = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For these rules, we can also observe that the distortion generally increases as k  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In contrast, the distortion of randomized rules remains virtually unchanged for any value of  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis is in complete accordance with our theoretical findings, where we established that these rules  induce the same probability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te experiments showcase that this does not only hold in  expectation, but also in practice (given sufficiently many runs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Another crucial observation is that, in terms of the absolute distortion numbers, randomization  does not seem to help;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' if anything, it makesthe distortion bounds worse!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis can be justified by the fact  that real-world instances like those from the Jester dataset display a large degree of homogeneity, which  results in the simple deterministic rules performing quite well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' On the other hand, randomization ofen  leads to suboptimal choices even on such “well-behaved” instances, demeaning the distortion bounds  on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Surprisingly, among ordinal voting rules, Borda seems to perform best across the board  even though the theoretical distortion of Borda is in fact unbounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='2  Experiments with Synthetic Datasets  We also perform experiments with datasets that are generated from probability distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In par-  ticular, and to be consistent with the Jester experiment presented above, we create instances with  100 agents and 8 alternatives, by first drawing the values of the agents from a certain distribution,  and then constructing the induced ordinal preference profile from those values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We use the following  distributions:  Uniform distribution in [1, 100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis is the simplest case, where all possible values are equally  likely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Beta distribution with α = 1/10 and β = 1/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis distribution has a symmetric convex pdf  function centered around a mean of 1/2, assigning higher probabilities to values very close to 1  or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Exponential distribution with exponent 4, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=', the pdf is f(x) = 4e4 for x ≥ 0 and f(x) = 0  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis distribution generates values close to 0 with high probability, and as the values  increase, the probability of them being generated decreases exponentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  For the rest of the experiment, we perform similar steps as in the case of the Jester dataset: We nor-  malize the values to sum up to 1, and run the set of mechanisms described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' For each ran-  domized mechanism we now perform 150 individual runs and calculate its expected welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We  calculate the average distortions over 500 runs of the experiment for k symmetric districts, where  k ∈ {1, 2, 5, 20, 25}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Note that the number of runs and the number of district sizes is slightly smaller  15  in this experiment, because it is more computationally intensive (as we need to calculate bounds for 3  different distributions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Again, we use Plurality as fover for deterministic and Uniform for random-  ized mechanisms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' the results for the other cases were similar and are not reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te results can be found in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Similarly to the Jester experiment, it is evident that the distor-  tion of the deterministic mechanisms becomes worse for k ≥ 2, whereas it remains prety much the  same for randomized mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Again, we observe that randomization results in worse distortion  bounds overall, and that Borda performs best among deterministic mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Interestingly, con-  trary to the Jester dataset, here we do not see a clear patern of the distortion increasing as k increases  for deterministic mechanisms (other than the jump from k = 1 to k = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Tis is probably due to the  fact that the synthetic instances are highly homogeneous, and with uniform random district partitions,  the districts end up being quite uniform, regardless of their number and size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Te role of unit-sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We remark here that normalizing the values to sum up to 1 effectively makes the  Uniform and Exponential distributions prety similar, and this is reflected in the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' To get a sense  of the effect of normalization, we also ran the experiments without it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' We observe that the distortions  for the exponential distribution are now larger than those of the uniform distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In general, the  distortion bounds still lie in the range [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='03, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='15] for all distributions, but their average values (over  all documented distortion bounds) are larger for all distributions except Uniform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' It is also the case  that for the Beta distribution, the bounds of deterministic mechanisms are much closer to those of  randomized ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of randomized mechanisms is still almost the same for any number  of districts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  6  Open Problems  From our results, an interesting technical challenge is to remove the requirement for a consistent tie-  breaking ordering from the statement of Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Similarly, we could atempt to remove unanimity  from the lower bound of Teorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' although unanimity is usually prety natural, removing it would  make the theorem stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' More interestingly, our result about point-voting schemes in Teorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='8  crucially does not depend on the normalization of the valuations, and hence also could be applied  verbatim to the metric distributed social choice seting studied by Anshelevich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' [2022], where  randomized mechanisms have never been considered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' this seems like a natural starting point for such  an investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  References  Ben Abramowitz, Elliot Anshelevich, and Wennan Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Awareness of voter passion greatly improves  the distortion of metric social choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the Te 15th Conference on Web and Internet  Economics (WINE), pages 3–16, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Peeking  behind the ordinal curtain: Improving distortion via cardinal queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Artificial Intelligence, 296:  103488, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' A few  queries go a long way: Information-distortion tradeoffs in matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Journal of Artificial Intelligence  Research, 74, 2022a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Don’t roll  the dice, ask twice: Te two-query distortion of matching problems and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of  the 36th Conference on Neural Information Processing Systems (NeurIPS), 2022b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  16  Elliot Anshelevich and Shreyas Sekar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Blind, greedy, and random: Algorithms for matching and clus-  tering using only ordinal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 30th AAAI Conference on Artificial Intel-  ligence (AAAI), pages 390–396, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Elliot Anshelevich, Onkar Bhardwaj, Edith Elkind, John Postl, and Piotr Skowron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Approximating  optimal social choice under metric preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Artificial Intelligence, 264:27–51, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Elliot Anshelevich, Aris Filos-Ratsikas, Nisarg Shah, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Distortion in so-  cial choice problems: Te first 15 years and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 30th International Joint  Conference on Artificial Intelligence (IJCAI), pages 4294–4301, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Elliot Anshelevich, Aris Filos-Ratsikas, and Alexandros A Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of distributed  metric social choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Artificial Intelligence, 308:103713, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Yoram Bachrach, Omer Lev, Yoad Lewenberg, and Yair Zick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Misrepresentation in district voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In  IJCAI, pages 81–87, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Salvador Barbera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Nice Decision Schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Springer Netherlands, 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Gerdus Benad`e, Swaprava Nath, Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia, and Nisarg Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Preference elicitation for partic-  ipatory budgeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI), pages  376–382, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Umang Bhaskar and Abheek Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' On the welfare of cardinal voting mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of  the 38th IARCS Annual Conference on Foundations of Sofware Technology and Teoretical Computer  Science (FSTTCS), pages 27:1–27:22, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Umang Bhaskar, Varsha Dani, and Abheek Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Truthful and near-optimal mechanisms for welfare  maximization in multi-winner elections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 32nd AAAI Conference on Artificial  Intelligence (AAAI), pages 925–932, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Allan Borodin, Omer Lev, Nisarg Shah, and Tyrone Strangway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Big city vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' the great outdoors: Voter  distribution and how it affects gerrymandering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In IJCAI, pages 98–104, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Allan Borodin, Omer Lev, Nisarg Shah, and Tyrone Strangway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Primarily about primaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceed-  ings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), pages 1804–1811, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Craig Boutilier, Ioannis Caragiannis, Simi Haber, Tyler Lu, Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia, and Or Sheffet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Optimal  social choice functions: A utilitarian view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Artificial Intelligence, 227:190–213, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Felix Brandt, Vincent Conitzer, Ulle Endriss, J´erˆome Lang, and Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia, editors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Handbook  of Computational Social Choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Cambridge University Press, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Ioannis Caragiannis, Swaprava Nath, Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia, and Nisarg Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Subset selection via implicit  utilitarian voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Journal of Artificial Intelligence Research, 58:123–152, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Ioannis Caragiannis, Nisarg Shah, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te metric distortion of multiwinner  voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI), pages 4900–4907,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Soroush Ebadian, Anson Kahng, Dominik Peters, and Nisarg Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Optimized distortion and propor-  tional fairness in voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 23rd ACM Conference on Economics and Computation  (EC), pages 563–600, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  17  Edith Elkind, Jiarui Gan, Svetlana Obraztsova, Zinovi Rabinovich, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Pro-  tecting elections by recounting ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Artificial Intelligence, 290:103401, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Aris Filos-Ratsikas and Peter Bro Miltersen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Truthful approximations to range voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings  of the 10th International Conference on Web and Internet Economics (WINE), pages 175–188, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Aris Filos-Ratsikas and Alexandros A Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Approximate mechanism design for distributed facil-  ity location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In International Symposium on Algorithmic Game Teory, pages 49–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Springer, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, and Jie Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Social welfare in one-sided match-  ings: Random priority and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 7th Symposium of Algorithmic Game Teory  (SAGT), pages 1–12, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Aris Filos-Ratsikas, Evi Micha, and Alexandros A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Voudouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of distributed voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Artificial Intelligence, 286:103343, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Allan Gibbard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Manipulation of schemes that mix voting with chance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Econometrica: Journal of the  Econometric Society, pages 665–681, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Vasilis Gkatzelis, Daniel Halpern, and Nisarg Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Resolving the optimal metric distortion conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  In Proceedings of the 61st IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages  1427–1438, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Ken Goldberg, Teresa Roeder, Dhruv Gupta, and Chris Perkins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Eigentaste: A constant time collabo-  rative filtering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' information retrieval, 4(2):133–151, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Aanund Hylland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Strategy proofness of voting procedures with loteries as outcomes and infinite sets  of strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Technical report, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Fatih Erdem Kizilkaya and David Kempe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Plurality veto: A simple voting rule achieving optimal metric  distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 31st International Joint Conference on Artificial Intelligence (IJCAI),  pages 349–355, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Omer Lev and Yoad Lewenberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' “reverse gerrymandering”: Manipulation in multi-group decision  making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 2069–  2076, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Yoad Lewenberg, Omer Lev, and Jeffrey S Rosenschein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Divide and conquer: Using geographic manip-  ulation to win district-based elections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 16th Conference on Autonomous Agents  and MultiAgent Systems, pages 624–632, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Debmalya Mandal, Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia, Nisarg Shah, and David P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Woodruff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Efficient and thrify vot-  ing by any means necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 32nd Annual Conference on Neural Information  Processing Systems (NeurIPS), pages 7178–7189, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Debmalya Mandal, Nisarg Shah, and David P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Woodruff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Optimal communication-distortion tradeoff  in voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In Proceedings of the 21st ACM Conference on Economics and Computation (EC), pages  795–813, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  Ariel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Procaccia and Jeffrey S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Rosenschein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' Te distortion of cardinal preferences in voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content=' In  International Workshop on Cooperative Information Agents (CIA), pages 317–331, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
+page_content='  18' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQflAQk/content/2301.03279v1.pdf'}
diff --git a/19AzT4oBgHgl3EQfDfqo/content/tmp_files/2301.00978v1.pdf.txt b/19AzT4oBgHgl3EQfDfqo/content/tmp_files/2301.00978v1.pdf.txt
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+arXiv:2301.00978v1  [math.NT]  3 Jan 2023
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Abstract. Let K be either a locally compact non-discrete field
+of characteristic p > 2 or K = Qp, and Q be a non-degenerate
+isotropic quadratic form with coefficients in K. We obtain asymp-
+totic estimates for the number of solutions in the two fold product
+of certain discrete set inside K, of the inequalities of the form
+|Q(x, y)| < δ for some δ > 0, where | · | is an ultrametric abso-
+lute value on K. The estimates are obtained in terms of continued
+fraction expansions of the coefficients of the quadratic form Q.
+Mathematics Subject Classification: 11E16, 11E08, 11D88, 11A55,
+11J70, 11K50, 37A44.
+Keywords: Quadratic forms, locally compact fields, asymptotic esti-
+mates, continued fractions.
+Contents
+1.
+Introduction
+1
+2.
+K has positive characteristic (> 2)
+3
+3.
+K is the field of p-adic numbers
+10
+References
+14
+1. Introduction
+The Oppenheim conjecture, solved by Margulis in 1987 (see [13]
+for more details), states that if Q is a real non-degenerate indefinite
+quadratic form which is not proportional to a form with rational coeffi-
+cients, then Q(Zn) is dense in R if n ≥ 3. After Oppenheim conjecture
+was settled, people got interested in studying finer questions related to
+the distribution of the values of Q on integral points. Given a quadratic
+form as above, and a, b, ρ ∈ R with ρ > 0, let
+NQ(a, b, ρ) := # {v ∈ Zn : a < Q(v) < b, v ∈ B(ρ)},
+B(ρ) being the ball of radius ρ around the origin in Rn. Also let
+VQ(a, b, ρ) := Vol ({v ∈ Rn : a < Q(v) < b, v ∈ B(ρ)}).
+1
+
+2
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Then it was shown by Dani and Margulis in [7] that
+lim inf
+ρ→∞
+NQ(a, b, ρ)
+VQ(a, b, ρ) = 1.
+Asymptotic upper bound for the quantity NQ(a,b,ρ)
+VQ(a,b,ρ) was found by Eskin,
+Margulis and Mozes (see [9] for instance), and combining the result of
+[7], they showed that if Q is a quadratic form as above such that the
+signature of Q is neither (2, 1) nor (2, 2), then
+lim
+ρ→∞
+NQ(a, b, ρ)
+VQ(a, b, ρ) = 1.
+The Oppenheim conjecture fails for binary quadratic forms due to
+the existence of badly approximable numbers. A real number α is called
+badly approximable if there exists c > 0 such that
+���α − p
+q
+��� > c
+q2 for any
+rational number p
+q. Now, let Q be the binary quadratic form defined
+by
+Q(x, y) = (x + αy)y,
+α being a badly approximable number. Then Q(Z2) avoids the neigh-
+bourhood (−c, c) of zero. Nevertheless, one can study the distribution
+of the values taken by such forms at integral points. This was done
+in [6] with the interval (a, b) being a neighbourhood of 0.
+In case
+of binary quadratic forms, the asymptotic estimates depend on the
+quadratic form under consideration, and they are given in terms of
+the partial quotients of the continued fraction expansions of the coeffi-
+cients of the quadratic form. There is a natural connection between the
+values of non-degenerate indefinite binary quadratic forms at integral
+points, and certain geometric and dynamical aspects of the orbits of
+geodesic flow associated with the modular surface. In [6], the authors
+explored this connection, and used a method of coding of geodesics on
+the modular surface via nearest integer continued fraction which was
+introduced by S. Katok and I. Ugarcovicci (see [10] for instance), to
+obtain the estimates (see [18] for a different proof which does not uses
+the mechinary of geodesic flow etc.). The method of [6] can be adopted
+to obtain similar type of estimates in terms of a more general class of
+continued farctions as well, see Remark 3.4 of [5] for more details.
+In the present article, we do a similar study for non-degenerate
+isotropic binary quadratic forms whose coefficients are coming from
+a non-discrete locally compact field K such that either K has char-
+acteristic p > 2, or K is the field of p-adic numbers. In the following
+sections, we first deal with the positive characteristic case and then con-
+sider quadratic forms with coefficients in Qp. Note that an analogue
+of Oppenheim conjecture holds in S-arithmetic setting for isotropic
+quadratic forms in n ≥ 3 variables (see [2] for more details) as well.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+3
+2. K has positive characteristic (> 2)
+By the classification of non-discrete locally compact fields, if K is
+of positive characteristic, then K is the Laurent series fields in one
+indeterminate over a finite field. Let p be an odd prime, q be a power of
+p, and Fq be the finite field of characteristic p consisting of q elements.
+We denote by Z the polynomial ring Fq[X] in one variable over Fq.
+Let Fq(X) be the field of rational functions with coefficients in Fq and
+K := Fq((X−1)) be the field of formal Laurent series in X−1 over Fq.
+More precisely, if α ∈ Fq((X−1)), then
+α =
+�
+j≥n0
+ajX−j,
+aj ∈ Fq, n0 ∈ Z.
+Whenever α ∈ Fq((X−1))\Fq(X), we call α an irrational element. We
+define a valuation ν on K as follows: if α =
+�
+n≥n0
+anX−n, then
+ν(α) := inf {j ∈ Z : aj ̸= 0}.
+This valuation gives rise to an absolute value on K as follows: if α(̸=
+0) ∈ K and ν(α) = dα, then
+|α| := qdα,
+and the absolute value of the zero element in K is 0.
+Then K is
+the completion of Fq(X) with respect to this absolute value. As ν is
+a non-Archimedean valuation, the absolute value defined above is an
+ultrametric absolute value. Being a locally compact field, K admits a
+Haar measure (see [14] for details) which we denote by µ. For a ∈ K
+and r ∈ Z, let
+B(a, qr) := {α ∈ K : |α − a| < qr}
+be the open disc around a of radius qr, then µ(B(a, qr)) = qr. Let µ⊗µ
+be the corresponding product measure on K2 which is denoted by η.
+As in the case of real numbers, any α in K has a unique continued
+fraction expansion
+α = b0 +
+1
+b1 +
+1
+b2 +
+1
+b3 + ....
+,
+also written as
+α = [b0, b1, b2, ....]
+with bj ∈ Z for j ≥ 0 and bj has positive degree for j ≥ 1. Given any
+α =
+�
+j≥n0
+ajX−j in K, let
+⌊α⌋ =
+
+
+
+
+
+
+
+0
+�
+j=n0
+ajX−j
+if
+n0 ≤ 0
+0
+if
+n0 ≥ 1.
+
+4
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Then the continued fraction algorithm is defined as follows:
+α0 := α, αn+1 := (αn − bn)−1 and bn = ⌊αn⌋.
+Here bn’s are called partial quotients and αn’s are called complete quo-
+tients of the continued fraction expansion of α (see [16] for more de-
+tails).
+Now let sn
+tn be the nth convergent of the continued fraction
+expansion of α, i.e.,
+sn
+tn
+= [b0, b1, b2, ..., bn].
+Then the sequences (sn)n≥0 and (tn)n≥0 in Z satisfy the following re-
+currence relations:
+(1)
+sn = bnsn−1 + sn−2,
+tn = bntn−1 + tn−2.
+They also satisfy the following equation:
+(2)
+sn+1tn − sntn+1 = (−1)n
+which tells us that sn and tn are coprime, i.e., they do not have any
+common factor other than the constant polynomials in Fq[X]. The fol-
+lowing equalities which are special features of continued fraction theory,
+will be quite useful for this article. If α, bn, sn, tn are as above, then
+(3)
+|tn| = |bn · · · b1| ; ∀n ≥ 1,
+(4)
+����α − sn
+tn
+���� =
+1
+|bn+1||tn|2,
+and
+(5)
+����α − sn
+tn
+���� =
+1
+|tn+1||tn|.
+Note that in the case of continued fraction for real numbers, inequal-
+ities hold instead of equalities in (4) and (5). This is because of the
+ultrametric nature of the absolute value on K. The following lemma is
+a simple characterization of the convergents of the continued fraction
+expansion of any element in K, the proof of which can be found in [16].
+Lemma 1. Let s, t ∈ Z with t ̸= 0. Then s
+t is a convergent to α if and
+only if
+(6)
+����α − s
+t
+���� < 1
+|t|2.
+Now, let us consider binary quadratic forms with coefficients in K.
+It is well-known that if Q is a non-degenerate isotropic quadratic form
+with coefficients in a field F of characteristic not equal to 2, then there
+exists a basis {v1, v2} of F 2 such that if a1, a2 ∈ F, then
+Q(a1v1 + a2v2) = a1a2.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+5
+This says in particular that if Q0 is the quadratic from on K2 defined
+by
+Q0(x, y) = xy for x, y ∈ K,
+then for any isotropic quadratic form Q on K2, there is a matrix AQ
+in SL(2, K) and γ in K, such that
+(7)
+Q(x, y) = γ Q0(AQ(x, y)).
+So, to study the asymptotic behaviour of the set of values of an isotropic
+quadratic form with coefficients in K, it is enough to consider quadratic
+form Q given as follows:
+Q(x, y) = (ax + by)(cx + dy)
+with a, b, c, d ∈ K, bc − ad = 1.
+Now let Q be a quadratic form of the type Q(x, y) = (ax+by)(cx+dy)
+with a, b, c, d ∈ K, bc − ad = 1 (there is no loss of generality because
+one may replace γ by −γ in (7)) such that ba is an irrational element of
+K. Also let p be the set of primitive elements of Z2, i.e., p is the set of
+those (s, t) in Z2 such that s and t do not have a common factor except
+constant polynomials. For fixed real numbers k and δ with k > 1 and
+0 < δ < 1, let
+G(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)| < δ, ||(s, t)|| ≤ ρ, |cs + dt| > k},
+where ||(s, t)|| = max{|s|, |t|}.
+Let α = −ba and β = ac, and the
+continued fraction expansion of α be given by
+α = [b0, b1, b2, ...]
+with sn
+tn being the nth convergent. Also let
+H(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)| < δ, ||(x, y)|| ≤ ρ, |cx + dy| > k}.
+In this article, we find asymptotic lower and upper bound of the quo-
+tient # G(ρ)
+η (H(ρ)) as ρ → ∞. Now let
+α− := lim inf
+n→∞
+1
+n
+n
+�
+j=1
+log |bj|
+and
+α+ := lim sup
+n→∞
+1
+n
+n
+�
+j=1
+log |bj|.
+Also for 0 < δ < 1, let
+e(δ) := lim inf
+n→∞
+1
+n#
+�
+j, 1 ≤ j ≤ n : |bj+1| ≥ 1
+δ
+�
+and
+f(δ) := lim sup
+n→∞
+1
+n#
+�
+j, 1 ≤ j ≤ n : |bj+1| ≥ 1
+δ
+�
+.
+The main result of this article is contained in the following theorem.
+
+6
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Theorem 2. Let Q be a quadratic form defined by
+Q(x, y) = (ax + by)(cx + dy) with a, b, c, d ∈ K, bc − ad = 1,
+and ba an irrational element of K. Also let G(ρ), H(ρ), α+, α−, e(δ),
+f(δ) be as defined above. If α− < ∞, then we have the followings:
+lim inf
+ρ→∞
+# G(ρ)
+η (H(ρ)) ≥ c e(δ)
+α+
+and
+lim sup
+ρ→∞
+# G(ρ)
+η (H(ρ)) ≤ c f(δ)
+α− ,
+where c is a constant depending on δ and q.
+Remark 3. Let
+I(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)| < δ, ||(s, t)|| ≤ ρ, |as + bt| > k}
+and
+J(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)| < δ, ||(x, y)|| ≤ ρ, |ax+by| > k}.
+Then one can obtain a similar estimates for # I(ρ)
+η (J(ρ)) in terms of the
+continued fraction expansion of −dc provided dc is an irrational element
+of K.
+Proof of Theorem 2:
+Let
+G′(ρ) := {(s, t) ∈ p : |t(tα − s)| < δ, |t| ≤ ρ}.
+It is easy to see that
+(8)
+Q(s, t) = (tα − s)(t + β(tα − s)).
+If |Q(s, t)| < δ with |cs+dt| > k then |as+bt| < δ
+k, which implies that
+|tα − s| < δ|a|
+k , i.e., |tα − s| is bounded. Now by (8),
+|Q(s, t)|
+|q(tα − s)| =
+�����1 + β
+t (tα − s)
+����� .
+Since |tα − s| is bounded, it follows that
+|Q(s, t)|
+|t(tα − s)| = 1 if |t| is suffi-
+ciently large. Note that when |tα − s| is bounded, ||(s, t)|| → ∞ if and
+only if |t| → ∞. Also, if |q(tα−s)| < δ, then clearly |tα−s| is bounded
+and
+|Q(s, t)|
+|t(tα − s)| = 1 for sufficiently large |t|. Combining all these facts,
+we can say that there exists a constant C > 0 such that
+#G
+′(ρ) − C ≤ #G(ρ) ≤ #G
+′(ρ) + C
+for sufficiently large ρ. Since 0 < δ < 1, it follows from Lemma 1, that if
+(s, t) ∈ G
+′(ρ), then s = sj and t = tj, where sj
+tj is a convergent of α in its
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+7
+continued fraction expansion. Also G
+′(ρ) = G
+′(|tn|) if |tn| ≤ ρ < |tn+1|.
+Note that if (sj, tj) ∈ G
+′(|tn|), then (asj, atj) ∈ G
+′(|tn|) as well for any
+a ∈ F∗
+q.
+Now let us calculate the measure of H(ρ). Let A be the set given by
+A := {(x, y) ∈ K2 : 0 < |xy| < δ, ||(x, y)|| ≤ ρ, |y| > k},
+then
+η(H(ρ)) = |det(M)| η(A)
+where M =
+�
+a
+b
+c
+d
+�
+. Since bc−ad = 1, we have that η(H(ρ)) = η(A).
+Note that for 0 < δ < 1, k > 1 and ρ ≥ k, there exist unique
+m0, m
+′
+0, t and i ∈ Z such that qm0 ≤ δ < qm0+1, qm
+′
+0 ≤
+√
+δ <
+qm
+′
+0+1, qm
+′
+0+t ≤ k < qm
+′
+0+t+1 and qm
+′
+0+t+i ≤ ρ < qm
+′
+0+t+i+1. Also for
+1 ≤ n ≤ i, let
+An := {(x, y) ∈ K2 : |x| ≤ qm0−m
+′
+0−t−n and |y| = qm
+′
+0+t+n}.
+Clearly An’s are disjoint, and it is easy to see that A = ∪i
+n=1An. Hence,
+η(A) =
+i�
+n=1 η(An). Now
+{y ∈ K : |y| ≤ qm
+′
+0+t+n}
+= {y ∈ K : |y| < qm
+′
+0+t+n} ∪ {y ∈ K : |y| = qm
+′
+0+t+n}.
+Therefore,
+η(An) = µ({x ∈ K : |x| ≤ qm0−m
+′
+0−t−n}) · µ({y ∈ K : |y| = qm
+′
+0+t+n})
+= µ({x ∈ K : |x| ≤ qm0−m
+′
+0−t−n})
+· (µ({y ∈ K : |y| ≤ qm
+′
+0+t+n}) − µ({y ∈ K : |y| < qm
+′
+0+t+n}))
+= (qm0−m
+′
+0−t−n+1) · (qm
+′
+0+t+n+1 − qm
+′
+0+t+n)
+= (qm0−m
+′
+0−t−n+1)(qm
+′
+0+t+n)(q − 1)
+= qm0+1(q − 1),
+and consequently,
+η(H(ρ)) = η(A) =
+i
+�
+n=1
+η(An) = iqm0+1(q − 1).
+Since qm′
+0+t+i ≤ ρ < qm′
+0+t+i+1, it follows that
+(m′
+0 + t + i) log q ≤ log ρ < (m′
+0 + t + i + 1) log q
+which implies that
+log ρ
+log q − m′
+0 − t − 1 < i ≤ log ρ
+log q − m′
+0 − t.
+
+8
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Hence,
+�log ρ
+log q − m
+′
+0 − t − 1
+�
+(q − 1)qm0+1 < η(H(ρ)) ≤
+�log ρ
+log q − m
+′
+0 − t
+�
+(q − 1)qm0+1.
+(9)
+Now,
+lim inf
+ρ→∞
+#G(ρ)
+η(H(ρ)) ≥ lim inf
+ρ→∞
+#G′(ρ) − C
+η(H(ρ))
+= lim inf
+n→∞
+#G′(|tn|) − C
+η(H(|tn|))
+(for |tn| ≤ ρ < |tn+1|)
+= lim inf
+n→∞
+1
+n(#G′(|tn|) − C)
+1
+n(η(H(|tn|)))
+≥
+lim inf
+n→∞
+1n(#G′(|tn|))
+lim sup
+n→∞
+1n(η(H(|tn|)))
+≥
+lim inf
+n→∞
+1
+n(q − 1) #
+�
+j : 1 ≤ j ≤ n, |bj| ≥ 1
+δ
+�
+lim sup
+n→∞
+1
+n
+�log |tn|
+log q
+− m′
+0 − t
+�
+qm0+1(q − 1)
+(by (4) and (9))
+≥
+lim inf
+n→∞
+1
+n #
+�
+j : 1 ≤ j ≤ n, |bj| ≥ 1
+δ
+�
+lim sup
+n→∞
+1
+n
+�log |b1b2 · · · bn|
+log q
+− m′
+0 − t
+�
+qm0+1
+(by (3))
+≥
+lim inf
+n→∞
+1
+n #
+�
+j : 1 ≤ j ≤ n, |bj| ≥ 1
+δ
+�
+lim sup
+n→∞
+1
+n
+
+
+
+
+
+n�
+j=1 log |bj|
+log q
+− m′
+0 − t
+
+
+
+
+ qm0+1
+= e(δ)
+α+
+log q
+qm0+1.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+9
+A similar calculation yields
+lim sup
+ρ→∞
+#G(ρ)
+η(H(ρ)) ≤ f(δ)
+α−
+log q
+qm0+1.
+Corollary 4. Let Q be a quadratic form as in Theorem 2, and 0 < δ <
+1 be fixed. Then there exist a subset K′ of K with µ(K′) = µ(K) such
+that if α = −ba ∈ K′, then
+lim
+ρ→∞
+#G(ρ)
+η(H(ρ)) =
+q − 1
+q⌈δ−1⌉+m0+1,
+where ⌈δ−1⌉ denotes the smallest integer greater or equal to δ−1.
+Proof. Let [b0, b1, b2, . . .] be the continued fraction expansion of α =
+−ba as above.
+It follows from Theorem 6 of [1] that there is a full
+measure subset K′ of K such that if α = −ba ∈ K′, then
+(10)
+lim
+n→∞ |b1b2 · · · bn| 1n = q
+q
+q − 1.
+This implies that
+lim
+n→∞
+1
+n
+n
+�
+j=1
+log |bj| =
+q
+q − 1 log q,
+and, therefore, α− = α+ =
+q
+q−1 log q. Also for any 0 < δ < 1, there
+exists a unique l ∈ N such that l = ⌈δ−1⌉. Then by Theorem 14 of
+[12], for α in a full measure set which without loss of generality we may
+assume to be K′,
+lim
+n→∞
+1
+n #{1 ⩽ j ⩽ n : |bj| ⩾ ql} =
+1
+ql−1
+which implies that e(δ) = f(δ) =
+1
+ql−1 =
+1
+q⌈δ−1⌉−1. Then it follows from
+Theorem 2 above that, if α = −ba ∈ K
+′, then
+lim
+ρ→∞
+#G(ρ)
+η(H(ρ)) =
+1
+q⌈δ−1⌉ − 1
+�
+q
+q − 1 log q
+� log q
+qm0+1
+=
+q − 1
+q⌈δ−1⌉ + m0 + 1.
+□
+Remark 5. Let Q, α be as in Theorem 2. Now, if the absolute values
+of the partial quotients in the continued fraction expansion of α are
+
+10
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+bounded by some real numbers, then it is easy to see that e(δ) = f(δ) =
+0 if δ is sufficiently small. In this case,
+lim
+ρ→∞
+#G(ρ)
+η(H(ρ)) = 0.
+3. K is the field of p-adic numbers
+In this section, we consider isotropic quadratic forms with coefficients
+in the field of p-adic numbers for a prime p. Recall that the field of
+p-adic numbers, denoted by Qp, is the collection of all formal series of
+the form
+�
+j≥n0
+ajpj, with n0 ∈ Z and aj ∈ {0, 1, . . ., p − 1}.
+The ultrametric absolute value on Qp is defined as follows: if
+α (̸= 0) =
+�
+j≥n0
+ajpj,
+then
+|α|p := p−νp(α), and |0|p = 0,
+where νp(α) := inf {j ∈ Z : aj ̸= 0}. The integer νp(α) is also known
+as the valuation of α. For α ∈ Qp and r ∈ Z, let
+B(a, pr) := {α ∈ K : |α − a|p < pr}
+be the open disc of radius pr around the point α. The Haar measure µ
+(say) on Qp is defined in such a way that µ(B(a, pr)) = pr. We denote
+by η again the product measure µ ⊗ µ on Qp × Qp.
+As in the case of real numbers and elements of Laurent series fields
+over finite fields, continued fraction expansion exists for p-adic num-
+bers as well. There are mainly two types of continued fractions for
+p-adic numbers, one of them was introduced by Schneider (see [17] for
+instance), and the other one was introduced by Ruban (see [15] for
+instance) and modified later by Brokwin (see [3], [4]). In this article,
+we are going to consider the continued fraction introduced by Ruban
+which has some similarity with the simple continued fraction for real
+numbers. From now on, unless otherwise stated, we will be considering
+Ruban’s continued fraction only. Let Z be the subset of Qp given by
+Z := {a0 + a1
+1
+p + . . . an
+1
+pn : ai ∈ {0, 1, . . ., p − 1} for 0 ≤ i ≤ n}.
+It is easy to see that Z is a discrete set in the topology coming from
+the p-adic abosolute value. For α (̸= 0) = �
+j≥n0
+ajpj, let
+⌊α⌋ =
+
+
+
+
+
+
+
+0
+�
+j=n0
+ajpj
+if
+n0 ≤ 0
+0
+if
+n0 ≥ 1.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+11
+Given α ∈ Qp, we define two sequences (αn) and (bn) as follows: α0 =
+α, b0 = ⌊α0⌋; for n ≥ 0, if bn = αn, then αn+1 and bn+1 are not defined,
+otherwise, αn+1 = (αn − bn)−1 and bn+1 = ⌊αn+1⌋. Any p-adic number
+α has a unique continued fraction expansion as α = [b0, b1, . . . , bn, . . . ]
+which can be obtained by using the algorithm discussed above. Note
+that the partial quotients bn’s are elements of Z. The nth convergent
+is given by sn
+tn = [b0, b1, . . . , bn] where sn and tn satisfy the recurrence
+relation as in (1), and equation (2) as well.
+The p-adic versions of
+equation (3), (4) and (5) are valid as well with the absolute value in
+the Laurent series field replaced by the p-adic absolute value. As we
+could not find a proper reference for a p-adic version of Lemma 1, we
+include a proof here following the proof of Lemma 1 given in [16].
+Lemma 6. Let s, t ∈ Z with t ̸= 0. Then s
+t is a convergent to α if and
+only if
+(11)
+����α − s
+t
+����
+p < 1
+|t|2p
+Proof. By the p-adic version of equation (4),
+����α − sn
+tn
+����
+p
+=
+1
+|bn+1|p |tn|2
+p
+<
+1
+|tn|2
+p
+for any convergent sn
+tn corresponding to the continued fraction expan-
+sion of α.
+Conversely, assume that s, t ∈ Z with t ̸= 0 such that
+����α − s
+t
+����
+p < 1
+|t|2
+p
+.
+There is a unique n such that |tn|p ≤ |t|p < |tn+1|p. Then
+����α − s
+t
+����
+p <
+1
+|t|p|tn|p
+,
+and
+����α − sn
+tn
+����
+p
+=
+1
+|tn|p|tn+1|p
+(by p-adic version of (5))
+<
+1
+|t|p|tn|p
+,
+so that
+����
+s
+t − sn
+tn
+����
+p
+=
+����
+s
+t − α + α − sn
+tn
+����
+p
+≤ max
+�����α − s
+t
+����
+p ,
+����α − sn
+tn
+����
+p
+�
+<
+1
+|t|p|tn|p
+.
+
+12
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+Thus, s
+t = sn
+tn .
+□
+Now, let Q be a non-degenerate isotropic binary quadratic form with
+coefficients in Qp. Since Qp has characteristic zero, as explained in the
+previous section, it is enough to consider Q defined by
+Q(x, y) = (ax + by)(cx + dy)
+with a, b, c, d in Qp and bc−ad = 1. We also assume that ba is not of the
+form s
+t for some s, t ∈ Z with t ̸= 0. Let p denote the set of all those
+(s, t) ∈ Z such that s and t does not have a common factor except the
+constant polynomials in 1p inside Z. For k > 1 and 0 < δ < 1, we
+define G(ρ) and H(ρ) as in the previous section as follows:
+G(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)|p < δ, ||(s, t)|| ≤ ρ, |cs + dt|p > k},
+H(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)|p < δ, ||(x, y)|| ≤ ρ, |cx+dy|p > k},
+here ||(s, t)|| = max { |s|p, |t|p }. Also let α = −ba and β = ac, and the
+continued fraction expansion of α be given by
+α = [b0, b1, b2, ...].
+The quantities e(δ), f(δ), α− and α+ are defined similarly as in the
+previous section with the absolute value replaced by the p-adic absolute
+value wherever applicable. Then an analogue of Theorem 2 holds in
+this set up as well.
+Theorem 7. With all the notations as above, if α− < ∞, then
+lim inf
+ρ→∞
+#G(ρ)
+η(H(ρ)) ≥ c e(δ)
+α+ ,
+and
+lim sup
+ρ→∞
+#G(ρ)
+η(H(ρ)) ≤ c f(δ)
+α− ,
+where c =
+log p
+pm0 + 1.
+Let X = B(0, 1) and T : X → X be the continued fraction map
+defined by
+T(α) = 1
+α −
+� 1
+α
+�
+.
+It is known that the map T is ergodic (see [15] for details) with respect
+to the Haar measure µ. As an application of the ergodicity, we obtain
+a result similar to Theorem 14 of [12].
+Lemma 8. Let α ∈ X and [0, b1, b2, . . . ] be the continued fraction
+expansion of α. Then for any natural number l,
+lim
+n→∞ #{1 ≤ j ≤ n : −νp(bj) ≥ l} =
+1
+pl−1
+almost everywhere with respect to the Haar measure µ.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+13
+Proof. Note that b1 = b1(α) can be thought of as a function on B(0, 1).
+Then it is easy to check that the function
+f(α) = χ[pl,∞)(|b1(α)|p), α ∈ B(0, 1)
+is integrable on B(0, 1). Now, by the pointwise ergodic theorem
+(see Theorem 2.30 of [8] for instance),
+lim
+n→∞
+1
+n#{1 ≤ j ≤ n : −νp(bj) ≥ l} = lim
+n→∞
+1
+n#{1 ≤ j ≤ n : |bj|p ≥ pl}
+= lim
+n→∞
+1
+n
+n
+�
+j=1
+χ[pl,∞)(|b1(T j(α))|p)
+=
+�
+B(0,1)
+χ[pl,∞)(|b1(α)|p)dµ
+= µ{α ∈ B(0, 1) : |b1(α)|p ≥ pl}
+= µ{α ∈ B(0, 1) : |α|p ≤ p−l}
+= p−l+1
+=
+1
+pl−1
+□
+Now, using Theorem 8 of [15] and Lemma 8 above, we obtain a p-adic
+version of Corollary 4.
+Corollary 9. Let Q be a quadratic form as in Theorem 7, and 0 < δ <
+1 be fixed. Then there exist a subset K
+′ of K with µ(K
+′) = µ(K) such
+that if α = −ba ∈ K
+′, then
+lim
+ρ→∞
+#G(ρ)
+η(H(ρ)) =
+p − 1
+p⌈δ−1⌉+m0+1.
+It is easy to see that a version of Remark 5 is true in the p-adic set
+up as well. As the statements are similar, we do not write it separately
+here. Rather, we give an example of a p-adic number whose continued
+fraction expansion consists of partial quotients with bounded absolute
+values. One may look at [11] and references cited there in for similar
+examples in Laurent series field over finite fields. Let α be the p-adic
+number given by α =
+�
+j≥−1 ajpj, with aj = 1 for all j ≥ −1. Let the
+continued fraction expansion of α be [b0, b1, b2, ...]. Then b0 = p0 + p−1
+
+14
+MANOJ CHOUDHURI AND PRASHANT J. MAKADIYA
+and |b0|p = p. Now
+α1 = (α0 − b0)−1
+=
+
+�
+j≥1
+pj
+
+
+−1
+= p−1 +
+�
+j≥0
+(p − 1)pj.
+Then b1 = (p − 1)p0 + p−1 and |b1|p = p. Again
+α2 = (α1 − b1)−1
+=
+
+�
+j≥1
+(p − 1)pj
+
+
+−1
+=
+�
+j≥−1
+(p − 1)pj.
+Then b2 = (p − 1)p0 + (p − 1)p−1 and |b2|p = p. Observe that α3 =
+(α2 − b2)−1 = α2, and hence |b3|p = p. In a similar manner we get
+αn+1 = αn, bn+1 = bn, |bn+1|p = p for n ≥ 3 as well. Therefore, the
+absolute values of all the partial quotients of the continued fraction
+expansion of α are bounded by p.
+Remark 10. As in the case of binary real quadratic forms, the Op-
+penheim conjecture fails to hold for non-degenerate isotropic quadratic
+form with coefficients in a non-discrete locally compact non-Archimedean
+field as well. To see this, let us consider the quadratic form Q given by
+Q(x, y) = (x + αy)y
+with α ∈ Fq((X−1)) (or Qp). Now if the partial quotients in the con-
+tinued fraction expansion of α have bounded absolute values, then us-
+ing Lemma 1 (or Lemma 6), it is easy to see that the set of values
+{|Q(s, t)| : s, t ∈ Z} (Z is either as in Section 1 or as in Section 2)
+avoids certain neighbourhood of zero.
+Acknowledgement . Prashant J. Makadiya acknowledges the support
+of Government of Gujarat thorugh the SHODH (ScHeme Of Developing
+High Quality Research) fellowship. Manoj Choudhuri thanks L. Singhal
+for helpful discussions.
+References
+[1] Val´erie Berth´e and Hitoshi Nakada. On continued fraction expansions in pos-
+itive characteristic: equivalence relations and some metric properties. Expo.
+Math., 18(4):257–284, 2000.
+[2] Armand Borel and Gopal Prasad. Values of isotropic quadratic forms at S-
+integral points. Compositio Math., 83(3):347–372, 1992.
+
+ON VALUES OF ISOTROPIC QUADRATIC FORMS
+15
+[3] Jerzy Browkin. Continued fractions in local fields. i. Demonstratio Math.,
+11(1):67–82, 1978.
+[4] Jerzy
+Browkin.
+Continued
+fractions
+in
+local
+fields.
+ii.
+Math.
+Comp.,
+70(235):1281–1292, 2001.
+[5] Manoj Choudhuri. On certain orbits of geodesic flow and (a, b)-continued frac-
+tions. Proc. Indian Acad. Sci. Math. Sci., 131(1):Paper No. 2, 19, 2021.
+[6] Manoj Choudhuri and S. G. Dani. On values of binary quadratic forms at
+integer points. Math. Res. Lett., 22(4):1023–1045, 2015.
+[7] S. G. Dani and G. A. Margulis. Limit distributions of orbits of unipotent flows
+and values of quadratic forms. In I. M. Gelfand Seminar, volume 16 of Adv.
+Soviet Math., pages 91–137. Amer. Math. Soc., Providence, RI, 1993.
+[8] Manfred Einsiedler and Thomas Ward. Ergodic theory with a view towards
+number theory, volume 259 of Graduate Texts in Mathematics. Springer-Verlag
+London, Ltd., London, 2011.
+[9] Alex Eskin, Gregory Margulis, and Shahar Mozes. On a quantitative ver-
+sion of the Oppenheim conjecture. Electron. Res. Announc. Amer. Math. Soc.,
+1(3):124–130, 1995.
+[10] Svetlana Katok and Ilie Ugarcovici. Arithmetic coding of geodesics on the
+modular surface via continued fractions. In European women in mathematics—
+Marseille 2003, volume 135 of CWI Tract, pages 59–77. Centrum Wisk. In-
+form., Amsterdam, 2005.
+[11] Alain Lasjaunias and Jean-Jacques Ruch. Algebraic and badly approximable
+power series over a finite field. Finite Fields Appl., 8(1):91–107, 2002.
+[12] Poj Lertchoosakul and Radhakrishnan Nair. On the metric theory of continued
+fractions in positive characteristic. Mathematika, 60(2):307–320, 2014.
+[13] G. A. Margulis. Oppenheim conjecture. In Fields Medallists’ lectures, volume 5
+of World Sci. Ser. 20th Century Math., pages 272–327. World Sci. Publ., River
+Edge, NJ, 1997.
+[14] Dinakar Ramakrishnan and Robert J. Valenza. Fourier analysis on number
+fields, volume 186 of Graduate Texts in Mathematics. Springer-Verlag, New
+York, 1999.
+[15] A. A. Ruban. Certain metric properties of the p-adic numbers. Sibirsk. Mat.
+ˇZ., 11:222–227, 1970.
+[16] Wolfgang M. Schmidt. On continued fractions and Diophantine approximation
+in power series fields. Acta Arith., 95(2):139–166, 2000.
+[17] Th. Schneider. ¨Uber p-adische Kettenbr¨uche. In Symposia Mathematica, Vol.
+IV (INDAM, Rome, 1968/69), pages 181–189. Academic Press, London, 1970.
+[18] David Simmons. The Hurwitz continued fraction expansion as applied to real
+numbers. Enseign. Math., 62(3-4):475–485, 2016.
+Institute of Infrastructure, Technology, Research and Manage-
+ment, Near Khokhara Circle, maninagar (East), Ahmedabad 380026,
+Gujarat, India.
+Email address: manojchoudhuri@iitram.ac.in
+Email address: prashant.makadiya.20pm@iitram.ac.in
+
diff --git a/19AzT4oBgHgl3EQfDfqo/content/tmp_files/load_file.txt b/19AzT4oBgHgl3EQfDfqo/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,382 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf,len=381
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='00978v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='NT]  3 Jan 2023  ON VALUES OF ISOTROPIC QUADRATIC FORMS  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let K be either a locally compact non-discrete field  of characteristic p > 2 or K = Qp, and Q be a non-degenerate  isotropic quadratic form with coefficients in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' We obtain asymp-  totic estimates for the number of solutions in the two fold product  of certain discrete set inside K, of the inequalities of the form  |Q(x, y)| < δ for some δ > 0, where | · | is an ultrametric abso-  lute value on K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The estimates are obtained in terms of continued  fraction expansions of the coefficients of the quadratic form Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Mathematics Subject Classification: 11E16, 11E08, 11D88, 11A55,  11J70, 11K50, 37A44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Keywords: Quadratic forms, locally compact fields, asymptotic esti-  mates, continued fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Introduction  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  K has positive characteristic (> 2)  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  K is the field of p-adic numbers  10  References  14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Introduction  The Oppenheim conjecture, solved by Margulis in 1987 (see [13]  for more details), states that if Q is a real non-degenerate indefinite  quadratic form which is not proportional to a form with rational coeffi-  cients, then Q(Zn) is dense in R if n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' After Oppenheim conjecture  was settled, people got interested in studying finer questions related to  the distribution of the values of Q on integral points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Given a quadratic  form as above, and a, b, ρ ∈ R with ρ > 0, let  NQ(a, b, ρ) := # {v ∈ Zn : a < Q(v) < b, v ∈ B(ρ)},  B(ρ) being the ball of radius ρ around the origin in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also let  VQ(a, b, ρ) := Vol ({v ∈ Rn : a < Q(v) < b, v ∈ B(ρ)}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  1  2  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Then it was shown by Dani and Margulis in [7] that  lim inf  ρ→∞  NQ(a, b, ρ)  VQ(a, b, ρ) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Asymptotic upper bound for the quantity NQ(a,b,ρ)  VQ(a,b,ρ) was found by Eskin,  Margulis and Mozes (see [9] for instance), and combining the result of  [7], they showed that if Q is a quadratic form as above such that the  signature of Q is neither (2, 1) nor (2, 2), then  lim  ρ→∞  NQ(a, b, ρ)  VQ(a, b, ρ) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  The Oppenheim conjecture fails for binary quadratic forms due to  the existence of badly approximable numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' A real number α is called  badly approximable if there exists c > 0 such that  ���α − p  q  ��� > c  q2 for any  rational number p  q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now, let Q be the binary quadratic form defined  by  Q(x, y) = (x + αy)y,  α being a badly approximable number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then Q(Z2) avoids the neigh-  bourhood (−c, c) of zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Nevertheless, one can study the distribution  of the values taken by such forms at integral points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' This was done  in [6] with the interval (a, b) being a neighbourhood of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  In case  of binary quadratic forms, the asymptotic estimates depend on the  quadratic form under consideration, and they are given in terms of  the partial quotients of the continued fraction expansions of the coeffi-  cients of the quadratic form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' There is a natural connection between the  values of non-degenerate indefinite binary quadratic forms at integral  points, and certain geometric and dynamical aspects of the orbits of  geodesic flow associated with the modular surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In [6], the authors  explored this connection, and used a method of coding of geodesics on  the modular surface via nearest integer continued fraction which was  introduced by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Katok and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Ugarcovicci (see [10] for instance), to  obtain the estimates (see [18] for a different proof which does not uses  the mechinary of geodesic flow etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The method of [6] can be adopted  to obtain similar type of estimates in terms of a more general class of  continued farctions as well, see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='4 of [5] for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  In the present article, we do a similar study for non-degenerate  isotropic binary quadratic forms whose coefficients are coming from  a non-discrete locally compact field K such that either K has char-  acteristic p > 2, or K is the field of p-adic numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In the following  sections, we first deal with the positive characteristic case and then con-  sider quadratic forms with coefficients in Qp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Note that an analogue  of Oppenheim conjecture holds in S-arithmetic setting for isotropic  quadratic forms in n ≥ 3 variables (see [2] for more details) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' K has positive characteristic (> 2)  By the classification of non-discrete locally compact fields, if K is  of positive characteristic, then K is the Laurent series fields in one  indeterminate over a finite field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let p be an odd prime, q be a power of  p, and Fq be the finite field of characteristic p consisting of q elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  We denote by Z the polynomial ring Fq[X] in one variable over Fq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Let Fq(X) be the field of rational functions with coefficients in Fq and  K := Fq((X−1)) be the field of formal Laurent series in X−1 over Fq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  More precisely, if α ∈ Fq((X−1)), then  α =  �  j≥n0  ajX−j,  aj ∈ Fq, n0 ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Whenever α ∈ Fq((X−1))\\Fq(X), we call α an irrational element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' We  define a valuation ν on K as follows: if α =  �  n≥n0  anX−n, then  ν(α) := inf {j ∈ Z : aj ̸= 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  This valuation gives rise to an absolute value on K as follows: if α(̸=  0) ∈ K and ν(α) = dα, then  |α| := qdα,  and the absolute value of the zero element in K is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then K is  the completion of Fq(X) with respect to this absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' As ν is  a non-Archimedean valuation, the absolute value defined above is an  ultrametric absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Being a locally compact field, K admits a  Haar measure (see [14] for details) which we denote by µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' For a ∈ K  and r ∈ Z, let  B(a, qr) := {α ∈ K : |α − a| < qr}  be the open disc around a of radius qr, then µ(B(a, qr)) = qr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let µ⊗µ  be the corresponding product measure on K2 which is denoted by η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  As in the case of real numbers, any α in K has a unique continued  fraction expansion  α = b0 +  1  b1 +  1  b2 +  1  b3 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='.  ,  also written as  α = [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='.]  with bj ∈ Z for j ≥ 0 and bj has positive degree for j ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Given any  α =  �  j≥n0  ajX−j in K, let  ⌊α⌋ =  \uf8f1  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f3  0  �  j=n0  ajX−j  if  n0 ≤ 0  0  if  n0 ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  4  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Then the continued fraction algorithm is defined as follows:  α0 := α, αn+1 := (αn − bn)−1 and bn = ⌊αn⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Here bn’s are called partial quotients and αn’s are called complete quo-  tients of the continued fraction expansion of α (see [16] for more de-  tails).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Now let sn  tn be the nth convergent of the continued fraction  expansion of α, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=',  sn  tn  = [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', bn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then the sequences (sn)n≥0 and (tn)n≥0 in Z satisfy the following re-  currence relations:  (1)  sn = bnsn−1 + sn−2,  tn = bntn−1 + tn−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  They also satisfy the following equation:  (2)  sn+1tn − sntn+1 = (−1)n  which tells us that sn and tn are coprime, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', they do not have any  common factor other than the constant polynomials in Fq[X].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The fol-  lowing equalities which are special features of continued fraction theory,  will be quite useful for this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' If α, bn, sn, tn are as above, then  (3)  |tn| = |bn · · · b1| ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' ∀n ≥ 1,  (4)  ����α − sn  tn  ���� =  1  |bn+1||tn|2,  and  (5)  ����α − sn  tn  ���� =  1  |tn+1||tn|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Note that in the case of continued fraction for real numbers, inequal-  ities hold instead of equalities in (4) and (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' This is because of the  ultrametric nature of the absolute value on K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The following lemma is  a simple characterization of the convergents of the continued fraction  expansion of any element in K, the proof of which can be found in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let s, t ∈ Z with t ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then s  t is a convergent to α if and  only if  (6)  ����α − s  t  ���� < 1  |t|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Now, let us consider binary quadratic forms with coefficients in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It is well-known that if Q is a non-degenerate isotropic quadratic form  with coefficients in a field F of characteristic not equal to 2, then there  exists a basis {v1, v2} of F 2 such that if a1, a2 ∈ F, then  Q(a1v1 + a2v2) = a1a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  5  This says in particular that if Q0 is the quadratic from on K2 defined  by  Q0(x, y) = xy for x, y ∈ K,  then for any isotropic quadratic form Q on K2, there is a matrix AQ  in SL(2, K) and γ in K, such that  (7)  Q(x, y) = γ Q0(AQ(x, y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  So, to study the asymptotic behaviour of the set of values of an isotropic  quadratic form with coefficients in K, it is enough to consider quadratic  form Q given as follows:  Q(x, y) = (ax + by)(cx + dy)  with a, b, c, d ∈ K, bc − ad = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Now let Q be a quadratic form of the type Q(x, y) = (ax+by)(cx+dy)  with a, b, c, d ∈ K, bc − ad = 1 (there is no loss of generality because  one may replace γ by −γ in (7)) such that ba is an irrational element of  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also let p be the set of primitive elements of Z2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', p is the set of  those (s, t) in Z2 such that s and t do not have a common factor except  constant polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' For fixed real numbers k and δ with k > 1 and  0 < δ < 1, let  G(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)| < δ, ||(s, t)|| ≤ ρ, |cs + dt| > k},  where ||(s, t)|| = max{|s|, |t|}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Let α = −ba and β = ac, and the  continued fraction expansion of α be given by  α = [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=']  with sn  tn being the nth convergent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also let  H(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)| < δ, ||(x, y)|| ≤ ρ, |cx + dy| > k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  In this article, we find asymptotic lower and upper bound of the quo-  tient # G(ρ)  η (H(ρ)) as ρ → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now let  α− := lim inf  n→∞  1  n  n  �  j=1  log |bj|  and  α+ := lim sup  n→∞  1  n  n  �  j=1  log |bj|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Also for 0 < δ < 1, let  e(δ) := lim inf  n→∞  1  n#  �  j, 1 ≤ j ≤ n : |bj+1| ≥ 1  δ  �  and  f(δ) := lim sup  n→∞  1  n#  �  j, 1 ≤ j ≤ n : |bj+1| ≥ 1  δ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  The main result of this article is contained in the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  6  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let Q be a quadratic form defined by  Q(x, y) = (ax + by)(cx + dy) with a, b, c, d ∈ K, bc − ad = 1,  and ba an irrational element of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also let G(ρ), H(ρ), α+, α−, e(δ),  f(δ) be as defined above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' If α− < ∞, then we have the followings:  lim inf  ρ→∞  # G(ρ)  η (H(ρ)) ≥ c e(δ)  α+  and  lim sup  ρ→∞  # G(ρ)  η (H(ρ)) ≤ c f(δ)  α− ,  where c is a constant depending on δ and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let  I(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)| < δ, ||(s, t)|| ≤ ρ, |as + bt| > k}  and  J(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)| < δ, ||(x, y)|| ≤ ρ, |ax+by| > k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then one can obtain a similar estimates for # I(ρ)  η (J(ρ)) in terms of the  continued fraction expansion of −dc provided dc is an irrational element  of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Proof of Theorem 2:  Let  G′(ρ) := {(s, t) ∈ p : |t(tα − s)| < δ, |t| ≤ ρ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It is easy to see that  (8)  Q(s, t) = (tα − s)(t + β(tα − s)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  If |Q(s, t)| < δ with |cs+dt| > k then |as+bt| < δ  k, which implies that  |tα − s| < δ|a|  k , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', |tα − s| is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now by (8),  |Q(s, t)|  |q(tα − s)| =  �����1 + β  t (tα − s)  ����� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Since |tα − s| is bounded, it follows that  |Q(s, t)|  |t(tα − s)| = 1 if |t| is suffi-  ciently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Note that when |tα − s| is bounded, ||(s, t)|| → ∞ if and  only if |t| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also, if |q(tα−s)| < δ, then clearly |tα−s| is bounded  and  |Q(s, t)|  |t(tα − s)| = 1 for sufficiently large |t|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Combining all these facts,  we can say that there exists a constant C > 0 such that  #G  ′(ρ) − C ≤ #G(ρ) ≤ #G  ′(ρ) + C  for sufficiently large ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Since 0 < δ < 1, it follows from Lemma 1, that if  (s, t) ∈ G  ′(ρ), then s = sj and t = tj, where sj  tj is a convergent of α in its  ON VALUES OF ISOTROPIC QUADRATIC FORMS  7  continued fraction expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also G  ′(ρ) = G  ′(|tn|) if |tn| ≤ ρ < |tn+1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Note that if (sj, tj) ∈ G  ′(|tn|), then (asj, atj) ∈ G  ′(|tn|) as well for any  a ∈ F∗  q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Now let us calculate the measure of H(ρ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let A be the set given by  A := {(x, y) ∈ K2 : 0 < |xy| < δ, ||(x, y)|| ≤ ρ, |y| > k},  then  η(H(ρ)) = |det(M)| η(A)  where M =  �  a  b  c  d  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Since bc−ad = 1, we have that η(H(ρ)) = η(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Note that for 0 < δ < 1, k > 1 and ρ ≥ k, there exist unique  m0, m  ′  0, t and i ∈ Z such that qm0 ≤ δ < qm0+1, qm  ′  0 ≤  √  δ <  qm  ′  0+1, qm  ′  0+t ≤ k < qm  ′  0+t+1 and qm  ′  0+t+i ≤ ρ < qm  ′  0+t+i+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also for  1 ≤ n ≤ i, let  An := {(x, y) ∈ K2 : |x| ≤ qm0−m  ′  0−t−n and |y| = qm  ′  0+t+n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Clearly An’s are disjoint, and it is easy to see that A = ∪i  n=1An.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Hence,  η(A) =  i�  n=1 η(An).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now  {y ∈ K : |y| ≤ qm  ′  0+t+n}  = {y ∈ K : |y| < qm  ′  0+t+n} ∪ {y ∈ K : |y| = qm  ′  0+t+n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Therefore,  η(An) = µ({x ∈ K : |x| ≤ qm0−m  ′  0−t−n}) · µ({y ∈ K : |y| = qm  ′  0+t+n})  = µ({x ∈ K : |x| ≤ qm0−m  ′  0−t−n})  (µ({y ∈ K : |y| ≤ qm  ′  0+t+n}) − µ({y ∈ K : |y| < qm  ′  0+t+n}))  = (qm0−m  ′  0−t−n+1) · (qm  ′  0+t+n+1 − qm  ′  0+t+n)  = (qm0−m  ′  0−t−n+1)(qm  ′  0+t+n)(q − 1)  = qm0+1(q − 1),  and consequently,  η(H(ρ)) = η(A) =  i  �  n=1  η(An) = iqm0+1(q − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Since qm′  0+t+i ≤ ρ < qm′  0+t+i+1, it follows that  (m′  0 + t + i) log q ≤ log ρ < (m′  0 + t + i + 1) log q  which implies that  log ρ  log q − m′  0 − t − 1 < i ≤ log ρ  log q − m′  0 − t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  8  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Hence,  �log ρ  log q − m  ′  0 − t − 1  �  (q − 1)qm0+1 < η(H(ρ)) ≤  �log ρ  log q − m  ′  0 − t  �  (q − 1)qm0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  (9)  Now,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  lim inf  ρ→∞  #G(ρ)  η(H(ρ)) ≥ lim inf  ρ→∞  #G′(ρ) − C  η(H(ρ))  = lim inf  n→∞  #G′(|tn|) − C  η(H(|tn|))  (for |tn| ≤ ρ < |tn+1|)  = lim inf  n→∞  1  n(#G′(|tn|) − C)  1  n(η(H(|tn|)))  ≥  lim inf  n→∞  1n(#G′(|tn|))  lim sup  n→∞  1n(η(H(|tn|)))  ≥  lim inf  n→∞  1  n(q − 1) #  �  j : 1 ≤ j ≤ n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' |bj| ≥ 1  δ  �  lim sup  n→∞  1  n  �log |tn|  log q  − m′  0 − t  �  qm0+1(q − 1)  (by (4) and (9))  ≥  lim inf  n→∞  1  n #  �  j : 1 ≤ j ≤ n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' |bj| ≥ 1  δ  �  lim sup  n→∞  1  n  �log |b1b2 · · · bn|  log q  − m′  0 − t  �  qm0+1  (by (3))  ≥  lim inf  n→∞  1  n #  �  j : 1 ≤ j ≤ n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' |bj| ≥ 1  δ  �  lim sup  n→∞  1  n  \uf8eb  \uf8ec  \uf8ec  \uf8ec  \uf8ed  n�  j=1 log |bj|  log q  − m′  0 − t  \uf8f6  \uf8f7  \uf8f7  \uf8f7  \uf8f8 qm0+1  = e(δ)  α+  log q  qm0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  9  A similar calculation yields  lim sup  ρ→∞  #G(ρ)  η(H(ρ)) ≤ f(δ)  α−  log q  qm0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let Q be a quadratic form as in Theorem 2, and 0 < δ <  1 be fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then there exist a subset K′ of K with µ(K′) = µ(K) such  that if α = −ba ∈ K′, then  lim  ρ→∞  #G(ρ)  η(H(ρ)) =  q − 1  q⌈δ−1⌉+m0+1,  where ⌈δ−1⌉ denotes the smallest integer greater or equal to δ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='] be the continued fraction expansion of α =  −ba as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It follows from Theorem 6 of [1] that there is a full  measure subset K′ of K such that if α = −ba ∈ K′, then  (10)  lim  n→∞ |b1b2 · · · bn| 1n = q  q  q − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  This implies that  lim  n→∞  1  n  n  �  j=1  log |bj| =  q  q − 1 log q,  and, therefore, α− = α+ =  q  q−1 log q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also for any 0 < δ < 1, there  exists a unique l ∈ N such that l = ⌈δ−1⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then by Theorem 14 of  [12], for α in a full measure set which without loss of generality we may  assume to be K′,  lim  n→∞  1  n #{1 ⩽ j ⩽ n : |bj| ⩾ ql} =  1  ql−1  which implies that e(δ) = f(δ) =  1  ql−1 =  1  q⌈δ−1⌉−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then it follows from  Theorem 2 above that, if α = −ba ∈ K  ′, then  lim  ρ→∞  #G(ρ)  η(H(ρ)) =  1  q⌈δ−1⌉ − 1  �  q  q − 1 log q  � log q  qm0+1  =  q − 1  q⌈δ−1⌉ + m0 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  □  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let Q, α be as in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now, if the absolute values  of the partial quotients in the continued fraction expansion of α are  10  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  bounded by some real numbers, then it is easy to see that e(δ) = f(δ) =  0 if δ is sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In this case,  lim  ρ→∞  #G(ρ)  η(H(ρ)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' K is the field of p-adic numbers  In this section, we consider isotropic quadratic forms with coefficients  in the field of p-adic numbers for a prime p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Recall that the field of  p-adic numbers, denoted by Qp, is the collection of all formal series of  the form  �  j≥n0  ajpj, with n0 ∈ Z and aj ∈ {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', p − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  The ultrametric absolute value on Qp is defined as follows: if  α (̸= 0) =  �  j≥n0  ajpj,  then  |α|p := p−νp(α), and |0|p = 0,  where νp(α) := inf {j ∈ Z : aj ̸= 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The integer νp(α) is also known  as the valuation of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' For α ∈ Qp and r ∈ Z, let  B(a, pr) := {α ∈ K : |α − a|p < pr}  be the open disc of radius pr around the point α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The Haar measure µ  (say) on Qp is defined in such a way that µ(B(a, pr)) = pr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' We denote  by η again the product measure µ ⊗ µ on Qp × Qp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  As in the case of real numbers and elements of Laurent series fields  over finite fields, continued fraction expansion exists for p-adic num-  bers as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' There are mainly two types of continued fractions for  p-adic numbers, one of them was introduced by Schneider (see [17] for  instance), and the other one was introduced by Ruban (see [15] for  instance) and modified later by Brokwin (see [3], [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In this article,  we are going to consider the continued fraction introduced by Ruban  which has some similarity with the simple continued fraction for real  numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' From now on, unless otherwise stated, we will be considering  Ruban’s continued fraction only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let Z be the subset of Qp given by  Z := {a0 + a1  1  p + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' an  1  pn : ai ∈ {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', p − 1} for 0 ≤ i ≤ n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It is easy to see that Z is a discrete set in the topology coming from  the p-adic abosolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' For α (̸= 0) = �  j≥n0  ajpj, let  ⌊α⌋ =  \uf8f1  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f3  0  �  j=n0  ajpj  if  n0 ≤ 0  0  if  n0 ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  11  Given α ∈ Qp, we define two sequences (αn) and (bn) as follows: α0 =  α, b0 = ⌊α0⌋;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' for n ≥ 0, if bn = αn, then αn+1 and bn+1 are not defined,  otherwise, αn+1 = (αn − bn)−1 and bn+1 = ⌊αn+1⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Any p-adic number  α has a unique continued fraction expansion as α = [b0, b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' , bn, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' ]  which can be obtained by using the algorithm discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Note  that the partial quotients bn’s are elements of Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The nth convergent  is given by sn  tn = [b0, b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' , bn] where sn and tn satisfy the recurrence  relation as in (1), and equation (2) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  The p-adic versions of  equation (3), (4) and (5) are valid as well with the absolute value in  the Laurent series field replaced by the p-adic absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' As we  could not find a proper reference for a p-adic version of Lemma 1, we  include a proof here following the proof of Lemma 1 given in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let s, t ∈ Z with t ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then s  t is a convergent to α if and  only if  (11)  ����α − s  t  ����  p < 1  |t|2p  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' By the p-adic version of equation (4),  ����α − sn  tn  ����  p  =  1  |bn+1|p |tn|2  p  <  1  |tn|2  p  for any convergent sn  tn corresponding to the continued fraction expan-  sion of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Conversely, assume that s, t ∈ Z with t ̸= 0 such that  ����α − s  t  ����  p < 1  |t|2  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  There is a unique n such that |tn|p ≤ |t|p < |tn+1|p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then  ����α − s  t  ����  p <  1  |t|p|tn|p  ,  and  ����α − sn  tn  ����  p  =  1  |tn|p|tn+1|p  (by p-adic version of (5))  <  1  |t|p|tn|p  ,  so that  ����  s  t − sn  tn  ����  p  =  ����  s  t − α + α − sn  tn  ����  p  ≤ max  �����α − s  t  ����  p ,  ����α − sn  tn  ����  p  �  <  1  |t|p|tn|p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  12  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  Thus, s  t = sn  tn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  □  Now, let Q be a non-degenerate isotropic binary quadratic form with  coefficients in Qp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Since Qp has characteristic zero, as explained in the  previous section, it is enough to consider Q defined by  Q(x, y) = (ax + by)(cx + dy)  with a, b, c, d in Qp and bc−ad = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' We also assume that ba is not of the  form s  t for some s, t ∈ Z with t ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let p denote the set of all those  (s, t) ∈ Z such that s and t does not have a common factor except the  constant polynomials in 1p inside Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' For k > 1 and 0 < δ < 1, we  define G(ρ) and H(ρ) as in the previous section as follows:  G(ρ) := {(s, t) ∈ p : 0 < |Q(s, t)|p < δ, ||(s, t)|| ≤ ρ, |cs + dt|p > k},  H(ρ) := {(x, y) ∈ K2 : 0 < |Q(x, y)|p < δ, ||(x, y)|| ≤ ρ, |cx+dy|p > k},  here ||(s, t)|| = max { |s|p, |t|p }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Also let α = −ba and β = ac, and the  continued fraction expansion of α be given by  α = [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  The quantities e(δ), f(δ), α− and α+ are defined similarly as in the  previous section with the absolute value replaced by the p-adic absolute  value wherever applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then an analogue of Theorem 2 holds in  this set up as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' With all the notations as above, if α− < ∞, then  lim inf  ρ→∞  #G(ρ)  η(H(ρ)) ≥ c e(δ)  α+ ,  and  lim sup  ρ→∞  #G(ρ)  η(H(ρ)) ≤ c f(δ)  α− ,  where c =  log p  pm0 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Let X = B(0, 1) and T : X → X be the continued fraction map  defined by  T(α) = 1  α −  � 1  α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It is known that the map T is ergodic (see [15] for details) with respect  to the Haar measure µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' As an application of the ergodicity, we obtain  a result similar to Theorem 14 of [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let α ∈ X and [0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' ] be the continued fraction  expansion of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then for any natural number l,  lim  n→∞ #{1 ≤ j ≤ n : −νp(bj) ≥ l} =  1  pl−1  almost everywhere with respect to the Haar measure µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  13  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Note that b1 = b1(α) can be thought of as a function on B(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then it is easy to check that the function  f(α) = χ[pl,∞)(|b1(α)|p), α ∈ B(0, 1)  is integrable on B(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now, by the pointwise ergodic theorem  (see Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='30 of [8] for instance),  lim  n→∞  1  n#{1 ≤ j ≤ n : −νp(bj) ≥ l} = lim  n→∞  1  n#{1 ≤ j ≤ n : |bj|p ≥ pl}  = lim  n→∞  1  n  n  �  j=1  χ[pl,∞)(|b1(T j(α))|p)  =  �  B(0,1)  χ[pl,∞)(|b1(α)|p)dµ  = µ{α ∈ B(0, 1) : |b1(α)|p ≥ pl}  = µ{α ∈ B(0, 1) : |α|p ≤ p−l}  = p−l+1  =  1  pl−1  □  Now, using Theorem 8 of [15] and Lemma 8 above, we obtain a p-adic  version of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Corollary 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let Q be a quadratic form as in Theorem 7, and 0 < δ <  1 be fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then there exist a subset K  ′ of K with µ(K  ′) = µ(K) such  that if α = −ba ∈ K  ′, then  lim  ρ→∞  #G(ρ)  η(H(ρ)) =  p − 1  p⌈δ−1⌉+m0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  It is easy to see that a version of Remark 5 is true in the p-adic set  up as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' As the statements are similar, we do not write it separately  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Rather, we give an example of a p-adic number whose continued  fraction expansion consists of partial quotients with bounded absolute  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' One may look at [11] and references cited there in for similar  examples in Laurent series field over finite fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let α be the p-adic  number given by α =  �  j≥−1 ajpj, with aj = 1 for all j ≥ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Let the  continued fraction expansion of α be [b0, b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Then b0 = p0 + p−1  14  MANOJ CHOUDHURI AND PRASHANT J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' MAKADIYA  and |b0|p = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now  α1 = (α0 − b0)−1  =  \uf8eb  \uf8ed�  j≥1  pj  \uf8f6  \uf8f8  −1  = p−1 +  �  j≥0  (p − 1)pj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then b1 = (p − 1)p0 + p−1 and |b1|p = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Again  α2 = (α1 − b1)−1  =  \uf8eb  \uf8ed�  j≥1  (p − 1)pj  \uf8f6  \uf8f8  −1  =  �  j≥−1  (p − 1)pj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Then b2 = (p − 1)p0 + (p − 1)p−1 and |b2|p = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Observe that α3 =  (α2 − b2)−1 = α2, and hence |b3|p = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In a similar manner we get  αn+1 = αn, bn+1 = bn, |bn+1|p = p for n ≥ 3 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Therefore, the  absolute values of all the partial quotients of the continued fraction  expansion of α are bounded by p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Remark 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' As in the case of binary real quadratic forms, the Op-  penheim conjecture fails to hold for non-degenerate isotropic quadratic  form with coefficients in a non-discrete locally compact non-Archimedean  field as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' To see this, let us consider the quadratic form Q given by  Q(x, y) = (x + αy)y  with α ∈ Fq((X−1)) (or Qp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Now if the partial quotients in the con-  tinued fraction expansion of α have bounded absolute values, then us-  ing Lemma 1 (or Lemma 6), it is easy to see that the set of values  {|Q(s, t)| : s, t ∈ Z} (Z is either as in Section 1 or as in Section 2)  avoids certain neighbourhood of zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Acknowledgement .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Prashant J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Makadiya acknowledges the support  of Government of Gujarat thorugh the SHODH (ScHeme Of Developing  High Quality Research) fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Manoj Choudhuri thanks L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Singhal  for helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  References  [1] Val´erie Berth´e and Hitoshi Nakada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On continued fraction expansions in pos-  itive characteristic: equivalence relations and some metric properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Expo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 18(4):257–284, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [2] Armand Borel and Gopal Prasad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Values of isotropic quadratic forms at S-  integral points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Compositio Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 83(3):347–372, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ON VALUES OF ISOTROPIC QUADRATIC FORMS  15  [3] Jerzy Browkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Continued fractions in local fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Demonstratio Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=',  11(1):67–82, 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [4] Jerzy  Browkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Continued  fractions  in  local  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=',  70(235):1281–1292, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [5] Manoj Choudhuri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On certain orbits of geodesic flow and (a, b)-continued frac-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Indian Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 131(1):Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' 2, 19, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [6] Manoj Choudhuri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Dani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On values of binary quadratic forms at  integer points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 22(4):1023–1045, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Dani and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Margulis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Limit distributions of orbits of unipotent flows  and values of quadratic forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Gelfand Seminar, volume 16 of Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Soviet Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', pages 91–137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', Providence, RI, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [8] Manfred Einsiedler and Thomas Ward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Ergodic theory with a view towards  number theory, volume 259 of Graduate Texts in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Springer-Verlag  London, Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', London, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [9] Alex Eskin, Gregory Margulis, and Shahar Mozes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On a quantitative ver-  sion of the Oppenheim conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Announc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=',  1(3):124–130, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [10] Svetlana Katok and Ilie Ugarcovici.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Arithmetic coding of geodesics on the  modular surface via continued fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In European women in mathematics—  Marseille 2003, volume 135 of CWI Tract, pages 59–77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Centrum Wisk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In-  form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', Amsterdam, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [11] Alain Lasjaunias and Jean-Jacques Ruch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Algebraic and badly approximable  power series over a finite field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Finite Fields Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 8(1):91–107, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [12] Poj Lertchoosakul and Radhakrishnan Nair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On the metric theory of continued  fractions in positive characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Mathematika, 60(2):307–320, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Margulis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Oppenheim conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In Fields Medallists’ lectures, volume 5  of World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' 20th Century Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', pages 272–327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', River  Edge, NJ, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [14] Dinakar Ramakrishnan and Robert J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Valenza.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Fourier analysis on number  fields, volume 186 of Graduate Texts in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Springer-Verlag, New  York, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Ruban.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Certain metric properties of the p-adic numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Sibirsk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  ˇZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 11:222–227, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [16] Wolfgang M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Schmidt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' On continued fractions and Diophantine approximation  in power series fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Acta Arith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 95(2):139–166, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [17] Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Schneider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' ¨Uber p-adische Kettenbr¨uche.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' In Symposia Mathematica, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  IV (INDAM, Rome, 1968/69), pages 181–189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Academic Press, London, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  [18] David Simmons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' The Hurwitz continued fraction expansion as applied to real  numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Enseign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content=', 62(3-4):475–485, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Institute of Infrastructure, Technology, Research and Manage-  ment, Near Khokhara Circle, maninagar (East), Ahmedabad 380026,  Gujarat, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='  Email address: manojchoudhuri@iitram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='in  Email address: prashant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='makadiya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='20pm@iitram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
+page_content='in' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfDfqo/content/2301.00978v1.pdf'}
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+arXiv:2301.02831v1  [cs.IT]  7 Jan 2023
+1
+Joint Beamforming and Phase Shift Design for
+Hybrid-IRS-aided Directional Modulation Network
+Rongen Dong, Hangjia He, Feng Shu, Riqing Chen, and Jiangzhou Wang, Fellow, IEEE
+Abstract—To make a good balance between performance,
+cost, and power consumption, a hybrid intelligent reflecting
+surface (IRS)-aided directional modulation (DM) network is
+investigated in this paper, where the hybrid IRS consists of
+passive and active reflecting elements. To maximize the achievable
+rate, two optimization algorithms, called maximum signal-to-
+noise ratio (SNR)-fractional programming (FP) (Max-SNR-FP)
+and maximum SNR-equal amplitude reflecting (EAR) (Max-
+SNR-EAR), are proposed to jointly design the beamforming
+vector and IRS phase shift matrix by alternately optimizing one
+and fixing another. The former employs the successive convex
+approximation and FP methods to solve the beamforming vector
+and hybrid IRS phase shift matrix, while the latter uses the
+maximum signal-to-leakage-noise ratio method and the criteria
+of phase alignment and EAR to design them. Simulation results
+show that the rates harvested by the proposed two methods
+are slightly lower than that of active IRS with higher power
+consumption, which are 35 percent higher than those of no IRS
+and random phase IRS, while passive IRS achieves only about
+17 percent rate gain over the latter. Moreover, compared to Max-
+SNR-FP, the proposed Max-SNR-EAR method makes an obvious
+complexity reduction at the cost of a slight rate performance loss.
+Index Terms—Intelligent reflecting surface, directional modu-
+lation, fractional programming, beamforming, phase shift
+I. INTRODUCTION
+Directional modulation (DM) is a promising solution to sig-
+nificantly improve the performance of physical layer security
+in wireless networks [1]. The design of DM synthesis is mainly
+implemented in the radio frequency (RF) frontend or baseband.
+For example, in [2], the signal was produced in a given
+direction by shifting the phase of each antenna element at the
+RF frontend. In [3], a multi-beam DM scenario was considered
+to maximize the secure rate (SR), where the precoder and
+the artificial noise (AN) were designed by maximizing signal-
+to-leakage-noise ratio and maximizing the signal-to-AN ratio
+methods, respectively.
+Intelligent reflecting surface (IRS), as a cost and energy-
+efficient solution to enhance the performance of the wire-
+less communication system, has been adopted to aid various
+This work was supported in part by the National Natural Science Foundation
+of China (Nos.U22A2002, and 62071234), the Major Science and Technology
+plan of Hainan Province under Grant ZDKJ2021022, and the Scientific
+Research Fund Project of Hainan University under Grant KYQD(ZR)-21008.
+Rongen Dong and Feng Shu are with the School of Information and Com-
+munication Engineering, Hainan University, Haikou, 570228, China (Email:
+shufeng0101@163.com).
+Hangjia He is with the School of Electronic and Optical Engineering,
+Nanjing University of Science and Technology, Nanjing, 210094, China.
+Riqing Chen is with the Digital Fujian Institute of Big Data for Agriculture,
+Fujian Agriculture and Forestry University, Fuzhou 350002, China (Email:
+riqing.chen@fafu.edu.cn).
+Jiangzhou Wang is with the School of Engineering, University of Kent,
+Canterbury CT2 7NT, U.K. (Email: j.z.wang@kent.ac.uk).
+wireless communication directions: unmanned aerial vehicle
+communication [4], single-cell wireless communication [5],
+multi-cell communication [6], etc. Recently, IRS-aided DM
+system have also been investigated. To maximize the SR
+of IRS-aided DM system, the general alternating iterative
+and null-space projection algorithms were proposed to jointly
+obtain the transmit beamforming vectors and IRS phase shift
+matrix in [7]. To maximize the receive power sum, the authors
+in [8] proposed the general alternating optimization and zero-
+forcing algorithms to jointly design the receive beamforming
+vectors and IRS phase shift matrix.
+However, all the above work was considered in the scenarios
+of passive IRS, and the system may not be able to guarantee
+a satisfactory achievable rate due to the presence of double
+path loss in the cascaded channels. To overcome the “double
+fading” effect and enhance the performance of the passive
+IRS-aided wireless network, the fully active IRS has been
+investigated [9], [10]. Due to the high power consumption and
+hardware design of active IRS, a hybrid active-passive IRS
+was proposed to overcome the limitation of passive and active
+IRSs [11], [12]. The main idea of the hybrid IRS is to employ
+some active elements to replace the one of the passive IRS,
+these active elements of hybrid IRS with signal amplification
+can efficiently compensate for the path loss and increase the
+achievable rate. To the best of the authors’ knowledge, the
+hybrid IRS-aided DM system have not been investigated yet.
+In this paper, we employ the hybrid IRS to further enhance
+the performance of passive IRS-aided DM network. The main
+contributions of this paper are summarized as follows:
+1) To make a good balance between performance, cost,
+and power consumption, a hybrid IRS-aided DM system
+model is proposed. To maximize the achievable rate,
+the optimization problem of maximizing the signal-to-
+noise ratio (SNR) is established, and the maximum SNR-
+fractional programming (FP) (Max-SNR-FP) scheme is
+proposed to jointly obtain the beamforming vector and
+hybrid IRS phase shift matrix by optimizing one and
+fixing another. In this scheme, the beamforming vector
+and passive IRS phase shift matrix are solved by the
+successive convex approximation algorithm, and the
+active IRS phase shift matrix is computed by the FP
+method.
+2) To reduce the high computational complexity of the
+above scheme, a low-complexity maximum SNR-equal
+amplitude reflecting (EAR) (Max-SNR-EAR) method is
+proposed. By utilizing the maximum signal-to-leakage-
+noise ratio (SLNR) method, the beamforming vector is
+
+2
+obtained. Moreover, the hybrid IRS phase shift matrix is
+computed based on the criteria of phase alignment and
+EAR. Simulation results show that the achievable rates
+harvested by both the proposed methods are higher than
+those of no IRS, random phase IRS, and passive IRS.
+In addition, the difference in achievable rates between
+these two methods is trivial when the number of hybrid
+IRS elements tends to large scale.
+The remainder of this paper is organized as follows. Section
+II describes the system model of hybrid IRS-aided DM net-
+work. The Max-SNR-FP scheme is presented in Section III.
+Section IV describes the Max-SNR-EAR scheme. Numerical
+simulation results are presented in Section V. Finally, we draw
+conclusions in Section VI.
+Notations: throughout this paper, boldface lower case and
+upper case letters represent vectors and matrices, respectively.
+Signs (·)T , (·)∗, (·)H, Tr(·), ℜ{·}, and diag{·} denote the
+transpose, conjugate, conjugate transpose, trace, real part,
+and diagonal operations, respectively. The sign | · | is the
+determinant of a matrix or the absolute value of a scalar. The
+symbol CN×N denotes the space of N × N complex-valued
+matrix. The notation IN is the N × N identity matrix.
+II. SYSTEM MODEL
+As shown in Fig. 1, a hybrid IRS-aided DM system is
+considered, where the base station (BS) is equipped with
+N antennas, and the user (Bob) is equipped with single
+antenna. The hybrid IRS is equipped with M elements, which
+consists of Ma active and Mp passive IRS reflecting elements
+(M = Ma + Mp, 1 ≤ Ma ≤ Mp). It is assumed that the
+active elements can tune both the phase and amplitude while
+the passive ones can only shift the phase of the incident
+signal. The signals reflected more than once on the hybrid IRS
+are negligible due to the severe path loss [6]. All channels
+are assumed to be line-of-sight channels since DM is only
+applicable to line-of-sight channels. It is assumed that all the
+channel state information is perfectly known through channel
+estimation [13].
+Fig. 1. System model of Hybrid-IRS-aided directional modulation network.
+Similar to the conventional passive IRS, it is assumed that
+each elements of hybrid IRS can independently reflect the inci-
+dent signals. Let us denote the set of the Ma active elements by
+Ω. Θ = diag{θ∗} = diag{θ1, · · · , θm, · · · , θM} ∈ CM×M,
+Ψ = diag{ψ∗} ∈ CM×M, and Φ = diag{φ∗} ∈ CM×M are
+the reflection coefficients of total elements, active elements,
+and passive elements of hybrid IRS, respectively, where
+θm =
+�
+|βm|ejµm,
+if m ∈ Ω,
+ejµm,
+otherwise,
+(1)
+µm
+∈ [0, 2π) is the phase, and |βm| is the amplifying
+coefficient and determined by the total power of the active
+elements. Let us define
+Ψ = EMaΘ, Φ = EMpΘ,
+(2)
+where
+EMa + EMp = IM, EMaEMp = 0M,
+(3)
+EMa is an M × M diagonal matrix whose non-zero elements
+are all unity and have positions determined by Ω.
+The transmitted signal at BS is
+s =
+√
+Pvx,
+(4)
+where P denotes the transmit power, v ∈ CN×1 and x are the
+beamforming vector and the information symbol, satisfying
+vHv = 1 and E[∥x∥2] = 1, respectively.
+Taking the path loss into consideration, the received signal
+at Bob is
+yb = (√ρsrbhH
+rbΘHsr + √ρsbhH
+sb)s + √ρrbhH
+rbΨnr + nb
+=
+√
+P(√ρsrbhH
+rbΨHsr + √ρsrbhH
+rbΦHsr + √ρsbhH
+sb)vx
++ √ρrbhH
+rbΨnr + nb,
+(5)
+where ρsrb = ρsrρrb is the equivalent path loss coefficient
+of BS-to-IRS channel and IRS-to-Bob channel, ρsb and ρrb
+are the path loss coefficient of BS-to-Bob channel and IRS-
+to-Bob channel, respectively. nr ∼ CN(0, σ2
+rIMa) and nb ∼
+CN(0, σ2
+b) denote the complex additive white Gaussian noise
+(AWGN) at the Ma active elements of the hybrid IRS and
+at Bob, respectively. hsb ∈ CN×1, hrb ∈ CM×1, and Hsr =
+hsrhH
+sr ∈ CM×N are the BS-to-Bob, IRS-to-Bob, and BS-to-
+IRS channels, respectively. Let us define the channel htr =
+h(θtr), the normalized steering vector h(θ) is
+h(θ) =
+1
+√
+N
+[ej2πΨθ(1), . . . , ej2πΨθ(n), . . . , ej2πΨθ(N)]T , (6)
+and the phase function Ψθ(n) is given by
+Ψθ(n)
+∆= −(n − (N + 1)/2)d cosθ
+λ
+, n = 1, . . . , N,
+(7)
+where θ represents the direction angle of arrival or departure,
+n denotes the index of antenna, d is the spacing of adjacent
+transmitting antennas, and λ represents the wavelength.
+In accordance with (5), the achievable rate at Bob can be
+written as
+Rb = log2 (1 + SNR) ,
+(8)
+where
+SNR = P|(√ρsrbhH
+rbΨHsr + √ρsrbhH
+rbΦHsr + √ρsbhH
+sb)v|2
+σ2r|√ρrbhH
+rbΨ|2 + σ2
+b
+.
+(9)
+
+Hybrid IRS
+Active
+Passive
+H
+H
+rb
+((())
+H
+5
+sb
+User
+(Bob)
+Base station3
+The transmit power of the active elements at the hybrid IRS
+is given by
+Pr = Tr
+�
+Ψ
+�
+ρsrPHsrvvHHH
+sr + σ2
+rIM
+�
+ΨH�
+,
+(10)
+which satisfies Pr ≤ P max
+r
+, where P max
+r
+represents the maxi-
+mum transmit power of Ma active elements.
+In this paper, we maximize the SNR by jointly optimizing
+beamforming vector v, passive IRS phase shift matrix Φ, and
+active IRS phase shift matrix Ψ. The optimization problem
+can be formulated as
+max
+v,Φ,Ψ
+SNR
+(11a)
+s.t.
+vHv = 1, Pr ≤ P max
+r
+,
+(11b)
+|Φ(m, m)| = 1, if m ̸∈ Ω,
+(11c)
+|Φ(m, m)| = 0, otherwise,
+(11d)
+|Ψ(m, m)| ≤ βmax, if m ∈ Ω,
+(11e)
+|Ψ(m, m)| = 0, otherwise,
+(11f)
+where βmax is the amplification budget. It is notes that this
+optimization problem is a non-convex problem with a constant
+modulus constraint, and it is challenging to solve it directly in
+general. In what follows, we propose the alternating optimiza-
+tion algorithm to design the beamforming vector and hybrid
+IRS phase shift matrix, respectively.
+III. PROPOSED MAX-SNR-FP SCHEME
+In this section, we construct a Max-SNR-FP method to
+jointly optimize the beamforming vector v, passive IRS phase
+shift matrix Φ, and active IRS phase shift matrix Ψ. In what
+follows, we will alternately solve for v, Φ, and Ψ.
+A. Optimize v given Φ and Ψ
+Firstly, we transform the power constraint in (11b) into a
+convex constraint with respect to v as follows
+Pr = vH �
+ρsrPHH
+srΨHΨHsr
+�
+v + Tr
+�
+σ2
+rΨΨH�
+≤ P max
+r
+.
+(12)
+Then, given Φ and Ψ, the optimal beamforming vector v can
+be found by solving the following problem
+max
+v
+vHA¯v
+s.t. vHv = 1, (12),
+(13)
+where
+A =(√ρsrbhH
+rbΦHsr + √ρsrbhH
+rbΨHsr + √ρsbhH
+sb)H
+(√ρsrbhH
+rbΦHsr + √ρsrbhH
+rbΨHsr + √ρsbhH
+sb).
+(14)
+It is clear that this problem is not convex, and in accordance
+with the Taylor series expansion, we have
+vHAv ≥ 2ℜ{¯vHAv} − ¯vHA¯v,
+(15)
+where ¯v is a given vector. Then (13) can be recasted as
+max
+v
+2ℜ{¯vHAv} − ¯vHA¯v
+s.t. vHv = 1, (12).
+(16)
+It is a convex optimization problem and can be solved by
+employing CVX tool.
+B. Optimize Φ given v and Ψ
+To simplify the SNR expression related to the phase shift
+matrix Φ, we regard v and Ψ as two constants, and define
+B = (√ρsrbhH
+rbΨHsr + √ρsbhH
+sb)v.
+(17)
+Then, the subproblem to optimize Φ can be expressed as
+max
+Φ
+|√ρsrbhH
+rbΦHsrv + B|2
+(18a)
+s.t. |Φ(m, m)| = 1, if m ̸∈ Ω,
+(18b)
+|Φ(m, m)| = 0, otherwise.
+(18c)
+By defining
+C = ρsrbdiag{hH
+rb}HsrvvHHH
+srdiag{hH
+rb}H,
+(19)
+and based on the fact that diag{a}b = diag{b}a for a, b ∈
+CM×1, the objective function in (18) can be recasted as
+φHCφ + 2ℜ{√ρsrbφHdiag{hH
+rb}HsrvB∗} + |B|2.
+(20)
+Based on the Taylor series expansion, we have
+φHCφ ≥ 2ℜ{ ¯φHCφ} − ¯φHC ¯φ,
+(21)
+where ¯φ is a given vector. For the unit modulus constraint
+(18b), it can be relaxed as
+|Φ(m, m)| ≤ 1, if m ̸∈ Ω.
+(22)
+At this point, the problem (18) can be rewritten as
+max
+Φ
+2ℜ{ ¯φHCφ} − ¯φHC ¯φ + |B|2 + 2ℜ{√ρsrbφH•
+diag{hH
+rb}HsrvB∗}
+s.t.
+(22), (18c).
+(23)
+We can find that it is a convex optimization problem and can
+be solved by employing CVX tool.
+C. Optimize Ψ given v and Φ
+To optimize Ψ, we regard v and Φ as two given constants,
+and transform the power constraint in (11b) into a convex
+constraint on ψ as follows
+Pr = Tr
+�
+Ψ
+�
+ρsrPHsrvvHHH
+sr + σ2IM
+�
+ΨH�
+= ψT (ρsrPdiag{vHHH
+sr}diag{Hsrv} + σ2
+rIM)ψ∗
+≤ P max
+r
+.
+(24)
+By neglecting the constant terms, the subproblem with respect
+to Ψ is given by
+max
+Ψ
+|(√ρsrbhH
+rbΨHsr + √ρsrbhH
+rbΦHsr + √ρsbhH
+sb)v|2
+σ2r|√ρrbhH
+rbΨ|2 + σ2
+b
+(25a)
+s.t.
+(11e), (11f), (24).
+(25b)
+Let us define
+D = (√ρsrbhH
+rbΦHsr + √ρsbhH
+sb)v.
+(26)
+Then, the objective function in (25) can be converted to
+ψHCψ + 2ℜ{ψH√ρsrbdiag{hH
+rb}HsrvD∗} + |D|2
+σ2rρrb|ψHdiag{hH
+rb}|2 + σ2
+b
+.
+(27)
+
+4
+At this point, the optimization problem (25) becomes a nonlin-
+ear fractional optimization problem. Based on the FP strategy
+in [14], we introduce a parameter τ and transform the objective
+function (27) as
+ψHCψ + 2ℜ{ψH√ρsrbdiag{hH
+rb}HsrvD∗} + |D|2
+− τ(σ2
+rρrb|ψHdiag{hH
+rb}|2 + σ2
+b).
+(28)
+The
+optimal
+solution
+can
+be
+achieved
+if
+and
+only
+if ψHCψ + 2ℜ{ψH√ρsrbdiag{hH
+rb}HsrvD∗} + |D|2 −
+τ(σ2
+rρrb|ψHdiag{hH
+rb}|2 + σ2
+b) = 0. We linearize the ψHCψ
+by employing Taylor series expansion at a given vector ¯ψ, the
+subproblem with respect to Ψ can be rewritten as
+max
+Ψ,τ
+2ℜ{ ¯ψHCψ} − ¯ψHC ¯ψ + 2ℜ{ψH√ρsrbdiag{hH
+rb}•
+HsrvD∗} + |D|2 − τ(σ2
+rρrb|ψHdiag{hH
+rb}|2 + σ2
+b)
+s.t.
+(11e), (11f), (24).
+(29)
+It should be noted that this problem is convex, which can be
+effectively solved by the CVX tool. The whole procedure of
+the Max-SNR-FP algorithm is described in Algorithm 1.
+Algorithm 1 Proposed Max-SNR-FP algorithm
+1: Initialize v(0), Φ(0), and Ψ(0), compute R(0)
+b
+based on (8).
+2: Set p = 0, threshold value ǫ.
+3: repeat
+4:
+Given Φ(p) and Ψ(p), solve (16) to determine v(p+1).
+5:
+Given v(p+1) and Ψ(p), solve (23) to determine Φ(p+1).
+6:
+Given v(p+1) and Φ(p+1), solve (29) to determine
+Ψ(p+1).
+7:
+Compute R(p+1)
+b
+using v(p+1), Φ(p+1), and Ψ(p+1).
+8:
+p = p + 1.
+9: until |R(p)
+b
+− R(p−1)
+b
+| ≤ ǫ.
+The computational complexity of the proposed Max-SNR-
+FP algorithm is O(L((M + 1)3 + 2MN 2 + 2M 2)In(1/ǫ) +
+M 3+N 3+5M 2+2MN+2M+2MN 2) float-point operations
+(FLOPs), where L is the numbers of alternating iterations, ǫ
+denotes the accuracy.
+IV. PROPOSED MAX-SNR-EAR SCHEME
+In the previous section, we proposed the Max-SNR-FP
+method to design the beamforming v, IRS phase shift matrices
+Φ and Ψ. However, it has a high computational complexity.
+To reduce the computational complexity, a low-complexity
+method named Max-SNR-EAR is proposed in what follows.
+A. Optimize v given Φ and Ψ
+Given IRS phase shift matrices Φ and Ψ, in accordance with
+the principle of maximizing SLNR in [15], the beamforming
+vector v can be optimized by solving the following problem
+max
+v
+SLNR =
+vHEv
+vH(σ2
+bIN)v
+s.t. vHv = 1, (12),
+(30)
+where
+E =ρsrbHH
+srΦHhrbhH
+rbΦHsr + ρsrbHH
+srΨHhrbhH
+rbΨHsr
++ hsbhH
+sb.
+(31)
+According to the Taylor series expansion and neglecting the
+constant terms, the problem (30) can be recasted as
+max
+v
+2ℜ{¯vHEv} − ¯vHE¯v
+s.t.
+vHv = 1, (12).
+(32)
+Note that it is a convex optimization problem and can be
+solved with CVX tool.
+B. Optimize Φ and Ψ given v
+Given beamforming vector v, we consider to design the
+phase of hybrid IRS firstly. The confidential message received
+by Bob through the cascade path is expressed as
+PρsrbhH
+rbΘHsrvvHHH
+srΘHhrb.
+(33)
+To maximize the confidential message of the cascade path, the
+phase alignment method is employed to design the hybrid IRS
+phase �θ, �θ is given by
+�θ = [e(−iarg(s1)), · · · , e(−iarg(sM))]T ,
+(34)
+where s = diag{hH
+rb}Hsrv, and si is the i-th element of s.
+Next, inspired by the amplitude design of fully active IRS
+in [9], we assume that all active IRS elements have the same
+amplitude. Based on the IRS power constraint in (11b), we
+have
+|β| =
+�
+P max
+r
+/Q,
+(35)
+where
+Q =Tr(�θH(ρsrPdiag{vHHH
+srEMa}diag{vHHH
+srEMa}H
++ σ2EMaEMa)�θ).
+(36)
+Based on (34) and (35), we can obtain the passive IRS phase
+shift matrix and active IRS phase shift matrix as follows
+Φ = EMpdiag{�θ}, Ψ = |β|EMadiag{�θ}.
+(37)
+Similar to Algorithm 1, we calculate v, Φ, and Ψ alternately
+until convergence, i.e., |R(p)
+b −R(p−1)
+b
+| ≤ ǫ. The computational
+complexity of Max-SNR-EAR algorithm is O(K(2M 2+N 3+
+2M 2 + 8N 2M + 2MN) FLOPs, where K is the numbers of
+alternating iterations.
+V. SIMULATION RESULTS AND DISCUSSIONS
+In this section, simulation results are presented to evaluate
+the performance of two proposed algorithms. Simulation de-
+fault parameters are chosen as follows: N = 8, M = 128,
+Ma = 32, d = λ/2, θsr = π/4, θsb = π/3, dsr = 200m,
+dsb = 220m, σ2
+b = −70dBm, σ2
+r = 2σ2
+b, P = 25dBm,
+P max
+r
+= 30dBm. The path loss at the distance d is modeled
+as g(d) = PL0 − 10γlog10
+d
+d0 , where PL0 = −30dB is the
+path loss reference distance d0 = 1m, and γ is the path loss
+exponent. The path loss exponents of all channels are chosen
+as 2. The positions of the IRS active elements are fixed to
+Ω = {1, · · · , Ma}.
+First, we make an investigation of the convergence be-
+haviour of the proposed Max-SNR-FP and Max-SNR-EAR
+algorithms. Fig. 2 shows the achievable rate versus the differ-
+ent BS power, i.e., P = 20dBm, 25dBm. It can be seen from
+the figure that both of the proposed algorithms converge within
+limited iterations. The proposed Max-SNR-EAR algorithm has
+a faster convergence rate than the Max-SNR-FP algorithm,
+regardless of P = 20dBm or 25dBm.
+
+5
+0
+5
+10
+15
+20
+25
+30
+13.5
+14
+14.5
+15
+15.5
+16
+16.5
+17
+Fig. 2. Convergence of the proposed algorithms at different BS power.
+Fig. 3 depicts the curves of the achievable rate versus the
+number of IRS phase shift elements, where Ma = M/2. We
+compare two proposed algorithms to the benchmark schemes:
+active IRS, passive IRS, no IRS, random phase IRS, and exist-
+ing method in [11]. The achievable rates of the proposed Max-
+SNR-FP and Max-SNR-EAR algorithms gradually increase
+as the number of IRS elements increases, and the former
+is better than the latter and existing method in [11]. The
+achievable rates of both the proposed algorithms are much
+better than that of the passive IRS, no IRS and random phase
+IRS. Moreover, the difference in achievable rates between both
+the proposed algorithms and active IRS gradually decreases
+when the number of IRS elements tends to large scale.
+3
+4
+5
+6
+7
+8
+11
+12
+13
+14
+15
+16
+17
+18
+19
+Fig. 3. Achievable rate versus the numbers of IRS phase shift elements.
+Fig. 4 plots the curves of the computational complexity
+versus the number of IRS elements. It can be found that the
+complexities of the proposed Max-SNR-FP method, proposed
+Max-SNR-EAR method, and existing method in [11] are
+similar at small-scale IRS. However, the complexities of the
+existing method in [11] and proposed Max-SNR-FP method
+are far higher than that of the proposed Max-SNR-EAR
+method when the number of IRS elements tends to large scale.
+VI. CONCLUSION
+In this paper, we have made an investigation of the hybrid
+IRS-aided DM network. To fully explore the advantages of
+hybrid IRS and maximize the achievable rate, the Max-SNR-
+FP and Max-SNR-EAR algorithms were proposed to jointly
+design the beamforming vector, passive IRS phase shift matrix,
+and active IRS phase shift matrix by alternately optimizing one
+and fixing rest. Simulation results showed that the achievable
+2
+3
+4
+5
+6
+7
+0
+2
+4
+6
+8
+10
+12
+14
+107
+Fig. 4. Computational complexity versus the numbers of IRS elements.
+rate of both proposed algorithms increases as the number of
+IRS elements increases, and is much better than those of
+the cases of random phase IRS, no IRS, and passive IRS.
+Moreover, the proposed Max-SNR-FP method outperforms the
+existing method in terms of the achievable rate and has lower
+complexity.
+REFERENCES
+[1] Q. Cheng, S. Wang, V. Fusco, F. Wnag, J. Zhu, and C. Gu, “Physical-
+layer security for frequency diverse array-based directional modulation
+in fluctuating two-ray fading channels,” IEEE Trans. Wirel. Commun.,
+vol. 20, no. 7, pp. 4190–4204, Jul. 2021.
+[2] M. P. Daly and J. T. Bemhard, “Directional modulation technique for
+phased arrays,” IEEE Trans. Antennas Propag, vol. 57, no. 9, pp. 2633–
+2640, Sep. 2009.
+[3] F. Shu, X. Wu, J. Li, R. Chen, and B. Vucetic, “Robust synthesis scheme
+for secure multi-beam directional modulation in broadcasting systems,”
+IEEE Access, vol. 4, pp. 6614–6623, Nov. 2016.
+[4] Y. Pan, C. Wang, C. Pan, H. Zhu, and J. Wang, “UAV-assisted and intel-
+ligent reflecting surfaces-supported terahertz communication,” Wireless
+Commun. Lett., vol. 10, no. 6, pp. 1256–1260, Jun. 2021.
+[5] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless
+network via joint active and passive beamforming,” IEEE Trans. Wirel.
+Commun., vol. 18, no. 11, pp. 5394–5409, Nov. 2019.
+[6] C. Pan, H. Ren, K. Wang, W. Xu, M. Elkashlan, A. Nallanathan, and
+L. Hanzo, “Multicell MIMO communications relaying on intelligent
+reflecting surfaces,” IEEE Trans. Wirel. Commun., vol. 19, no. 8, pp.
+5218–5233, Aug. 2020.
+[7] F. Shu, Y. Teng, J. Li, M. Huang, W. Shi, J. Li, Y. Wu, and J. Wang,
+“Enhanced secrecy rate maximization for directional modulation net-
+works via IRS,” IEEE Trans. Commun., vol. 69, no. 12, pp. 8388–8401,
+Dec. 2021.
+[8] R. Dong, S. Jiang, X. Hua, Y. Teng, F. Shu, and J. Wang, “Low-
+complexity joint phase adjustment and receive beamforming for di-
+rectional modulation networks via IRS,” IEEE open journal of the
+Communications Society, vol. 3, pp. 1234–1243, Aug. 2022.
+[9] Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V. Poor,
+“Active RIS vs. passive RIS: which will previal in 6G?” arXiv preprint
+arXiv: 2103.15154, 2021.
+[10] K. Liu, Z. Zhang, L. Dai, s. Xu, and F. Yang, “Active reconfigurable
+intelligent surface: Fully-connected or sub-connected?” IEEE Commun.
+Lett., vol. 26, no. 1, pp. 167–171, Jan. 2022.
+[11] N. T. Nguyen, V.-D. Nguyen, Q. Wu, A. T¨olli, S. Chatzinotas, and
+M. Juntti, “Hybrid active-passive reconfigurable intelligent surface-
+assisted multi-user MISO systems,” 2022 IEEE 23rd International
+Workshop on Signal Processing Advances in Wireless Communication
+(SPAWC), pp. 1–5, Jul. 2022.
+[12] N. T. Nguyen, Q.-D. Vu, K. Lee, and M. Juntti, “Hybrid relay-reflecting
+intelligent surface-assisted wireless communications,” IEEE Trans. Veh.
+Technol., Mar. 2022.
+[13] Z. Wang, L. Liu, and S. Cui, “Channel estimation for intelligent reflect-
+ing surface assisted multiuser communications: Framework, algorithms,
+and analysis,” IEEE Trans. Wirel. Commun., vol. 19, no. 10, pp. 6607–
+6620, Oct. 2020.
+[14] W. Dinkelbach, “On nonlinear fractional programming,” Manage Sci.,
+vol. 13, no. 7, pp. 492–498, Mar. 1967.
+
+6
+[15] M. Sadek, A. Tarighat, and A. H. Sayed, “A leakage-based precoding
+scheme for downlink multi-user MIMO channels,” IEEE Trans. Wirel.
+Commun., vol. 6, no. 5, pp. 1711–1721, May. 2007.
+
diff --git a/1tE0T4oBgHgl3EQf_wKi/content/tmp_files/load_file.txt b/1tE0T4oBgHgl3EQf_wKi/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d1bfc28259a53f7c1f93e1108efe17c7413692ba
--- /dev/null
+++ b/1tE0T4oBgHgl3EQf_wKi/content/tmp_files/load_file.txt
@@ -0,0 +1,380 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf,len=379
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='02831v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='IT]  7 Jan 2023  1  Joint Beamforming and Phase Shift Design for  Hybrid-IRS-aided Directional Modulation Network  Rongen Dong, Hangjia He, Feng Shu, Riqing Chen, and Jiangzhou Wang, Fellow, IEEE  Abstract—To make a good balance between performance,  cost, and power consumption, a hybrid intelligent reflecting  surface (IRS)-aided directional modulation (DM) network is  investigated in this paper, where the hybrid IRS consists of  passive and active reflecting elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To maximize the achievable  rate, two optimization algorithms, called maximum signal-to-  noise ratio (SNR)-fractional programming (FP) (Max-SNR-FP)  and maximum SNR-equal amplitude reflecting (EAR) (Max-  SNR-EAR), are proposed to jointly design the beamforming  vector and IRS phase shift matrix by alternately optimizing one  and fixing another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The former employs the successive convex  approximation and FP methods to solve the beamforming vector  and hybrid IRS phase shift matrix, while the latter uses the  maximum signal-to-leakage-noise ratio method and the criteria  of phase alignment and EAR to design them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Simulation results  show that the rates harvested by the proposed two methods  are slightly lower than that of active IRS with higher power  consumption, which are 35 percent higher than those of no IRS  and random phase IRS, while passive IRS achieves only about  17 percent rate gain over the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Moreover, compared to Max-  SNR-FP, the proposed Max-SNR-EAR method makes an obvious  complexity reduction at the cost of a slight rate performance loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Index Terms—Intelligent reflecting surface, directional modu-  lation, fractional programming, beamforming, phase shift  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' INTRODUCTION  Directional modulation (DM) is a promising solution to sig-  nificantly improve the performance of physical layer security  in wireless networks [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The design of DM synthesis is mainly  implemented in the radio frequency (RF) frontend or baseband.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  For example, in [2], the signal was produced in a given  direction by shifting the phase of each antenna element at the  RF frontend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' In [3], a multi-beam DM scenario was considered  to maximize the secure rate (SR), where the precoder and  the artificial noise (AN) were designed by maximizing signal-  to-leakage-noise ratio and maximizing the signal-to-AN ratio  methods, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Intelligent reflecting surface (IRS), as a cost and energy-  efficient solution to enhance the performance of the wire-  less communication system, has been adopted to aid various  This work was supported in part by the National Natural Science Foundation  of China (Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='U22A2002, and 62071234), the Major Science and Technology  plan of Hainan Province under Grant ZDKJ2021022, and the Scientific  Research Fund Project of Hainan University under Grant KYQD(ZR)-21008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Rongen Dong and Feng Shu are with the School of Information and Com-  munication Engineering, Hainan University, Haikou, 570228, China (Email:  shufeng0101@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Hangjia He is with the School of Electronic and Optical Engineering,  Nanjing University of Science and Technology, Nanjing, 210094, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Riqing Chen is with the Digital Fujian Institute of Big Data for Agriculture,  Fujian Agriculture and Forestry University, Fuzhou 350002, China (Email:  riqing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='chen@fafu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='cn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Jiangzhou Wang is with the School of Engineering, University of Kent,  Canterbury CT2 7NT, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' (Email: j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='wang@kent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='uk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  wireless communication directions: unmanned aerial vehicle  communication [4], single-cell wireless communication [5],  multi-cell communication [6], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Recently, IRS-aided DM  system have also been investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To maximize the SR  of IRS-aided DM system, the general alternating iterative  and null-space projection algorithms were proposed to jointly  obtain the transmit beamforming vectors and IRS phase shift  matrix in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To maximize the receive power sum, the authors  in [8] proposed the general alternating optimization and zero-  forcing algorithms to jointly design the receive beamforming  vectors and IRS phase shift matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  However, all the above work was considered in the scenarios  of passive IRS, and the system may not be able to guarantee  a satisfactory achievable rate due to the presence of double  path loss in the cascaded channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To overcome the “double  fading” effect and enhance the performance of the passive  IRS-aided wireless network, the fully active IRS has been  investigated [9], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Due to the high power consumption and  hardware design of active IRS, a hybrid active-passive IRS  was proposed to overcome the limitation of passive and active  IRSs [11], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The main idea of the hybrid IRS is to employ  some active elements to replace the one of the passive IRS,  these active elements of hybrid IRS with signal amplification  can efficiently compensate for the path loss and increase the  achievable rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To the best of the authors’ knowledge, the  hybrid IRS-aided DM system have not been investigated yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  In this paper, we employ the hybrid IRS to further enhance  the performance of passive IRS-aided DM network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The main  contributions of this paper are summarized as follows:  1) To make a good balance between performance, cost,  and power consumption, a hybrid IRS-aided DM system  model is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To maximize the achievable rate,  the optimization problem of maximizing the signal-to-  noise ratio (SNR) is established, and the maximum SNR-  fractional programming (FP) (Max-SNR-FP) scheme is  proposed to jointly obtain the beamforming vector and  hybrid IRS phase shift matrix by optimizing one and  fixing another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' In this scheme, the beamforming vector  and passive IRS phase shift matrix are solved by the  successive convex approximation algorithm, and the  active IRS phase shift matrix is computed by the FP  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  2) To reduce the high computational complexity of the  above scheme, a low-complexity maximum SNR-equal  amplitude reflecting (EAR) (Max-SNR-EAR) method is  proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' By utilizing the maximum signal-to-leakage-  noise ratio (SLNR) method, the beamforming vector is  2  obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Moreover, the hybrid IRS phase shift matrix is  computed based on the criteria of phase alignment and  EAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Simulation results show that the achievable rates  harvested by both the proposed methods are higher than  those of no IRS, random phase IRS, and passive IRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  In addition, the difference in achievable rates between  these two methods is trivial when the number of hybrid  IRS elements tends to large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  The remainder of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Section  II describes the system model of hybrid IRS-aided DM net-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The Max-SNR-FP scheme is presented in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Section IV describes the Max-SNR-EAR scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Numerical  simulation results are presented in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Finally, we draw  conclusions in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Notations: throughout this paper, boldface lower case and  upper case letters represent vectors and matrices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Signs (·)T , (·)∗, (·)H, Tr(·), ℜ{·}, and diag{·} denote the  transpose, conjugate, conjugate transpose, trace, real part,  and diagonal operations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The sign | · | is the  determinant of a matrix or the absolute value of a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The  symbol CN×N denotes the space of N × N complex-valued  matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The notation IN is the N × N identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' SYSTEM MODEL  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1, a hybrid IRS-aided DM system is  considered, where the base station (BS) is equipped with  N antennas, and the user (Bob) is equipped with single  antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The hybrid IRS is equipped with M elements, which  consists of Ma active and Mp passive IRS reflecting elements  (M = Ma + Mp, 1 ≤ Ma ≤ Mp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' It is assumed that the  active elements can tune both the phase and amplitude while  the passive ones can only shift the phase of the incident  signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The signals reflected more than once on the hybrid IRS  are negligible due to the severe path loss [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' All channels  are assumed to be line-of-sight channels since DM is only  applicable to line-of-sight channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' It is assumed that all the  channel state information is perfectly known through channel  estimation [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' System model of Hybrid-IRS-aided directional modulation network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Similar to the conventional passive IRS, it is assumed that  each elements of hybrid IRS can independently reflect the inci-  dent signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Let us denote the set of the Ma active elements by  Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Θ = diag{θ∗} = diag{θ1, · · · , θm, · · · , θM} ∈ CM×M,  Ψ = diag{ψ∗} ∈ CM×M, and Φ = diag{φ∗} ∈ CM×M are  the reflection coefficients of total elements, active elements,  and passive elements of hybrid IRS, respectively, where  θm =  �  |βm|ejµm,  if m ∈ Ω,  ejµm,  otherwise,  (1)  µm  ∈ [0, 2π) is the phase, and |βm| is the amplifying  coefficient and determined by the total power of the active  elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Let us define  Ψ = EMaΘ, Φ = EMpΘ,  (2)  where  EMa + EMp = IM, EMaEMp = 0M,  (3)  EMa is an M × M diagonal matrix whose non-zero elements  are all unity and have positions determined by Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  The transmitted signal at BS is  s =  √  Pvx,  (4)  where P denotes the transmit power, v ∈ CN×1 and x are the  beamforming vector and the information symbol, satisfying  vHv = 1 and E[∥x∥2] = 1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Taking the path loss into consideration, the received signal  at Bob is  yb = (√ρsrbhH  rbΘHsr + √ρsbhH  sb)s + √ρrbhH  rbΨnr + nb  =  √  P(√ρsrbhH  rbΨHsr + √ρsrbhH  rbΦHsr + √ρsbhH  sb)vx  + √ρrbhH  rbΨnr + nb,  (5)  where ρsrb = ρsrρrb is the equivalent path loss coefficient  of BS-to-IRS channel and IRS-to-Bob channel, ρsb and ρrb  are the path loss coefficient of BS-to-Bob channel and IRS-  to-Bob channel, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' nr ∼ CN(0, σ2  rIMa) and nb ∼  CN(0, σ2  b) denote the complex additive white Gaussian noise  (AWGN) at the Ma active elements of the hybrid IRS and  at Bob, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' hsb ∈ CN×1, hrb ∈ CM×1, and Hsr =  hsrhH  sr ∈ CM×N are the BS-to-Bob, IRS-to-Bob, and BS-to-  IRS channels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Let us define the channel htr =  h(θtr), the normalized steering vector h(θ) is  h(θ) =  1  √  N  [ej2πΨθ(1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' , ej2πΨθ(n), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' , ej2πΨθ(N)]T , (6)  and the phase function Ψθ(n) is given by  Ψθ(n)  ∆= −(n − (N + 1)/2)d cosθ  λ  , n = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' , N,  (7)  where θ represents the direction angle of arrival or departure,  n denotes the index of antenna, d is the spacing of adjacent  transmitting antennas, and λ represents the wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  In accordance with (5), the achievable rate at Bob can be  written as  Rb = log2 (1 + SNR) ,  (8)  where  SNR = P|(√ρsrbhH  rbΨHsr + √ρsrbhH  rbΦHsr + √ρsbhH  sb)v|2  σ2r|√ρrbhH  rbΨ|2 + σ2  b  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (9)  Hybrid IRS  Active  Passive  H  H  rb  ((())  H  5  sb  User  (Bob)  Base station3  The transmit power of the active elements at the hybrid IRS  is given by  Pr = Tr  �  Ψ  �  ρsrPHsrvvHHH  sr + σ2  rIM  �  ΨH�  ,  (10)  which satisfies Pr ≤ P max  r  , where P max  r  represents the maxi-  mum transmit power of Ma active elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  In this paper, we maximize the SNR by jointly optimizing  beamforming vector v, passive IRS phase shift matrix Φ, and  active IRS phase shift matrix Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The optimization problem  can be formulated as  max  v,Φ,Ψ  SNR  (11a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  vHv = 1, Pr ≤ P max  r  ,  (11b)  |Φ(m, m)| = 1, if m ̸∈ Ω,  (11c)  |Φ(m, m)| = 0, otherwise,  (11d)  |Ψ(m, m)| ≤ βmax, if m ∈ Ω,  (11e)  |Ψ(m, m)| = 0, otherwise,  (11f)  where βmax is the amplification budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' It is notes that this  optimization problem is a non-convex problem with a constant  modulus constraint, and it is challenging to solve it directly in  general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' In what follows, we propose the alternating optimiza-  tion algorithm to design the beamforming vector and hybrid  IRS phase shift matrix, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' PROPOSED MAX-SNR-FP SCHEME  In this section, we construct a Max-SNR-FP method to  jointly optimize the beamforming vector v, passive IRS phase  shift matrix Φ, and active IRS phase shift matrix Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' In what  follows, we will alternately solve for v, Φ, and Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Optimize v given Φ and Ψ  Firstly, we transform the power constraint in (11b) into a  convex constraint with respect to v as follows  Pr = vH �  ρsrPHH  srΨHΨHsr  �  v + Tr  �  σ2  rΨΨH�  ≤ P max  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (12)  Then, given Φ and Ψ, the optimal beamforming vector v can  be found by solving the following problem  max  v  vHA¯v  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' vHv = 1, (12),  (13)  where  A =(√ρsrbhH  rbΦHsr + √ρsrbhH  rbΨHsr + √ρsbhH  sb)H  (√ρsrbhH  rbΦHsr + √ρsrbhH  rbΨHsr + √ρsbhH  sb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (14)  It is clear that this problem is not convex, and in accordance  with the Taylor series expansion, we have  vHAv ≥ 2ℜ{¯vHAv} − ¯vHA¯v,  (15)  where ¯v is a given vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Then (13) can be recasted as  max  v  2ℜ{¯vHAv} − ¯vHA¯v  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' vHv = 1, (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (16)  It is a convex optimization problem and can be solved by  employing CVX tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Optimize Φ given v and Ψ  To simplify the SNR expression related to the phase shift  matrix Φ, we regard v and Ψ as two constants, and define  B = (√ρsrbhH  rbΨHsr + √ρsbhH  sb)v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (17)  Then, the subproblem to optimize Φ can be expressed as  max  Φ  |√ρsrbhH  rbΦHsrv + B|2  (18a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' |Φ(m, m)| = 1, if m ̸∈ Ω,  (18b)  |Φ(m, m)| = 0, otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (18c)  By defining  C = ρsrbdiag{hH  rb}HsrvvHHH  srdiag{hH  rb}H,  (19)  and based on the fact that diag{a}b = diag{b}a for a, b ∈  CM×1, the objective function in (18) can be recasted as  φHCφ + 2ℜ{√ρsrbφHdiag{hH  rb}HsrvB∗} + |B|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (20)  Based on the Taylor series expansion, we have  φHCφ ≥ 2ℜ{ ¯φHCφ} − ¯φHC ¯φ,  (21)  where ¯φ is a given vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' For the unit modulus constraint  (18b), it can be relaxed as  |Φ(m, m)| ≤ 1, if m ̸∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (22)  At this point, the problem (18) can be rewritten as  max  Φ  2ℜ{ ¯φHCφ} − ¯φHC ¯φ + |B|2 + 2ℜ{√ρsrbφH•  diag{hH  rb}HsrvB∗}  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (22), (18c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (23)  We can find that it is a convex optimization problem and can  be solved by employing CVX tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Optimize Ψ given v and Φ  To optimize Ψ, we regard v and Φ as two given constants,  and transform the power constraint in (11b) into a convex  constraint on ψ as follows  Pr = Tr  �  Ψ  �  ρsrPHsrvvHHH  sr + σ2IM  �  ΨH�  = ψT (ρsrPdiag{vHHH  sr}diag{Hsrv} + σ2  rIM)ψ∗  ≤ P max  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (24)  By neglecting the constant terms, the subproblem with respect  to Ψ is given by  max  Ψ  |(√ρsrbhH  rbΨHsr + √ρsrbhH  rbΦHsr + √ρsbhH  sb)v|2  σ2r|√ρrbhH  rbΨ|2 + σ2  b  (25a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (11e), (11f), (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (25b)  Let us define  D = (√ρsrbhH  rbΦHsr + √ρsbhH  sb)v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (26)  Then, the objective function in (25) can be converted to  ψHCψ + 2ℜ{ψH√ρsrbdiag{hH  rb}HsrvD∗} + |D|2  σ2rρrb|ψHdiag{hH  rb}|2 + σ2  b  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (27)  4  At this point, the optimization problem (25) becomes a nonlin-  ear fractional optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Based on the FP strategy  in [14], we introduce a parameter τ and transform the objective  function (27) as  ψHCψ + 2ℜ{ψH√ρsrbdiag{hH  rb}HsrvD∗} + |D|2  − τ(σ2  rρrb|ψHdiag{hH  rb}|2 + σ2  b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (28)  The  optimal  solution  can  be  achieved  if  and  only  if ψHCψ + 2ℜ{ψH√ρsrbdiag{hH  rb}HsrvD∗} + |D|2 −  τ(σ2  rρrb|ψHdiag{hH  rb}|2 + σ2  b) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' We linearize the ψHCψ  by employing Taylor series expansion at a given vector ¯ψ, the  subproblem with respect to Ψ can be rewritten as  max  Ψ,τ  2ℜ{ ¯ψHCψ} − ¯ψHC ¯ψ + 2ℜ{ψH√ρsrbdiag{hH  rb}•  HsrvD∗} + |D|2 − τ(σ2  rρrb|ψHdiag{hH  rb}|2 + σ2  b)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (11e), (11f), (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (29)  It should be noted that this problem is convex, which can be  effectively solved by the CVX tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The whole procedure of  the Max-SNR-FP algorithm is described in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Algorithm 1 Proposed Max-SNR-FP algorithm  1: Initialize v(0), Φ(0), and Ψ(0), compute R(0)  b  based on (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  2: Set p = 0, threshold value ǫ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  3: repeat  4:  Given Φ(p) and Ψ(p), solve (16) to determine v(p+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  5:  Given v(p+1) and Ψ(p), solve (23) to determine Φ(p+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  6:  Given v(p+1) and Φ(p+1), solve (29) to determine  Ψ(p+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  7:  Compute R(p+1)  b  using v(p+1), Φ(p+1), and Ψ(p+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  8:  p = p + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  9: until |R(p)  b  − R(p−1)  b  | ≤ ǫ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  The computational complexity of the proposed Max-SNR-  FP algorithm is O(L((M + 1)3 + 2MN 2 + 2M 2)In(1/ǫ) +  M 3+N 3+5M 2+2MN+2M+2MN 2) float-point operations  (FLOPs), where L is the numbers of alternating iterations, ǫ  denotes the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' PROPOSED MAX-SNR-EAR SCHEME  In the previous section, we proposed the Max-SNR-FP  method to design the beamforming v, IRS phase shift matrices  Φ and Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' However, it has a high computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  To reduce the computational complexity, a low-complexity  method named Max-SNR-EAR is proposed in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Optimize v given Φ and Ψ  Given IRS phase shift matrices Φ and Ψ, in accordance with  the principle of maximizing SLNR in [15], the beamforming  vector v can be optimized by solving the following problem  max  v  SLNR =  vHEv  vH(σ2  bIN)v  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' vHv = 1, (12),  (30)  where  E =ρsrbHH  srΦHhrbhH  rbΦHsr + ρsrbHH  srΨHhrbhH  rbΨHsr  + hsbhH  sb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (31)  According to the Taylor series expansion and neglecting the  constant terms, the problem (30) can be recasted as  max  v  2ℜ{¯vHEv} − ¯vHE¯v  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  vHv = 1, (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (32)  Note that it is a convex optimization problem and can be  solved with CVX tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Optimize Φ and Ψ given v  Given beamforming vector v, we consider to design the  phase of hybrid IRS firstly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The confidential message received  by Bob through the cascade path is expressed as  PρsrbhH  rbΘHsrvvHHH  srΘHhrb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (33)  To maximize the confidential message of the cascade path, the  phase alignment method is employed to design the hybrid IRS  phase �θ, �θ is given by  �θ = [e(−iarg(s1)), · · · , e(−iarg(sM))]T ,  (34)  where s = diag{hH  rb}Hsrv, and si is the i-th element of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Next, inspired by the amplitude design of fully active IRS  in [9], we assume that all active IRS elements have the same  amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Based on the IRS power constraint in (11b), we  have  |β| =  �  P max  r  /Q,  (35)  where  Q =Tr(�θH(ρsrPdiag{vHHH  srEMa}diag{vHHH  srEMa}H  + σ2EMaEMa)�θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (36)  Based on (34) and (35), we can obtain the passive IRS phase  shift matrix and active IRS phase shift matrix as follows  Φ = EMpdiag{�θ}, Ψ = |β|EMadiag{�θ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  (37)  Similar to Algorithm 1, we calculate v, Φ, and Ψ alternately  until convergence, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', |R(p)  b −R(p−1)  b  | ≤ ǫ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The computational  complexity of Max-SNR-EAR algorithm is O(K(2M 2+N 3+  2M 2 + 8N 2M + 2MN) FLOPs, where K is the numbers of  alternating iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' SIMULATION RESULTS AND DISCUSSIONS  In this section, simulation results are presented to evaluate  the performance of two proposed algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Simulation de-  fault parameters are chosen as follows: N = 8, M = 128,  Ma = 32, d = λ/2, θsr = π/4, θsb = π/3, dsr = 200m,  dsb = 220m, σ2  b = −70dBm, σ2  r = 2σ2  b, P = 25dBm,  P max  r  = 30dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The path loss at the distance d is modeled  as g(d) = PL0 − 10γlog10  d  d0 , where PL0 = −30dB is the  path loss reference distance d0 = 1m, and γ is the path loss  exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The path loss exponents of all channels are chosen  as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The positions of the IRS active elements are fixed to  Ω = {1, · · · , Ma}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  First, we make an investigation of the convergence be-  haviour of the proposed Max-SNR-FP and Max-SNR-EAR  algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2 shows the achievable rate versus the differ-  ent BS power, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', P = 20dBm, 25dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' It can be seen from  the figure that both of the proposed algorithms converge within  limited iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The proposed Max-SNR-EAR algorithm has  a faster convergence rate than the Max-SNR-FP algorithm,  regardless of P = 20dBm or 25dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  5  0  5  10  15  20  25  30  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='5  14  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='5  15  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='5  16  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='5  17  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Convergence of the proposed algorithms at different BS power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 3 depicts the curves of the achievable rate versus the  number of IRS phase shift elements, where Ma = M/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' We  compare two proposed algorithms to the benchmark schemes:  active IRS, passive IRS, no IRS, random phase IRS, and exist-  ing method in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The achievable rates of the proposed Max-  SNR-FP and Max-SNR-EAR algorithms gradually increase  as the number of IRS elements increases, and the former  is better than the latter and existing method in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' The  achievable rates of both the proposed algorithms are much  better than that of the passive IRS, no IRS and random phase  IRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Moreover, the difference in achievable rates between both  the proposed algorithms and active IRS gradually decreases  when the number of IRS elements tends to large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  3  4  5  6  7  8  11  12  13  14  15  16  17  18  19  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Achievable rate versus the numbers of IRS phase shift elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 4 plots the curves of the computational complexity  versus the number of IRS elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' It can be found that the  complexities of the proposed Max-SNR-FP method, proposed  Max-SNR-EAR method, and existing method in [11] are  similar at small-scale IRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' However, the complexities of the  existing method in [11] and proposed Max-SNR-FP method  are far higher than that of the proposed Max-SNR-EAR  method when the number of IRS elements tends to large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' CONCLUSION  In this paper, we have made an investigation of the hybrid  IRS-aided DM network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' To fully explore the advantages of  hybrid IRS and maximize the achievable rate, the Max-SNR-  FP and Max-SNR-EAR algorithms were proposed to jointly  design the beamforming vector, passive IRS phase shift matrix,  and active IRS phase shift matrix by alternately optimizing one  and fixing rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Simulation results showed that the achievable  2  3  4  5  6  7  0  2  4  6  8  10  12  14  107  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Computational complexity versus the numbers of IRS elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  rate of both proposed algorithms increases as the number of  IRS elements increases, and is much better than those of  the cases of random phase IRS, no IRS, and passive IRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Moreover, the proposed Max-SNR-FP method outperforms the  existing method in terms of the achievable rate and has lower  complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  REFERENCES  [1] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Cheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Fusco, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wnag, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Zhu, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Gu, “Physical-  layer security for frequency diverse array-based directional modulation  in fluctuating two-ray fading channels,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 4190–4204, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Daly and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Bemhard, “Directional modulation technique for  phased arrays,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Antennas Propag, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 57, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2633–  2640, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [3] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Shu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Chen, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Vucetic, “Robust synthesis scheme  for secure multi-beam directional modulation in broadcasting systems,”  IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 6614–6623, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Pan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Pan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Zhu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, “UAV-assisted and intel-  ligent reflecting surfaces-supported terahertz communication,” Wireless  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1256–1260, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [5] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wu and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Zhang, “Intelligent reflecting surface enhanced wireless  network via joint active and passive beamforming,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 5394–5409, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Pan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Ren, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Xu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Elkashlan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Nallanathan, and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Hanzo, “Multicell MIMO communications relaying on intelligent  reflecting surfaces,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  5218–5233, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [7] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Shu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Teng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Huang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang,  “Enhanced secrecy rate maximization for directional modulation net-  works via IRS,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 8388–8401,  Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Dong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Jiang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Hua, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Teng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Shu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, “Low-  complexity joint phase adjustment and receive beamforming for di-  rectional modulation networks via IRS,” IEEE open journal of the  Communications Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1234–1243, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [9] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Dai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Yang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Schober, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Poor,  “Active RIS vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' passive RIS: which will previal in 6G?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' arXiv preprint  arXiv: 2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='15154, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [10] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Dai, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Xu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Yang, “Active reconfigurable  intelligent surface: Fully-connected or sub-connected?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 167–171, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Nguyen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Nguyen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' T¨olli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Chatzinotas, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Juntti, “Hybrid active-passive reconfigurable intelligent surface-  assisted multi-user MISO systems,” 2022 IEEE 23rd International  Workshop on Signal Processing Advances in Wireless Communication  (SPAWC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1–5, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Nguyen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Vu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Lee, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Juntti, “Hybrid relay-reflecting  intelligent surface-assisted wireless communications,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Veh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Liu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Cui, “Channel estimation for intelligent reflect-  ing surface assisted multiuser communications: Framework, algorithms,  and analysis,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 6607–  6620, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  [14] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Dinkelbach, “On nonlinear fractional programming,” Manage Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 492–498, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  6  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Sadek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Tarighat, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Sayed, “A leakage-based precoding  scheme for downlink multi-user MIMO channels,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 1711–1721, May.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE0T4oBgHgl3EQf_wKi/content/2301.02831v1.pdf'}
diff --git a/1tFLT4oBgHgl3EQfqC-n/content/tmp_files/2301.12138v1.pdf.txt b/1tFLT4oBgHgl3EQfqC-n/content/tmp_files/2301.12138v1.pdf.txt
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@@ -0,0 +1,2874 @@
+Mapping a topology-disorder phase diagram with a quantum simulator 
+Xue-Gang Li1†, Hui-Kai Xu1‡, Jun-Hua Wang1§, Ling-Zhi Tang2, Dan-Wei Zhang2*, 
+Chu-Hong Yang1, Tang Su1, Chen-Lu Wang1, Zhen-Yu Mi1, Wei-Jie Sun1, Xue-Hui 
+Liang1, Mo Chen1, Cheng-Yao Li1, Ying-Shan Zhang1, Ke-Huan Linghu1, Jia-Xiu 
+Han1, Wei-Yang Liu1, Yu-Long Feng1, Pei Liu3, Guang-Ming Xue1, Jing-Ning 
+Zhang1*, Yi-Rong Jin1*, Shi-Liang Zhu2, Hai-Feng Yu1, Qi-Kun Xue1,3 
+1Beijing Academy of Quantum Information Sciences; Beijing 100193, China  
+2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum 
+Materials, School of Physics and Telecommunication Engineering, South China 
+Normal University; Guangzhou 510006, China  
+3State Key Laboratory of Low Dimensional Quantum Physics and Department of 
+Physics, Tsinghua University, Beijing 100084, China 
+ 
+†, ‡, §These authors contributed equally to this work 
+*Corresponding author. Email: danweizhang@m.scnu.edu.cn (D.W.Z); 
+zhangjn@baqis.ac.cn (J.N.Z.); jinyr@baqis.ac.cn (Y.R.J.). 
+The competition and interplay of topology and disorder has been one of the most 
+famous topics in the field of condensed matter physics. In addition to the 
+intuitive tendency to bring the system into a topologically trivial and localized 
+phase1, it has been discovered that disorder can also induce nontrivial topology2,3 
+and transport4,5. To reveal rich and diverse phase structures, mapping phase 
+diagrams plays an important role in both theoretical and experimental sides. 
+Quantum simulation6,7 provides a prospective way to study the target model, 
+explore the phase diagram and reveal the underlying mechanism. Thanks to the 
+unprecedented controllability, superconducting quantum simulators have been 
+introduced to investigate complex many-body physics8,9 and bring thought 
+experiments into reality10. To our best knowledge, the effort to map a phase 
+diagram with a rich structure is still lacking. Here we report a systematic 
+experimental study of the topology-disorder phase diagram with 32 qubits on a 
+
+programmable analog quantum simulator. We implement one-dimensional (1D) 
+disordered dimerized tight-binding models over a wide parameter range and 
+observe diverse phases, including the topological Anderson insulator (TAI) and 
+the inverse Anderson localization (IAL). Our experiment manifests the 
+efficiency, accuracy and flexibility of the superconducting-circuit device and 
+paves the way to the demonstration and understanding of many-body 
+phenomena with noisy intermediate-scale quantum simulators. 
+Topology and disorder both lie in the heart of condensed matter physics, due to their 
+intrinsic relation with symmetry and ubiquitous existence in nature. Exploring exotic 
+topological phases has attracted intense interest in both theoretical and experimental 
+aspects since the discovery of the quantum Hall effect11. As is well known, topology 
+is protected by generic symmetries, and thus is robust against disorder. However, 
+strong disorders eventually destroy topology due to Anderson localization1. This 
+intuitive picture has been broken by the discovery of the TAI2,3, which originates from 
+the investigation of HgTe/CdTe quantum wells12 and is then generalized to various 
+disordered systems13-18. Besides the disorder-induced topology, the disorder also 
+imposes a dramatic influence on transport. In contrast to the intuition that disorder 
+leads to localization, the inverse Anderson localization (IAL), induced by adding 
+disorders to a flat-band system, has also been predicted in 3D diamond lattices4 and 
+2D photonic cages5. It has been recently proposed19 that a dimerized tight-binding 
+chain with off-diagonal quasiperiodic disorder hosts multiple topologies and disorder-
+related phenomena, including the TAI and the Anderson transition. Moreover, this 
+model exhibits the IAL in the fully dimerized limit and thus provides a theoretically 
+fundamental and experimentally feasible testbed for the investigation of the interplay 
+between topology and disorder. 
+Due to the lack of continuous and precise control of system parameters, it is 
+challenging to observe rich phase diagrams caused by topology and disorder 
+competition in real materials. Quantum simulation6 provides an ideal platform to 
+explore topology and localization physics. For instance, the TAI with bulk dynamics 
+
+was observed with ultracold atoms20 and photonic crystals21,22. However, to our best 
+knowledge, a systematic experimental study of the topology-disorder phase diagram 
+with a quantum simulator is still lacking, which puts forward requirements on high 
+levels of flexibility and efficiency. The superconducting quantum simulator, as an 
+artificial quantum system, features excellent scalability and versatility and has been 
+vastly exploited to simulate quantum dynamics, ranging from strongly-correlated 
+quantum walks8 to many-body localization9 and even quantum supremacy23,24. In this 
+work, we experimentally map out the topology-disorder phase diagram of a dimerized 
+tight-binding chain with off-diagonal quasi-periodic disorder, using a 32-qubit chain 
+selected out of 62 functional qubits in a superconducting quantum simulator. With 
+precise parameterized calibration, we efficiently implement hundreds of target 
+Hamiltonians over a wide range in the parameter plane and observe various phases 
+with different topological and localization properties, including the TAI and the IAL. 
+ 
+Programmable quantum simulator 
+The device used in this experiment is shown in Fig. 1.  Benefiting from the flip-chip 
+and air bridge techniques, the flux crosstalk is greatly suppressed. In our device, the 
+crosstalk is lower than 0.2% for all nearest-neighbor qubit-qubit pairs and qubit-
+coupler pairs, and thus can be negligible. However, in such a compact layout, 
+unwanted couplings between spatially close qubits are still visible25,26, which blurs the 
+boundary between extended and localized phases in off-diagonally disordered models. 
+We adopt a novel qubit design, named flipmon27, to overcome this problem. The 
+average value of the residual XY coupling strengths between diagonal qubit pairs is 
+measured to be about 2π × 30 kHz28, corresponding to a swapping period of about 
+16.67 μs, much larger than the characteristic time (1.5 μs ) in this experiment. In this 
+device, the decoherence times ������������1 and ������������2
+∗ at the maximum frequency, averaged over 
+all 62 functional qubits, are measured to be about 14.9 μs and 6.7 μs, respectively.  
+To accurately engineer the target Hamiltonians as many as possible in our experiment, 
+we perform an efficient calibration procedure. We first align the frequencies of 32 
+
+activated qubits, then parametrize the coupling strength of each nearest-neighbor 
+qubit pair, and finally, compensate for the coupler-induced dispersive shifts of 
+qubits28. After calibration, we can simulate the dynamic evolution of 18 Hamiltonians 
+per hour. Meanwhile, the average classical fidelity of different Hamiltonians under 
+different evolution times is 91%, which is comparable to the previous results8.  
+ 
+Fig. 1. Programmable analog quantum simulator. a, Photograph of the 
+superconducting quantum device. b, Photographs of the chip and the carrier of a five-
+qubit unit. The chip contains elements with high-quality factors, including flipmon 
+qubits in orange, readout resonators in blue, and couplers in green, while the carrier 
+contains elements with low-quality factors, including control lines in grey and Purcell 
+filters in red, which are covered by air bridges. The flipmon consists of two capacitive 
+electrodes, with one on the chip and the other on the carrier. c, Qubit layout. The 
+device contains 62 functional qubits and 105 couplers, among which 32 qubits and 
+couplers are activated to form a quantum simulator.   
+ 
+Generalized Su-Schrieffer-Heeger model 
+To investigate the interplay between topology and disorder, we use this simulator to 
+realize the generalized Su-Schrieffer-Heeger (gSSH) model29. The model describes 
+
+a
+C
+Chip
+Carrier
+4mm
+Qubit:
+Active
+Inactive
+Broken
+Coupler:
+b
+Active
+Inactive
+Chip
+Bouple
+0.5mm
+Qubit
+Indiumpoint
+Carrier
+0.5mm
+Airbridge
+XYZline
+Purcell filterspin-less fermions moving in disordered dimerized chains, as shown in Fig. 2a. The 
+target Hamiltonian reads, 
+�������������gSSH/ℏ = � ������������������������
+′
+������������c
+������������=1
+�������������������������,������������
+† �������������������������,������������ + ������������ � �������������������������,������������
+† �������������������������+1,������������
+������������c−1
+������������=1
++ ℎ. ������������. ,
+(1) 
+where �������������������������,������������(α ∈ A, B) is the fermionic annihilation operator for the α-site in the ������������������������ℎ 
+unit cell with ������������������������ being the number of cells. We adopt the configuration that the 
+inter-cell tunneling strength ������������ is homogeneous, while the intra-cell tunneling strength 
+������������′ is modulated by quasi-periodic disorders, 
+������������������������
+′ = ������������′ + ������������ cos(2������������������������������������ + ������������) ,
+(2) 
+with W quantifying the disorder strength and δ being an arbitrary phase. Here ������������ is 
+an irrational number and is chosen to be �√5 − 1�/2. The topological and localized 
+properties of this 1D disordered chiral system19,28 are characterized by the real-space 
+winding number and the spectral-averaged inverse participation ratio, denoted by ν 
+and aIPR, respectively. Note that while δ has no physical meaning in the 
+thermodynamic limit, it generates different disorder realizations for the cases with 
+finite-size systems, which are averaged to recover the thermodynamic results. 
+The competition between topology and disorder gives rise to a rich phase diagram28, 
+with four phases of different values of ������������ and aIPR, as shown in Fig. 2b. In the clean 
+limit (������������ = 0), the topological and trivial phases, both extended, are separated by a 
+critical point at ������������′/������������ = 1, and these two phases extend to the weak disorder regime. 
+As the disorder becomes stronger, the nontrivial topology breaks down and the bulk 
+states become localized. Theoretically, it has been predicted that the critical disorder 
+strength to induce a localization transition is well below that to break a nontrivial 
+topology2. As a result, there exists a topological localized phase, or the TAI, between 
+the topological extended and the trivial localized phase. Strikingly, the topological 
+localized phase extends to the regime where the system is topologically trivial in the 
+clean limit. This can be understood by the disorder-induced renormalization of the 
+model parameter in the critical regime3. More importantly, this model also exhibits 
+
+the IAL in the fully dimerized limit with ������������′ = 0, where the transport is solely due to 
+disorder and has not been observed hitherto. 
+ 
+ 
+Fig. 2. Generalized Su-Schriffer-Heeger (gSSH) model and typical dynamics in 
+various phases. a, Schematic illustration of the gSSH model. The inter-cell tunneling 
+(red dashed lines) is homogeneous, while the intra-cell tunneling (gray solid lines) is 
+modulated with quasi-periodic disorders (gray explosive shapes). b, Numerical phase 
+diagram. The parameter plane is presented by the average normalized intra-cell 
+coupling strength ������������′/������������ and the normalized disorder strength ������������/������������. This model 
+supports the topological extended (topo. ext.) phase, the trivial extended (triv. ext.) 
+phase, the topological localized (topo. loc.) phase and the trivial localized (triv. loc.) 
+phase. The TAI manifests itself in the topological localized phase. On the horizontal 
+axis with ������������′ = 0, the origin point features the flat-band localization (FBL), while the 
+IAL emerges in the topological extended region with ������������/������������ ∈ (0,2). c, Typical density 
+evolution of single-excitation quantum walks as the function of the evolution time ������������ 
+and qubit site index ranging from 1 to 32. Each row contains two quantum walks, 
+initially excited at the edge (site 1) and in the bulk of the chain (site 15), and 
+corresponding to a parameter point (yellow star) in b, respectively. 
+ 
+Dynamical extraction 
+We begin with mapping the fermionic system to a spin system by the Jordan-Wigner 
+transformation and then engineer the native Hamiltonian of the 32-qubit quantum 
+simulator. The frequencies of the active qubits are biased to the reference point 
+
+Population
+a
+c
+A
+A
+A
+0.0
+1.0
+1.2
+n
+B
+B
+C
+B
+n-1
+n
+n+1
+0.0
+b
+1.2
+2
+(sr)
+0.0
+七
+1.2
+TAI
+0.0
+IAL
+0
+1.2
+0
+2
+3
+WIJ
+FBL
+Topo.ext.
+Triv.ext.
+0.0
+1
+15
+32
+15
+32
+Topo.loc.
+Triv. loc.
+Site index������������ref = 2π × 5.495 GHz, and the nearest-neighbor couplings are tuned to ������������ and ������������������������
+′  
+according to Eq. (2). We fix the inter-cell tunneling strength to be ������������ = 2π × 1.5 
+MHz and let the ratio ������������′/������������ (������������/������������) vary in the range [0,2] ([0,4]). This parameter 
+range covers various phases in Fig. 2b. For each Hamiltonian, we prepare two initial 
+states, with the single-excitation at the edge and in the bulk. The experimental data of 
+density evolution, obtained from projective measurement after turning on the target 
+Hamiltonian and evolving the system for a time period ������������, intuitively reflect the 
+topological and localization properties, as shown in Fig. 2c. From top to bottom, the 
+four representative systems, with model parameters marked by yellow stars in Fig. 2b, 
+are chosen from the trivial extended, the topological extended, the trivial localized 
+and the topological localized phases, respectively. The difference between extended 
+and localized phases is intuitively demonstrated in the time evolution of bulk 
+excitations. As to the topological characteristics, the edge excitations for topological 
+phases remain at the edge throughout the evolution no matter whether the bulk states 
+are extended or localized. Moreover, the edge excitation in topological phases mainly 
+couples to nearby sites in the same sublattice.  
+Having shown the typical behavior of each phase, we then quantitatively extract the 
+topological and localized properties, i.e. ������������ and aIPR, with the quantum simulator. 
+For each quantum-walk experiment, we calculate the time-averaged expectation 
+values of the chiral displacement operator and the survival probability, denoted as �������������������������  
+and �������������������������,  
+������������������������� = 1
+������������ � �������������(������������′)����������������������������������������(������������′)�������������������������′
+������������
+0
+,
+(3) 
+������������������������� = 1
+������������ � |⟨������������, ������������|������������(������������′)⟩|2������������������������′
+������������
+0
+,
+(4) 
+where the chiral ������������� and the position ������������� operators are defined by �������������|������������, ������������⟩ = ������������������������ |������������, ������������⟩ 
+with ������������������������/������������ = ±1 and �������������|������������, ������������⟩ = ������������|������������, ������������⟩, respectively. Here |������������, ������������⟩ is the initial state 
+
+which prepares a single excitation on the α-site in the ������������������������ℎ unit cell and |������������(������������)⟩ =
+exp�−�������������������������gSSH������������/ℏ�|������������, ������������⟩.  
+To diminish the impact of the finite-size effect, we construct 8 disordered realizations 
+and 4 initial single-excitation states for a target model. Fig. 3a (3b) show the 
+dynamics of �������������������������  (�������������������������) for these 32 quantum-walk instances for a gSSH model in the 
+trivial localized phase with (������������/������������, ������������/������������′) = (3,1.25), where the instance-averaged 
+⟨������������̅������������⟩ (⟨������������̅������������⟩) is also shown by green squares. Although the evolutions of �������������������������  and ������������������������� 
+depend on the specific disorder realization and initial state, ⟨������������̅������������⟩ and ⟨������������̅������������⟩, after 
+taking average over the 32 quantum-walk instances, converge to the real-space 
+winding number and the spectral-averaged IPR28, respectively. 
+We then implement the gSSH model in other three phases and show the results in 
+Figs. 3c and 3d. We observe that the topological indices ⟨������������̅������������⟩ almost converge to 
+their corresponding values in the long-time limit, saying ν = 1(0) for topological 
+(trivial) phases, while the circumstance is more complicated for the extraction of the 
+localized property. Theoretically, ⟨������������̅������������⟩ should vanish in the long-time limit for 
+infinite systems in the extended phases. In our experiment, however, it remains finite 
+due to the small size of our simulator. We observe that ⟨������������̅������������⟩ quickly becomes flat for 
+localized phases (orange and green dots in Fig. 3d), while it keeps decreasing during 
+the evolution for extended phases (red and blue dots in Fig. 3d). Besides, the values of 
+⟨������������̅������������⟩ at the longest evolution time ������������ = 1.5 μs separate enough to discriminate the 
+extended and localized phases. 
+
+ 
+Fig. 3. Dynamical extraction of topological and localization properties. a, Time-
+averaged chiral displacement ������������������������� . b, Time-averaged survival probability ������������������������� . Each 
+dashed line is �������������������������  a or ������������������������� b for a single quantum-walk instance, while these instances 
+are generated by setting ������������ ∈ [0, … ,7] × 2π/8 and placing the initial excitation at 
+sites 15, 16, 17 and 18. The data points are obtained by averaging over different 
+quantum-walk instances. c, Averaged chiral displacement and d, survival probability 
+for different phases. In c and d, the solid lines are numerical results without fitting 
+parameters30. For all experimental results (markers), the error bars are the standard 
+deviation of the mean propagated from the sampling error in the projective 
+measurement with 1024 repetition times. Solid lines are obtained by ideal numerical 
+simulation. 
+ 
+Experimental phase diagram 
+With the above method of distinguishing topology and localization or not, we take 
+advantage of the programmable and efficient superconducting quantum simulator to 
+obtain the phase diagram. We sweep the model parameters over a wide range in the 
+topology-disorder plane and summarize our experimental results in Fig. 4. Here we 
+
+a
+b
+(WU.JJ)= (3, 1.25)
+(WU, /U) = (3, 1.25)
+2
+0.6
+0
+0.4
+0.3
+0.2
+0.0
+0.5
+1.0
+1.5
+0.0
+0.5
+1.0
+1.5
+t (μs)
+t (μs)
+{(0.5, 2)
+F (3,1.25)
+(WU,J'I) =
+( (1,0.5)
+(0.1,0.6)
+c
+1.0
+0.5
+0.0
+0.5
+S
+0.2
+0.1
+0
+0.2
+0.5
+1
+1.5 2
+3
+4.5
+t (μs)define the values at ������������ = 1.5 ������������s as the experimental results for 〈������������̅∞〉 and 〈������������̅∞〉, which 
+serve as the experimental indices for the topological and localization properties. 
+Guided by the theoretical phase diagram in Fig. 2b, we choose 114 points unevenly 
+distributed in the ������������-������������′ parameter space, and experimentally obtain the real-space 
+winding number and the spectral-averaged IPR in the long-time limit, i.e. 〈������������̅∞〉 and 
+〈������������̅∞〉, as shown in Figs. 4a and 4c. The experimental data for 〈������������̅∞〉 (〈������������̅∞〉) show clear 
+edges between topological and trivial (extended and localized) phases in Fig. 4a and 
+4c, which are consistent with the theoretically-obtained phase boundaries in Fig. 2b. 
+For better comparison, we also put corresponding numerical results, obtained from 
+numerically evolving the Schrödinger equation without free fitting parameters, in 
+Figs. 4b and 4d. Two representative cross-sections of the parameter space are shown 
+in Figs. 4E and 4F, with ������������′/J = 1.25 and 0, respectively. Fig. 4e shows nontrivial 
+topology emerges from trivial states in the clean limit as the disorder strength 
+increases, indicated by the sudden rise of 〈������������̅∞〉 to near unity in the regime ������������/������������ ∈
+(1.25, 2). Together with 〈������������̅∞〉, which shows the system becomes increasingly 
+localized, it provides convincing evidence of the TAI. In Fig. 4f, we observe the 
+crossover from the FBL at ������������ = 0 to the topological extended phase lying on the 
+fully dimerized limit with ������������′ = 0. The formation of this phase is attributed to the IAL. 
+As the disorder strength further increases, both the TAI and the IAL give up to the 
+trivial localized phase. As 〈������������̅∞〉 and 〈������������̅∞〉 gradually change when the target model 
+goes across phase boundaries, we claim that these are the manifestation of phase 
+transitions in the finite-time evolution of a finite-size system. 
+
+ 
+Fig. 4. Experimental results for the topology-disorder phase diagram. a, 
+Averaged chiral displacement ⟨������������̅∞⟩ in the long-time limit. b, Numerical results for  
+⟨������������̅∞⟩. c, Averaged survival probability ⟨������������̅∞⟩ in the long-time limit. d, Numerical 
+results for ⟨������������̅∞⟩. Each plaquette in a and c represents a data point on the parameter 
+plane. Numerical phase boundaries adopted from Fig. 2b are also shown, where the 
+black dashed line separates topological and trivial phases, the white dashed-dotted 
+line separates the extended and localized phases, and the pink solid line on the 
+horizontal axis marks the trivial extended phase due to the IAL. Numerical results in 
+b and d are obtained by evolving the Schrödinger equation with the target 
+Hamiltonian for a duration of 1.5 μs. e, Disorder-induced topology. f, Disorder-
+induced transport. The shaded areas mark the parameter ranges for the topological 
+localized e and extended f phases, respectively. The lines are numerical simulation 
+data, and the data points are experimental data with the error bars obtained in the 
+same way as Fig. 3. 
+ 
+Outlook 
+With the inherent 2D geometry of the qubit lattice and strongly interacting multi-
+excitations, it is anticipated that our quantum simulator can be straightforwardly 
+
+a
+b
+2
+1.0
+0.5
+0.0
+0
+C
+2
+0.3
+0.2
+0.1
+0
+0
+1
+2
+3
+4
+0
+1
+2
+3
+4
+WIJ
+WIJ
+e
+1.0
+.4
+0.3
+sim
+0.5
+0.2
+exp
+IS
+0.0
+0.1
+f
+JJ=0
+0.5
+1.0
+sim
+0.4
+exp.
+00
+0.5
+0.3
+C
+IS
+0.2
+0.0
+0
+1
+2
+3
+4
+WJextended to realize quantum many-body models in quasi-1D or 2D systems with 
+computationally hard features. This work significantly improves the near-term 
+prospects of superconducting quantum simulators to explore exotic phases or quantum 
+dynamics elusive in condensed matter systems, such as 2D many-body localization31 
+and fractional topological states of photons32. 
+ 
+Note added  
+Recently, we noticed another work on the experimental observation of inverse 
+Anderson transition in ultra-cold atoms33. 
+ 
+References and Notes 
+1. Anderson, P. W. Absence of Diffusion in Certain Random Lattices. Phys. 
+Rev. 109, 1492-1505 (1958). 
+2. Li, J., Chu, R.-L., Jain, J. K. & Shen, S.-Q. Topological Anderson Insulator. 
+Phys. Rev. Lett. 102, 136806 (2009). 
+3. Groth, C. W. et al. Theory of the Topological Anderson Insulator. Phys. Rev. 
+Lett. 103, 196805 (2009). 
+4. Goda, M., Nishino, S. & Matsuda, H. Inverse Anderson Transition Caused by 
+Flatbands. Phys. Rev. Lett. 96, 126401 (2006). 
+5. Longhi, S. Inverse Anderson transition in photonic cages. Opt. Lett. 46, 2872-
+2875 (2021). 
+6. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 
+467-488 (1982). 
+7. Türeci, H. E., Houck, A. A. & Koch, J. On-chip quantum simulation with 
+superconducting circuits, Nat. Phys. 8, 292-299 (2012). 
+8. Yan, Z. et al. Strongly correlated quantum walks with a 12-qubit 
+superconducting processor. Science 364, 753-756 (2019). 
+9. Guo, Q. et al. Observation of energy-resolved many-body localization. Nat. 
+Phys. 17, 234-239 (2021). 
+10. Jafferis, D. et al. Traversable wormhole dynamics on a quantum processor. 
+Nature 612, 51–55 (2022). 
+11. Prange, R. E. & Girvin, S. M., Ed., The quantum Hall effect (Springer, 1990). 
+12. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and 
+topological phase transition in HgTe quantum wells. Science 314, 1757-1761 
+(2006). 
+13. Guo, H. M., Rosenberg, G., Refael, G. & Franz, M. Topological Anderson 
+Insulator in Three Dimensions. Phys. Rev. Lett. 105, 216601 (2010). 
+
+14. Mondragon-Shem, I., Hughes, T. L., Song, J. & Prodan, E. Topological 
+Criticality in the Chiral-Symmetric AIII Class at Strong Disorder. Phys. Rev. 
+Lett. 113, 046802 (2014). 
+15. Altland, A. et al. Quantum Criticality of Quasi-One-Dimensional Topological 
+Anderson Insulators. Phys. Rev. Lett. 112, 206602 (2014). 
+16. Titum, P., Lindner, N. H., Rechtsman, M. C. & Refael, G. Disorder-Induced 
+Floquet Topological Insulators. Phys. Rev. Lett. 114, 056801 (2015). 
+17. Zhang, D.-W. et al. Non-Hermitian topological Anderson insulators. Sci. 
+China-Phys. Mech. Astron. 63, 267062 (2020). 
+18. Lin, Q. et al. Observation of non-Hermitian topological Anderson insulator in 
+quantum dynamics. Nat. Commun. 13, 3229 (2022). 
+19. Tang, L.-Z., Liu, S.-N., Zhang, G.-Q. & Zhang, D.-W. Topological Anderson 
+insulators with different bulk states in quasiperiodic chains. Phys. Rev. A 105, 
+063327 (2022). 
+20. Meier, E. J. et al. Observation of the topological Anderson insulator in 
+disordered atomic wires. Science 362, 929-933 (2018). 
+21. Stützer, S. et al. Photonic topological Anderson insulators. Nature 560, 461-
+465 (2018). 
+22. Liu, G.-G. et al. Topological Anderson Insulator in Disordered Photonic 
+Crystals. Phys. Rev. Lett. 125, 133603 (2020). 
+23. Arute, F. et al. Quantum supremacy using a programmable superconducting 
+processor. Nature 574, 505-510 (2019). 
+24. Wu, Y. et al. Strong Quantum Computational Advantage Using a 
+Superconducting Quantum Processor. Phys. Rev. Lett. 127, 180501 (2021). 
+25. Chen, Z. et al. Exponential suppression of bit or phase errors with cyclic error 
+correction. Nature 595, 383-387 (2021). 
+26. Zhang, P. et al. Many-body Hilbert space scarring on a superconducting 
+processor. Nat. Phys. (2022). 
+27. Li, X. et al. Vacuum-gap transmon qubits realized using flip-chip technology. 
+Appl. Phys. Lett. 119, 184003 (2021). 
+28. See Supplementary Materials. 
+29. Su, W. P., Schrieffer & J. R., Heeger, A. J., Solitons in Polyacetylene, Phys. 
+Rev. Lett. 42, 1698 (1979). 
+30. Johansson, J. R., Nation, P. D. & Nori, F., QuTiP: An open-source Python 
+framework for the dynamics of open quantum systems, Comput. Phys. 
+Commun. 183, 1760 (2012). 
+31. Choi, J. yoon et al. Exploring the many-body localization transition in two 
+dimensions, Science 352, 1547 (2016). 
+
+32. Roushan, P. et al. Chiral ground-state currents of interacting photons in a 
+synthetic magnetic field, Nat. Phys. 13, 146-151 (2016). 
+33. Li, H. et al. Aharonov-Bohm Caging and Inverse Anderson transition in 
+Ultracold Atoms, Phys. Rev. Lett. 129, 220403 (2022). 
+ 
+Acknowledgments 
+We acknowledge support from the National Natural Science Foundation of China 
+(grant nos. 11890704, 12174126, 12104055, 12104056 and 12004042), Natural 
+Science Foundation of Beijing (grant no. Z190012), Guangdong Basic and 
+Applied Basic Research Foundation (grant no. 2021A1515010315) and Key Area 
+Research and Development Program of Guangdong Province (grant no. 
+2018B030326001). 
+ 
+Author contributions 
+D.W.Z, J.N.Z, Y.R.J, and H.F.Y conceived the experiments. X.G.L, H.K.X, J.H.W 
+carried out the measurement. X.G.L, C.H.Y, T.S, C.L.W, Z.Y.M, W.J.S, X.H.L, M.C, 
+C.Y.L and G.M.X designed and made the sample. Y.L.F, P.L and H.K.X wrote the 
+measurement software. J.H.W, W.Y.L, K.H.L and Y.R.J built the measurement setup. 
+L.Z.T, D.W.Z and J.N.Z performed the analytic calculations. J.N.Z, D.W.Z, Y.S.Z, 
+J.X.H, X.G.L and H.F.Y wrote the manuscript in consultation with S.L.Z and Q.K.X. 
+All authors discussed the results and contributed to the writing of the manuscript. 
+ 
+Competing interests 
+Authors declare that they have no competing interests. 
+ 
+Data and materials availability 
+All data are available in the main text or the supplementary materials.  
+ 
+Supplementary Materials 
+Materials and Methods 
+Supplementary Text 
+Figs. S1 to S20 
+References 
+ 
+
+1 
+ 
+Supplementary Materials for 
+ 
+Realization of the topological Anderson insulator in a superconducting quantum 
+simulator 
+Xue-Gang Li1†, Hui-Kai Xu1‡, Jun-Hua Wang1§, Ling-Zhi Tang2, Dan-Wei Zhang2*, Chu-Hong Yang1, 
+Tang Su1, Chen-Lu Wang1, Zhen-Yu Mi1, Wei-Jie Sun1, Xue-Hui Liang1, Mo Chen1, Cheng-Yao Li1, 
+Ying-Shan Zhang1, Ke-Huan Linghu1, Jia-Xiu Han1, Wei-Yang Liu1, Yu-Long Feng1, Pei Liu3, Guang-
+Ming Xue1, Jing-Ning Zhang1*, Yi-Rong Jin1*, Shi-Liang Zhu2, Hai-Feng Yu1, Qi-Kun Xue1,3 
+1Beijing Academy of Quantum Information Sciences; Beijing 100193, China  
+2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of 
+Physics and Telecommunication Engineering, South China Normal University; Guangzhou 510006, 
+China  
+3State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua 
+University, Beijing 100084, China 
+ 
+†, ‡, §These authors contributed equally to this work 
+*Corresponding author. Email: danweizhang@m.scnu.edu.cn (D.W.Z); zhangjn@baqis.ac.cn 
+(J.N.Z.); jinyr@baqis.ac.cn (Y.R.J.). 
+ 
+ 
+This PDF file includes: 
+ 
+Materials and Methods 
+Supplementary Text 
+Figs. S1 to S20 
+ 
+ 
+
+2 
+ 
+Materials and Methods 
+ 
+1 Device and measurement setup  
+ 
+1.1 Design 
+The device consists of 63 tunable qubits and 105 tunable couplers. The qubits are arranged in a 
+2-dimensional square lattice with a coupler between each of the two nearest qubit pairs. A 
+schematic of the circuit of a unit cell is shown in Fig. S1(a). The qubits adopt "flipmon" design, 
+which is considered for advantages including improved vacuum energy participation ratio, 
+reduced unwanted crosstalk, more freedom of circuit wiring, and natural compatibility with flip-
+chip technology. For more details, please refer to (32). 
+Each qubit includes an asymmetric SQUID, with a control line grounded nearby for tuning its 
+frequency with persistent bias or fast DC pulse. The control line also acts as a microwave drive 
+line utilizing its weak capacitive coupling to the qubit. A meandered quarter-wave coplanar 
+waveguide (CPW) resonator is dispersively coupled to each qubit for readout, and up to six 
+resonators share a common bandpass filter for suppression of the Purcell effect. We put the 
+resonator frequencies far under the qubit’s idle frequencies, in the range of 4.1 - 4.6 GHz, with 
+a separation of ≈ 50 MHz between each other. Qubits can be tuned down to a frequency near 
+their readout resonators to realize a fast reset. As the readout resonators have a high decay rate 
+(������������ ∼ 2 MHz), the qubit states can quickly decay to the ground state within 200 ns due to the 
+Purcell effect. The tunable coupler is a grounded qubit between two neighboring qubits. The 
+tunable couplers have much higher frequencies (about 8 GHz) at their optimal points. By 
+choosing appropriate qubits and coupler frequencies, the effective coupling strength between 
+adjacent qubits can be continuously tuned from positive to negative (33), thus can be turned off. 
+Fig. S1(b) shows a photograph of another device with the same design. It contains a top chip, 
+where all elements with high-quality factors, including qubits, couplers, and readout resonators, 
+are allocated, and a carrier chip, with other elements, including the bandpass Purcell filters and 
+the control lines. All the Purcell filters and control lines are covered with tunnel-like air-
+bridges, which are shown in FIG.S1(c). Those bridges form Faraday cages that prevent the 
+leakage of electromagnetic fields, thus protecting the qubits and couplers from coupling to 
+spurious fields. 
+ 
+1.2 Fabrication 
+The carrier and the qubit chip were fabricated separately with almost the same processes, 
+except that the Josephson junctions had to be added to the top chip. About 200 nm thick 
+Tantalum (Ta) films were deposited on a pre-annealed sapphire wafer by sputtering. The base 
+circuits, including all the CPW transmission lines, resonators, and capacitors, were defined by 
+laser direct writing lithography (DWL). They were then transferred to the Ta film using 
+reactive ion etching (RIE) with SF6 gas. Before and after the etching process, oxygen ashing 
+was performed in order to remove the residual photoresist. The wafers were then immersed in 
+N-methyl-pyrrolidone (NMP) for several hours, followed by ultrasonic cleaning. The 
+
+3 
+ 
+Al/AlOx/Al junctions were fabricated using standard Dolan-bridge (34) shadow evaporation 
+technology as follows: the junction regions were first defined by electron beam lithography 
+with double-layer resists. After development, Dolan-bridges were formed with under-cut 
+structures. Then the wafers were transferred to an ultra-high vacuum four-chamber electron 
+beam evaporation system (AdnanoTek® JEB-4), wherein the evaporation chamber about 17 
+nm Al was deposited with a tilted angle of 40 - 60 degrees to form the bottom electrodes, and 
+then transferred into the oxidation chamber to form a thin AlOx barrier layer, and finally 
+transferred back for normal deposition of Al top electrodes of about 19 nm. Right before the 
+deposition, an in-situ argon ion milling was adopted to remove the surface oxide of the Ta 
+films. 
+After deposition, the wafers were soaked in NMP bath of 80∘C for at least two hours, with a 
+gentle ultrasonic for thorough lift-off. The tunnel-like bridges were fabricated following the 
+reflowing process (35) with two differences. First, we increased the thickness of the air-bridge 
+film to 500 nm to ensure enough structural strength to sustain subsequent processes. Second, 
+the area for wet etching is 6 μm wide surrounding the air-bridges, which ensures that the 
+bridges are separated from the excess aluminum films. Another lift-off was performed similar 
+to that in the Josephson junction process but without ultrasonic. As there was quite an amount 
+of residual reflowed resist around the bridges, an ozone treatment at 80∘C for one hour is 
+required after lift-off. 
+The final step was to fabricate indium bumps on both chips and then bonded them together via 
+flip-chip technology. Indium bumps with diameters of 20 - 30 μm were patterned on both 
+wafers by DWL. Approximately 10 μm-thick indium was then grown by thermal evaporation 
+after an in-situ argon ion milling. Resist, and excess indium films were stripped away after 
+soaking in NMP for one day. The carrier and the chip wafers were then diced into different 
+sizes and bonded with a bonding force of 150-180 N in a flip-chip bonder (SET ACCμRATM M). 
+Before bonding, all the chips were treated in H2/N2/He plasma to reduce oxidation of the 
+bump surface. 
+ 
+1.3 Experiment setup 
+Our experiment setup is summarized in Fig. S2. To reduce the requirement of wirings and 
+electronic resources, we used only one control line for each qubit, combining the ������������������������ and ������������ 
+control signals together. Furthermore, we developed a so-called single-sideband (SSB) 
+technology, which is more compact than the traditional IQ mixing scheme and requires only 
+half of Digital-to-Analog Converter (DAC) channels, to generate the qubit drive signal (also 
+known as ������������������������ control). To obtain a single-tone drive pulse, the baseband waveforms (IF tone) 
+were first generated by a 2 GSa/s DAC and then mixed with a continuous microwave source 
+(LO tone). Two sidebands with frequencies of ������������������������������������ ± ������������������������������������ would appear after mixing, with an 
+unwanted LO leakage in the spectrum. On the condition that ������������������������������������ was high enough (for 
+example, > 200 MHz), we could use a proper bandpass filter to select only one sideband as the 
+control signal. We tested the spectral purity of such SSB technology and could obtain a 
+Spurious Free Dynamic Range (SFDR) of over 50 dB, which was comparable to or even better 
+than that generated by calibrated IQ mixing method. In addition, as the imaging and leaking LO 
+
+4 
+ 
+signals were deeply filtered out, such a scheme required no time-consuming repeated 
+calibrations, which were needed in the traditional IQ mixing scheme. 
+The flux biases (also known as ������������ control) of the qubits and tunable couplers were generated 
+directly from 2 GSa/s DACs, followed by the 1  GHz lowpass filters. For qubit XY and Z 
+control simultaneously, the Z pulses were further combined with the ������������������������ pulses by using a 
+diplexer. The stimulation signals of the readout resonators were generated by the traditional IQ 
+mixing scheme. All those input signals reached the device at the mixing-chamber (MXC) stage 
+of a dilution refrigerator, with different attenuation at each temperature stage, shown in Fig. S2. 
+The filtering configurations under the MXC stage were different for different kinds of signals. 
+For the ������������������������������������ control of a qubit, the highly attenuated signal was filtered first by a 10 GHz 
+lowpass filter and then an infrared (IR) filter (using Eccosorb® CR124 as the absorber). The 
+CR124 IR filter can attenuate the ������������������������ control signals for about 20 - 50 dB (depending on the 
+filter length) while affecting the DC pulses, (i.e. the ������������ control signals) negligibly. In addition, 
+it could heavily absorb electromagnetic waves from 10 GHz to the infrared band. For the ������������ 
+control of couplers, it first passed through a 500  MHz lowpass filter and then a CR110 IR filter 
+(using Eccosorb® CR110 as the absorber). The CR110 filter was similar to the CR124 IR 
+filter, except that its attenuation was much more gentle. To suppress thermal photon noise, we 
+added 69 dB attenuation, 10 GHz low pass filtering, and CR110 IR filtering to each 
+measurement input line in series. 
+The output of the qubit measurement signal passed through 10 GHz low pass filter and three 
+isolators to prevent out-band and in-band noises, respectively, from coming down to the chip. It 
+was then pre-amplified by a High-Electron-Mobility Transistor (HEMT) at the 4 K stage. After 
+coming out of the fridge, the signal was further amplified by two microwave amplifiers and 
+then down-converted to the IF band by an IQ mixer. The converted IQ signals were filtered and 
+amplified and finally digitized by 1 GSa/s analog-to-digital converters (ADCs) for 
+demodulation. In order to prevent spurious radiation and flux noise, a light-tight oxygen-free 
+copper shield and a cryoperm shield were added outside the device. In addition, we applied 
+another μ-metal shield (between the 50 K shield and the vacuum can), and the residual 
+magnetic field around the position of the device was measured at room temperature to be less 
+than 20 nT. 
+ 
+2 Experiment setup 
+ 
+2.1 Characterization 
+Some key parameters of all the qubits (63 qubits, with one non-working) are depicted in Fig. 
+S3. Readout frequencies are in the range of 4.1 - 4.6 GHz ( Fig. S3(a)). The maximum 
+frequencies of the qubits are in the range of 5.3 - 5.8 GHz ( Fig. S3(b)). The relaxation times ������������1 
+and Ramsey decay times ������������2
+∗ at maximum frequencies are listed in Fig. S3(c) and (d). We find 
+that the coherence of the qubits is much lowered when compared to our previous works (36). 
+We address the possible reasons as follows: First, as the circuit complexity increases, a lot of 
+unwanted modes are introduced, which may weakly interact with the qubits and lead to stronger 
+decoherence. Second, although the flipmon design can increase the vacuum energy 
+
+5 
+ 
+participation ratio, it also increases losses from the metal-air interface. Finally, the combination 
+of ������������������������ and ������������ control signals renders the filtering of control lines not sufficient, since we must 
+ensure that both the low-frequency Z pulses and high-frequency microwave ������������������������ pulses could 
+be transmitted. The first two problems can be alleviated by improved design, and the third 
+problem may require a more careful and optimized filtering scheme design. 
+Among the 62 available qubits, we chose 32 activated qubits in a chain, marked as ������������1 − ������������32 in 
+Fig. S4(a), to simulate the gSSH model in our experiment. All the activated qubits are 
+initialized or excited at their idle frequencies (shown in Fig. S4(b)). During evolution time, they 
+are tuned to their reference point. Meanwhile, inactivated qubits are always far-detuned and 
+negligibly coupled to activated qubits. We can measure the ������������1 and ������������2
+∗ at reference points of 
+activated qubits (shown in Fig. S4(c) and (d)). Here, ������������1 and ������������2
+∗ are different from those at 
+maximum frequencies. ������������2
+∗ are remarkably lowered because the working points are chosen 
+away from the flux sweet spot and thus more sensitive to flux noise. 
+We also care about readout fidelity, which determines the amount of data that needs to be 
+averaged to obtain results with a reasonable error bar. When multiple qubits are measured 
+simultaneously, their fidelities tend to be lower than when they are measured individually due 
+to crosstalk. In Fig. S5, we show that the simultaneous readout fidelities of ground and excited 
+states of the activated qubits are 97% and 89.9% on average, respectively. Thanks to the 
+relatively low noise temperature of the HEMT amplifiers, we found that adequate simultaneous 
+readout fidelities can be obtained without Josephson parametric amplifiers. Furthermore, we 
+mitigate the influence of decoherence through shelving technique (37) on some of the qubits. 
+ 
+2.2 Crosstalk and distortion 
+We minimized the effect of ������������������������ crosstalk by carefully choosing the frequency and duration of 
+the drive pulses. For ������������, we measured the crosstalk of nearest qubits and couplers, and the 
+results showed that the average crosstalk strength between different flux control lines in our 
+chip was less than 0.2% (Fig. S6). As a result, we ignored ������������ crosstalk in the experiment. 
+The non-ideality of electronics and wirings makes the ������������-control signal sensed by the qubits 
+severely distorted. In order to obtain accurate control over the qubit, we corrected the distorted 
+signal by the method of deconvolution (38). The experimental pulse sequence for measuring the 
+distortion of the ������������-control signal is shown in the inset of Fig. S7. First, a square wave was 
+applied on the qubit’s ������������-control line, with a large enough amplitude and a long enough pulse 
+duration. Following that, we applied the qubit phase tomography as a distortion detector where 
+a short square wave was inserted between two ������������/2 pulses. In order to extract the distortion 
+more accurately, the duration of the ������������/2 pulse was set to be short, and the amplitude of the 
+short square wave was carefully selected so that the frequency of the qubit was tuned to a flux-
+sensitive point. Then, we measured the qubit phase for different delay times between the large 
+square wave and the detector, shown in Fig. S7 (black line). We calculated the frequency 
+deviation of the qubit according to the measured phase and the duration of the short square 
+wave. Combining with the information of the qubit spectrum, we obtained the trailing 
+amplitude after the large square wave, and then we could pre-distorted the input signal to 
+
+6 
+ 
+correct the distortion. After the correction, the measured phase was expected to be a constant 
+value at different delay times, as shown in Fig. S7 (red line). 
+2.3 Timing alignment 
+We calibrated the timing between different control channels to make the control more accurate. 
+Firstly, we aligned the timing between a single qubit’s ������������������������ and ������������ control, and the pulse 
+sequence was shown in Fig. S8(a). We fixed the time duration between two ������������ pulses on the 
+������������������������ control and applied a square wave on the ������������ control with the same duration. We measured 
+the population of a qubit as a function of the delay between ������������������������ and ������������ control. When the ������������ 
+pulse was exactly halfway between the two ������������ pulses, the population of the qubit should return 
+to zero, shown in Fig. S8(d). Secondly, we aligned the ������������ control timing between the two 
+adjacent qubits by implementing the ������������������������������������������������������������-like experiment. For example, the pulse sequence 
+of ������������23 − ������������24 − ������������24 was shown in Fig. S8(b). Note that, the square wave duration of the 
+coupler was set larger. When the two ������������ pulses were aligned correctly, the population exchange 
+between the two qubits reached the maximum (Fig. S8(e)). Finally, the alignment between ������������ 
+pulses of the adjacent coupler and qubit was done with a similar method, shown in Fig. S8(c), 
+(f). 
+ 
+2.4 Coupling strength 
+Accurately determining the effective coupling strength between the two nearest neighboring 
+qubits is very important, and the experimental pulse sequence is shown in Fig. S9(a). Firstly, 
+we decoupled the surrounding qubits and couplers, and we prepared the initial state as |100⟩ 
+by applying a ������������ pulse on the ������������19, which described the energy-eigenstates of the qubit-coupler-
+qubit (������������19 − ������������19 − ������������18) systems. Then, we observed that the population swapped as a function 
+of the time, between two qubits shown in Fig. S9(b). The typical chevron pattern could indicate 
+the oscillation point which was the maximum population swapping point. We fixed the 
+oscillation point and then measured the population swapping as a function of the coupler flux 
+bias, shown in Fig. S9(c). We extracted the effective coupling strength by fitting each line 
+along y-axis, which varied from 0 MHz to -14 MHz. Because of the limited evolution time up to 
+2 ������������s, the extracted coupling strength from -14 MHz to -0.25 MHz was more accurate. 
+Continuous parameterization of the effective coupling strength is very important for us to 
+quickly simulate the target Hamiltonians. In our experiment, we chose the 20th-order 
+polynomial to fit the extracted coupling strength from -14 MHz to -0.25 MHz as a function of 
+the coupler flux bias. We believed that the extracted coupling strength of 0 MHz was also 
+accurate, so we continuously parameterized the coupling strength by linear interpolation from -
+0.25 MHz to 0 MHz. Fig. S9(d) showed a total of 32 parameterized coupling strengths between 
+the nearest neighboring qubit pairs. 
+ 
+2.5 Frequency alignment 
+We biased all qubits to the reference point with frequency ωref = 2π × 5.395 GHz for the 
+quantum walk experiment. Firstly, we fixed one qubit at the reference point and applied an 
+iSWAP sequence (Fig. S9) between a qubit and its nearest neighboring qubit. During the 
+
+7 
+ 
+iSWAP experiment, the coupling strength between the two qubits was set to be 1.5 MHz, and 
+the rest qubits were decoupled from these two. We repeated this two-qubit frequency alignment 
+sequentially along the qubit chain. Due to its inherent many-body nature, when all the qubits 
+and couplers were set to the points we characterized above, the alignment was not perfect. Fig. 
+S13 has shown that the coupling of a qubit to a coupler can deviate the qubit’s frequency from 
+the reference point by -10 MHz. Here, we parameterized the deviated qubit frequency as a 
+function of the coupler bias by a 40th polynomial. Then we compensated for this deviation with 
+an extra qubit bias. After this compensation, we can see that the qubit frequency became nearly 
+constant with the coupler bias. Due to the limited compensation accuracy of this method, we 
+only compensated the qubit bias within the range of coupling strength from -9.5 MHz to -
+0.25 MHz. 
+ 
+2.6 Consistency of target couplings to parameterized couplings 
+Although we can accurately parameterize the coupling strength between each nearest-neighbor 
+qubit pair when all other qubits are decoupled, it is still a challenge to parameterize the 
+coupling strength when all qubits and couplers are activated due to the intrinsic many-body 
+nature of our device. Thus we evaluated the extension of our pair-wise coupling strength 
+parameterization to the whole qubit chain with a quantum walk. We implemented the 32-qubit 
+single-excitation quantum walk using the target Hamiltonian, where all couplings were set to be 
+the same target strength. For example, we performed quantum walk experiments with six 
+different initial states, with the target coupling strength set to be 2 MHz. The results of up to 
+300 ns evolution were shown in Fig. S10. The left column has shown the theoretical simulations 
+of the quantum walks using the target Hamiltonian. The middle column contained the 
+experimental result of the quantum walks of the parameterized Hamiltonian. To accurately 
+extract the actual coupling strength of each qubit pair, we optimized the Hamiltonian to match 
+the experiment result, where the coupling strengths were the fitting parameters. The results 
+were plotted in the right column. We could see good consistency with the target. Repeating this 
+procedure with different target coupling strengths, we were able to check the consistency of the 
+experimentally extracted coupling strength with the target coupling strength, shown in Fig. S10. 
+It was clear that the pair-wise couplings were well in control when the target coupling strength 
+was not over 4 MHz. 
+ 
+2.7 Residual couplings 
+In our experiment, we can only turn off the coupling strength between nearest-neighbor qubit 
+pairs. The residual couplings between diagonal next-nearest neighbor (NNN) qubits may also 
+have an impact on our experimental results. Here, we applied the ������������������������������������������������������������ experiment to NNN 
+qubit pairs to figure out the residual coupling strength. Due to the limited coherence time, we 
+could only observe a very small population swapping. The swapping between the NNN qubit 
+pair(������������26 and ������������28) with the maximum residual coupling strength is shown in Fig. S12. The 
+maximum population swapping corresponds to a swapping time of 5.05 ������������s, and thus we can 
+infer that the coupling strength was no larger than 0.05 MHz. Such a small unwanted coupling 
+strength was owing to the flipmon design. In our quantum walk experiment in the main text, the 
+
+8 
+ 
+evolution time is set to be 1.5 ������������s, less than the 5.05 ������������s, and then the residual couplings do not 
+pose a significant impact on our experiment. 
+ 
+2.8 Demonstration of the single-excitation quantum walks 
+After all above calibrations, we excited the Q25 to the excited state and set all the coupling 
+strengths between adjacent qubits to be 2π × 2 MHz and measured the population evolution of 
+each qubit. The result of the single-excitation quantum walk was shown in Fig. S14. The 
+population evolution of the qubits was clear and the remain imperfections were attributed to the 
+alignment errors, the imperfect Z pulse distortions, and the residual couplings to the 
+environment. 
+ 
+3 Experimental realization of topological Anderson insulators 
+ 
+3.1 Static phase diagram: topology and localization 
+We provide some details of obtaining the static phase diagram of the generalized SSH model 
+(�������������gSSH) with quasi-periodic hopping disorders (39), as shown in Fig. 1 in the main text. To this 
+end, we first determine the topological phase diagram in the ������������-������������′ parameter space [see Fig. 
+S15(a)]. Then we determine the delocalization-localization transition, which separates the 
+extended phase and the (partially and fully) localized phase. Moreover, we study the interplay 
+of flat-band localization and Anderson localization in the fully dimerized limit with ������������′/������������ = 0, 
+and obtain the localization phase diagram (see Fig. S17(h)). By combining these results, we 
+finally obtain the complete phase diagram with respect to the topology and localization in the 
+model. Note that we have confirmed that the following numerical results obtained for the single 
+configuration of ������������ = 0 are preserved for other values of ������������ ≠ 0. This is due to the fact that the 
+lattice size ������������ = 2������������������������ = 1220 in our numerical simulations is large enough for self-averaging. 
+The topological phase diagram is shown in Fig. S15(a), which is obtained for a sufficiently 
+large lattice of size ������������ = 1220 with negligible finite-size effects. Here we numerically calculate 
+the real-space winding number ������������ for �������������gSSH as functions of dimensionless parameters ������������/������������ 
+and ������������′/������������. Following Ref. , the real-space winding number as the topological marker is given by 
+������������ =
+1
+2|ℬ| � T������������������������
+������������∈ℬ
+�����������������������������������������, ���������������, 
+where T������������������������ is the trace operator inside the ������������-th unit cell within a small region (������������������������/8 unit cells 
+in our simulations) in the center of the lattice, and ℬ denotes the corresponding collection of 
+bulk cells away from the boundary. Here ������������� = ∑ ��������������������������,+⟩⟨������������������������,+� − �������������������������,−⟩⟨������������������������,−��
+������������
+ is the flat-band 
+Hamiltonian, ������������� = ������������3
+⊗������������������������ is the chiral operator, and ������������� is the unit cell operator with 
+�������������|������������, ������������⟩ = ������������|������������, ������������⟩, �������������, ������������⟩ = �������������������������,������������
+† �v������������������������⟩ (������������ ∈ [1, ������������������������] ), and |v������������������������⟩ as the vacuum state of the 
+system. 
+
+9 
+ 
+In the clean limit with ������������/������������ = 0, there exists a topological transition between topological phase 
+with ������������ = 1 and trivial phase with ������������ = 0 at ������������′/������������ = 1. With increasing quasi-periodic disorder 
+strength up to ������������/������������ ≲ 2, the parameter region for the topological phase enlarges. This gives 
+rise to the TAI phase induced by moderate disorders from the trivial phase for 1 < ������������′/������������ ≲ 2 
+and large ������������������������. To further reveal the topological phase transition, we numerically compute the 
+bulk gap ������������������������ = ������������������������������������+1 − ������������������������������������ under the periodic boundary condition in Fig. S15(b). One can 
+find that the topological phase is gapped, and the bulk gap closes at topological transition 
+points. When ������������ is large enough (������������ ≳ 2), the system is in the trivial gapless Anderson 
+insulators with vanishing ������������������������. To be more clear, we show ������������������������ under the open boundary 
+condition and ������������ with varying ������������ and fixed ������������′/������������ = 1.1 in Fig. S15(c). In the gapped TAI phase 
+region (0.65 ≲ ������������/������������ ≲ 2.0) with ������������ = 1, a pair of disorder-induced zero-energy edge modes 
+inside the bulk gap exhibits due to the bulk-boundary correspondence. 
+The whole topological phase boundary can be determined from the localization length of zero-
+energy modes, which diverges at topological transition points, owing to their delocalization 
+character in one-dimensional chiral chains (40). For �������������gSSH, we can denote the wave function of 
+the zero-energy eigenstate as ������������0 = {������������1,������������, ������������1,������������, ������������2,������������, ������������2,������������ ⋯ ������������������������������������,������������, ������������������������������������,������������}������������, which is governed 
+by the Schrödinger equation 
+�������������gSSH������������0 = 0, #(1) 
+Eq.(1) leads to ������������������������������������,������������ + ������������������������
+′ ������������������������+1,������������ = 0 and ������������������������
+′ ������������������������,������������ + ������������������������������������+1,������������ = 0. Then the corresponding 
+probability distribution can be obtained as 
+������������������������,������������
+= (−1)������������ � ������������������������
+′
+������������
+������������
+������������=1
+������������1,������������, #(2)
+������������������������,������������
+= (−1)������������ � ������������
+������������������������+1
+′
+������������
+������������=1
+������������1,������������, #(3)
+ 
+Using the transform matrix method, one can obtain the inverse of the localization length ������������ in 
+the ������������������������ → ∞ limit 
+������������−1 = max � lim
+������������������������→∞
+1
+������������������������
+ln�������������������������������������,�������������, lim
+������������������������→∞
+1
+������������������������
+ln�������������������������������������,�������������� , #(4) 
+By setting ������������1,������������ = ������������1,������������ = 1, we obtain 
+lim
+������������������������→∞
+1
+������������������������
+ln�������������������������������������,�������������
+= lim
+������������������������→∞
+1
+������������������������
+ln�������������������������������������,�������������
+=∣ lim
+������������������������→∞
+1
+������������������������
+�(ln|������������| − ln ∣ ������������������������
+′|)
+������������������������
+������������=1
+|, #(5)
+ 
+By substituting Eq. (4) into Eq. (5), one can obtain 
+
+10 
+ 
+������������−1 =∣ lim
+������������������������→∞
+1
+������������������������
+�(ln|������������| − ln ∣ ������������������������
+′|)
+������������������������
+������������=1
+|, #(6) 
+The numerical results of ������������−1 ≈ 0 for ������������ = 2������������������������ = 1220 is shown in Fig. S15(a) as the white 
+dashed line, corresponding to the divergence of the localization length with ������������ → ∞. The results 
+demonstrate that the divergence of the zero-energy modes perfectly matches the topological 
+phase boundaries. 
+The emergence of the TAI phase from a trivial phase in the clean limit in the topological phase 
+diagram originates in the disorder-induced renormalization of the topological term. This 
+mechanism can be revealed based on the self-consistent Born approximation (SCBA) for weak 
+and moderate disorders (41). Under the SCBA, the disorder-induced self-energy term can be 
+viewed as an additional renormalization term for a clean Hamiltonian. For �������������gSSH, one can 
+obtain the self-energy ������������(������������) from the self-consistent equation 
+1
+������������������������ − ℋ(������������) − ������������(������������) = ⟨
+1
+������������������������ − ������������eff(������������, ������������)⟩������������, #(7) 
+where ������������������������ ≡ 0 denotes Fermi energy, ℋ(������������) = [������������′ + ������������cos(������������)]������������1 + ������������sin(������������)������������2 denotes the 
+momentum-space Hamiltonian in clean limit, ������������(������������) = ������������1(������������)������������1 is the simplified self-energy 
+under the symmetry of the Hamiltonian, and the ⟨⋯ ⟩������������ stands for averaging overall disorder 
+realizations. In our model, the disorder satisfies the form ������������(������������)������������1 with ������������(������������) = ������������cos(2������������������������������������), 
+and the effective Hamiltonian reads ������������eff = ℋ(������������) + ������������(������������)������������1. The renormalized hopping 
+constant is ������������′� = ������������′ + ������������1(������������), which gives rise to the modified topological phase transition 
+points satisfying the equation ������������′�(������������′, ������������)/������������ = 1. For a given ������������ and other parameters, the self-
+energy ������������1 can be obtained by numerically solving the self-consistent equation. Thus, the 
+topological phase boundary on the ������������-������������′ plane can be obtained. We plot the numerical result of 
+the topological phase boundary based on the SCBA analysis for 0 < ������������ < 2 as the black solid 
+line in Fig. S15(a), which agrees well with that determined by ������������. 
+The basic mechanism of the TAI phase induced by quasi-periodic disorders here is the same as 
+that of TAIs in random disordered systems (41,42). However, they have different gap and 
+localization properties. In particular, the TAI induced by random disorders in the SSH model is 
+gapless and only contains fully localized bulk states (40,43,44). This is due to the common 
+wisdom that all states are Anderson localized without localization transition in 1D random 
+uncorrelated disordered systems (45). In sharp contrast, the TAI phase in this quasiperiodic 
+SSH model is gapped and can have bulk states of different localization properties (39). The 
+gapped TAI in the moderate disorder region has been shown in Fig. S15(b, c). The 
+corresponding disorder-induced edge modes are protected by a finite bulk gap, different from 
+those being embedded in the gapless bulk spectra of the TAI in random disordered systems. 
+Thus, the mid-gap edge modes of the TAI in this quasi-periodic system are easier to detect in 
+experiments. 
+On the other hand, there exists Anderson transition in this quasi-periodic system, such that the 
+TAI phase can have extended, partially or fully localized bulk states. To see this point, we can 
+numerically compute the local density of states at site ������������ of a lattice of length ������������ = 2������������������������ by 
+following Refs. (46,47): 
+
+11 
+ 
+������������(������������, ������������) = 1
+������������ �|������������������������(������������)|2
+������������
+������������=1
+������������(������������ − ������������������������), #(8) 
+where ������������������������(������������) denotes the probability amplitude of the ������������-th normalized eigenstate at ������������-th site in 
+real space. From the local density of states, one can obtain its arithmetic mean ������������a������������������������(������������) and 
+geometric mean ������������t������������������������(������������) as 
+������������a������������������������(������������) = ⟨������������(������������, ������������)⟩������������,  ������������t������������������������(������������) = exp[⟨ln������������(������������, ������������)⟩������������], #(9) 
+Here ⟨⋯ ⟩������������ denotes the average over the site ������������ of the lattice. The localized and extended 
+eigenstates around energy ������������ can be characterizes as ������������t������������������������(������������)/������������a������������������������(������������) → 0 and 
+������������t������������������������(������������)/������������a������������������������(������������) ≠ 0 in the large ������������ limit, respectively. Fig. S15(d) shows three typical TAI 
+phases with extended states, the coexistence of extended and localized states, and localized 
+states, from top to bottom. 
+To further study the localization properties of bulk states, we can numerically compute the real-
+space inverse participation ratio (IPR) of the ������������-th eigenstate IPR������������ and the mean IPR averaged 
+over the energy spectrum: 
+IPR������������ = �|������������������������(������������)|4
+������������
+������������=1
+,  IPR = 1
+������������ � IPR������������
+������������
+������������=1
+, #(10) 
+For an extended (������������-th) eigenstate, one has IPR������������ ∼ ������������−1 and IPR������������ ∼ 0 in the large ������������ limit, 
+while IPR������������ ∼ ������������(1) for a localized eigenstate. Thus, one can define the extended phase as all 
+of the eigenstates being extended with IPR ∼ ������������−1 ∼ 0 in the large ������������ limit, while the localized 
+phase for part or all of the eigenstates being localized with IPR ≠ 0 and independent of ������������. The 
+extended and localized phases are separated by Anderson transition points with critical disorder 
+strengths. By determining the critical disorder strengths of Anderson transition points, we can 
+obtain the boundary between extended and localized phases and thus the localization phase 
+diagram on the ������������-������������′ parameter plane. To this end, we first numerically compute IPR for a 
+large lattice (������������ = 2������������������������ = 1220) as functions of ������������ and ������������′, as shown in Fig. S16(a). The result 
+indicates two parameter regions of the extended phase with IPR ∼ 0, one with small ������������ and 
+the other around the ������������′ = 0 axis, and otherwise for the localized phase. 
+We first consider the parameter regime with ������������′ ≠ 0 and study the particular case of ������������′ = 0 
+later. To determine the Anderson transition point, we can take the finite-size analysis of IPR 
+with respect to the quasi-periodic disorder strength ������������ for fixed ������������′/������������. For instance, we show 
+the results of IPR with respect to ������������ for fixed ������������′/������������ = 1.1 and ������������ = 2������������������������ = {288,754,1220} in 
+Fig. S16(b). One can see clearly that by increasing ������������, three lines approach a critical point that 
+separates the extended phase region with vanishing IPR ∼ 0 and the localized phase region 
+with finite IPR (indicated by the grey dashed line). To be more clearly, we show the 
+corresponding logarithm plots as lgIPR(������������) ≡ log10IPR(������������) in the inset of Fig. S16(b). As 
+excepted, the results show a sharp increase of lgIPR(������������) near the AT point, after (before) 
+which the values of lgIPR(������������) are almost independent (dependent) of ������������ for the localized 
+
+12 
+ 
+(extended) phase. In view of the sharp change near the AT, we use the corresponding derivation 
+∂lgIPR/ ∂������������ to further determine the critical point, as shown in Fig. S16(c). The peak of the 
+derivation indicates the Anderson transition point. The peak becomes sharper with increasing 
+the lattice size, but its location is the same for different lattice sizes. For other values of ������������′/������������, 
+the critical disorder strengths of the Anderson transition points can also be extracted in this 
+way, with three other examples shown in Fig. S16(d). Following this procedure of the finite-
+size analysis, we finally obtain the boundary between the extended and localized phases, which 
+is plotted as the white dashed-dotted line in Fig. S16(a). 
+We proceed to study the localization properties of the system when ������������′ = 0. In the clean case 
+with ������������ = ������������′ = 0, the SSH chain is in the fully dimerized limit and has two topological flat 
+bands with energies ������������ = ±������������ and winding numbers ������������ = ∓1. In this clean limit, the system 
+contains compact localized states, and the transport is prevented due to the diverging effective 
+mass in the two flat bands. This localization phenomenon is named flat-band localization. 
+However, the flat bands are very sensitive to perturbations from hopping disorders ������������, which 
+actually destroys the fully dimerized bonds and recovers the intra-cell hopping. Thus, one can 
+accept that the localization of compact states is broken under small ������������ and the disorder can 
+prohibit transport. When the disorder effect is dominant, one can expect the system will enter 
+the AL phase. Therefore, there exists a competition between flat-band localization and 
+Anderson localization, which can lead to the so-called inverse Anderson transition 
+(localization ) with the striking disorder-induced (insulator-metal transition (transport) (48). 
+As shown in Fig. S17(a), we plot the eigenenergy spectrum of a finite chain (under the periodic 
+boundary condition) for various ������������. One can see that when turning on the hopping disorder and 
+increasing its strength ������������, the energy spectrum changes from the flat bands at ������������ = 0 to 
+dispersive bands, which becomes gapless when ������������/������������ ≥ 2. To show the interplay between flat-
+band localization and Anderson localization and obtain the Anderson transition point, we 
+numerically compute lgIPR and ∂lgIPR/ ∂������������ as a function of ������������, as shown in Figs. S17(b) 
+and S17(c), respectively. The results demonstrate the FBL phase at ������������ = 0, the extended phase 
+for 0 < ������������/������������ ≲ 2, and the localized phase for ������������/������������ ≳ 2 with the Anderson transition point at 
+������������/������������ ≈ 2. We further perform the finite-size scaling of IPR to confirm the two localization 
+phases and the extended phase in Figs. S17(d) and S17(e), respectively. To reveal the interplay 
+between the flat-band localization and Anderson localization with the disorder-induced 
+transport, we can use the time-averaged survival probability ������������������������ (see Eq. (7) in the main text) 
+and the time-averaged mean square displacement ������������ exacted from the spreading dynamics of a 
+single-site excitation. The time-averaged mean square displacement is given by 
+������������ = 1
+������������ � �� (������������ − ������������0)2
+������������
+��������������������������,������������(������������′)�
+2 + �������������������������,������������(������������′)�
+2��
+1/2
+������������
+0
+������������������������′, #(11) 
+which reflects the mean width of the quantum walk over the evolution time ������������ with the initial 
+state being localized at a single site (site A or B) of the ������������0-th unit cell. The typical results of 
+numerical simulations for a finite lattice with ������������ = 2������������������������ = 1220 and ������������0 = ������������������������/2 = 305 are 
+shown in Figs. S17(f) and S17(g). Fig. S17(f) show ������������ as a function of ������������ for different disorder 
+strengths ������������. Owing to the FBL at the clean limit, the breathing dynamics between two sites of 
+the ������������0-th unit cell exhibit when ������������ = 0. The ballistic transport is enabled and enhanced when 
+
+13 
+ 
+0 < ������������/������������ < 2 as the inverse Anderson localization, and is prevented when ������������/������������ > 2 due to 
+the AL. Moreover, we simulate the evolution dynamics up to a sufficiently long time ������������ =
+400 ℏ/������������ (but with negligible edge effects), and compute ������������������������ and ������������ as a function of ������������ in Fig. 
+S17(g). The numerical results show the non-monotonous transport (localization) property with 
+respect to the disorder strength, which agrees well with the analysis of the interplay between the 
+flat-band localization and Anderson localization. 
+Based on these numerical results and analysis of the localization properties, we obtain the 
+localization phase diagram in the whole ������������-������������′ parameter space, as shown in Fig. S17(h). By 
+combining the topological and localization phase diagrams in Figs. S15(a) and S17(h), we 
+finally obtain the complete static phase diagram of the generalized SSH model quasi-periodic 
+hopping disorders [see Fig. 1(b) in the main text]. 
+ 
+3.2 Extracting Topological and Localization properties from Quantum walks 
+The extraction of the real-space winding number is following the procedure in Ref. (49) and 
+Ref. (44). Here we review the derivation of the local topological markers and their relation to 
+the density evolution in the quantum-walk experiments. 
+The definition of the real-space winding number is mathematically expressed in Eq. (3) in the 
+main text, which can be understood as taking the average of an operator, ������������� = ����������������������������������������, ��������������, over 
+the bulk-state region and different modulation realizations. Note the flat-band Hamiltonian ������������� 
+can be written in terms of the projectors ������������������������� = ∑ �������������������������,±⟩⟨������������������������,�������������
+������������
+ with ������������ = ± as ������������� = ������������� − 2�������������−, 
+where ������������� = �������������+ + �������������− is the identity operator. Then the topological marker ������������(������������) can be obtained 
+as the sum of the expectation of the operator ������������� in basis states in the ������������-th unit cell, 
+������������(������������)
+=
+� �������������, ���������������������������������������, �������������
+������������=������������,������������
+=
+4 � �������������, ��������������������������−���������������������������������������−�������������, �������������
+������������=������������,������������
+=
+4 � �� ��������������, ������������|������������������������,−��
+2
+������������
+�������������������������,−����������������������������������������������������,−�
+������������=������������,������������
++ � �������������, ������������|������������������������,−�
+������������≠������������′
+�������������������������′,−|������������, ��������������������������������������,−����������������������������������������������������′,−��
+≃
+� � ��������������, ������������|��������������������������
+2
+������������
+������������=������������,������������
+��������������������������2����������������������������������������������������, #(12)
+ 
+where in the last line of the above equation, the summation is over the whole spectrum, and the 
+off-diagonal terms are omitted since their contributions are negligibly small. Note that here we 
+use a single index ������������ to traverse the whole spectrum of the target Hamiltonian, i.e. 
+�������������g�������������������������������������������������������������⟩ = �������������������������������������������������⟩, for notation simplicity. The real-space winding number is then obtained as 
+
+14 
+ 
+the average of the topological markers over unit cells in the bulk-state region and different 
+modulation realizations. 
+In a single-excitation quantum-walk experiment, the time-averaged expectation of the chiral 
+displacement 2�������������������������� can be evaluated as follows, 
+������������‾������������
+=
+1
+������������ � �������������������������,������������(������������′)�2���������������������������������������������������,������������(������������′)�
+������������
+0
+������������������������′
+=
+� ��������������, ������������|��������������������������
+2
+������������
+��������������������������2����������������������������������������������������
++ℏ � �������������������������������������������������−������������������������′�������������/ℏ − 1
+������������������������������������� − ������������������������′�������������
+������������≠������������′
+× �������������, ������������|���������������������������������������������������2���������������������������������������������������′��������������������������′|������������, �������������, #(13)
+ 
+with �������������������������,������������(������������′)⟩ = ������������−�������������������������g������������������������������������������������′/ℏ�������������, ������������⟩, where the first term corresponds to the dominant part of 
+the real-space winding number in Eq. (12) and the second term tends to zero as the evolution 
+time increases. With this observation, it is clear that the real-space winding number can be 
+calculated with quantum-walk experiments as follows, 
+������������ =
+1
+2|ℬ| � � lim
+������������→∞
+������������
+������������∈ℬ
+������������‾������������ ≡ ⟨������������‾∞⟩, #(14) 
+where ℬ denotes the collection of cell indices in the bulk-state region. 
+Now we turn to extract the spectral-averaged IPR from the experimental data of quantum 
+walks. We notice that, for each quantum-walk experiment, the second-order moment of the 
+survival probability can be evaluated as follows, 
+������������‾������������
+=
+1
+������������ � ��������������, ������������|������������������������,������������(������������′)��
+2
+������������
+0
+������������������������′
+=
+1
+������������ � �� ������������−������������������������������������������������′
+������������
+��������������, ������������|��������������������������
+2�
+2
+������������
+0
+������������������������′
+=
+� ��������������, ������������|��������������������������
+4
+������������
++ ℏ � �������������������������������������������������−������������������������′�������������/ℏ − 1
+������������������������������������� − ������������������������′�������������
+������������≠������������′
+× ��������������, ������������|��������������������������
+2��������������, ������������|������������������������′��
+2, #(15)
+ 
+It is clear that the second term in Eq. (15) is proportional to the inverse of the evolution time, 
+and thus it tends to zero in the long-time limit. In other words, the averaged survival probability 
+converges to the first term, which is a time-independent value, in the long-time limit, 
+������������‾∞ ≡ lim
+������������→∞������������‾������������ = � ��������������, ������������|��������������������������
+4
+������������
+, #(16) 
+
+15 
+ 
+Comparing Eq. (16) with Eq. (10), we find that the spectral-averaged IPR can be obtained by 
+averaging ������������‾∞ over all excitation positions, 
+a������������������������������������ = 1
+������������ � ������������‾∞
+������������,������������
+, #(17) 
+With the introduction of the modulation phase ������������, it is reasonable to assume that modulation-
+averaged observables still retain translational invariance in the quasi-periodically modulated 
+system. To mitigate the finite-size effect, we restrict the single excitations in the bulk-state 
+region ℬ with |ℬ| ≪ ������������������������. Moreover, in consideration of the finite coherence times in 
+experiment, we use experimentally measured values of ������������‾������������ and ������������‾������������ at the longest evolution time 
+������������������������ = 1.5 μs as the experimental data for ������������‾∞ and ������������‾∞. Fig. S18 shows the experimental pulse 
+sequence for a quantum walk, and Fig. S19 shows an example of the experimentally measured 
+density evolution data for all of the quantum-walk instances. We finally arrive at the following 
+expressions for ⟨������������‾∞⟩ and ⟨������������‾∞⟩ as 
+⟨������������‾∞⟩
+=
+1
+2|ℬ|������������������������
+�
+������������∈ℬ,������������
+� �������������������������,������������(������������′)�2���������������������������������������������������,������������(������������′)�
+������������������������
+0
+������������������������′, #(18)
+ 
+and 
+⟨������������‾∞⟩
+=
+1
+2|ℬ|������������������������
+� � ��������������, ������������|������������������������,������������(������������′)��
+2
+������������������������
+0
+������������∈ℬ,������������
+������������������������′, #(19) 
+with the average over disorder realizations being taken implicitly. 
+ 
+3.3 Error Mitigation 
+To mitigate readout and leakage errors, we combine the subspace readout-error mitigation 
+proposed in Ref. (50) and postselection of the single-excitation subspace. Here we briefly 
+outline the procedure. 
+The essential idea of readout-error mitigation lies in the assumption that there exists an 
+assignment matrix ������������ which relates the ideal and measured probability distributions, ������������⃗i������������������������ =
+�������������0
+i������������������������, … , ������������2������������−1
+i������������������������ �
+������������ and ������������⃗m������������������������ = �������������0
+m������������������������, … , ������������2������������−1
+m������������������������ �
+������������, in the following way, 
+������������⃗m������������������������ = ������������������������⃗i������������������������, #(20) 
+where ������������ is a 2������������ × 2������������ matrix, with ������������ referring to the number of involved qubits. With the 
+assumption that the readout crosstalk errors are negligible, the matrix ������������ and its inversion can 
+be constructed from a single-qubit readout-calibration matrix ������������������������, 
+������������ =⊗
+������������
+������������=1 ������������������������, ������������−1 =⊗
+������������
+������������=1 ������������������������
+−1, #(21) 
+
+16 
+ 
+with the matrix elements of ������������������������ being [������������������������]������������,������������′ = ������������������������′→������������
+(������������)
+ and ������������������������
+−1 being the inverse of ������������������������. Here 
+������������������������′→������������
+(������������)
+ is the probability of obtaining ������������ in the projective measurement after preparing the 
+state |������������′⟩, with ������������, ������������′ ∈ {0,1}. Note that ������������−1 is also a 2������������ × 2������������ matrix, whose matrix elements 
+can be directly constructed from ������������������������
+−1 as [������������−1]������������,������������ = ∏
+[������������������������
+−1]������������������������,������������������������
+������������
+������������=1
+ with ������������ and ������������ being 
+bitstring strings, i.e. ������������ = ������������������������ … ������������1 and ������������ = ������������������������ … ������������1 in the binary format. For small systems, we 
+can straightforwardly obtain the reconstructed quasiprobability ������������⃗q������������������������ = ������������−1������������⃗m������������������������, with ������������⃗q������������������������ 
+being defined similarly as ������������⃗i������������������������. Note that the direct inversion approach generates 
+quasiprobability that may contain negative values due to sampling errors in realistic 
+experimental scenarios. This problem can be surmounted by introducing numerical techniques 
+like the maximum likelihood analysis or the bounded minimization approach. Here in this 
+experiment, however, we are only concerned with expectation values, especially the density 
+distribution, and thus are satisfied with the direct-inversion approach, since it has been proved 
+in Ref. (51) that the error-mitigated quasiprobability distribution provides an unbiased estimate 
+for expectation values. 
+For intermediate-scale quantum systems consisting of tens of qubits, however, it is infeasible to 
+experimentally measure ������������⃗m������������������������ and perform matrix multiplication in the whole Hilbert space 
+with exponentially large dimensionalities. With the observation that ������������⃗m������������������������ can have at most ������������ 
+non-zero entries, where ������������ is the number of shots in each experiment, Ref. (50) proposed to 
+mitigate readout error in the subspace spanned by the computational basis states corresponding 
+to the non-zero entries in ������������⃗m������������������������. Moreover, in our experiment, we only concern with the 
+probability distribution in the single-excitation subspace, since the target Hamiltonian 
+conserves the particle number. Taking these aspects into account, we use the following 
+subspace formula to obtain the unnormalized readout-error-mitigated quasiprobability 
+distribution in the single-excitation subspace, 
+�������������′q������������������������ = ������������̃−1�������������m������������������������, #(22) 
+where ������������̃−1 is a ������������ × ������������′ matrix, with ������������′ ≤ ������������ being the number of non-zeros entries in ������������⃗m������������������������. 
+Finally, the quasiprobability distribution can be naturally normalized by �������������q������������������������ = �������������′q������������������������/∑�������������′q������������������������. 
+Fig. S20 shows a representative example of the error-mitigation procedure. After applying the 
+above-mentioned error-mitigation technique, the interference pattern becomes clearer and the 
+background residual excitation originating from assignment errors is also suppressed. 
+ 
+3.4 Reference 
+32. X. Li, et al., Applied Physics Letters 119, 184003 (2021). 
+33. F. Yan, et al., Phys. Rev. Applied 10, 054062 (2018). 
+34. G. Dolan, Applied Physics Letters 31, 337 (1977). 
+35. Z. Chen, et al., Applied Physics Letters 104, 052602 (2014). 
+36. C. Wang, et al., npj Quantum Information 8, 1 (2022). 
+
+17 
+ 
+37. F. Mallet, et al., Nature Physics 5, 791 (2009). 
+38. F. Bao, et al., Phys. Rev. Lett. 129, 010502 (2022) 
+39. L.-Z. Tang, S.-N. Liu, G.-Q. Zhang, D.-W. Zhang, Phys. Rev. A 105, 063327 (2022). 
+40. I. Mondragon-Shem, T. L. Hughes, J. Song, E. Prodan, Phys. Rev. Lett. 113, 046802 (2014). 
+41. C. W. Groth, M. Wimmer, A. R. Akhmerov, J. Tworzydło, C. W. J. Beenakker, Phys. Rev. 
+Lett. 103, 196805 (2009). 
+42. J. Li, R.-L. Chu, J. K. Jain, S.-Q. Shen, Phys. Rev. Lett. 102, 136806 (2009). 
+43. A. Altland, D. Bagrets, L. Fritz, A. Kamenev, H. Schmiedt, Phys. Rev. Lett. 112, 206602 
+(2014). 
+44. E. J. Meier, et al., Science 362, 929 (2018). 
+45. P. W. Anderson, Phys. Rev. 109, 1492 (1958). 
+46. Y.-Y. Zhang, R.-L. Chu, F.-C. Zhang, S.-Q. Shen, Phys. Rev. B 85, 035107 (2012). 
+47. S.-Q. Shen, Topological Insulators (Springer,New York, 2013). 
+48. M. Goda, S. Nishino, H. Matsuda, Phys. Rev. Lett. 96, 126401 (2006). 
+49. F. Cardano, et al., Nat. Commun. 8 (2017). 
+50. P. D. Nation, H. Kang, N. Sundaresan, J. M. Gambetta, PRX Quantum 2, 040326 (2021). 
+51. S. Bravyi, S. Sheldon, A. Kandala, D. C. Mckay, J. M. Gambetta, Phys. Rev. A 103, 042605 
+(2021). 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+18 
+ 
+ 
+ 
+ 
+ 
+Figure S1: (a) A schematic circuit of a unit cell of our device. Each flipmon qubit (blue) is capacitively 
+coupled with four couplers (orange) and four adjacent qubits. The frequencies of all qubits and couplers 
+can be tuned by the flux of SQUID loops. (b) A photograph of another device with the same design. (c) 
+A photograph of the tunnel-like air-bridge and indium bumps. 
+
+(a)
+Qubit
+Coupler
+(b)
+4mm
+(c)
+tOμum
+EHT= 5.00 AV
+SignefA = SE2
+Dafe: 3 Mar 2021
+WD =14.9 mm
+Mag*721X
+Time: 19.44:45
+ZEIS19 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S2: A schematic of the measurement system, including cryogenic and room temperature 
+wiring, various microwave devices, measurement electronics, and electromagnetic shielding. 
+ 
+ 
+ 
+ 
+
+2GSa/s
+2GSa/s
+MW
+MW
+DAC
+DAC
+MW
+MW
+Qubit
+Coupler
+Measurement
+-3dB
+Qubit
+t Amp
+Amp
+XY Control
+Z Control
+Z Control
+Input
+5-6GHz 
+1GHz
+1GHz
+Measurement
+500MHz
+Output
+300K
+IF Amp
+50K
+OdB
+OdB
+OdB
+1GSa/s
+ADC
+3K
+-20dB
+-20dB
+-20dB
+HEMT
+Still
+-6dB
+-6dB
+-6dB
+Cold
+Plate
+-3dB
+-3dB
+-3dB
+Attenuator
+OdB
+Low-pass filter
+MC
+OdB
+OdB
+-20dB
+-20dB
+Band-pass filter
+x3
+/
+IR filter
+10GHz
+500MHz
+10GHz
+OdB
+CR124
+Circulator
+CR110
+CR110
+10GHz
+CR110 
+Amplifier
+×63
+×105
+×11
+IQ mixer
+×11
+Mixer
+Diplexer
+Oxygen-free Copper
+Cryoperm20 
+ 
+ 
+Figure S3: The (a) frequencies of readout resonators, (b) maximum frequencies of the qubits, relaxation 
+times T1 and (d) Ramsey decay times T2∗ available qubits in the chip at the maximum frequencies of 
+all. 
+ 
+ 
+ 
+ 
+ 
+ 
+
+(a)
+4.166
+4.235
+4.372
+4.416
+4.460
+(b)
+5.505
+5.782
+5.530
+5.508
+5.707
+.35
+4.168
+4.179
+4.249
+4.385
+4.427
+4.472
+5.635
+5.452
+5.466
+5.615
+5.436
+5.548
+4.181
+4.190
+4.270
+4.408
+4.448
+4.488
+5.500
+5.553
+5.556
+5.588
+5.500
+5.425
+4.194
+4.207
+4.291
+4.429
+4.463
+4.502
+5.642
+5.636
+5.710
+5.580
+5.361
+5.504
+4.201
+4.209
+4.297
+4.444
+4.481
+4.517
+5.736
+5.689
+5.529
+5.521
+5.509
+5.339
+4.211
+4.233
+4.317
+4.456
+4.487
+4.520
+5.663
+5.458
+5.489
+5.601
+5.473
+5.348
+4.209
+4.217
+4.311
+4.458
+4.498
+4.513
+5.474
+5.708
+5.493
+5.498
+5.553
+5.415
+4.211
+4.226
+4.316
+4.487
+4.521
+5.526
+5.724
+5.474
+5.519
+5.435
+4.202
+4.212
+4.299
+4.445
+4.482
+4.516
+5.606
+5.608
+5.444
+5.612
+5.616
+5.452
+4.192
+4.205
+4.292
+4.426
+4.461
+4.496
+5.504
+5.615
+5.595
+5.438
+5.580
+5.617
+4.269
+4.397
+4.447
+5.529
+5.714
+5.579
+4
+4.2
+4.4
+4.6
+5.2
+5.4
+5.6
+5.8
+Readout frequency (GHz)
+Max fo1 (GHz)
+(c)
+22.37
+25.71
+23.11
+21.26
+5.65
+20.09
+(d)
+6.98
+9.01
+9.35
+11.70
+5.40
+5.09
+22.46
+29.23
+5.62
+13.02
+11.99
+0.5
+3.94
+16.10
+.6.75
+15.40
+.33
+9.80
+14.15
+23.17
+29.14
+15.32
+11.70
+5.77
+11.80
+17.90
+9.03
+16.10
+4.22
+16.81
+15.95
+8.76
+14.90
+17.82
+13.49
+4.84
+2.68
+1.66
+L.01
+2.38
+.64
+21.51
+4.54
+23.24
+23.58
+16.64
+6T
+5.64
+.43
+8.44
+3.88
+67
+16.38
+15.46
+17.66
+18.00
+14.40
+9.55
+9.13
+4.29
+6.75
+4.93
+10.80
+19.00
+6.66
+11.65
+8.15
+3.27
+24.26
+9.04
+6.72
+14.70
+3.93
+3.58
+15.80
+0.41
+17.66
+17.57
+20.42
+12.18
+12.09
+3.60
+2.88
+10.20
+7.12
+10.75
+17.12
+16.05
+26.05
+11.19
+15.20
+6.49
+5.43
+12.20
+5.43
+8.59
+7.11
+5.44
+5.55
+4.01
+12.34
+18.81
+10.03
+11.07
+3.23
+5.45
+2.22
+1.52
+10.20
+8.25
+8.63
+13
+5.85
+22.63
+12.62
+2
+8
+16
+24
+30
+0
+5
+10
+15
+19
+Ti (μs)
+T2 (μs)21 
+ 
+ 
+ 
+Figure S4: The characteristics of activated qubits (dark grey) in our experiments. The activated couplers 
+(blue) are tuned to simulate the gSSH Hamiltonian. The inactivated qubits and couplers (light grey) are 
+at idle point throughout the experiment. The empty circle marks the only dead qubit. (a) Locations of 
+activated qubits ������������1 − Q32. (b) Idle frequencies of activated qubits.  (c) The relaxation times T1 of 
+activated qubits at the reference point. (d) The Ramsey decay times T2
+∗ of activated qubits at the 
+reference point. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S5: Simultaneous readout fidelities of ground (blue bars) and excited (orange bars) states of all 
+the activated qubits. The average fidelity for the ground (excited) state is 0.97 (0.899), marked by the 
+red (green) dashed line. Inset: A typical scattering plot of the readout signal (for Q19) in the I/Q plane. 
+
+Activequbits
+Idlefrequencies
+Ti at reference point
+T2 at reference point
+(a)
+Q23
+Q25
+(b)
+5.5575.529
+(c)
+19.6
+27.0
+(d)
+2.92.6
+Q22
+Q24Q26
+5.4165.4875.623
+9.0
+15.83.3
+1.8
+3.41.5
+Q21
+Q29Q27
+5.486
+5.5955.459
+16.6
+10.714.6
+2.3
+2.13.2
+Q20
+5.606
+5.6965.421
+7.1
+8.619.3
+0.9
+0.61.9
+Q19
+Q31]
+Q1
+5.689 5.5385.497
+14.54.5
+18.6
+1.5
+1.92.5
+Q18
+Q32
+Q2
+5.5075.3855.625
+23.3
+2.5
+Q17
+Q3
+5.709
+5.562
+19.3
+14.2
+2.0
+2.2
+Q16
+Q10
+Q4
+5.6245.485
+5.471
+17.017.5
+16.5
+1.33.1
+2.5
+Q15Q11
+Qg
+Q5
+5.5575.4105.404 5.652
+10.419.510.116.1
+2.04.04.11.7
+Q14
+Q12
+Q：Q6
+5.6495.6405.4765.512
+4.58.88.214.2
+1.51.72.61.8
+Q13
+Q7
+5.603
+5.638
+17.3
+16.6
+1.0
+1.00.970 ± 0.023
+0.899 ± 0.035
+Q19
+0.994
+Ground
+0.937
+Excited22 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S6: The Z crosstalk between adjacent qubits and adjacent coupler-qubit pairs. (a) The 
+crosstalk from Qi+1 to Qi. (b) The crosstalk from Qi−1 to Qi. (c) The crosstalk from Ci to Qi. 
+(D) The crosstalk from Ci+1 to Qi. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S7: The correction of the distorted Z-control signal. The measured trailings of a distorted square 
+wave (solid black) and a corrected square wave (solid red). Inset: the experimental sequence for 
+measuring the distortion of the Z-control signal. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+(a)
+Qi+1→Qi
+(b)
+Qi-1→Qi
+0.2
+0.0
+0.2
+(c)
+Ci-→Qi
+(d)
+Ci+1→Qi
+0.2
+0.0
+0.2
+1
+07
+Q1
+03'0
+T/2
+Tomo
+Phase
+-2
+XY
+Delay
+Z
+-4
+Z distortion
+Z distortion (corrected)
+-6
+0
+5
+10
+15
+20
+Delay (μs)23 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S8: The timing calibrations in the experiment. (a), (b), (c) show the pulse sequences for the 
+timing alignments between qubit’s XY control and Z control, Z control between two adjacent qubits, 
+Z control between a qubit and its nearest couplers, respectively. (d), (e), (f) shows the corresponding 
+typical experimental data (dots), respectively. The solid lines are the experimental data filtered by a 
+fifth-order low-pass Butterworth filter. 
+
+T
+T
+(a)
+(c) Q23 XY
+T
+Delay
+XY
+Q23 Z
+Q23 Z
+Delayi
+Z
+C24 Z
+C24 Z
+Delay
+Q24 Z
+Q24 Z
+(e)
+(f)
+0.9
+0.9
+ Population
+0.8 ns
+0.4
+0.6
+0.6
+-0.2 ns
+Q23
+0.2 ns
+Q23
+Q24
+Q24
+0.2
+0.3
+Total
+0.3
+Total
+Q23
+0.0
+0.0
+0.0
+-50
+-10
+30
+70
+100-50
+0
+50 100
+-100-50
+0
+50
+100
+Delay (ns)
+Delay (ns)
+Delay (ns)24 
+ 
+ 
+ 
+Figure S9: Demonstration of the tunable coupling strength between the nearest qubit pairs. (a) The 
+sequence of iSW AP experiment. (b) The typical iSWAP oscillation between two qubits (Q19 and Q18), 
+when the coupling (C19) is 2π *1.5 MHz. (c) The oscillation frequency can be tuned by the flux bias of 
+the C19 (10 times the flux bias followed by exponential amplifying for clarity here). (d) The coupling 
+strengths of a total of 32 qubit-coupler-qubit triples as a function of coupler bias. These curves are then 
+parameterized by the 20th-order polynomial fitting. Blue dots (orange curves) are experimentally 
+extracted (parameterized) coupling strength.
+
+(a)
+(b)
+(c)
+Q19 - C19 - Q18
+Q19 - C19 - Q18
+TT
+2.0
+0.9
+1.0
+0.9
+Q19 XY
+Population
+[Q19 bias
+Q1g Z
+0.5
+[↑ Cig bias
+C1g Z
+t
+Q18 Z
+0.1
+0.1
+0.0
+0.0
+-0.227
+-0.224
+-0.221
+-0.218
+1.0
+3.0
+5.0
+6.7
+(d)
+Q1g bias (a. u.)
+Cig bias (a. u. )
+12 +
+13
+14
+13 -
+Q1-C1-Q32
+Q2-C2-Q1
+Q4-C4-Q3
+0
+0
+0
+0
+-0.14
+-0.07
+0.00
+0.00
+0.07
+0.15
+-0.06
+-0.03
+0.00
+-0.18
+-0.09
+0.00
+13
+13
+14
+13
+Q5-C5-Q4
+Q6-C6-Q5
+9-
+Q8-C8-Q7
+0
+0
+0
+0
+0.00
+0.05
+0.11
+0.00
+0.07
+0.13
+-0.16
+-0.08
+0.00
+-0.12
+-0.06
+0.00
+15
+13
+14
+14
+80-60-60
+Q10-C10-Qg
+Q11-C11-Q10
+Q12-C12-Q11
+0
+0
+0
+/2π)
+-0.13
+-0.06
+0.00
+-0.15
+-0.07
+0.00
+-0.14
+-0.07
+0.00
+0.00
+0.08
+0.15
+(MHz)
+12
+13
+12
+13
+Q13-C13-Q12
+Q14-C14-Q13
+Q15-C15-Q14
+Q16-C16-Q15
+strength (
+0
+0
+0
+0
+0.18
+-0.09
+0.00
+-0.12
+-0.06
+0.00
+0.00
+0.07
+0.15
+0.17
+-0.08
+0.00
+16
+Coupling 
+14
+13
+13
+Q17-C17-Q16
+Q18-C18-Q17
+Q19-C19-Q18
+Q20-C20-Q19
+0
+0
+0-
+0
+0.00
+0.07
+0.14
+0.00
+0.09
+0.18
+0.00
+0.10
+0.20
+0.00
+0.11
+0.22
+14
+13
+12
+14
+Q21-C21-Q20
+Q22-C22-Q21
+Q23-C23-Q22
+Q24-C24-Q23
+0
+0
+0
+0.00
+0.12
+0.24
+-0.23
+-0.12
+0.00
+-0.25
+-0.13
+0.00
+0.00
+0.07
+0.15
+13
+13
+14
+14
+Q25-C25-Q24
+Q26-C26-Q25
+Q27-C27-Q26
+Q28-C28-Q27
+0
+0
+0
+0
+-0.19
+0.09
+0.00
+0.00
+0.10
+0.21
+0.00
+0.10
+0.19
+-0.15
+-0.08
+0.00
+15
+15
+12
+15
+Q29-C29-Q28
+Q30-C30-Q29
+Q31-C31-Q30
+Q32-C32-Q31
+70
+0 +
+Q：
+0.00
+0.03
+0.06
+0.00
+0.05
+0.10
+-0.32
+-0.16
+0.00
+0.00
+0.10
+0.19
+Coupler bias (a.u.)25 
+ 
+ 
+ 
+Figure S10: (a) Theoretical 32-qubit quantum walk of the target Hamiltonian where all nearest- neighbor 
+coupling strengths are set to be 2 MHz. (b) Measured 32-qubit quantum walk of the experimental 
+Hamiltonian where all pairwise coupling strengths are parameterized as 2 MHz. 
+(c) Fitted 32-qubit quantum walk by optimizing the Hamiltonian to approximate the actual evolution 
+in (b). 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S11: The comparison between parameterized coupling strength and target coupling strength. 
+Blue dots are the approximate coupling strength from the optimization of the coupling strength of 32 
+qubit pairs in the Hamiltonian. Yellow dots are their average. 
+
+(a)
+(b)
+(c)
+1.0
+0.2
+0.1
+0
+0.8
+0.2
+0.1
+0
+0.2
+0.6
+0.1
+(sn)
+0
+0.2
+0.1
+0.4
+0
+0.2
+0.1
+0.2
+0
+0.2
+0.1
+0
+0.0
+1
+6
+11
+16
+21
+26
+31
+1
+6
+11
+21
+26
+31
+1
+6
+11
+16
+21
+26
+31
+SiteFitted
+Average
+8
+6
+(MHz)
+4
+2
+0
+0
+2
+4
+6
+8
+Target (MHz)26 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S12: Demonstration of the residual coupling between two diagonal qubits when all couplers are 
+set at zero bias. The qubits Q27 in (a) and Q29 in (b) with the shortest characteristic swapping time is 
+larger than 5.05 µs, marked by the red dashed line. The corresponding characteristic coupling strength 
+is less than 0.05 MHz, manifesting the upper limit of the residual coupling. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S13: Calibration of the effect of the coupler bias on the qubit frequency. (a) Experimental pulse 
+sequence. (b) The solid blue circle and green diamond lines are experimental phase shifts on Q10 when 
+we sweep the coupler bias from strong to weak coupling (blue circles for C10 and green diamonds for 
+C11). The solid orange squares (C10) and red stars (C11) are calibrated data. 
+ 
+
+(a)
+Q27
+(b)
+Q29
+10
+0.85
+0.25
+Population
+(srl)
+5.050us
+5.050us
+t
+5
+0.55
+0.15
+0.05
+1
+0.30
+-0.044-0.043
+-0.042
+-0.044
+-0.043
+-0.042
+Q2z bias (a.u.)
+Q2z bias (a.u.)T/2
+Tr/2
+(a)
+Q10XY
+Q10 Z
+Couperbias
+C10/C11Z
+(b)
+Deviated frequency (MHz)
+0
+Ci0 - Q10 data
+Ci0 - Q1o fitted
+5
+Cio- Q1o corrected
+C11 - Q10 data
+C11-Q1ofitted
+C11 - Q1o corrected
+-10
+-0.15
+-0.1
+-0.05
+0.0
+Coupler bias (a.u.)27 
+ 
+ 
+ 
+Figure S14: Demonstration of quantum walks on qubits chains with single-excitation at Q25. The 
+evolution time is 1 µs and all coupling strength are set to be 2π*2 MHz. We add two more qubits Q33 
+and Q34 (between Q2 and Q3) here. 
+ 
+ 
+ 
+Figure S15: (Color online) (a) Topological phase diagram. Real-space winding number ν as 
+functions of W and J′. Here the white dashed and black solid lines denote the topological phase 
+boundaries, which are determined by the divergence of the localization length of zero-energy states 
+and by the flat-band localization (SCBA) analysis, respectively. (b) Energy gap ∆E/J as functions 
+of W and J′. (c) Middle 100 eigenenergies as a function of W for J′/J = 1.1 under the open boundary 
+condition. The TAI regime with ν = 1 and disorder-induced mid-gap edge modes is colored. (d) 
+Averaged DOS ρave (red dashed line) and typical DOS ρtype (blue solid line) as a function of energy 
+E for the TAI phase at (J′/J, W/J) = (1.02, 0.5), (1.1, 1), and (1.5, 1.9) from top to bottom. The 
+lattice size in (a-d) is L = 2Nc = 1220 with negligible finite-size effects. The energy unit is set as J 
+= 1. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+edge modes 
+ 
+
+1.0
+1.0
+0.8
+0.6
+0.5
+0.2
+0.0
+0.0
+6
+9
+Oubit2
+L
+1.5
+0.8
+0.6
+1
+0.4
+0.5
+0.2
+0
+0
+-
+W/.J
+2Dta
+0.5AE/J
+2
+1.5
+1.5
+1
+1
+0.5
+0.5
+0
+0
+0
+1
+2
+/A0.2
+-0.2
+V=0
+=1
+V=0
+0
+1
+2
+f/M28 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S16: (Color online) (a) Averaged inverse participation ratio IPR
+����� as a function of W and J′/J for 
+L = 1220. The white dash-dotted line denotes the boundary between the extended 
+and the localized phases obtained from numerically determining critical disorder strengths of 
+AT points. (b) IPR
+����� and (c) ∂ lg IPR
+�����/∂W as a function of W for L = {288, 754, 1220} with 
+J′/J = 1.1. The inset in (b) shows the corresponding logarithm plot lg IPR
+�����(W). The grey 
+dashed lines indicate the critical disorder strength of the AT point extracted from the finite- 
+size analysis in this case. (d) ∂ lg IPR
+�����/∂W as a function of W for J′/J = {0.1, 0.5, 2.0} and 
+L = 1220. The energy unit is set as J = 1.
+(a) 
+(b) 
+(c) 
+(d) 
+
+2
+TPR
+1.5
+0.3
+0.2
+0.5
+0. 1
+0
+0
+0
+2
+r/A10.25
+-1
+0.2 
+HdI
+0.15
+-3
+0.1
+0
+0.5 W/J
+0.05
+L = 288
+F9 = T
+L = 1220
+0
+0
+0.5.
+r/M50
+L = 288
+40
+L = 754
+Me/
+L = 1220
+30
+20
+10
+0
+0
+0.5
+W/J80
+J°/J = 0.1
+ J°/J = 0.5
+Me/
+60
+. J'/J = 2.0
+TPR/
+40
+20
+0
+A
+0
+0.5
+W/J29 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure S17: (Color online) (a) Eigenenergy spectrum for lattice size L = 1220 and disorder strengths 
+W/J ∈ {0, 0.5, 1, 1.5, 2, 2.5, 3}, with the cases of W/J = 0 and W/J = 2 in the insets. (b) lg IPR
+����� and (c) 
+∂lg IPR
+�����/∂W as a function of W for L = {288, 754, 1220}. The insets show the corresponding results 
+for a smaller region near W = 0. The flat-band localization at W = 0 and the Anderson transition (AT) 
+at W ≈ 2.0 are labeled. (d) Finite-size scaling of IPR
+����� with respect to the lattice size L = 2Nc for the 
+flat-band localization (W/J = 0) and AL (W/J = 3) phases. (e) The same as (d) for the extended phase 
+with W/J ∈ {10−6, 10−4, 10−2, 1}. (f) Time-averaged mean square displacement D� as a function of 
+evolution time t for L = 1220 and different values of W. (g) Time-averaged survival probability St� and 
+the mean square displacement D� as a function of W for L = 1220 after a long evolution time t = 400 
+ℏ/J. (h) Localization phase diagram on the whole W -J′plane 
+ 
+ 
+
+(a)
+(b)
+0
+(c)
+(d) 0.6
+4
+FBL
+AT
+W/J=0
+AT
+FBL
+-0.5
+Me/
+0.5
+80-0
+2 
+9
+0
+5
+R
+IPI
+0.1 ;
+HdI
+0.4
+0-W/J=0
+W/J
+-1
+0.05
+-50
+0
+500
+1000
+-20
+-W/J=3
+E
+0
+-100
+2/ W/J=2
+0.3
+-1.5
+-150
+-2
+L = 288
+AL
+-40
+: FBL
+L = 754
+-200
+0.2
+-2
+L = 1220
+0
+0.05
+0.1
+500
+1000
+-4 
+0.1
+2
+0
+2
+4
+0
+2
+4
+0
+500
+1000
+0
+4
+6
+W/J
+Eigenvalue index
+W/ J
+I-T
+×10-3
+(e) 0.04
+(f) 4
+(g) 0.8
+15
+(h) 2
+W/J= 0.0
+W/J = 0.1
+W/J= 10-6
+3
+W/J = 1.0
+0.03
+-W/J= 10-4
+W/J=2.0
+0.6
+1.5
+-W/J= 10-2
+W/J = 3.0
+10
+R
+W/J=1
+ID
+W/J=4.0
+2
+s 0.4
+D
+Localized
+5
+0.01
+1
+0.2
+0.5
+FBL
+AT
+0 L
+0
+0
+0
+00
+0
+2
+4
+6
+0
+10
+20
+30
+0
+2
+4
+0
+2
+×10-3
+W/J
+W/J
+L-1
+time t (h/.J)30 
+ 
+ 
+ 
+Figure S18: Pulse sequence for the quantum-walk experiment. Initially, all the qubits (couplers) are 
+biased at the idle (turning-off) frequencies. To prepare the single-excitation initial state, we apply a π-
+pulse, composed of two π/2-pulses with the same phase, to a chosen qubit. To turn on the target 
+Hamiltonian, we bias all of the qubits to the reference frequency ωref , and set the coupler frequencies 
+according to the calibrated functional relations between flux bias and the effective coupling strength. 
+After the system evolves for a duration t, we first bias the couplers back to the turning-off points and 
+perform simultaneous projective measurement on all the qubits in the σˆz–basis. 
+
+C1 ... C32
+Q1 .. Q32 
+ 
+ 
+ 
+Figure S19: Experimental data of single-excitation quantum walks for a parameter point 
+(W /J, J′/J) = (3, 1.25) in the W -J′ plane. The energy unit is chosen to be J = 2π *1.5 MHz, 
+and the duration of the walks is t f = 1.5 μs. The single excitation is placed at n = 15, . . . , 
+18 from the left to the right columns, while the modulation phase is set to be δ = 2qπ/8 
+with q = 0, 1, . . . 7 from the top to the bottom rows. 
+ 
+ 
+
+excitedsite:14,phase:0.0*2n
+excited site:15, phase:0.0*2n
+xcited site:16,phase:0.0*2m
+excited site:17,phase:0.0*2n
+:0.125*2
+site:15.phase:0.125*2
+te:16.phase:0.125*2n
+se:0.125*2m
+excited site:14.phase:0.25*2n
+excited site:15.,phase:0.25*2m
+excited site:16,phase:0.25*2m
+excited site:17.phase:0.25*2n
+excitedsite:14.phase:0.375*2n
+excitedsite:16.phase:0.375*2
+excitedsite:17,phase:0.375*2n
+time (μs)
+excited site:14,phase:0.5*2n
+excited site:15.phase:0.5*2n
+excited site:16,phase:0.5*2n
+excited site:17.phase:0.5*2n
+excited site:14, phase:0.625*2n
+excited site:15.phase:0.625*2n
+excited site:16. phase:0.625*2n
+excited site:17.phase:0.625*2
+excited site:14,phase:0.75*2n
+excited site:15, phase:0.75*2m
+excited site:17,phase:0.75*2n
+excitedsite:14,phase:0.875*2nt
+excitedsite:15,phase:0.875*2
+excited site:16.phase:0.875*2
+excited site:17.phase:0.875*2
+site 
+ 
+ 
+ 
+ 
+ 
+Figure S20: Performance of the error mitigation techniques. Density evolution of raw 
+experi- mental data (a) and error-mitigated data (b). The dimensionless parameters for 
+this quantum- walk experiment is (W/J, J′/J) = (1, 0) and the phase of the disorder 
+realization is δ = 0. 
+
+(a)
+Orignal data
+(b) error mitgated data
+.5
+0.9
+0.9
+1.0
+0.6
+Population
+(sr)
+0.6
+t
+0.5
+0.3
+0.3
+0.0
+0.0
+0.0
+1
+10
+20
+32
+1
+10
+20
+32
+Site index
\ No newline at end of file
diff --git a/1tFLT4oBgHgl3EQfqC-n/content/tmp_files/load_file.txt b/1tFLT4oBgHgl3EQfqC-n/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d49228cdef0a2bfd330eef852188e1c5eeb67c7d
--- /dev/null
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf,len=2192
+page_content='Mapping a topology-disorder phase diagram with a quantum simulator  Xue-Gang Li1†, Hui-Kai Xu1‡, Jun-Hua Wang1§, Ling-Zhi Tang2, Dan-Wei Zhang2*,  Chu-Hong Yang1, Tang Su1, Chen-Lu Wang1, Zhen-Yu Mi1, Wei-Jie Sun1, Xue-Hui  Liang1, Mo Chen1, Cheng-Yao Li1, Ying-Shan Zhang1, Ke-Huan Linghu1, Jia-Xiu  Han1, Wei-Yang Liu1, Yu-Long Feng1, Pei Liu3, Guang-Ming Xue1, Jing-Ning  Zhang1*, Yi-Rong Jin1*, Shi-Liang Zhu2, Hai-Feng Yu1, Qi-Kun Xue1,3  1Beijing Academy of Quantum Information Sciences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Beijing 100193, China  2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum  Materials, School of Physics and Telecommunication Engineering, South China  Normal University;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Guangzhou 510006, China  3State Key Laboratory of Low Dimensional Quantum Physics and Department of  Physics, Tsinghua University, Beijing 100084, China  †, ‡, §These authors contributed equally to this work  Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Email: danweizhang@m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='scnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='cn (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  zhangjn@baqis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='cn (J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' jinyr@baqis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='cn (Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The competition and interplay of topology and disorder has been one of the most  famous topics in the field of condensed matter physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In addition to the  intuitive tendency to bring the system into a topologically trivial and localized  phase1, it has been discovered that disorder can also induce nontrivial topology2,3  and transport4,5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To reveal rich and diverse phase structures, mapping phase  diagrams plays an important role in both theoretical and experimental sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Quantum simulation6,7 provides a prospective way to study the target model,  explore the phase diagram and reveal the underlying mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thanks to the  unprecedented controllability, superconducting quantum simulators have been  introduced to investigate complex many-body physics8,9 and bring thought  experiments into reality10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To our best knowledge, the effort to map a phase  diagram with a rich structure is still lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here we report a systematic  experimental study of the topology-disorder phase diagram with 32 qubits on a  programmable analog quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We implement one-dimensional (1D)  disordered dimerized tight-binding models over a wide parameter range and  observe diverse phases, including the topological Anderson insulator (TAI) and  the inverse Anderson localization (IAL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Our experiment manifests the  efficiency, accuracy and flexibility of the superconducting-circuit device and  paves the way to the demonstration and understanding of many-body  phenomena with noisy intermediate-scale quantum simulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Topology and disorder both lie in the heart of condensed matter physics, due to their  intrinsic relation with symmetry and ubiquitous existence in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Exploring exotic  topological phases has attracted intense interest in both theoretical and experimental  aspects since the discovery of the quantum Hall effect11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As is well known, topology  is protected by generic symmetries, and thus is robust against disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' However,  strong disorders eventually destroy topology due to Anderson localization1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This  intuitive picture has been broken by the discovery of the TAI2,3, which originates from  the investigation of HgTe/CdTe quantum wells12 and is then generalized to various  disordered systems13-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Besides the disorder-induced topology, the disorder also  imposes a dramatic influence on transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In contrast to the intuition that disorder  leads to localization, the inverse Anderson localization (IAL), induced by adding  disorders to a flat-band system, has also been predicted in 3D diamond lattices4 and  2D photonic cages5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' It has been recently proposed19 that a dimerized tight-binding  chain with off-diagonal quasiperiodic disorder hosts multiple topologies and disorder-  related phenomena, including the TAI and the Anderson transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, this  model exhibits the IAL in the fully dimerized limit and thus provides a theoretically  fundamental and experimentally feasible testbed for the investigation of the interplay  between topology and disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Due to the lack of continuous and precise control of system parameters, it is  challenging to observe rich phase diagrams caused by topology and disorder  competition in real materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Quantum simulation6 provides an ideal platform to  explore topology and localization physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For instance, the TAI with bulk dynamics  was observed with ultracold atoms20 and photonic crystals21,22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' However, to our best  knowledge, a systematic experimental study of the topology-disorder phase diagram  with a quantum simulator is still lacking, which puts forward requirements on high  levels of flexibility and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The superconducting quantum simulator, as an  artificial quantum system, features excellent scalability and versatility and has been  vastly exploited to simulate quantum dynamics, ranging from strongly-correlated  quantum walks8 to many-body localization9 and even quantum supremacy23,24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In this  work, we experimentally map out the topology-disorder phase diagram of a dimerized  tight-binding chain with off-diagonal quasi-periodic disorder, using a 32-qubit chain  selected out of 62 functional qubits in a superconducting quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' With  precise parameterized calibration, we efficiently implement hundreds of target  Hamiltonians over a wide range in the parameter plane and observe various phases  with different topological and localization properties, including the TAI and the IAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Programmable quantum simulator  The device used in this experiment is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Benefiting from the flip-chip  and air bridge techniques, the flux crosstalk is greatly suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In our device, the  crosstalk is lower than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2% for all nearest-neighbor qubit-qubit pairs and qubit-  coupler pairs, and thus can be negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' However, in such a compact layout,  unwanted couplings between spatially close qubits are still visible25,26, which blurs the  boundary between extended and localized phases in off-diagonally disordered models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We adopt a novel qubit design, named flipmon27, to overcome this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  average value of the residual XY coupling strengths between diagonal qubit pairs is  measured to be about 2π × 30 kHz28, corresponding to a swapping period of about  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='67 μs, much larger than the characteristic time (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 μs ) in this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In this  device, the decoherence times ������������1 and ������������2  ∗ at the maximum frequency, averaged over  all 62 functional qubits, are measured to be about 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='9 μs and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='7 μs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  To accurately engineer the target Hamiltonians as many as possible in our experiment,  we perform an efficient calibration procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We first align the frequencies of 32  activated qubits, then parametrize the coupling strength of each nearest-neighbor  qubit pair, and finally, compensate for the coupler-induced dispersive shifts of  qubits28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After calibration, we can simulate the dynamic evolution of 18 Hamiltonians  per hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Meanwhile, the average classical fidelity of different Hamiltonians under  different evolution times is 91%, which is comparable to the previous results8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Programmable analog quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' a, Photograph of the  superconducting quantum device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' b, Photographs of the chip and the carrier of a five-  qubit unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The chip contains elements with high-quality factors, including flipmon  qubits in orange, readout resonators in blue, and couplers in green, while the carrier  contains elements with low-quality factors, including control lines in grey and Purcell  filters in red, which are covered by air bridges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The flipmon consists of two capacitive  electrodes, with one on the chip and the other on the carrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' c, Qubit layout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  device contains 62 functional qubits and 105 couplers, among which 32 qubits and  couplers are activated to form a quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Generalized Su-Schrieffer-Heeger model  To investigate the interplay between topology and disorder, we use this simulator to  realize the generalized Su-Schrieffer-Heeger (gSSH) model29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The model describes  a  C  Chip  Carrier  4mm  Qubit:  Active  Inactive  Broken  Coupler:  b  Active  Inactive  Chip  Bouple  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5mm  Qubit  Indiumpoint  Carrier  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5mm  Airbridge  XYZline  Purcell filterspin-less fermions moving in disordered dimerized chains, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  target Hamiltonian reads,  �������������gSSH/ℏ = � ������������������������  ′  ������������c  ������������=1  �������������������������,������������  † �������������������������,������������ + ������������ � �������������������������,������������  † �������������������������+1,������������  ������������c−1  ������������=1  + ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ,  (1)  where �������������������������,������������(α ∈ A, B) is the fermionic annihilation operator for the α-site in the ������������������������ℎ  unit cell with ������������������������ being the number of cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We adopt the configuration that the  inter-cell tunneling strength ������������ is homogeneous, while the intra-cell tunneling strength  ������������′ is modulated by quasi-periodic disorders,  ������������������������  ′ = ������������′ + ������������ cos(2������������������������������������ + ������������) ,  (2)  with W quantifying the disorder strength and δ being an arbitrary phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here ������������ is  an irrational number and is chosen to be �√5 − 1�/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The topological and localized  properties of this 1D disordered chiral system19,28 are characterized by the real-space  winding number and the spectral-averaged inverse participation ratio, denoted by ν  and aIPR, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that while δ has no physical meaning in the  thermodynamic limit, it generates different disorder realizations for the cases with  finite-size systems, which are averaged to recover the thermodynamic results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The competition between topology and disorder gives rise to a rich phase diagram28,  with four phases of different values of ������������ and aIPR, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In the clean  limit (������������ = 0), the topological and trivial phases, both extended, are separated by a  critical point at ������������′/������������ = 1, and these two phases extend to the weak disorder regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  As the disorder becomes stronger, the nontrivial topology breaks down and the bulk  states become localized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Theoretically, it has been predicted that the critical disorder  strength to induce a localization transition is well below that to break a nontrivial  topology2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As a result, there exists a topological localized phase, or the TAI, between  the topological extended and the trivial localized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Strikingly, the topological  localized phase extends to the regime where the system is topologically trivial in the  clean limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This can be understood by the disorder-induced renormalization of the  model parameter in the critical regime3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' More importantly, this model also exhibits  the IAL in the fully dimerized limit with ������������′ = 0, where the transport is solely due to  disorder and has not been observed hitherto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Generalized Su-Schriffer-Heeger (gSSH) model and typical dynamics in  various phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' a, Schematic illustration of the gSSH model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The inter-cell tunneling  (red dashed lines) is homogeneous, while the intra-cell tunneling (gray solid lines) is  modulated with quasi-periodic disorders (gray explosive shapes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' b, Numerical phase  diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The parameter plane is presented by the average normalized intra-cell  coupling strength ������������′/������������ and the normalized disorder strength ������������/������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This model  supports the topological extended (topo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=') phase, the trivial extended (triv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=')  phase, the topological localized (topo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=') phase and the trivial localized (triv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=')  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The TAI manifests itself in the topological localized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' On the horizontal  axis with ������������′ = 0, the origin point features the flat-band localization (FBL), while the  IAL emerges in the topological extended region with ������������/������������ ∈ (0,2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' c, Typical density  evolution of single-excitation quantum walks as the function of the evolution time ������������  and qubit site index ranging from 1 to 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Each row contains two quantum walks,  initially excited at the edge (site 1) and in the bulk of the chain (site 15), and  corresponding to a parameter point (yellow star) in b, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Dynamical extraction  We begin with mapping the fermionic system to a spin system by the Jordan-Wigner  transformation and then engineer the native Hamiltonian of the 32-qubit quantum  simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The frequencies of the active qubits are biased to the reference point  Population  a  c  A  A  A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  n  B  B  C  B  n-1  n  n+1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  2  (sr)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  七  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  TAI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  IAL  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0  2  3  WIJ  FBL  Topo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='ext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Triv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='ext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1  15  32  15  32  Topo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Triv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Site index������������ref = 2π × 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='495 GHz, and the nearest-neighbor couplings are tuned to ������������ and ������������������������  ′  according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We fix the inter-cell tunneling strength to be ������������ = 2π × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  MHz and let the ratio ������������′/������������ (������������/������������) vary in the range [0,2] ([0,4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This parameter  range covers various phases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For each Hamiltonian, we prepare two initial  states, with the single-excitation at the edge and in the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The experimental data of  density evolution, obtained from projective measurement after turning on the target  Hamiltonian and evolving the system for a time period ������������, intuitively reflect the  topological and localization properties, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' From top to bottom, the  four representative systems, with model parameters marked by yellow stars in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b,  are chosen from the trivial extended, the topological extended, the trivial localized  and the topological localized phases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The difference between extended  and localized phases is intuitively demonstrated in the time evolution of bulk  excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As to the topological characteristics, the edge excitations for topological  phases remain at the edge throughout the evolution no matter whether the bulk states  are extended or localized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, the edge excitation in topological phases mainly  couples to nearby sites in the same sublattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Having shown the typical behavior of each phase, we then quantitatively extract the  topological and localized properties, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������ and aIPR, with the quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  For each quantum-walk experiment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' we calculate the time-averaged expectation  values of the chiral displacement operator and the survival probability,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' denoted as �������������������������  and �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������������������� = 1  ������������ � �������������(������������′)����������������������������������������(������������′)�������������������������′  ������������  0  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (3)  ������������������������� = 1  ������������ � |⟨������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������(������������′)⟩|2������������������������′  ������������  0  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (4)  where the chiral ������������� and the position ������������� operators are defined by �������������|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩ = ������������������������ |������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩  with ������������������������/������������ = ±1 and �������������|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩ = ������������|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here |������������, ������������⟩ is the initial state  which prepares a single excitation on the α-site in the ������������������������ℎ unit cell and |������������(������������)⟩ =  exp�−�������������������������gSSH������������/ℏ�|������������, ������������⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  To diminish the impact of the finite-size effect, we construct 8 disordered realizations  and 4 initial single-excitation states for a target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3a (3b) show the  dynamics of �������������������������  (�������������������������) for these 32 quantum-walk instances for a gSSH model in the  trivial localized phase with (������������/������������, ������������/������������′) = (3,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25), where the instance-averaged  ⟨������������̅������������⟩ (⟨������������̅������������⟩) is also shown by green squares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Although the evolutions of �������������������������  and �������������������������  depend on the specific disorder realization and initial state, ⟨������������̅������������⟩ and ⟨������������̅������������⟩, after  taking average over the 32 quantum-walk instances, converge to the real-space  winding number and the spectral-averaged IPR28, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We then implement the gSSH model in other three phases and show the results in  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3c and 3d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We observe that the topological indices ⟨������������̅������������⟩ almost converge to  their corresponding values in the long-time limit, saying ν = 1(0) for topological  (trivial) phases, while the circumstance is more complicated for the extraction of the  localized property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Theoretically, ⟨������������̅������������⟩ should vanish in the long-time limit for  infinite systems in the extended phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In our experiment, however, it remains finite  due to the small size of our simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We observe that ⟨������������̅������������⟩ quickly becomes flat for  localized phases (orange and green dots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3d), while it keeps decreasing during  the evolution for extended phases (red and blue dots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Besides, the values of  ⟨������������̅������������⟩ at the longest evolution time ������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 μs separate enough to discriminate the  extended and localized phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Dynamical extraction of topological and localization properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' a, Time-  averaged chiral displacement ������������������������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' b, Time-averaged survival probability ������������������������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Each  dashed line is �������������������������  a or ������������������������� b for a single quantum-walk instance, while these instances  are generated by setting ������������ ∈ [0, … ,7] × 2π/8 and placing the initial excitation at  sites 15, 16, 17 and 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The data points are obtained by averaging over different  quantum-walk instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' c, Averaged chiral displacement and d, survival probability  for different phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In c and d, the solid lines are numerical results without fitting  parameters30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For all experimental results (markers), the error bars are the standard  deviation of the mean propagated from the sampling error in the projective  measurement with 1024 repetition times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Solid lines are obtained by ideal numerical  simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Experimental phase diagram  With the above method of distinguishing topology and localization or not, we take  advantage of the programmable and efficient superconducting quantum simulator to  obtain the phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We sweep the model parameters over a wide range in the  topology-disorder plane and summarize our experimental results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here we  a  b  (WU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='JJ)= (3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25)  (WU, /U) = (3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25)  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  t (μs)  t (μs)  {(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 2)  F (3,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content="25)  (WU,J'I) =  ( (1,0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6)  c  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 2  3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  t (μs)define the values at ������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 ������������s as the experimental results for 〈������������̅∞〉 and 〈������������̅∞〉, which  serve as the experimental indices for the topological and localization properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Guided by the theoretical phase diagram in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b, we choose 114 points unevenly  distributed in the ������������-������������′ parameter space, and experimentally obtain the real-space  winding number and the spectral-averaged IPR in the long-time limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 〈������������̅∞〉 and  〈������������̅∞〉, as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4a and 4c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The experimental data for 〈������������̅∞〉 (〈������������̅∞〉) show clear  edges between topological and trivial (extended and localized) phases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4a and  4c, which are consistent with the theoretically-obtained phase boundaries in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  For better comparison, we also put corresponding numerical results, obtained from  numerically evolving the Schrödinger equation without free fitting parameters, in  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4b and 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Two representative cross-sections of the parameter space are shown  in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4E and 4F, with ������������′/J = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25 and 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4e shows nontrivial  topology emerges from trivial states in the clean limit as the disorder strength  increases, indicated by the sudden rise of 〈������������̅∞〉 to near unity in the regime ������������/������������ ∈  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Together with 〈������������̅∞〉, which shows the system becomes increasingly  localized, it provides convincing evidence of the TAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4f, we observe the  crossover from the FBL at ������������ = 0 to the topological extended phase lying on the  fully dimerized limit with ������������′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The formation of this phase is attributed to the IAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  As the disorder strength further increases, both the TAI and the IAL give up to the  trivial localized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As 〈������������̅∞〉 and 〈������������̅∞〉 gradually change when the target model  goes across phase boundaries, we claim that these are the manifestation of phase  transitions in the finite-time evolution of a finite-size system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Experimental results for the topology-disorder phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' a,  Averaged chiral displacement ⟨������������̅∞⟩ in the long-time limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' b, Numerical results for  ⟨������������̅∞⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' c, Averaged survival probability ⟨������������̅∞⟩ in the long-time limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' d, Numerical  results for ⟨������������̅∞⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Each plaquette in a and c represents a data point on the parameter  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Numerical phase boundaries adopted from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2b are also shown, where the  black dashed line separates topological and trivial phases, the white dashed-dotted  line separates the extended and localized phases, and the pink solid line on the  horizontal axis marks the trivial extended phase due to the IAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Numerical results in  b and d are obtained by evolving the Schrödinger equation with the target  Hamiltonian for a duration of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 μs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' e, Disorder-induced topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' f, Disorder-  induced transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The shaded areas mark the parameter ranges for the topological  localized e and extended f phases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The lines are numerical simulation  data, and the data points are experimental data with the error bars obtained in the  same way as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Outlook  With the inherent 2D geometry of the qubit lattice and strongly interacting multi-  excitations, it is anticipated that our quantum simulator can be straightforwardly  a  b  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0  C  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  0  0  1  2  3  4  0  1  2  3  4  WIJ  WIJ  e  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  sim  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  exp  IS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  f  JJ=0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  sim  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  C  IS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0  1  2  3  4  WJextended to realize quantum many-body models in quasi-1D or 2D systems with  computationally hard features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This work significantly improves the near-term  prospects of superconducting quantum simulators to explore exotic phases or quantum  dynamics elusive in condensed matter systems, such as 2D many-body localization31  and fractional topological states of photons32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Note added  Recently, we noticed another work on the experimental observation of inverse  Anderson transition in ultra-cold atoms33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  References and Notes  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Anderson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Absence of Diffusion in Certain Random Lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 109, 1492-1505 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Chu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Jain, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Shen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Topological Anderson Insulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 102, 136806 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Groth, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Theory of the Topological Anderson Insulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 103, 196805 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Goda, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Nishino, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Matsuda, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Inverse Anderson Transition Caused by  Flatbands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 96, 126401 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Longhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Inverse Anderson transition in photonic cages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 46, 2872-  2875 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Feynman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Simulating physics with computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 21,  467-488 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Türeci, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Houck, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Koch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' On-chip quantum simulation with  superconducting circuits, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 8, 292-299 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Yan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Strongly correlated quantum walks with a 12-qubit  superconducting processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Science 364, 753-756 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Guo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Observation of energy-resolved many-body localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 17, 234-239 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Jafferis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Traversable wormhole dynamics on a quantum processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Nature 612, 51–55 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Prange, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Girvin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', The quantum Hall effect (Springer, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Bernevig, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Hughes, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Quantum spin Hall effect and  topological phase transition in HgTe quantum wells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Science 314, 1757-1761  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Guo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Rosenberg, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Refael, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Franz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Topological Anderson  Insulator in Three Dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 105, 216601 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Mondragon-Shem, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Hughes, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Song, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Prodan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Topological  Criticality in the Chiral-Symmetric AIII Class at Strong Disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 113, 046802 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Altland, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Quantum Criticality of Quasi-One-Dimensional Topological  Anderson Insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 112, 206602 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Titum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Lindner, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Rechtsman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Refael, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Disorder-Induced  Floquet Topological Insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 114, 056801 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Non-Hermitian topological Anderson insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  China-Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 63, 267062 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Observation of non-Hermitian topological Anderson insulator in  quantum dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 13, 3229 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Tang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Topological Anderson  insulators with different bulk states in quasiperiodic chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A 105,  063327 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Meier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Observation of the topological Anderson insulator in  disordered atomic wires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Science 362, 929-933 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Stützer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Photonic topological Anderson insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nature 560, 461-  465 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Topological Anderson Insulator in Disordered Photonic  Crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 125, 133603 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Arute, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Quantum supremacy using a programmable superconducting  processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nature 574, 505-510 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Strong Quantum Computational Advantage Using a  Superconducting Quantum Processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 127, 180501 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Exponential suppression of bit or phase errors with cyclic error  correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nature 595, 383-387 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Many-body Hilbert space scarring on a superconducting  processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Vacuum-gap transmon qubits realized using flip-chip technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 119, 184003 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' See Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Su, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Schrieffer & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Heeger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Solitons in Polyacetylene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 42, 1698 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Johansson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Nation, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' & Nori, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', QuTiP: An open-source Python  framework for the dynamics of open quantum systems, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 183, 1760 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' yoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Exploring the many-body localization transition in two  dimensions, Science 352, 1547 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Roushan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chiral ground-state currents of interacting photons in a  synthetic magnetic field, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 13, 146-151 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Aharonov-Bohm Caging and Inverse Anderson transition in  Ultracold Atoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 129, 220403 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Acknowledgments  We acknowledge support from the National Natural Science Foundation of China  (grant nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 11890704, 12174126, 12104055, 12104056 and 12004042), Natural  Science Foundation of Beijing (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Z190012), Guangdong Basic and  Applied Basic Research Foundation (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 2021A1515010315) and Key Area  Research and Development Program of Guangdong Province (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2018B030326001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Author contributions  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Y conceived the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='X, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='W  carried out the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Y, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='S, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='W, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='S, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='C,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='X designed and made the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='F, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J built the measurement setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='Z performed the analytic calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='Z, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='H, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Y wrote the manuscript in consultation with S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='Z and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  All authors discussed the results and contributed to the writing of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Competing interests  Authors declare that they have no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Data and materials availability  All data are available in the main text or the supplementary materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Supplementary Materials  Materials and Methods  Supplementary Text  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S1 to S20  References  1  Supplementary Materials for  Realization of the topological Anderson insulator in a superconducting quantum  simulator  Xue-Gang Li1†,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Hui-Kai Xu1‡,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Jun-Hua Wang1§,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Ling-Zhi Tang2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Dan-Wei Zhang2*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chu-Hong Yang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Tang Su1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chen-Lu Wang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Zhen-Yu Mi1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Wei-Jie Sun1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Xue-Hui Liang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Mo Chen1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Cheng-Yao Li1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Ying-Shan Zhang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Ke-Huan Linghu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Jia-Xiu Han1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Wei-Yang Liu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Yu-Long Feng1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Pei Liu3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Guang-  Ming Xue1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Jing-Ning Zhang1*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Yi-Rong Jin1*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Shi-Liang Zhu2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Hai-Feng Yu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Qi-Kun Xue1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  1Beijing Academy of Quantum Information Sciences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Beijing 100193, China  2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of  Physics and Telecommunication Engineering, South China Normal University;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Guangzhou 510006,  China  3State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua  University, Beijing 100084, China  †, ‡, §These authors contributed equally to this work  Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Email: danweizhang@m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  This PDF file includes:  Materials and Methods  Supplementary Text  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S1 to S20  2  Materials and Methods  1 Device and measurement setup  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 Design  The device consists of 63 tunable qubits and 105 tunable couplers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The qubits are arranged in a  2-dimensional square lattice with a coupler between each of the two nearest qubit pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A  schematic of the circuit of a unit cell is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The qubits adopt "flipmon" design,  which is considered for advantages including improved vacuum energy participation ratio,  reduced unwanted crosstalk, more freedom of circuit wiring, and natural compatibility with flip-  chip technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For more details, please refer to (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Each qubit includes an asymmetric SQUID, with a control line grounded nearby for tuning its  frequency with persistent bias or fast DC pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The control line also acts as a microwave drive  line utilizing its weak capacitive coupling to the qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A meandered quarter-wave coplanar  waveguide (CPW) resonator is dispersively coupled to each qubit for readout, and up to six  resonators share a common bandpass filter for suppression of the Purcell effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We put the  resonator frequencies far under the qubit’s idle frequencies, in the range of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 - 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6 GHz, with  a separation of ≈ 50 MHz between each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Qubits can be tuned down to a frequency near  their readout resonators to realize a fast reset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As the readout resonators have a high decay rate  (������������ ∼ 2 MHz), the qubit states can quickly decay to the ground state within 200 ns due to the  Purcell effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The tunable coupler is a grounded qubit between two neighboring qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  tunable couplers have much higher frequencies (about 8 GHz) at their optimal points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' By  choosing appropriate qubits and coupler frequencies, the effective coupling strength between  adjacent qubits can be continuously tuned from positive to negative (33), thus can be turned off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S1(b) shows a photograph of another device with the same design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' It contains a top chip,  where all elements with high-quality factors, including qubits, couplers, and readout resonators,  are allocated, and a carrier chip, with other elements, including the bandpass Purcell filters and  the control lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' All the Purcell filters and control lines are covered with tunnel-like air-  bridges, which are shown in FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='S1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Those bridges form Faraday cages that prevent the  leakage of electromagnetic fields, thus protecting the qubits and couplers from coupling to  spurious fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2 Fabrication  The carrier and the qubit chip were fabricated separately with almost the same processes,  except that the Josephson junctions had to be added to the top chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' About 200 nm thick  Tantalum (Ta) films were deposited on a pre-annealed sapphire wafer by sputtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The base  circuits, including all the CPW transmission lines, resonators, and capacitors, were defined by  laser direct writing lithography (DWL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' They were then transferred to the Ta film using  reactive ion etching (RIE) with SF6 gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Before and after the etching process, oxygen ashing  was performed in order to remove the residual photoresist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The wafers were then immersed in  N-methyl-pyrrolidone (NMP) for several hours, followed by ultrasonic cleaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  3  Al/AlOx/Al junctions were fabricated using standard Dolan-bridge (34) shadow evaporation  technology as follows: the junction regions were first defined by electron beam lithography  with double-layer resists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After development, Dolan-bridges were formed with under-cut  structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then the wafers were transferred to an ultra-high vacuum four-chamber electron  beam evaporation system (AdnanoTek® JEB-4), wherein the evaporation chamber about 17  nm Al was deposited with a tilted angle of 40 - 60 degrees to form the bottom electrodes, and  then transferred into the oxidation chamber to form a thin AlOx barrier layer, and finally  transferred back for normal deposition of Al top electrodes of about 19 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Right before the  deposition, an in-situ argon ion milling was adopted to remove the surface oxide of the Ta  films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  After deposition, the wafers were soaked in NMP bath of 80∘C for at least two hours, with a  gentle ultrasonic for thorough lift-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The tunnel-like bridges were fabricated following the  reflowing process (35) with two differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' First, we increased the thickness of the air-bridge  film to 500 nm to ensure enough structural strength to sustain subsequent processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Second,  the area for wet etching is 6 μm wide surrounding the air-bridges, which ensures that the  bridges are separated from the excess aluminum films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Another lift-off was performed similar  to that in the Josephson junction process but without ultrasonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As there was quite an amount  of residual reflowed resist around the bridges, an ozone treatment at 80∘C for one hour is  required after lift-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The final step was to fabricate indium bumps on both chips and then bonded them together via  flip-chip technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Indium bumps with diameters of 20 - 30 μm were patterned on both  wafers by DWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Approximately 10 μm-thick indium was then grown by thermal evaporation  after an in-situ argon ion milling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Resist, and excess indium films were stripped away after  soaking in NMP for one day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The carrier and the chip wafers were then diced into different  sizes and bonded with a bonding force of 150-180 N in a flip-chip bonder (SET ACCμRATM M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Before bonding, all the chips were treated in H2/N2/He plasma to reduce oxidation of the  bump surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3 Experiment setup  Our experiment setup is summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To reduce the requirement of wirings and  electronic resources, we used only one control line for each qubit, combining the ������������������������ and ������������  control signals together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Furthermore, we developed a so-called single-sideband (SSB)  technology, which is more compact than the traditional IQ mixing scheme and requires only  half of Digital-to-Analog Converter (DAC) channels, to generate the qubit drive signal (also  known as ������������������������ control).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To obtain a single-tone drive pulse, the baseband waveforms (IF tone)  were first generated by a 2 GSa/s DAC and then mixed with a continuous microwave source  (LO tone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Two sidebands with frequencies of ������������������������������������ ± ������������������������������������ would appear after mixing, with an  unwanted LO leakage in the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' On the condition that ������������������������������������ was high enough (for  example, > 200 MHz), we could use a proper bandpass filter to select only one sideband as the  control signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We tested the spectral purity of such SSB technology and could obtain a  Spurious Free Dynamic Range (SFDR) of over 50 dB, which was comparable to or even better  than that generated by calibrated IQ mixing method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In addition, as the imaging and leaking LO  4  signals were deeply filtered out, such a scheme required no time-consuming repeated  calibrations, which were needed in the traditional IQ mixing scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The flux biases (also known as ������������ control) of the qubits and tunable couplers were generated  directly from 2 GSa/s DACs, followed by the 1  GHz lowpass filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For qubit XY and Z  control simultaneously, the Z pulses were further combined with the ������������������������ pulses by using a  diplexer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The stimulation signals of the readout resonators were generated by the traditional IQ  mixing scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' All those input signals reached the device at the mixing-chamber (MXC) stage  of a dilution refrigerator, with different attenuation at each temperature stage, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The filtering configurations under the MXC stage were different for different kinds of signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  For the ������������������������������������ control of a qubit, the highly attenuated signal was filtered first by a 10 GHz  lowpass filter and then an infrared (IR) filter (using Eccosorb® CR124 as the absorber).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  CR124 IR filter can attenuate the ������������������������ control signals for about 20 - 50 dB (depending on the  filter length) while affecting the DC pulses, (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' the ������������ control signals) negligibly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In addition,  it could heavily absorb electromagnetic waves from 10 GHz to the infrared band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For the ������������  control of couplers, it first passed through a 500  MHz lowpass filter and then a CR110 IR filter  (using Eccosorb® CR110 as the absorber).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The CR110 filter was similar to the CR124 IR  filter, except that its attenuation was much more gentle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To suppress thermal photon noise, we  added 69 dB attenuation, 10 GHz low pass filtering, and CR110 IR filtering to each  measurement input line in series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The output of the qubit measurement signal passed through 10 GHz low pass filter and three  isolators to prevent out-band and in-band noises, respectively, from coming down to the chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' It  was then pre-amplified by a High-Electron-Mobility Transistor (HEMT) at the 4 K stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After  coming out of the fridge, the signal was further amplified by two microwave amplifiers and  then down-converted to the IF band by an IQ mixer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The converted IQ signals were filtered and  amplified and finally digitized by 1 GSa/s analog-to-digital converters (ADCs) for  demodulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In order to prevent spurious radiation and flux noise, a light-tight oxygen-free  copper shield and a cryoperm shield were added outside the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In addition, we applied  another μ-metal shield (between the 50 K shield and the vacuum can), and the residual  magnetic field around the position of the device was measured at room temperature to be less  than 20 nT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2 Experiment setup  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 Characterization  Some key parameters of all the qubits (63 qubits, with one non-working) are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Readout frequencies are in the range of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 - 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6 GHz ( Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S3(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The maximum  frequencies of the qubits are in the range of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3 - 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='8 GHz ( Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S3(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The relaxation times ������������1  and Ramsey decay times ������������2  ∗ at maximum frequencies are listed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S3(c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We find  that the coherence of the qubits is much lowered when compared to our previous works (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We address the possible reasons as follows: First, as the circuit complexity increases, a lot of  unwanted modes are introduced, which may weakly interact with the qubits and lead to stronger  decoherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Second, although the flipmon design can increase the vacuum energy  5  participation ratio, it also increases losses from the metal-air interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Finally, the combination  of ������������������������ and ������������ control signals renders the filtering of control lines not sufficient, since we must  ensure that both the low-frequency Z pulses and high-frequency microwave ������������������������ pulses could  be transmitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The first two problems can be alleviated by improved design, and the third  problem may require a more careful and optimized filtering scheme design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Among the 62 available qubits, we chose 32 activated qubits in a chain, marked as ������������1 − ������������32 in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S4(a), to simulate the gSSH model in our experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' All the activated qubits are  initialized or excited at their idle frequencies (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' During evolution time, they  are tuned to their reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Meanwhile, inactivated qubits are always far-detuned and  negligibly coupled to activated qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We can measure the ������������1 and ������������2  ∗ at reference points of  activated qubits (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S4(c) and (d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here, ������������1 and ������������2  ∗ are different from those at  maximum frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������2  ∗ are remarkably lowered because the working points are chosen  away from the flux sweet spot and thus more sensitive to flux noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We also care about readout fidelity, which determines the amount of data that needs to be  averaged to obtain results with a reasonable error bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' When multiple qubits are measured  simultaneously, their fidelities tend to be lower than when they are measured individually due  to crosstalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S5, we show that the simultaneous readout fidelities of ground and excited  states of the activated qubits are 97% and 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='9% on average, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thanks to the  relatively low noise temperature of the HEMT amplifiers, we found that adequate simultaneous  readout fidelities can be obtained without Josephson parametric amplifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Furthermore, we  mitigate the influence of decoherence through shelving technique (37) on some of the qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2 Crosstalk and distortion  We minimized the effect of ������������������������ crosstalk by carefully choosing the frequency and duration of  the drive pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For ������������, we measured the crosstalk of nearest qubits and couplers, and the  results showed that the average crosstalk strength between different flux control lines in our  chip was less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2% (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As a result, we ignored ������������ crosstalk in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The non-ideality of electronics and wirings makes the ������������-control signal sensed by the qubits  severely distorted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In order to obtain accurate control over the qubit, we corrected the distorted  signal by the method of deconvolution (38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The experimental pulse sequence for measuring the  distortion of the ������������-control signal is shown in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' First, a square wave was  applied on the qubit’s ������������-control line, with a large enough amplitude and a long enough pulse  duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Following that, we applied the qubit phase tomography as a distortion detector where  a short square wave was inserted between two ������������/2 pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In order to extract the distortion  more accurately, the duration of the ������������/2 pulse was set to be short, and the amplitude of the  short square wave was carefully selected so that the frequency of the qubit was tuned to a flux-  sensitive point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then, we measured the qubit phase for different delay times between the large  square wave and the detector, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S7 (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We calculated the frequency  deviation of the qubit according to the measured phase and the duration of the short square  wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Combining with the information of the qubit spectrum, we obtained the trailing  amplitude after the large square wave, and then we could pre-distorted the input signal to  6  correct the distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After the correction, the measured phase was expected to be a constant  value at different delay times, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S7 (red line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3 Timing alignment  We calibrated the timing between different control channels to make the control more accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Firstly, we aligned the timing between a single qubit’s ������������������������ and ������������ control, and the pulse  sequence was shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S8(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We fixed the time duration between two ������������ pulses on the  ������������������������ control and applied a square wave on the ������������ control with the same duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We measured  the population of a qubit as a function of the delay between ������������������������ and ������������ control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' When the ������������  pulse was exactly halfway between the two ������������ pulses, the population of the qubit should return  to zero, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S8(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Secondly, we aligned the ������������ control timing between the two  adjacent qubits by implementing the ������������������������������������������������������������-like experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For example, the pulse sequence  of ������������23 − ������������24 − ������������24 was shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S8(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that, the square wave duration of the  coupler was set larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' When the two ������������ pulses were aligned correctly, the population exchange  between the two qubits reached the maximum (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S8(e)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Finally, the alignment between ������������  pulses of the adjacent coupler and qubit was done with a similar method, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S8(c),  (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4 Coupling strength  Accurately determining the effective coupling strength between the two nearest neighboring  qubits is very important, and the experimental pulse sequence is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S9(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Firstly,  we decoupled the surrounding qubits and couplers, and we prepared the initial state as |100⟩  by applying a ������������ pulse on the ������������19, which described the energy-eigenstates of the qubit-coupler-  qubit (������������19 − ������������19 − ������������18) systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then, we observed that the population swapped as a function  of the time, between two qubits shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S9(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The typical chevron pattern could indicate  the oscillation point which was the maximum population swapping point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We fixed the  oscillation point and then measured the population swapping as a function of the coupler flux  bias, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S9(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We extracted the effective coupling strength by fitting each line  along y-axis, which varied from 0 MHz to -14 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Because of the limited evolution time up to  2 ������������s, the extracted coupling strength from -14 MHz to -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25 MHz was more accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Continuous parameterization of the effective coupling strength is very important for us to  quickly simulate the target Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In our experiment, we chose the 20th-order  polynomial to fit the extracted coupling strength from -14 MHz to -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25 MHz as a function of  the coupler flux bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We believed that the extracted coupling strength of 0 MHz was also  accurate, so we continuously parameterized the coupling strength by linear interpolation from -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25 MHz to 0 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S9(d) showed a total of 32 parameterized coupling strengths between  the nearest neighboring qubit pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 Frequency alignment  We biased all qubits to the reference point with frequency ωref = 2π × 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='395 GHz for the  quantum walk experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Firstly, we fixed one qubit at the reference point and applied an  iSWAP sequence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S9) between a qubit and its nearest neighboring qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' During the  7  iSWAP experiment, the coupling strength between the two qubits was set to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 MHz, and  the rest qubits were decoupled from these two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We repeated this two-qubit frequency alignment  sequentially along the qubit chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Due to its inherent many-body nature, when all the qubits  and couplers were set to the points we characterized above, the alignment was not perfect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  S13 has shown that the coupling of a qubit to a coupler can deviate the qubit’s frequency from  the reference point by -10 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here, we parameterized the deviated qubit frequency as a  function of the coupler bias by a 40th polynomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then we compensated for this deviation with  an extra qubit bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After this compensation, we can see that the qubit frequency became nearly  constant with the coupler bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Due to the limited compensation accuracy of this method, we  only compensated the qubit bias within the range of coupling strength from -9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 MHz to -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6 Consistency of target couplings to parameterized couplings  Although we can accurately parameterize the coupling strength between each nearest-neighbor  qubit pair when all other qubits are decoupled, it is still a challenge to parameterize the  coupling strength when all qubits and couplers are activated due to the intrinsic many-body  nature of our device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thus we evaluated the extension of our pair-wise coupling strength  parameterization to the whole qubit chain with a quantum walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We implemented the 32-qubit  single-excitation quantum walk using the target Hamiltonian, where all couplings were set to be  the same target strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For example, we performed quantum walk experiments with six  different initial states, with the target coupling strength set to be 2 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The results of up to  300 ns evolution were shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The left column has shown the theoretical simulations  of the quantum walks using the target Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The middle column contained the  experimental result of the quantum walks of the parameterized Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To accurately  extract the actual coupling strength of each qubit pair, we optimized the Hamiltonian to match  the experiment result, where the coupling strengths were the fitting parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The results  were plotted in the right column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We could see good consistency with the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Repeating this  procedure with different target coupling strengths, we were able to check the consistency of the  experimentally extracted coupling strength with the target coupling strength, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  It was clear that the pair-wise couplings were well in control when the target coupling strength  was not over 4 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='7 Residual couplings  In our experiment, we can only turn off the coupling strength between nearest-neighbor qubit  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The residual couplings between diagonal next-nearest neighbor (NNN) qubits may also  have an impact on our experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here, we applied the ������������������������������������������������������������ experiment to NNN  qubit pairs to figure out the residual coupling strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Due to the limited coherence time, we  could only observe a very small population swapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The swapping between the NNN qubit  pair(������������26 and ������������28) with the maximum residual coupling strength is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  maximum population swapping corresponds to a swapping time of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05 ������������s, and thus we can  infer that the coupling strength was no larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Such a small unwanted coupling  strength was owing to the flipmon design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In our quantum walk experiment in the main text, the  8  evolution time is set to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 ������������s, less than the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05 ������������s, and then the residual couplings do not  pose a significant impact on our experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='8 Demonstration of the single-excitation quantum walks  After all above calibrations, we excited the Q25 to the excited state and set all the coupling  strengths between adjacent qubits to be 2π × 2 MHz and measured the population evolution of  each qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The result of the single-excitation quantum walk was shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  population evolution of the qubits was clear and the remain imperfections were attributed to the  alignment errors, the imperfect Z pulse distortions, and the residual couplings to the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  3 Experimental realization of topological Anderson insulators  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 Static phase diagram: topology and localization  We provide some details of obtaining the static phase diagram of the generalized SSH model  (�������������gSSH) with quasi-periodic hopping disorders (39), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 1 in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To this  end, we first determine the topological phase diagram in the ������������-������������′ parameter space [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  S15(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then we determine the delocalization-localization transition, which separates the  extended phase and the (partially and fully) localized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, we study the interplay  of flat-band localization and Anderson localization in the fully dimerized limit with ������������′/������������ = 0,  and obtain the localization phase diagram (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(h)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' By combining these results, we  finally obtain the complete phase diagram with respect to the topology and localization in the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that we have confirmed that the following numerical results obtained for the single  configuration of ������������ = 0 are preserved for other values of ������������ ≠ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This is due to the fact that the  lattice size ������������ = 2������������������������ = 1220 in our numerical simulations is large enough for self-averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The topological phase diagram is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(a), which is obtained for a sufficiently  large lattice of size ������������ = 1220 with negligible finite-size effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here we numerically calculate  the real-space winding number ������������ for �������������gSSH as functions of dimensionless parameters ������������/������������  and ������������′/������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' , the real-space winding number as the topological marker is given by  ������������ =  1  2|ℬ| � T������������������������  ������������∈ℬ  �����������������������������������������, ���������������,  where T������������������������ is the trace operator inside the ������������-th unit cell within a small region (������������������������/8 unit cells  in our simulations) in the center of the lattice, and ℬ denotes the corresponding collection of  bulk cells away from the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here ������������� = ∑ ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='+⟩⟨������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='+� − �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−⟩⟨������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−��  ������������  is the flat-band  Hamiltonian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������� = ������������3  ⊗������������������������ is the chiral operator,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' and ������������� is the unit cell operator with  �������������|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩ = ������������|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩ = �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  † �v������������������������⟩ (������������ ∈ [1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������������������] ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' and |v������������������������⟩ as the vacuum state of the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  9  In the clean limit with ������������/������������ = 0, there exists a topological transition between topological phase  with ������������ = 1 and trivial phase with ������������ = 0 at ������������′/������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' With increasing quasi-periodic disorder  strength up to ������������/������������ ≲ 2, the parameter region for the topological phase enlarges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This gives  rise to the TAI phase induced by moderate disorders from the trivial phase for 1 < ������������′/������������ ≲ 2  and large ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To further reveal the topological phase transition, we numerically compute the  bulk gap ������������������������ = ������������������������������������+1 − ������������������������������������ under the periodic boundary condition in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' One can  find that the topological phase is gapped, and the bulk gap closes at topological transition  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' When ������������ is large enough (������������ ≳ 2), the system is in the trivial gapless Anderson  insulators with vanishing ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To be more clear, we show ������������������������ under the open boundary  condition and ������������ with varying ������������ and fixed ������������′/������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In the gapped TAI phase  region (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='65 ≲ ������������/������������ ≲ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0) with ������������ = 1, a pair of disorder-induced zero-energy edge modes  inside the bulk gap exhibits due to the bulk-boundary correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The whole topological phase boundary can be determined from the localization length of zero-  energy modes, which diverges at topological transition points, owing to their delocalization  character in one-dimensional chiral chains (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For �������������gSSH, we can denote the wave function of  the zero-energy eigenstate as ������������0 = {������������1,������������, ������������1,������������, ������������2,������������, ������������2,������������ ⋯ ������������������������������������,������������, ������������������������������������,������������}������������, which is governed  by the Schrödinger equation  �������������gSSH������������0 = 0, #(1)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (1) leads to ������������������������������������,������������ + ������������������������  ′ ������������������������+1,������������ = 0 and ������������������������  ′ ������������������������,������������ + ������������������������������������+1,������������ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then the corresponding  probability distribution can be obtained as  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  = (−1)������������ � ������������������������  ′  ������������  ������������  ������������=1  ������������1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(2)  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  = (−1)������������ � ������������  ������������������������+1  ′  ������������  ������������=1  ������������1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(3)  Using the transform matrix method,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' one can obtain the inverse of the localization length ������������ in  the ������������������������ → ∞ limit  ������������−1 = max � lim  ������������������������→∞  1  ������������������������  ln�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='�������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' lim  ������������������������→∞  1  ������������������������  ln�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='�������������� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(4)  By setting ������������1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������ = ������������1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������ = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' we obtain  lim  ������������������������→∞  1  ������������������������  ln�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='�������������  = lim  ������������������������→∞  1  ������������������������  ln�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='�������������  =∣ lim  ������������������������→∞  1  ������������������������  �(ln|������������| − ln ∣ ������������������������  ′|)  ������������������������  ������������=1  |,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(5)  By substituting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (4) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (5), one can obtain  10  ������������−1 =∣ lim  ������������������������→∞  1  ������������������������  �(ln|������������| − ln ∣ ������������������������  ′|)  ������������������������  ������������=1  |, #(6)  The numerical results of ������������−1 ≈ 0 for ������������ = 2������������������������ = 1220 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(a) as the white  dashed line, corresponding to the divergence of the localization length with ������������ → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The results  demonstrate that the divergence of the zero-energy modes perfectly matches the topological  phase boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The emergence of the TAI phase from a trivial phase in the clean limit in the topological phase  diagram originates in the disorder-induced renormalization of the topological term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This  mechanism can be revealed based on the self-consistent Born approximation (SCBA) for weak  and moderate disorders (41).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Under the SCBA, the disorder-induced self-energy term can be  viewed as an additional renormalization term for a clean Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For �������������gSSH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' one can  obtain the self-energy ������������(������������) from the self-consistent equation  1  ������������������������ − ℋ(������������) − ������������(������������) = ⟨  1  ������������������������ − ������������eff(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������)⟩������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(7)  where ������������������������ ≡ 0 denotes Fermi energy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ℋ(������������) = [������������′ + ������������cos(������������)]������������1 + ������������sin(������������)������������2 denotes the  momentum-space Hamiltonian in clean limit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������(������������) = ������������1(������������)������������1 is the simplified self-energy  under the symmetry of the Hamiltonian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' and the ⟨⋯ ⟩������������ stands for averaging overall disorder  realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In our model, the disorder satisfies the form ������������(������������)������������1 with ������������(������������) = ������������cos(2������������������������������������),  and the effective Hamiltonian reads ������������eff = ℋ(������������) + ������������(������������)������������1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The renormalized hopping  constant is ������������′� = ������������′ + ������������1(������������), which gives rise to the modified topological phase transition  points satisfying the equation ������������′�(������������′, ������������)/������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For a given ������������ and other parameters, the self-  energy ������������1 can be obtained by numerically solving the self-consistent equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thus, the  topological phase boundary on the ������������-������������′ plane can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We plot the numerical result of  the topological phase boundary based on the SCBA analysis for 0 < ������������ < 2 as the black solid  line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(a), which agrees well with that determined by ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The basic mechanism of the TAI phase induced by quasi-periodic disorders here is the same as  that of TAIs in random disordered systems (41,42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' However, they have different gap and  localization properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In particular, the TAI induced by random disorders in the SSH model is  gapless and only contains fully localized bulk states (40,43,44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This is due to the common  wisdom that all states are Anderson localized without localization transition in 1D random  uncorrelated disordered systems (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In sharp contrast, the TAI phase in this quasiperiodic  SSH model is gapped and can have bulk states of different localization properties (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  gapped TAI in the moderate disorder region has been shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(b, c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  corresponding disorder-induced edge modes are protected by a finite bulk gap, different from  those being embedded in the gapless bulk spectra of the TAI in random disordered systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Thus, the mid-gap edge modes of the TAI in this quasi-periodic system are easier to detect in  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  On the other hand, there exists Anderson transition in this quasi-periodic system, such that the  TAI phase can have extended, partially or fully localized bulk states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To see this point, we can  numerically compute the local density of states at site ������������ of a lattice of length ������������ = 2������������������������ by  following Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (46,47):  11  ������������(������������, ������������) = 1  ������������ �|������������������������(������������)|2  ������������  ������������=1  ������������(������������ − ������������������������), #(8)  where ������������������������(������������) denotes the probability amplitude of the ������������-th normalized eigenstate at ������������-th site in  real space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' From the local density of states,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' one can obtain its arithmetic mean ������������a������������������������(������������) and  geometric mean ������������t������������������������(������������) as  ������������a������������������������(������������) = ⟨������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������)⟩������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������t������������������������(������������) = exp[⟨ln������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������)⟩������������],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(9)  Here ⟨⋯ ⟩������������ denotes the average over the site ������������ of the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The localized and extended  eigenstates around energy ������������ can be characterizes as ������������t������������������������(������������)/������������a������������������������(������������) → 0 and  ������������t������������������������(������������)/������������a������������������������(������������) ≠ 0 in the large ������������ limit, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(d) shows three typical TAI  phases with extended states, the coexistence of extended and localized states, and localized  states, from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  To further study the localization properties of bulk states,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' we can numerically compute the real-  space inverse participation ratio (IPR) of the ������������-th eigenstate IPR������������ and the mean IPR averaged  over the energy spectrum:  IPR������������ = �|������������������������(������������)|4  ������������  ������������=1  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  IPR = 1  ������������ � IPR������������  ������������  ������������=1  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(10)  For an extended (������������-th) eigenstate,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' one has IPR������������ ∼ ������������−1 and IPR������������ ∼ 0 in the large ������������ limit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  while IPR������������ ∼ ������������(1) for a localized eigenstate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thus, one can define the extended phase as all  of the eigenstates being extended with IPR ∼ ������������−1 ∼ 0 in the large ������������ limit, while the localized  phase for part or all of the eigenstates being localized with IPR ≠ 0 and independent of ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  extended and localized phases are separated by Anderson transition points with critical disorder  strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' By determining the critical disorder strengths of Anderson transition points, we can  obtain the boundary between extended and localized phases and thus the localization phase  diagram on the ������������-������������′ parameter plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To this end, we first numerically compute IPR for a  large lattice (������������ = 2������������������������ = 1220) as functions of ������������ and ������������′, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The result  indicates two parameter regions of the extended phase with IPR ∼ 0, one with small ������������ and  the other around the ������������′ = 0 axis, and otherwise for the localized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We first consider the parameter regime with ������������′ ≠ 0 and study the particular case of ������������′ = 0  later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To determine the Anderson transition point, we can take the finite-size analysis of IPR  with respect to the quasi-periodic disorder strength ������������ for fixed ������������′/������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For instance, we show  the results of IPR with respect to ������������ for fixed ������������′/������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 and ������������ = 2������������������������ = {288,754,1220} in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' One can see clearly that by increasing ������������, three lines approach a critical point that  separates the extended phase region with vanishing IPR ∼ 0 and the localized phase region  with finite IPR (indicated by the grey dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To be more clearly, we show the  corresponding logarithm plots as lgIPR(������������) ≡ log10IPR(������������) in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' As  excepted, the results show a sharp increase of lgIPR(������������) near the AT point, after (before)  which the values of lgIPR(������������) are almost independent (dependent) of ������������ for the localized  12  (extended) phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In view of the sharp change near the AT, we use the corresponding derivation  ∂lgIPR/ ∂������������ to further determine the critical point, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The peak of the  derivation indicates the Anderson transition point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The peak becomes sharper with increasing  the lattice size, but its location is the same for different lattice sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For other values of ������������′/������������,  the critical disorder strengths of the Anderson transition points can also be extracted in this  way, with three other examples shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Following this procedure of the finite-  size analysis, we finally obtain the boundary between the extended and localized phases, which  is plotted as the white dashed-dotted line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S16(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  We proceed to study the localization properties of the system when ������������′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In the clean case  with ������������ = ������������′ = 0, the SSH chain is in the fully dimerized limit and has two topological flat  bands with energies ������������ = ±������������ and winding numbers ������������ = ∓1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In this clean limit, the system  contains compact localized states, and the transport is prevented due to the diverging effective  mass in the two flat bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This localization phenomenon is named flat-band localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  However, the flat bands are very sensitive to perturbations from hopping disorders ������������, which  actually destroys the fully dimerized bonds and recovers the intra-cell hopping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Thus, one can  accept that the localization of compact states is broken under small ������������ and the disorder can  prohibit transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' When the disorder effect is dominant, one can expect the system will enter  the AL phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Therefore, there exists a competition between flat-band localization and  Anderson localization, which can lead to the so-called inverse Anderson transition  (localization ) with the striking disorder-induced (insulator-metal transition (transport) (48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(a), we plot the eigenenergy spectrum of a finite chain (under the periodic  boundary condition) for various ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' One can see that when turning on the hopping disorder and  increasing its strength ������������, the energy spectrum changes from the flat bands at ������������ = 0 to  dispersive bands, which becomes gapless when ������������/������������ ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To show the interplay between flat-  band localization and Anderson localization and obtain the Anderson transition point, we  numerically compute lgIPR and ∂lgIPR/ ∂������������ as a function of ������������, as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(b)  and S17(c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The results demonstrate the FBL phase at ������������ = 0, the extended phase  for 0 < ������������/������������ ≲ 2, and the localized phase for ������������/������������ ≳ 2 with the Anderson transition point at  ������������/������������ ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We further perform the finite-size scaling of IPR to confirm the two localization  phases and the extended phase in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(d) and S17(e), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To reveal the interplay  between the flat-band localization and Anderson localization with the disorder-induced  transport, we can use the time-averaged survival probability ������������������������ (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (7) in the main text)  and the time-averaged mean square displacement ������������ exacted from the spreading dynamics of a  single-site excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The time-averaged mean square displacement is given by  ������������ = 1  ������������ � �� (������������ − ������������0)2  ������������  ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�  2 + �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�  2��  1/2  ������������  0  ������������������������′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(11)  which reflects the mean width of the quantum walk over the evolution time ������������ with the initial  state being localized at a single site (site A or B) of the ������������0-th unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The typical results of  numerical simulations for a finite lattice with ������������ = 2������������������������ = 1220 and ������������0 = ������������������������/2 = 305 are  shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(f) and S17(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(f) show ������������ as a function of ������������ for different disorder  strengths ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Owing to the FBL at the clean limit, the breathing dynamics between two sites of  the ������������0-th unit cell exhibit when ������������ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The ballistic transport is enabled and enhanced when  13  0 < ������������/������������ < 2 as the inverse Anderson localization, and is prevented when ������������/������������ > 2 due to  the AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, we simulate the evolution dynamics up to a sufficiently long time ������������ =  400 ℏ/������������ (but with negligible edge effects), and compute ������������������������ and ������������ as a function of ������������ in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  S17(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The numerical results show the non-monotonous transport (localization) property with  respect to the disorder strength, which agrees well with the analysis of the interplay between the  flat-band localization and Anderson localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Based on these numerical results and analysis of the localization properties, we obtain the  localization phase diagram in the whole ������������-������������′ parameter space, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S17(h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' By  combining the topological and localization phase diagrams in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S15(a) and S17(h), we  finally obtain the complete static phase diagram of the generalized SSH model quasi-periodic  hopping disorders [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 1(b) in the main text].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2 Extracting Topological and Localization properties from Quantum walks  The extraction of the real-space winding number is following the procedure in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (49) and  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here we review the derivation of the local topological markers and their relation to  the density evolution in the quantum-walk experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The definition of the real-space winding number is mathematically expressed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (3) in the  main text, which can be understood as taking the average of an operator, ������������� = ����������������������������������������, ��������������, over  the bulk-state region and different modulation realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note the flat-band Hamiltonian �������������  can be written in terms of the projectors ������������������������� = ∑ �������������������������,±⟩⟨������������������������,�������������  ������������  with ������������ = ± as ������������� = ������������� − 2�������������−,  where ������������� = �������������+ + �������������− is the identity operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Then the topological marker ������������(������������) can be obtained  as the sum of the expectation of the operator ������������� in basis states in the ������������-th unit cell,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������(������������)  =  � �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ���������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' �������������  ������������=������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  =  4 � �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ��������������������������−���������������������������������������−�������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' �������������  ������������=������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  =  4 � �� ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−��  2  ������������  �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−����������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−�  ������������=������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  + � �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−�  ������������≠������������′  �������������������������′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ��������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−����������������������������������������������������′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='−��  ≃  � � ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|��������������������������  2  ������������  ������������=������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  ��������������������������2����������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(12)  where in the last line of the above equation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' the summation is over the whole spectrum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' and the  off-diagonal terms are omitted since their contributions are negligibly small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that here we  use a single index ������������ to traverse the whole spectrum of the target Hamiltonian, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  �������������g�������������������������������������������������������������⟩ = �������������������������������������������������⟩, for notation simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The real-space winding number is then obtained as  14  the average of the topological markers over unit cells in the bulk-state region and different  modulation realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  In a single-excitation quantum-walk experiment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' the time-averaged expectation of the chiral  displacement 2�������������������������� can be evaluated as follows,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������‾������������  =  1  ������������ � �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�2���������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�  ������������  0  ������������������������′  =  � ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|��������������������������  2  ������������  ��������������������������2����������������������������������������������������  +ℏ � �������������������������������������������������−������������������������′�������������/ℏ − 1  ������������������������������������� − ������������������������′�������������  ������������≠������������′  × �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|���������������������������������������������������2���������������������������������������������������′��������������������������′|������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' �������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(13)  with �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)⟩ = ������������−�������������������������g������������������������������������������������′/ℏ�������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' where the first term corresponds to the dominant part of  the real-space winding number in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (12) and the second term tends to zero as the evolution  time increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' With this observation, it is clear that the real-space winding number can be  calculated with quantum-walk experiments as follows,  ������������ =  1  2|ℬ| � � lim  ������������→∞  ������������  ������������∈ℬ  ������������‾������������ ≡ ⟨������������‾∞⟩, #(14)  where ℬ denotes the collection of cell indices in the bulk-state region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Now we turn to extract the spectral-averaged IPR from the experimental data of quantum  walks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We notice that,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' for each quantum-walk experiment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' the second-order moment of the  survival probability can be evaluated as follows,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������‾������������  =  1  ������������ � ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)��  2  ������������  0  ������������������������′  =  1  ������������ � �� ������������−������������������������������������������������′  ������������  ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|��������������������������  2�  2  ������������  0  ������������������������′  =  � ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|��������������������������  4  ������������  + ℏ � �������������������������������������������������−������������������������′�������������/ℏ − 1  ������������������������������������� − ������������������������′�������������  ������������≠������������′  × ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|��������������������������  2��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������������������′��  2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(15)  It is clear that the second term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (15) is proportional to the inverse of the evolution time,  and thus it tends to zero in the long-time limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' In other words, the averaged survival probability  converges to the first term, which is a time-independent value, in the long-time limit,  ������������‾∞ ≡ lim  ������������→∞������������‾������������ = � ��������������, ������������|��������������������������  4  ������������  , #(16)  15  Comparing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (16) with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (10), we find that the spectral-averaged IPR can be obtained by  averaging ������������‾∞ over all excitation positions,  a������������������������������������ = 1  ������������ � ������������‾∞  ������������,������������  , #(17)  With the introduction of the modulation phase ������������, it is reasonable to assume that modulation-  averaged observables still retain translational invariance in the quasi-periodically modulated  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To mitigate the finite-size effect, we restrict the single excitations in the bulk-state  region ℬ with |ℬ| ≪ ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, in consideration of the finite coherence times in  experiment, we use experimentally measured values of ������������‾������������ and ������������‾������������ at the longest evolution time  ������������������������ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 μs as the experimental data for ������������‾∞ and ������������‾∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S18 shows the experimental pulse  sequence for a quantum walk, and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S19 shows an example of the experimentally measured  density evolution data for all of the quantum-walk instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We finally arrive at the following  expressions for ⟨������������‾∞⟩ and ⟨������������‾∞⟩ as  ⟨������������‾∞⟩  =  1  2|ℬ|������������������������  �  ������������∈ℬ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  � �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�2���������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)�  ������������������������  0  ������������������������′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(18)  and  ⟨������������‾∞⟩  =  1  2|ℬ|������������������������  � � ��������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������|������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������(������������′)��  2  ������������������������  0  ������������∈ℬ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������  ������������������������′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(19)  with the average over disorder realizations being taken implicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3 Error Mitigation  To mitigate readout and leakage errors, we combine the subspace readout-error mitigation  proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (50) and postselection of the single-excitation subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here we briefly  outline the procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  The essential idea of readout-error mitigation lies in the assumption that there exists an  assignment matrix ������������ which relates the ideal and measured probability distributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������⃗i������������������������ =  �������������0  i������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' … ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������2������������−1  i������������������������ �  ������������ and ������������⃗m������������������������ = �������������0  m������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' … ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������2������������−1  m������������������������ �  ������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' in the following way,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������⃗m������������������������ = ������������������������⃗i������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(20)  where ������������ is a 2������������ × 2������������ matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' with ������������ referring to the number of involved qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' With the  assumption that the readout crosstalk errors are negligible,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' the matrix ������������ and its inversion can  be constructed from a single-qubit readout-calibration matrix ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  ������������ =⊗  ������������  ������������=1 ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������−1 =⊗  ������������  ������������=1 ������������������������  −1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' #(21)  16  with the matrix elements of ������������������������ being [������������������������]������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='������������′ = ������������������������′→������������  (������������)  and ������������������������  −1 being the inverse of ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here  ������������������������′→������������  (������������)  is the probability of obtaining ������������ in the projective measurement after preparing the  state |������������′⟩, with ������������, ������������′ ∈ {0,1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that ������������−1 is also a 2������������ × 2������������ matrix, whose matrix elements  can be directly constructed from ������������������������  −1 as [������������−1]������������,������������ = ∏  [������������������������  −1]������������������������,������������������������  ������������  ������������=1  with ������������ and ������������ being  bitstring strings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ������������ = ������������������������ … ������������1 and ������������ = ������������������������ … ������������1 in the binary format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' For small systems, we  can straightforwardly obtain the reconstructed quasiprobability ������������⃗q������������������������ = ������������−1������������⃗m������������������������, with ������������⃗q������������������������  being defined similarly as ������������⃗i������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Note that the direct inversion approach generates  quasiprobability that may contain negative values due to sampling errors in realistic  experimental scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' This problem can be surmounted by introducing numerical techniques  like the maximum likelihood analysis or the bounded minimization approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here in this  experiment, however, we are only concerned with expectation values, especially the density  distribution, and thus are satisfied with the direct-inversion approach, since it has been proved  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (51) that the error-mitigated quasiprobability distribution provides an unbiased estimate  for expectation values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  For intermediate-scale quantum systems consisting of tens of qubits, however, it is infeasible to  experimentally measure ������������⃗m������������������������ and perform matrix multiplication in the whole Hilbert space  with exponentially large dimensionalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' With the observation that ������������⃗m������������������������ can have at most ������������  non-zero entries, where ������������ is the number of shots in each experiment, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (50) proposed to  mitigate readout error in the subspace spanned by the computational basis states corresponding  to the non-zero entries in ������������⃗m������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Moreover, in our experiment, we only concern with the  probability distribution in the single-excitation subspace, since the target Hamiltonian  conserves the particle number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Taking these aspects into account, we use the following  subspace formula to obtain the unnormalized readout-error-mitigated quasiprobability  distribution in the single-excitation subspace,  �������������′q������������������������ = ������������̃−1�������������m������������������������, #(22)  where ������������̃−1 is a ������������ × ������������′ matrix, with ������������′ ≤ ������������ being the number of non-zeros entries in ������������⃗m������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Finally, the quasiprobability distribution can be naturally normalized by �������������q������������������������ = �������������′q������������������������/∑�������������′q������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S20 shows a representative example of the error-mitigation procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' After applying the  above-mentioned error-mitigation technique, the interference pattern becomes clearer and the  background residual excitation originating from assignment errors is also suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4 Reference  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Li, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Applied Physics Letters 119, 184003 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Yan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Applied 10, 054062 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Dolan, Applied Physics Letters 31, 337 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Applied Physics Letters 104, 052602 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Wang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', npj Quantum Information 8, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  17  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Mallet, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Nature Physics 5, 791 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Bao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 129, 010502 (2022)  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content=' A 105, 063327 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Hughes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Song, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 113, 046802 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Groth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Wimmer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Akhmerov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Tworzydło, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Beenakker, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 103, 196805 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Jain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Shen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 102, 136806 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Altland, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Bagrets, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Fritz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Kamenev, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Schmiedt, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 112, 206602  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Meier, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Science 362, 929 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Anderson, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 109, 1492 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Chu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Shen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' B 85, 035107 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Shen, Topological Insulators (Springer,New York, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Goda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nishino, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Matsuda, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 96, 126401 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Cardano, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 8 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Nation, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Kang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Sundaresan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Gambetta, PRX Quantum 2, 040326 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Bravyi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Sheldon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Kandala, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Mckay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Gambetta, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' A 103, 042605  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  18  Figure S1: (a) A schematic circuit of a unit cell of our device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Each flipmon qubit (blue) is capacitively  coupled with four couplers (orange) and four adjacent qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='MC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='62  2  8  16  24  30  0  5  10  15  19  Ti (μs)  T2 (μs)21  Figure S4: The characteristics of activated qubits (dark grey) in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The activated couplers  (blue) are tuned to simulate the gSSH Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The inactivated qubits and couplers (light grey) are  at idle point throughout the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The empty circle marks the only dead qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (a) Locations of  activated qubits ������������1 − Q32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) Idle frequencies of activated qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (c) The relaxation times T1 of  activated qubits at the reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d) The Ramsey decay times T2  ∗ of activated qubits at the  reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Figure S5: Simultaneous readout fidelities of ground (blue bars) and excited (orange bars) states of all  the activated qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The average fidelity for the ground (excited) state is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='899), marked by the  red (green) dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Inset: A typical scattering plot of the readout signal (for Q19) in the I/Q plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Activequbits  Idlefrequencies  Ti at reference point  T2 at reference point  (a)  Q23  Q25  (b)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='994  Ground  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='937  Excited22  Figure S6: The Z crosstalk between adjacent qubits and adjacent coupler-qubit pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (a) The  crosstalk from Qi+1 to Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) The crosstalk from Qi−1 to Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (c) The crosstalk from Ci to Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (D) The crosstalk from Ci+1 to Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Figure S7: The correction of the distorted Z-control signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The measured trailings of a distorted square  wave (solid black) and a corrected square wave (solid red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Inset: the experimental sequence for  measuring the distortion of the Z-control signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (a)  Qi+1→Qi  (b)  Qi-1→Qi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='2  (c)  Ci-→Qi  (d)  Ci+1→Qi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content="2  1  07  Q1  03'0  T/2  Tomo  Phase  2  XY  Delay  Z  4  Z distortion  Z distortion (corrected)  6  0  5  10  15  20  Delay (μs)23  Figure S8: The timing calibrations in the experiment." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (a), (b), (c) show the pulse sequences for the  timing alignments between qubit’s XY control and Z control, Z control between two adjacent qubits,  Z control between a qubit and its nearest couplers, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d), (e), (f) shows the corresponding  typical experimental data (dots), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The solid lines are the experimental data filtered by a  fifth-order low-pass Butterworth filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  T  T  (a)  (c) Q23 XY  T  Delay  XY  Q23 Z  Q23 Z  Delayi  Z  C24 Z  C24 Z  Delay  Q24 Z  Q24 Z  (e)  (f)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='9  Population  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='8 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2 ns  Q23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2 ns  Q23  Q24  Q24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  Total  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  Total  Q23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='0  50  10  30  70  100-50  0  50 100  100-50  0  50  100  Delay (ns)  Delay (ns)  Delay (ns)24  Figure S9: Demonstration of the tunable coupling strength between the nearest qubit pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (a) The  sequence of iSW AP experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) The typical iSWAP oscillation between two qubits (Q19 and Q18),  when the coupling (C19) is 2π *1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (c) The oscillation frequency can be tuned by the flux bias of  the C19 (10 times the flux bias followed by exponential amplifying for clarity here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d) The coupling  strengths of a total of 32 qubit-coupler-qubit triples as a function of coupler bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' These curves are then  parameterized by the 20th-order polynomial fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Blue dots (orange curves) are experimentally  extracted (parameterized) coupling strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (a)  (b)  (c)  Q19 - C19 - Q18  Q19 - C19 - Q18  TT  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='00  15  15  12  15  Q29-C29-Q28  Q30-C30-Q29  Q31-C31-Q30  Q32-C32-Q31  70  0 +  Q：  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='19  Coupler bias (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' )25  Figure S10: (a) Theoretical 32-qubit quantum walk of the target Hamiltonian where all nearest- neighbor  coupling strengths are set to be 2 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) Measured 32-qubit quantum walk of the experimental  Hamiltonian where all pairwise coupling strengths are parameterized as 2 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (c) Fitted 32-qubit quantum walk by optimizing the Hamiltonian to approximate the actual evolution  in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Figure S11: The comparison between parameterized coupling strength and target coupling strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Blue dots are the approximate coupling strength from the optimization of the coupling strength of 32  qubit pairs in the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Yellow dots are their average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (a)  (b)  (c)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='1  (sn)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='4  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1  6  11  16  21  26  31  1  6  11  21  26  31  1  6  11  16  21  26  31  SiteFitted  Average  8  6  (MHz)  4  2  0  0  2  4  6  8  Target (MHz)26  Figure S12: Demonstration of the residual coupling between two diagonal qubits when all couplers are  set at zero bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The qubits Q27 in (a) and Q29 in (b) with the shortest characteristic swapping time is  larger than 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05 µs, marked by the red dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The corresponding characteristic coupling strength  is less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05 MHz, manifesting the upper limit of the residual coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Figure S13: Calibration of the effect of the coupler bias on the qubit frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (a) Experimental pulse  sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) The solid blue circle and green diamond lines are experimental phase shifts on Q10 when  we sweep the coupler bias from strong to weak coupling (blue circles for C10 and green diamonds for  C11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The solid orange squares (C10) and red stars (C11) are calibrated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (a)  Q27  (b)  Q29  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25  Population  (srl)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='050us  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='050us  t  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='044-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='043  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='042  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='044  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='043  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='042  Q2z bias (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=')  Q2z bias (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' )T/2  Tr/2  (a)  Q10XY  Q10 Z  Couperbias  C10/C11Z  (b)  Deviated frequency (MHz)  0  Ci0 - Q10 data  Ci0 - Q1o fitted  5  Cio- Q1o corrected  C11 - Q10 data  C11-Q1ofitted  C11 - Q1o corrected  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  Coupler bias (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' )27  Figure S14: Demonstration of quantum walks on qubits chains with single-excitation at Q25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  evolution time is 1 µs and all coupling strength are set to be 2π*2 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' We add two more qubits Q33  and Q34 (between Q2 and Q3) here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  Figure S15: (Color online) (a) Topological phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Real-space winding number ν as  functions of W and J′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Here the white dashed and black solid lines denote the topological phase  boundaries, which are determined by the divergence of the localization length of zero-energy states  and by the flat-band localization (SCBA) analysis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) Energy gap ∆E/J as functions  of W and J′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (c) Middle 100 eigenenergies as a function of W for J′/J = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 under the open boundary  condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The TAI regime with ν = 1 and disorder-induced mid-gap edge modes is colored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d)  Averaged DOS ρave (red dashed line) and typical DOS ρtype (blue solid line) as a function of energy  E for the TAI phase at (J′/J, W/J) = (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1, 1), and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='9) from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The  lattice size in (a-d) is L = 2Nc = 1220 with negligible finite-size effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The energy unit is set as J  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  edge modes  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='0  6  9  Oubit2  L  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='2  0  0 W/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J  2Dta  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5AE/J  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content='5  1  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0  0  0  1  2  /A0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  V=0  =1  V=0  0  1  2  f/M28  Figure S16: (Color online) (a) Averaged inverse participation ratio IPR  ����� as a function of W and J′/J for  L = 1220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The white dash-dotted line denotes the boundary between the extended  and the localized phases obtained from numerically determining critical disorder strengths of  AT points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) IPR  ����� and (c) ∂ lg IPR  �����/∂W as a function of W for L = {288, 754, 1220} with  J′/J = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The inset in (b) shows the corresponding logarithm plot lg IPR  �����(W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The grey  dashed lines indicate the critical disorder strength of the AT point extracted from the finite-  size analysis in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d) ∂ lg IPR  �����/∂W as a function of W for J′/J = {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0} and  L = 1220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The energy unit is set as J = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  2  TPR  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 1  0  0  0  2  r/A10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  HdI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='15  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 W/J  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  L = 288  F9 = T  L = 1220  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  r/M50  L = 288  40  L = 754  Me/  L = 1220  30  20  10  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  W/J80  J°/J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  J°/J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  Me/  60  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=" J'/J = 2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  TPR/  40  20  0  A  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  W/J29  Figure S17: (Color online) (a) Eigenenergy spectrum for lattice size L = 1220 and disorder strengths  W/J ∈ {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 2, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5, 3}, with the cases of W/J = 0 and W/J = 2 in the insets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (b) lg IPR  ����� and (c)  ∂lg IPR  �����/∂W as a function of W for L = {288, 754, 1220}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The insets show the corresponding results  for a smaller region near W = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The flat-band localization at W = 0 and the Anderson transition (AT)  at W ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0 are labeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (d) Finite-size scaling of IPR  ����� with respect to the lattice size L = 2Nc for the  flat-band localization (W/J = 0) and AL (W/J = 3) phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (e) The same as (d) for the extended phase  with W/J ∈ {10−6, 10−4, 10−2, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (f) Time-averaged mean square displacement D� as a function of  evolution time t for L = 1220 and different values of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (g) Time-averaged survival probability St� and  the mean square displacement D� as a function of W for L = 1220 after a long evolution time t = 400  ℏ/J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' (h) Localization phase diagram on the whole W -J′plane  (a)  (b)  0  (c)  (d) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6  4  FBL  AT  W/J=0  AT  FBL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  Me/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  80-0  2  9  0  5  R  IPI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  HdI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  0-W/J=0  W/J  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  50  0  500  1000  20  W/J=3  E  0  100  2/ W/J=2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  150  2  L = 288  AL  40  : FBL  L = 754  200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  2  L = 1220  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  500  1000  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  2  0  2  4  0  2  4  0  500  1000  0  4  6  W/J  Eigenvalue index  W/ J  I-T  ×10-3  (e) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='04  (f) 4  (g) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='8  15  (h) 2  W/J= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  W/J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='1  W/J= 10-6  3  W/J = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='03  W/J= 10-4  W/J=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  W/J= 10-2  W/J = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  10  R  W/J=1  ID  W/J=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0  2  s 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='4  D  Localized  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='01  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5  FBL  AT  0 L  0  0  0  00  0  2  4  6  0  10  20  30  0  2  4  0  2  ×10-3  W/J  W/J  L-1  time t (h/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='J)30  Figure S18: Pulse sequence for the quantum-walk experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' Initially, all the qubits (couplers) are  biased at the idle (turning-off) frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To prepare the single-excitation initial state, we apply a π-  pulse, composed of two π/2-pulses with the same phase, to a chosen qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' To turn on the target  Hamiltonian, we bias all of the qubits to the reference frequency ωref , and set the coupler frequencies  according to the calibrated functional relations between flux bias and the effective coupling strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  After the system evolves for a duration t, we first bias the couplers back to the turning-off points and  perform simultaneous projective measurement on all the qubits in the σˆz–basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  C1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' C32  Q1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='. Q32  Figure S19: Experimental data of single-excitation quantum walks for a parameter point  (W /J, J′/J) = (3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='25) in the W -J′ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The energy unit is chosen to be J = 2π *1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 MHz,  and the duration of the walks is t f = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='5 μs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' The single excitation is placed at n = 15, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' ,  18 from the left to the right columns, while the modulation phase is set to be δ = 2qπ/8  with q = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content=' 7 from the top to the bottom rows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='  excitedsite:14,phase:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0*2n  excited site:15, phase:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0*2n  xcited site:16,phase:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0*2m  excited site:17,phase:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='0*2n  :0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='125*2  site:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='phase:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
+page_content='125*2  te:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+page_content=' Density evolution of raw  experi- mental data (a) and error-mitigated data (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tFLT4oBgHgl3EQfqC-n/content/2301.12138v1.pdf'}
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+Prepared for submission to JINST
+Computational Models for High-Power Cyclotrons and
+FFAs
+Andreas Adelmann
+,𝑎 Chris T. Rogers,𝑏
+𝑎Paul Scherrer Institut,
+Forschungsstrasse 111 CH-5232 Villigen, Switzerland
+𝑏STFC Rutherford Appleton Laboratory,
+Harwell Science and Innovation Campus, Didcot, OX11 0QX, United Kingdom
+E-mail: andreas.adelmann@psi.ch, chris.rogers@stfc.ac.uk
+Abstract: A summary of numerical modeling capabilities regarding high power cyclotrons and
+fixed field alternating gradient machines is presented. This paper focuses on techniques made
+available by the OPAL simulation code.
+Keywords: High Power Cyclotrons, High Power FFAs, Computational Models, OPAL
+1Corresponding author.
+arXiv:2301.01460v1  [physics.acc-ph]  4 Jan 2023
+
+Contents
+1
+Overview on Computational Models
+1
+1.1
+Single particle modeling
+1
+1.2
+Large Scale Multiparticle Modeling
+2
+1.3
+Surrogate Model Construction
+2
+2
+Physics Modeling
+2
+2.1
+Modeling H- Injection and Painting in Vertical and Horizontal FFAs
+2
+2.2
+Beam stripping interactions
+5
+2.3
+Spiral inflector modeling
+5
+2.4
+Neighboring Turn Modeling
+5
+3
+Path Forward
+6
+1
+Overview on Computational Models
+In all high-power particle accelerators "one of the major limitations is particle losses. Losses may
+be controlled, resulting in beam particles impinging on dedicated equipment such as collimators, or
+uncontrolled, resulting in beam particles striking other equipment around the accelerator. Uncon-
+trolled losses can damage and activate any equipment in the accelerator and so must be minimized.
+Controlled losses need to be carefully considered and also minimized. The amount and cause
+of loss are investigated by modeling accelerators using simulation codes that model numerically
+the behaviour of beams. A review of available numerical codes can be found in the article of
+Smirnov [1]. In this paper modeling capabilities available in OPAL are discussed in more detail
+[2].
+1.1
+Single particle modeling
+For conventional cyclotrons (and FFAs) the single particle tool box is established and many different
+codes variants exists [1]. For cyclotrons and (horizontal FFAs) the existing tools seem to be
+comfortable and accurate. New machines like vertical FFAs, currently studied for example at the
+Rutherford Appleton Laboratory (RAL) [3], require non–trivial modifications to the existing codes.
+These modifications are on the way for example in the code OPAL [2] and expected to be available
+in second quarter of 2022.
+Recently, in the context of very high field and ultra compact H− cyclotrons beam stripping
+losses of ion beams by interactions with residual gas and electromagnetic fields are evaluated [4].
+The beam stripping algorithm, implemented in OPAL, evaluates the interaction of hydrogen ions
+with residual gas and electromagnetic fields. In the first case, the cross sections of the processes
+are estimated according to the energy by means of analytical functions (see Sec. II-A c[4]). The
+– 1 –
+
+implementation allows the user to set the pressure, temperature, and composition of the residual
+gas, which could be selected for the calculations as either molecular hydrogen (H+
+2) or dry air in the
+usual proportion. For precise simulations, a two-dimensional pressure field map from an external
+file can be imported into OPAL, providing more realistic vacuum conditions.
+Concerning electromagnetic stripping, the electric dissociation lifetime is evaluated through
+the theoretical formalism (see Sec. II-B [4]). In both instances, the individual probability at each
+integration step for every particle is assessed.
+A stochastic process is used to evaluate if an interaction occurs. In this case the particle will
+be stripped and removed from the beam, or optionally transformed to a secondary heavy particle,
+dependent on the interaction. In this case, the secondary particle will continue its movement but
+with the new particle properties.
+1.2
+Large Scale Multiparticle Modeling
+In general, modeling losses in high intensity accelerators require 3D space-charge and sufficient
+simulation particles. Recent investigations [5] propose a sparse grid-based adaptive noise reduction
+strategy for electrostatic particle-in-cell (PIC) simulations. By projecting the charge density onto
+sparse grids, high-frequency particle noise is reduced and hence an optimal number of grid points
+and simulation particles can be obtained. For a 3D Penning trap simulation, a maximum speedup
+of 2.8 and 15 times memory reduction has been obtained. This method is already integrated into
+OPAL.
+1.3
+Surrogate Model Construction
+Cheap to evaluate surrogate models have gained a lot of interest lately. Statistical [6] or machine
+learning techniques are used [7]. These models can for example replace a computationally heavy
+model in a multi-objective optimization [8] or in the future be part of an on-line model. Some
+surrogate modeling algorithms may include an intrinsic estimator for the model uncertainty [9].
+2
+Physics Modeling
+In this section we show latest additions to the open source code OPAL [2] regarding cyclotron and
+FFA modeling capabilities.
+2.1
+Modeling H- Injection and Painting in Vertical and Horizontal FFAs
+Fixed Field Accelerators (FFAs) have fixed magnetic fields, like cyclotrons, but increase bending
+field with momentum and hence more compact designs can be realized. FFAs offer the power
+efficiency of cyclotrons combined with the energy reach of synchrotrons.
+FFAs have never been used for high power proton acceleration, however in OPAL the necessary
+models are available for design. Single particle tracking has been benchmarked against the KURNS
+FFA [10]. A design for a 3-12 MeV H- FFA prototype ring is being pursued at RAL as a prototype for
+a MW-class neutron spallation source [3]. Scaling horizontal orbit excursion (hFFA) and a vertical
+orbit excursion (vFFA) FFA are both under consideration. Both are non–isochronous machines
+using RF cavities with variable resonant frequency. Injection is planned using charge exchange of
+H− to H+ and phase space painting.
+– 2 –
+
+In hFFAs, magnetic rigidity varies with radius. The dipole field varies as [11]
+𝐵𝑧(𝑧 = 0) = 𝐵0(𝜓)
+� 𝑟
+𝑟0
+� 𝑘
+.
+(2.1)
+𝐵0(𝜓) is the dipole field as a function of a normalised azimuthal coordinate 𝜓, 𝑟 is the radial
+coordinate, 𝑟0 is a nominal (user-defined) radius, and 𝑘 is the field index. The field away from
+the midplane, at 𝑧 ≠ 0, may be calculated using a recursion relation arising from consideration
+of Maxwell’s equations in free space. OPAL has capability to calculate the expansion to arbitrary
+order, within machine precision. The normalised azimuthal coordinate
+𝜓 = 𝜙 − tan(𝛿) ln
+� 𝑟
+𝑟0
+�
+(2.2)
+is a measure of distance around the ring. Here 𝜙 is the geometrical azimuthal angle and 𝛿 is the
+spiral angle; for a sector FFA magnet 𝛿 = 0 and 𝜓 = 𝜙. The arrangement of fields in this way
+guarantees that single particle trajectories and optical parameters at all orders scale exactly with
+momentum.
+In vFFAs, magnetic rigidity varies with height.
+As particles are accelerated, the closed
+orbit changes height. Successive acceleration kicks add incoherently, so overall the beam follows
+the closed orbit with no appreciable emittance growth.
+Rectangular vFFA magnets have been
+implemented in OPAL, with a dipole field that varies as [12]
+𝐵0(𝑥𝑣 = 0) = 𝐵0(𝑠𝑣)𝑒𝑚𝑧𝑣 .
+(2.3)
+𝑧𝑣 is the height, 𝑠𝑣 is a nominal longitudinal coordinate and 𝑥𝑣 is a nominal horizontal coordinate
+in the rectangular coordinate system of the magnet. 𝐵0 describes the dipole field variation with
+longitudinal distance.
+A tanh model is available for vFFA fields.
+𝑚 is the vFFA field index,
+roughly equivalent to the field index 𝑘 in hFFAs. Fields away from the plane having 𝑥𝑣 = 0 are
+calculated using a field expansion derived from consideration of Maxwell’s laws. It is noted that
+the focusing in the magnet body is, to linear order, skew quadrupole. The fringe field has solenoid
+components parallel to 𝑠𝑣 that may be significant for short magnets. This arrangement of fields
+guarantees that trajectories and optical functions are identical as momentum increases, barring a
+vertical displacement. In particular, the path length of the beam is independent of momentum, the
+momentum compaction factor is exactly 0 and ultra-relativistic particles are isochronous.
+In order to model injection into the FFA, OPAL was extended with models for:
+• horizontal & vertical FFA magnets as described above;
+• variable frequency RF cavities;
+• arbitrary order multipoles with maxwellian fringe fields;
+• foil model (scattering and energy loss);
+• pulsed injected beam; and
+• pulsed multipoles.
+– 3 –
+
+ 
+ 
+H Bump 4
+catch H+ (x’)
+H Bump 5
+catch H+ (x)
+ 
+H Bump 2 moves H+ 
+bump orbit (r’)
+H Bump 1
+moves H+ 
+bump orbit
+(r)
+Merge H- and H+ in D 
+magnet
+Foil
+H- injection 
+Septum
+Vertical painting in
+injection line to select
+z, z’
+H = horizontal 
+bump
+H- 
+D F
+D = Defocusing
+F = Focusing
+Figure 1: Injection system for the hFFA (Left) field map of the hFFA, calculated using OPAL, with
+labels indicating the position of injection equipment (top right) closed orbits for different bump
+magnets (bottom right) required bump magnet fields.
+All but the latter two features are available in the latest version of OPAL. This enabled a fully
+four-dimensional simulation of the injection system, including consideration of effects such as
+appropriate phasing of the pulsed dipoles and transverse breathing of the beam arising due to initial
+longitudinal mismatch at injection.
+As an example, a schematic of an injection system and associated parameters for the 3-12 MeV
+test ring is shown for a horizontal FFA in Fig. 1. Owing to the compact nature of the ring, the
+injection system is spread across a number of cells. H− are brought into the ring and onto a foil.
+Bump magnets in the ring distort the proton closed orbit so that particles passing through the foil are
+returned to a nominal closed orbit. The foil is placed inside the defocusing (D) dipole magnet so that
+the distorted H+ closed orbit and H− beam, initially separated, are brought onto the same trajectory.
+Electrons are stripped from the H− leaving H+ (protons). The bump magnets are slowly varied, so
+that the proton closed orbit is moved away from the injection point for the H− and newly injected
+particles are at higher horizontal amplitude. In the H− injection line, pulsed magnets move the H−
+upwards so that newly injected particles are at higher vertical amplitude. Overall, a correlation is
+introduced between horizontal and vertical amplitude. Sample trajectories and bump magnet field
+strengths for the magnets in the ring are shown in Fig. 1. In this example vertical bumpers are not
+considered - they are all kept at 0 T field. The beam following injection is shown in fig. 2.
+– 4 –
+
+roΦ [m] for ro = 4.0 m
+0
+N
+4
+6
+8
+10
+12
+4.075
+4.050
+4.025
+4.000
+[m]
+3.975
+3.950
+3.925
+3.900
+3.875
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+[o] Φ0.00
+h bump 1
+hbump2
+hbump 3
+-0.02
+h bump 4
+hbump5
+0.04
+vbump 1
+[1] 
+v bump 2
+field
+0.06
+vbump3
+Bump
+v bump 4
+vbump 5
+-0.08
+-0.10
+0.12
+3900
+3920
+3940
+3960
+3980
+4000
+4020
+4040
+4060
+Radial position[mm]Orbit
+E
+4
+0.4
+B
+2
+0.2
+w
+0
+0.0
+-2
+0.2
+-0.4
+4
+-2
+0
+2
+4
+x [m]Figure 2: Beam (left) after injection is completed, but still on a distorted orbit (right) following
+collapse of the bump. 𝑥 is the position of the beam relative to the ring centre and 𝑦 is the height of
+the particle above the midplane. Particles are coloured according to the injection turn.
+2.2
+Beam stripping interactions
+Beam transmission optimization and loss characterization, where beam stripping interactions are
+a key issue, play an important role in the design and operation of compact cyclotrons. A beam
+stripping model has been implemented in the three-dimensional object-oriented parallel code OPAL-
+cycl, a flavor of the OPAL framework. The model includes Monte Carlo methods for interaction
+with residual gas and dissociation by electromagnetic stripping. The model has been verified with
+theoretical models and it has been applied to the AMIT cyclotron according to design conditions
+[4].
+2.3
+Spiral inflector modeling
+In [13] a spiral inflector model implemented in OPAL is presented, that enables us to run highly
+realistic simulations of the spiral inflector system of a compact cyclotron (c.f. Fig. 3). A new
+geometry class and field solver can handle the complicated boundary conditions posed by the
+electrode system in the central region of the cyclotron both in terms of particle termination, and
+calculation of self-fields. Results are benchmarked against the analytical solution of a coasting
+beam. As a practical example, the spiral inflector and the first revolution in a 1 MeV/amu test
+cyclotron, located at Best Cyclotron Systems, Inc., are modeled and compared to the simulation
+results [14, 15]. In conclusion, OPAL can handle realistic and arbitrary boundary geometries.
+Simulated injection efficiencies and beam shape compare well with measured efficiencies and a
+preliminary measurement of the beam distribution after injection.
+2.4
+Neighboring Turn Modeling
+This article presents a hardware architecture independent implementation of an adaptive mesh
+refinement Poisson solver that is integrated into the electrostatic Particle-In-Cell beam dynamics
+code OPAL. The Poisson solver is solely based on second generation Trilinos packages to ensure the
+desired hardware portability. Based on the massively parallel framework AMREX, formerly known
+– 5 –
+
+20
+[ww]
+0
+y
+-20
+3900
+3925
+3950
+3975
+4000
+4025
+4050
+4075
+4100
+x[mm]
+0.02
+0.24
+0.01
+0.22
+0.00
+0.20
+0.01
+0.18
+-0.02
+3900
+3950
+4000
+4050
+4100
+-20
+0
+20
+x[mm]
+y[mm]20
+[ww]
+0
+y
+-20
+3900
+3925
+3950
+3975
+4000
+4025
+4050
+4075
+4100
+x[mm]
+0.02
+0.24
+0.01
+0.22
+0.00
+0.20
+0.01
+0.18
+-0.02
+3900
+3950
+4000
+4050
+4100
+-20
+0
+20
+x[mm]
+y[mm]Figure 3: Spiral inflector with selected particle trajectories from an OPAL simulation.
+The
+beam enters axially (from the top) through an aperture (grey) and is bent into the mid-plane by a
+combination of the electrostatic field generated by the spiral electrodes (green and blue) and the
+cyclotron’s main magnetic field. Then it is accelerated by the two Dees (copper, Dummy-Dees not
+shown) [13].
+Figure 4: Integrated projection of the electric field component 𝐸𝑥 onto the xy-plane showing 7
+adjacent particle bunches [16].
+as BoxLib, the new adaptive mesh refinement interface provides several refinement policies in order
+to enable precise large-scale neighbouring bunch simulations in high intensity cyclotrons. The
+solver is validated with a built-in multigrid solver of AMREX and a test problem with analytical
+solution. The parallel scalability is presented as well as an example of a neighbouring bunch
+simulation that covers the scale of the later anticipated physics simulation [16].
+3
+Path Forward
+While statistical and machine learning techniques have a lot of potential, high fidelity physics
+simulations will always be used to, for example, produce the training set. In case of high-intensity
+machines we will need large numbers of particles and the associated fine mesh to solve the PDE in
+question. It is imperative that we make use of existing and future high performance infrastructure.
+– 6 –
+
+7.5
+102
+5.0
+(N)
+2.5
+cm
+101
+0
+2.5
+101
+5.0
+7.5
+1cm
+-102
+-10
+-5
+0
+5
+10
+x (cm)A performance portable implementation [16] is of utmost importance. The OPAL collaboration [2]
+is in the progress to completely rewrite the code according to the sketch in Fig. 5. With this new
+architecture we will be able to make efficient use of Exascale-Architecture that will come online
+soon. The core algorithms of OPAL are already performance portable as demonstrated in [17].
+Figure 5: Outlook of the future OPAL architecture, targeting in a performance portable way future
+exascale architectures.
+Acknowledgments
+The authors acknowledge the OPAL developer team for their continued support of this open source,
+community-driven code.
+References
+[1] V. Smirnov. Computer codes for beam dynamics analysis of cyclotronlike accelerators. Phys. Rev.
+Accel. Beams, 20:124801, 12 2017. doi: 10.1103/PhysRevAccelBeams.20.124801. URL
+https://link.aps.org/doi/10.1103/PhysRevAccelBeams.20.124801.
+[2] The OPAL Framework: Version 2.4, 2021.
+http://amas.web.psi.ch/opal/Documentation/2.4/index.html.
+[3] S. Machida, D. J. Kelliher, J-B. Lagrange, and C. T. Rogers. Optics design of vertical excursion
+fixed-field alternating gradient accelerators. Phys. Rev. Accel. Beams, 24:021601, 2 2021. doi:
+10.1103/PhysRevAccelBeams.24.021601. URL
+https://link.aps.org/doi/10.1103/PhysRevAccelBeams.24.021601.
+[4] P. Calvo, I. Podadera, D. Gavela, C. Oliver, A. Adelmann, J. Snuverink, and A. Gsell. Beam stripping
+interactions in compact cyclotrons. Phys. Rev. Accel. Beams, 24:090101, 11 2021. doi:
+10.1103/PhysRevAccelBeams.24.090101. URL
+https://link.aps.org/doi/10.1103/PhysRevAccelBeams.24.090101.
+[5] Sriramkrishnan Muralikrishnan, Antoine J. Cerfon, Matthias Frey, Lee F. Ricketson, and Andreas
+Adelmann. Sparse grid-based adaptive noise reduction strategy for particle-in-cell schemes. Journal
+of Computational Physics: X, 11:100094, 2021. ISSN 2590-0552. doi:
+– 7 –
+
+OPAL
+Kokkos aware Profiling and
+Trilinos
+IPPL
+Kokkos-Tools
+Debugging Tools)
+(Linear Solvers, Load Balancing,
+(Particles & Fields)
+Discretization,DistributedLinearAlgebra)
+Training)
+Kokkos-Kernels
+heFFTe
+(Sparse/DenseBLAS,GraphKernelsTensorKernels)
+Algorithms
+Containers
+(Random,Sort)
+(Map,CrsGraph, Mem Pool)
+Kokkos Core
+(Parallel Execution, Data Allocation, Data Transfer)
+std:thread
+OpenMP
+CUDA
+ROCmhttps://doi.org/10.1016/j.jcpx.2021.100094. URL
+https://www.sciencedirect.com/science/article/pii/S2590055221000111.
+[6] Andreas Adelmann. On nonintrusive uncertainty quantification and surrogate model construction in
+particle accelerator modeling. SIAM/ASA Journal on Uncertainty Quantification, 7(2):383–416, 2019.
+[7] Renato Bellotti, Romana Boiger, and Andreas Adelmann. Fast, efficient and flexible particle
+accelerator optimisation using densely connected and invertible neural networks. Information, 12(9),
+2021. doi: 10.3390/info12090351. URL https://www.mdpi.com/2078-2489/12/9/351.
+[8] Auralee Edelen, Nicole Neveu, Yannick Huber, Matthias Frey, and Andreas Adelmannn. Machine
+learning to enable orders of magnitude speedup in multi-objective optimization of particle accelerator
+systems’. Phys. Rev. AB, 23:044601, 2020. doi: 10.1103/PhysRevAccelBeams.23.044601. URL
+https://link.aps.org/doi/10.1103/PhysRevAccelBeams.23.044601.
+[9] Matthias Frey and Andreas Adelmann. Global sensitivity analysis on numerical solver parameters of
+particle-in-cell models in particle accelerator systems. Computer Physics Communications, 258:
+107577, 2021. ISSN 0010-4655. doi: https://doi.org/10.1016/j.cpc.2020.107577. URL
+http://www.sciencedirect.com/science/article/pii/S0010465520302770.
+[10] Suzanne Sheehy et al. Progress on Simulation of Fixed Field Alternating Gradient Accelerators. In
+6th International Particle Accelerator Conference, page MOPJE077, 2015. doi:
+10.18429/JACoW-IPAC2015-MOPJE077.
+[11] K. R. Symon, D. W. Kerst, L. W. Jones, L. J. Laslett, and K. M. Terwilliger. Fixed-field
+alternating-gradient particle accelerators. Phys. Rev., 103:1837–1859, Sep 1956. doi:
+10.1103/PhysRev.103.1837. URL https://link.aps.org/doi/10.1103/PhysRev.103.1837.
+[12] Stephen Brooks. Vertical orbit excursion fixed field alternating gradient accelerators. Phys. Rev. ST
+Accel. Beams, 16:084001, Aug 2013. doi: 10.1103/PhysRevSTAB.16.084001. URL
+https://link.aps.org/doi/10.1103/PhysRevSTAB.16.084001.
+[13] Daniel Winklehner, Andreas Adelmann, Achim Gsell, Tulin Kaman, and Daniela Campo. Realistic
+simulations of a cyclotron spiral inflector within a particle-in-cell framework. Physical Review
+Accelerators and Beams, 20(12):124201, 12 2017. doi: 10.1103/PhysRevAccelBeams.20.124201.
+URL https://link.aps.org/doi/10.1103/PhysRevAccelBeams.20.124201.
+[14] Daniel Winklehner, Andreas Adelmann, Achim Gsell, Tulin Kaman, and Daniela Campo. Realistic
+simulations of a cyclotron spiral inflector within a particle-in-cell framework. Phys. Rev. Accel.
+Beams, 20:124201, Dec 2017. doi: 10.1103/PhysRevAccelBeams.20.124201. URL
+https://link.aps.org/doi/10.1103/PhysRevAccelBeams.20.124201.
+[15] J. Alonso, S. Axani, L. Calabretta, D. Campo, L. Celona, J.M. Conrad, A. Day, G. Castro,
+F. Labrecque, and D. Winklehner. The isodar high intensity h2+ transport and injection tests. Journal
+of Instrumentation, 10(10):T10003, oct 2015. doi: 10.1088/1748-0221/10/10/T10003. URL
+https://dx.doi.org/10.1088/1748-0221/10/10/T10003.
+[16] Matthias Frey, Andreas Adelmann, and Uldis Locans. On architecture and performance of adaptive
+mesh refinement in an electrostatics particle-in-cell code (vol 247, 106912, 2020). COMPUTER
+PHYSICS COMMUNICATIONS, 265, 2021.
+[17] Sriramkrishnan Muralikrishnan, Matthias Frey, Alessandro Vinciguerra, Michael Ligotino, Antoine J.
+Cerfon, Miroslav Stoyanov, Rahulkumar Gayatri, and Andreas Adelmann. Alpine: A set of
+performance portable plasma physics particle-in-cell mini-apps for exascale computing, 2022. URL
+arXiv:2205.11052.
+– 8 –
+
diff --git a/5tAzT4oBgHgl3EQff_wz/content/tmp_files/load_file.txt b/5tAzT4oBgHgl3EQff_wz/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fdea4f54a240d4498c6acb1099926bd460291126
--- /dev/null
+++ b/5tAzT4oBgHgl3EQff_wz/content/tmp_files/load_file.txt
@@ -0,0 +1,430 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf,len=429
+page_content='Prepared for submission to JINST  Computational Models for High-Power Cyclotrons and  FFAs  Andreas Adelmann  ,𝑎 Chris T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Rogers,𝑏  𝑎Paul Scherrer Institut,  Forschungsstrasse 111 CH-5232 Villigen, Switzerland  𝑏STFC Rutherford Appleton Laboratory,  Harwell Science and Innovation Campus, Didcot, OX11 0QX, United Kingdom  E-mail: andreas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='adelmann@psi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='ch, chris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='rogers@stfc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='uk  Abstract: A summary of numerical modeling capabilities regarding high power cyclotrons and  fixed field alternating gradient machines is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' This paper focuses on techniques made  available by the OPAL simulation code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Keywords: High Power Cyclotrons, High Power FFAs, Computational Models, OPAL  1Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='01460v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='acc-ph]  4 Jan 2023  Contents  1  Overview on Computational Models  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1  Single particle modeling  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='2  Large Scale Multiparticle Modeling  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='3  Surrogate Model Construction  2  2  Physics Modeling  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1  Modeling H- Injection and Painting in Vertical and Horizontal FFAs  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='2  Beam stripping interactions  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='3  Spiral inflector modeling  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='4  Neighboring Turn Modeling  5  3  Path Forward  6  1  Overview on Computational Models  In all high-power particle accelerators "one of the major limitations is particle losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Losses may  be controlled, resulting in beam particles impinging on dedicated equipment such as collimators, or  uncontrolled, resulting in beam particles striking other equipment around the accelerator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Uncon-  trolled losses can damage and activate any equipment in the accelerator and so must be minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Controlled losses need to be carefully considered and also minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The amount and cause  of loss are investigated by modeling accelerators using simulation codes that model numerically  the behaviour of beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' A review of available numerical codes can be found in the article of  Smirnov [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In this paper modeling capabilities available in OPAL are discussed in more detail  [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1  Single particle modeling  For conventional cyclotrons (and FFAs) the single particle tool box is established and many different  codes variants exists [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' For cyclotrons and (horizontal FFAs) the existing tools seem to be  comfortable and accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' New machines like vertical FFAs, currently studied for example at the  Rutherford Appleton Laboratory (RAL) [3], require non–trivial modifications to the existing codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  These modifications are on the way for example in the code OPAL [2] and expected to be available  in second quarter of 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Recently, in the context of very high field and ultra compact H− cyclotrons beam stripping  losses of ion beams by interactions with residual gas and electromagnetic fields are evaluated [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  The beam stripping algorithm, implemented in OPAL, evaluates the interaction of hydrogen ions  with residual gas and electromagnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In the first case, the cross sections of the processes  are estimated according to the energy by means of analytical functions (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' II-A c[4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The  – 1 –  implementation allows the user to set the pressure, temperature, and composition of the residual  gas, which could be selected for the calculations as either molecular hydrogen (H+  2) or dry air in the  usual proportion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' For precise simulations, a two-dimensional pressure field map from an external  file can be imported into OPAL, providing more realistic vacuum conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Concerning electromagnetic stripping, the electric dissociation lifetime is evaluated through  the theoretical formalism (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' II-B [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In both instances, the individual probability at each  integration step for every particle is assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  A stochastic process is used to evaluate if an interaction occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In this case the particle will  be stripped and removed from the beam, or optionally transformed to a secondary heavy particle,  dependent on the interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In this case, the secondary particle will continue its movement but  with the new particle properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='2  Large Scale Multiparticle Modeling  In general, modeling losses in high intensity accelerators require 3D space-charge and sufficient  simulation particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Recent investigations [5] propose a sparse grid-based adaptive noise reduction  strategy for electrostatic particle-in-cell (PIC) simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' By projecting the charge density onto  sparse grids, high-frequency particle noise is reduced and hence an optimal number of grid points  and simulation particles can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' For a 3D Penning trap simulation, a maximum speedup  of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='8 and 15 times memory reduction has been obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' This method is already integrated into  OPAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='3  Surrogate Model Construction  Cheap to evaluate surrogate models have gained a lot of interest lately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Statistical [6] or machine  learning techniques are used [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' These models can for example replace a computationally heavy  model in a multi-objective optimization [8] or in the future be part of an on-line model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Some  surrogate modeling algorithms may include an intrinsic estimator for the model uncertainty [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  2  Physics Modeling  In this section we show latest additions to the open source code OPAL [2] regarding cyclotron and  FFA modeling capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1  Modeling H- Injection and Painting in Vertical and Horizontal FFAs  Fixed Field Accelerators (FFAs) have fixed magnetic fields, like cyclotrons, but increase bending  field with momentum and hence more compact designs can be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' FFAs offer the power  efficiency of cyclotrons combined with the energy reach of synchrotrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  FFAs have never been used for high power proton acceleration, however in OPAL the necessary  models are available for design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Single particle tracking has been benchmarked against the KURNS  FFA [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' A design for a 3-12 MeV H- FFA prototype ring is being pursued at RAL as a prototype for  a MW-class neutron spallation source [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Scaling horizontal orbit excursion (hFFA) and a vertical  orbit excursion (vFFA) FFA are both under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Both are non–isochronous machines  using RF cavities with variable resonant frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Injection is planned using charge exchange of  H− to H+ and phase space painting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  – 2 –  In hFFAs, magnetic rigidity varies with radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The dipole field varies as [11]  𝐵𝑧(𝑧 = 0) = 𝐵0(𝜓)  � 𝑟  𝑟0  � 𝑘  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1)  𝐵0(𝜓) is the dipole field as a function of a normalised azimuthal coordinate 𝜓, 𝑟 is the radial  coordinate, 𝑟0 is a nominal (user-defined) radius, and 𝑘 is the field index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The field away from  the midplane, at 𝑧 ≠ 0, may be calculated using a recursion relation arising from consideration  of Maxwell’s equations in free space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' OPAL has capability to calculate the expansion to arbitrary  order, within machine precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The normalised azimuthal coordinate  𝜓 = 𝜙 − tan(𝛿) ln  � 𝑟  𝑟0  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='2)  is a measure of distance around the ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Here 𝜙 is the geometrical azimuthal angle and 𝛿 is the  spiral angle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' for a sector FFA magnet 𝛿 = 0 and 𝜓 = 𝜙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The arrangement of fields in this way  guarantees that single particle trajectories and optical parameters at all orders scale exactly with  momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  In vFFAs, magnetic rigidity varies with height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  As particles are accelerated, the closed  orbit changes height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Successive acceleration kicks add incoherently, so overall the beam follows  the closed orbit with no appreciable emittance growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Rectangular vFFA magnets have been  implemented in OPAL, with a dipole field that varies as [12]  𝐵0(𝑥𝑣 = 0) = 𝐵0(𝑠𝑣)𝑒𝑚𝑧𝑣 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='3)  𝑧𝑣 is the height, 𝑠𝑣 is a nominal longitudinal coordinate and 𝑥𝑣 is a nominal horizontal coordinate  in the rectangular coordinate system of the magnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 𝐵0 describes the dipole field variation with  longitudinal distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  A tanh model is available for vFFA fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  𝑚 is the vFFA field index,  roughly equivalent to the field index 𝑘 in hFFAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Fields away from the plane having 𝑥𝑣 = 0 are  calculated using a field expansion derived from consideration of Maxwell’s laws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' It is noted that  the focusing in the magnet body is, to linear order, skew quadrupole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The fringe field has solenoid  components parallel to 𝑠𝑣 that may be significant for short magnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' This arrangement of fields  guarantees that trajectories and optical functions are identical as momentum increases, barring a  vertical displacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In particular, the path length of the beam is independent of momentum, the  momentum compaction factor is exactly 0 and ultra-relativistic particles are isochronous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  In order to model injection into the FFA, OPAL was extended with models for:  horizontal & vertical FFA magnets as described above;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  variable frequency RF cavities;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  arbitrary order multipoles with maxwellian fringe fields;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  foil model (scattering and energy loss);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  pulsed injected beam;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' and  pulsed multipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  – 3 –  H Bump 4  catch H+ (x’)  H Bump 5  catch H+ (x)  H Bump 2 moves H+  bump orbit (r’)  H Bump 1  moves H+  bump orbit  (r)  Merge H- and H+ in D  magnet  Foil  H- injection  Septum  Vertical painting in  injection line to select  z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' z’  H = horizontal  bump  H-  D F  D = Defocusing  F = Focusing  Figure 1: Injection system for the hFFA (Left) field map of the hFFA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' calculated using OPAL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' with  labels indicating the position of injection equipment (top right) closed orbits for different bump  magnets (bottom right) required bump magnet fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  All but the latter two features are available in the latest version of OPAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' This enabled a fully  four-dimensional simulation of the injection system, including consideration of effects such as  appropriate phasing of the pulsed dipoles and transverse breathing of the beam arising due to initial  longitudinal mismatch at injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  As an example, a schematic of an injection system and associated parameters for the 3-12 MeV  test ring is shown for a horizontal FFA in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Owing to the compact nature of the ring, the  injection system is spread across a number of cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' H− are brought into the ring and onto a foil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Bump magnets in the ring distort the proton closed orbit so that particles passing through the foil are  returned to a nominal closed orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The foil is placed inside the defocusing (D) dipole magnet so that  the distorted H+ closed orbit and H− beam, initially separated, are brought onto the same trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Electrons are stripped from the H− leaving H+ (protons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The bump magnets are slowly varied, so  that the proton closed orbit is moved away from the injection point for the H− and newly injected  particles are at higher horizontal amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In the H− injection line, pulsed magnets move the H−  upwards so that newly injected particles are at higher vertical amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Overall, a correlation is  introduced between horizontal and vertical amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Sample trajectories and bump magnet field  strengths for the magnets in the ring are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In this example vertical bumpers are not  considered - they are all kept at 0 T field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The beam following injection is shown in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  – 4 –  roΦ [m] for ro = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='0 m  0  N  4  6  8  10  12  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='075  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='050  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='025  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='000  [m]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='975  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='950  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='925  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='900  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='875  0  20  40  60  80  100  120  140  160  180  [o] Φ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='00  h bump 1  hbump2  hbump 3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='02  h bump 4  hbump5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='04  vbump 1  [1]  v bump 2  field  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='06  vbump3  Bump  v bump 4  vbump 5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='4  4  2  0  2  4  x [m]Figure 2: Beam (left) after injection is completed, but still on a distorted orbit (right) following  collapse of the bump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 𝑥 is the position of the beam relative to the ring centre and 𝑦 is the height of  the particle above the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Particles are coloured according to the injection turn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='2  Beam stripping interactions  Beam transmission optimization and loss characterization, where beam stripping interactions are  a key issue, play an important role in the design and operation of compact cyclotrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' A beam  stripping model has been implemented in the three-dimensional object-oriented parallel code OPAL-  cycl, a flavor of the OPAL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The model includes Monte Carlo methods for interaction  with residual gas and dissociation by electromagnetic stripping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The model has been verified with  theoretical models and it has been applied to the AMIT cyclotron according to design conditions  [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='3  Spiral inflector modeling  In [13] a spiral inflector model implemented in OPAL is presented, that enables us to run highly  realistic simulations of the spiral inflector system of a compact cyclotron (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' A new  geometry class and field solver can handle the complicated boundary conditions posed by the  electrode system in the central region of the cyclotron both in terms of particle termination, and  calculation of self-fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Results are benchmarked against the analytical solution of a coasting  beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' As a practical example, the spiral inflector and the first revolution in a 1 MeV/amu test  cyclotron, located at Best Cyclotron Systems, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=', are modeled and compared to the simulation  results [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In conclusion, OPAL can handle realistic and arbitrary boundary geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Simulated injection efficiencies and beam shape compare well with measured efficiencies and a  preliminary measurement of the beam distribution after injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='4  Neighboring Turn Modeling  This article presents a hardware architecture independent implementation of an adaptive mesh  refinement Poisson solver that is integrated into the electrostatic Particle-In-Cell beam dynamics  code OPAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The Poisson solver is solely based on second generation Trilinos packages to ensure the  desired hardware portability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Based on the massively parallel framework AMREX, formerly known  – 5 –  20  [ww]  0  y  20  3900  3925  3950  3975  4000  4025  4050  4075  4100  x[mm]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='02  3900  3950  4000  4050  4100  20  0  20  x[mm]  y[mm]Figure 3: Spiral inflector with selected particle trajectories from an OPAL simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  The  beam enters axially (from the top) through an aperture (grey) and is bent into the mid-plane by a  combination of the electrostatic field generated by the spiral electrodes (green and blue) and the  cyclotron’s main magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Then it is accelerated by the two Dees (copper, Dummy-Dees not  shown) [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Figure 4: Integrated projection of the electric field component 𝐸𝑥 onto the xy-plane showing 7  adjacent particle bunches [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  as BoxLib, the new adaptive mesh refinement interface provides several refinement policies in order  to enable precise large-scale neighbouring bunch simulations in high intensity cyclotrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The  solver is validated with a built-in multigrid solver of AMREX and a test problem with analytical  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The parallel scalability is presented as well as an example of a neighbouring bunch  simulation that covers the scale of the later anticipated physics simulation [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  3  Path Forward  While statistical and machine learning techniques have a lot of potential, high fidelity physics  simulations will always be used to, for example, produce the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In case of high-intensity  machines we will need large numbers of particles and the associated fine mesh to solve the PDE in  question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' It is imperative that we make use of existing and future high performance infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  – 6 –  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='5  102  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='0  (N)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='5  cm  101  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='5  101  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='5  1cm  102  10  5  0  5  10  x (cm)A performance portable implementation [16] is of utmost importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The OPAL collaboration [2]  is in the progress to completely rewrite the code according to the sketch in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' With this new  architecture we will be able to make efficient use of Exascale-Architecture that will come online  soon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The core algorithms of OPAL are already performance portable as demonstrated in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Figure 5: Outlook of the future OPAL architecture, targeting in a performance portable way future  exascale architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Acknowledgments  The authors acknowledge the OPAL developer team for their continued support of this open source,  community-driven code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  References  [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Smirnov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Computer codes for beam dynamics analysis of cyclotronlike accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content=' Machida, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='  [9] Matthias Frey and Andreas Adelmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='  [10] Suzanne Sheehy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Progress on Simulation of Fixed Field Alternating Gradient Accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' In  6th International Particle Accelerator Conference, page MOPJE077, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='  [11] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Symon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Kerst, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Jones, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Laslett, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Terwilliger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Fixed-field  alternating-gradient particle accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content=', 103:1837–1859, Sep 1956.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='  [12] Stephen Brooks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Vertical orbit excursion fixed field alternating gradient accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' ST  Accel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Beams, 16:084001, Aug 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1103/PhysRevSTAB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='1103/PhysRevSTAB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='084001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  [13] Daniel Winklehner, Andreas Adelmann, Achim Gsell, Tulin Kaman, and Daniela Campo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Realistic  simulations of a cyclotron spiral inflector within a particle-in-cell framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Physical Review  Accelerators and Beams, 20(12):124201, 12 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='124201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='1103/PhysRevAccelBeams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='124201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  [14] Daniel Winklehner, Andreas Adelmann, Achim Gsell, Tulin Kaman, and Daniela Campo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Realistic  simulations of a cyclotron spiral inflector within a particle-in-cell framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Accel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Beams, 20:124201, Dec 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1103/PhysRevAccelBeams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='124201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='124201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Alonso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Axani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Calabretta, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Campo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Celona, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Conrad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Day, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Castro,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Labrecque, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Winklehner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' The isodar high intensity h2+ transport and injection tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Journal  of Instrumentation, 10(10):T10003, oct 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1088/1748-0221/10/10/T10003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' URL  https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='1088/1748-0221/10/10/T10003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  [16] Matthias Frey, Andreas Adelmann, and Uldis Locans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' On architecture and performance of adaptive  mesh refinement in an electrostatics particle-in-cell code (vol 247, 106912, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' COMPUTER  PHYSICS COMMUNICATIONS, 265, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  [17] Sriramkrishnan Muralikrishnan, Matthias Frey, Alessandro Vinciguerra, Michael Ligotino, Antoine J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  Cerfon, Miroslav Stoyanov, Rahulkumar Gayatri, and Andreas Adelmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' Alpine: A set of  performance portable plasma physics particle-in-cell mini-apps for exascale computing, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content=' URL  arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='11052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
+page_content='  – 8 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5tAzT4oBgHgl3EQff_wz/content/2301.01460v1.pdf'}
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+This is a post-peer-review, pre-copyedit version of an article published in Autonomous Robots.
+The final authenticated version is available online at: http://dx.doi.org/10.1007/s10514-017-9682-5
+Long-Term Online Multi-Session Graph-Based SPLAM with
+Memory Management
+Mathieu Labb´e · Fran¸cois Michaud
+Abstract For long-term simultaneous planning, local-
+ization and mapping (SPLAM), a robot should be able
+to continuously update its map according to the dy-
+namic changes of the environment and the new areas
+explored. With limited onboard computation capabili-
+ties, a robot should also be able to limit the size of the
+map used for online localization and mapping. This pa-
+per addresses these challenges using a memory manage-
+ment mechanism, which identifies locations that should
+remain in a Working Memory (WM) for online pro-
+cessing from locations that should be transferred to
+a Long-Term Memory (LTM). When revisiting previ-
+ously mapped areas that are in LTM, the mechanism
+can retrieve these locations and place them back in WM
+for online SPLAM. The approach is tested on a robot
+equipped with a short-range laser rangefinder and a
+RGB-D camera, patrolling autonomously 10.5 km in
+an indoor environment over 11 sessions while having
+encountered 139 people.
+Keywords SLAM · path planning · pose graph ·
+multi-session · loop closure detection
+1 Introduction
+The ability to simultaneously map an environment, lo-
+calize itself in it, and plan paths using this information
+This work was supported by the Natural Sciences and Engi-
+neering Research Council of Canada (NSERC), the Canada
+Research Chair program and the Canadian Foundation for
+Innovation.
+M. Labb´e
+E-mail: mathieu.m.labbe@usherbrooke.ca
+F. Michaud
+E-mail: francois.michaud@usherbrooke.ca
+Interdisciplinary Institute for Technological Innovation (3IT),
+Universit´e de Sherbrooke, Sherbrooke, Qu´ebec, Canada
+is known as Simultaneous Planning, Localization And
+Mapping, or SPLAM (Stachniss, 2009). This task can
+be particularly complex when done online on a robot
+with limited computing resources in large, unstructured
+and dynamic environments. Since SPLAM can be seen
+as an extension of Simultaneous Localization And Map-
+ping (SLAM), many approaches exist (Thrun et al.,
+2005). Our interest lies with graph-based SLAM ap-
+proaches (Grisetti et al., 2010), for which combining
+a lightweight topological map over a detailed metrical
+map reveals to be more suitable for large-scale mapping
+and navigation (Konolige et al., 2011).
+Two important challenges in graph-based SPLAM
+are :
+– Multi-session mapping, also known as the kidnapped
+robot problem or the initial state problem: when
+turned on, a robot does not know its relative po-
+sition to a map previously created, making it im-
+possible to plan a path to a previously visited loca-
+tion. A solution is to have the robot localize itself
+in a previously-built map before initiating mapping.
+This solution has the advantage of always using the
+same referential, resulting in only one map is created
+across the sessions. However, the robot must start
+in a portion already mapped of the environment.
+Another approach is to initialize a new map with
+its own referential on startup, and when a previ-
+ously visited location is encountered, a transforma-
+tion between the two maps can be computed. The
+transformations between the maps can be saved ex-
+plicitly with special nodes called anchor nodes (Mc-
+Donald et al., 2012; Kim et al., 2010), or implicitly
+with links added between each map (Konolige and
+Bowman, 2009; Latif et al., 2013). This process is
+referred to as loop closure detection. Loop closure
+detection approaches that are independent of the
+arXiv:2301.00050v1  [cs.RO]  30 Dec 2022
+
+2
+Mathieu Labb´e, Fran¸cois Michaud
+robot’s estimated position (Ho and Newman, 2006)
+can intrinsically detect if the current location is a
+new location or a previously visited one among all
+the mapping sessions conducted in the past. Popular
+loop closure detection approaches are appearance-
+based (Garcia-Fidalgo and Ortiz, 2015), exploiting
+the distinctiveness of images of the environment.
+The underlying idea is that loop closure detection
+is done by comparing all previous images with the
+new one. When loop closures are found between the
+maps, a global map can be created by combining
+the maps from each session. In graph-based SLAM,
+graph pose optimization approaches (Folkesson and
+Christensen, 2007; Grisetti et al., 2007; Kummerle
+et al., 2011; Johannsson et al., 2013) use these loop
+closures to reduce odometry errors inside each map
+and in between the maps.
+– Long-term mapping in dynamic environments. Per-
+sistent (Milford and Wyeth, 2010), lifelong (Kono-
+lige and Bowman, 2009) or continuous (Pirker et al.,
+2011) are terms generally used to describe SLAM
+approaches working in such conditions. Continu-
+ously updating and adding new data to the map in
+unbounded or dynamic environments will inevitably
+increase the map size over time. Online simulta-
+neous planning, localization and mapping requires
+that new incoming data be processed faster than
+the time to acquire them. For example, if data are
+acquired at 1 Hz, updating the map should be done
+in less than 1 sec. As the map grows, the time re-
+quired for loop closure detection and graph opti-
+mization increases, and eventually limits the size of
+the environment that can be mapped and used on-
+line.
+To address these challenges, we introduce SPLAM-
+MM, a graph-based SPLAM with a memory manage-
+ment (MM) mechanism. As demonstrated in (Labbe
+and Michaud, 2013), memory management can be used
+to limit the size of the map so that loop closure detec-
+tions are always processed under a fixed time limit, thus
+satisfying online requirements for long-term and large-
+scale environment mapping. The idea behind SPLAM-
+MM is to limit the number of nodes available for
+loop closure detection and graph optimization, keeping
+enough observations in the map for successful online
+localization and planning while still having the ability
+to generate a global representation of the environment
+that can adapt to changes over time.
+The paper is organized as follows. Section 2 reviews
+graph-based SLAM approaches that reduce the size of
+the map when revisiting the same environment while
+continuously adapting to dynamic changes. Section 3
+describes the implementation and the operating prin-
+ciples associated with the use of memory management
+with a graph-based SPLAM approach, which extends
+our previous metric-based SLAM approach (Labbe and
+Michaud, 2014) with a new planning capability. The
+implementation integrates four algorithms: loop clo-
+sure detection (Labbe and Michaud, 2013), graph opti-
+mization (Grisetti et al., 2007), metrical path planner
+(Marder-Eppstein et al., 2010) and a custom topological
+path planner. Section 4 presents experimental results of
+11 SPLAM sessions using the AZIMUT-3 robot in an
+indoor environment over 10.5 km. Section 5 discusses
+strengths and limitations of SPLAM-MM, and Section
+6 concludes the paper.
+2 Related Work
+Lifelong appearance-based SLAM requires dealing with
+dynamic environments. Glover et al. (2010) present an
+appearance-based SLAM approach that had to oper-
+ate in different lighting conditions over three weeks.
+An interesting observation from their experiments is
+that even when revisiting the same locations, the map
+still grows: in dynamic environments, the loop closure
+detector is sometimes unable to detect loop closures,
+duplicating locations in the map. A map management
+approach is therefore required to limit map size. In
+highly dynamic environments, multiple views of the
+same location may also be required for proper local-
+ization. Churchill and Newman (2012) present a graph-
+based SLAM approach where visual experiences of the
+same locations are kept in the map, to increase localiza-
+tion robustness to dynamic changes caused for instance
+by outdoor illumination conditions. If localization fails
+when revisiting an area, new experiences are added to
+the map. Even if adding new visual experiences to the
+map happens less often over time (as the robot explores
+the same location), there is no mechanism to limit this.
+Pirker et al. (2011) present a continuous monocular
+SLAM approach where new key frames are added to
+the map only when the environment has changed, to
+keep its size proportional to the explored space. But if
+the environment changes very often, there is no mech-
+anism to limit the number of key frames over the same
+physical location.
+Some
+SLAM
+approaches
+can
+handle
+dynamic
+changes of the environment while limiting the size of
+the map for long-term operation. Biber et al. (2005)
+present a sample-based representation for maps, to han-
+dle changes at different timescales, tracking both sta-
+tionary and non-stationary elements of the environ-
+ment. The idea is to refresh samples stored for each
+timescale with new sensor measurements. Map growth
+is then indirectly limited as older memories fade at
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+3
+different rates depending on the timescale. Walcott-
+Bryant et al. (2012) describe Dynamic Pose-Graph
+SLAM (DPG-SLAM), a long-term mapping approach
+that detects static and dynamic changes of the environ-
+ment through time. To keep consistency of the graph
+while reducing its size, nodes that are not observable
+anymore are removed. Johannsson et al. (2013) also re-
+move unobservable nodes to limit the size of the map
+over time when revisiting the same area. Similar nodes
+of the graph are merged together while keeping only the
+new loop closure detection. However, the graph size is
+not bounded when exploring new areas. Krajn´ık et al.
+(2016) present an occupancy grid approach where each
+cell in the map estimates its occupancy value depend-
+ing on periodical and cyclic changes occurring in the
+environment. This increases localization and navigation
+accuracy in dynamic environments compared to static
+maps, as the predicted map represents the correct state
+of the environment at that time of the day (e.g., doors
+can change to be opened or closed). The maximum
+data kept for each cell is bounded by some parameters
+(depending on the smallest and longest cyclic periods
+that should be detected), thus keeping memory usage
+fixed. However, the approach assumes that the navi-
+gation phase always occur in the same environment as
+the first mapping cycle, without possibility to extend it
+afterward.
+These problems of lifelong SLAM are also addressed
+in some SPLAM approaches. Milford and Wyeth (2010)
+present a solution to limit the size of the map (called
+experience map) while revisiting the same area: close
+nodes are merged together up to a maximum density
+threshold. This approach has the advantage of mak-
+ing the map size independent of the operating time,
+but the diversity of the observations on each location is
+somewhat lost. Konolige et al. (2011) use a view-based
+graph SLAM approach (Konolige and Bowman, 2009)
+in a SPLAM context. The approach preserves diversity
+of the images referring to the same location so that the
+map can handle dynamic changes over time, and forget-
+ting images limits the size of the graph over time when
+revisiting the same area. However, the graph still grows
+when visiting new areas.
+Overall, these approaches reduce map size when re-
+visiting the same area, while continuously adapting to
+dynamic changes. This makes them independent or al-
+most independent of the operation time of the robot in
+these conditions, but they are all limited to a maximum
+size of the environment that can be mapped online. The
+SPLAM-MM approach deals specifically with this lim-
+itation.
+Fig. 1 The AZIMUT-3 robot equipped with a URG-04LX
+laser range finder and a Xtion PRO LIVE sensor.
+3 Memory Management for SPLAM
+The underlying representation of SPLAM-MM is a
+graph with nodes and links. The nodes contain the fol-
+lowing information:
+– ID: unique time index of the node.
+– Weight: an indication of the importance of the node,
+used for memory management.
+– Bag-of-words (BOW): visual words used for loop
+closure detections. They are SURF features (Bay
+et al., 2008) quantized to an incremental vocabu-
+lary based on KD-Trees.
+– Sensor data: used to find similarities between nodes
+and to construct maps. For this paper, our imple-
+mentation of SPLAM-MM is using the AZIMUT-3
+robot (Ferland et al., 2010), equipped with an URG-
+04LX laser rangefinder and a Xtion Pro Live RGB-D
+camera, as shown by Fig. 1. The sensory data used
+are:
+– Pose: the position of the robot computed by its
+odometry system (e.g., the value given by wheel
+odometry), expressed in (x, y, θ) coordinates.
+– RGB image: used to extract visual words.
+– Depth image: used to find 3D position of the vi-
+sual words. The depth image is registered with
+the RGB image, i.e., each depth pixel corre-
+sponds exactly to the same RGB pixel.
+– Laser scan: used for loop closure transformations
+and odometry refinements, and by the Proximity
+Detection module.
+The links store rigid transformations (i.e., Eucledian
+transformation derived from odometry or loop closures)
+between nodes. There are four types of links:
+
+URG-04LX
+Xtion PRO LIVE
+AZIMUT-34
+Mathieu Labb´e, Fran¸cois Michaud
+Motion Controller 
+Waypoints 
+ Graph-based SLAM-MM 
+WM 
+STM 
+ SPLAM-MM 
+Graph-based 
+ SLAM-MM 
+Wheel Odometry 
+Laser Rangefinder 
+RGB-D Camera 
+Motion Controller 
+Topological Path 
+Planner (TPP) 
+Twist 
+Pose 
+Scan 
+RGB-D  
+Image 
+Local Map 
+Upcoming Node IDs 
+Metrical Path 
+Planner (MPP) 
+Pose 
+User 
+Goal 
+Appearance-based Loop 
+Closure Detection 
+Graph 
+Optimization 
+New  
+Link(s) 
+New 
+Node 
+Local Map 
+Proximity Detection 
+Sensor Data 
+Sensors 
+Global Map 
+LTM 
+Transferred 
+Nodes 
+Retrieved  
+Nodes 
+Global Map 
+Upcoming Node IDs  
+Patrol 
+Goal 
+Status 
+Waypoints 
+Topological Path 
+Planner (TPP) 
+Twist 
+Metrical Path 
+Planner (MPP) 
+Pose 
+User 
+Goal 
+Patrol 
+Goal 
+Status 
+Fig. 2 Memory management and control architecture of SPLAM-MM.
+– Neighbor link: created between a new node and the
+previous one.
+– Loop closure link: added when a loop closure is de-
+tected between the new node and one in the map.
+– Proximity link: added when two close nodes are
+aligned together.
+– Temporary link: used for path planning purposes. It
+is used to keep the planned path connected to the
+current map.
+Figure 2 presents a high-level representation of
+SPLAM-MM. Basically, it consists of a graph-based
+SLAM module with memory management, to which
+path planners are added. Memory management involves
+the use of a Working Memory (WM) and a Long-Term
+Memory (LTM). WM is where maps, which are graphs
+of nodes and links, are processed. To satisfy online con-
+straints, nodes can be transferred and retrieved from
+LTM. More specifically, the WM size indirectly depends
+on a fixed time limit T: when the time required to up-
+date the map (i.e., the time required to execute the pro-
+cesses in the Graph-based SLAM-MM block) reaches
+T, some nodes of the map are transferred from WM to
+LTM, thus keeping WM size nearly constant and pro-
+cessing time around T. However, when a loop closure is
+detected, neighbors in LTM with the loop closure node
+can be retrieved from LTM to WM for further loop clo-
+sure detections. In other words, when a robot revisits
+an area which was previously transferred to LTM, it
+can incrementally retrieve the area if a least one node
+of this area is still in WM. When some LTM nodes are
+retrieved, nodes in WM from other areas in the map
+can be transferred to LTM, to limit map size in WM
+and therefore keeping processing time around T.
+Therefore, the choice of which nodes to keep in
+WM is key in SPLAM-MM. The objective is to have
+enough nodes in WM from each mapping session for
+loop closure detections and to keep a maximum num-
+ber of nodes in WM for generating a map usable to
+follow correctly a planned path, while still satisfying
+online processing. Two heuristics are used to establish
+the compromise between selection of which nodes to
+keep in WM and online processing:
+– Heuristic 1 is inspired from observations made by
+psychologists (Atkinson and Shiffrin, 1968; Badde-
+ley, 1997) that people remember more the areas
+where they spent most of their time, compared to
+those where they spent less time. In terms of mem-
+ory management, this means that the longer the
+robot is at a particular location, the larger the
+weight of the corresponding node should be. Old-
+est and less weighted nodes in WM are transferred
+to LTM before the others, thus keeping in WM only
+the nodes seen for longer periods of time. As demon-
+strated in (Labbe and Michaud, 2013), this heuristic
+reveals to be quite efficient in establishing the com-
+promise between search time and space, as driven by
+the environment and the experiences of the robot.
+– Heuristic 2 is used to identifies nodes that should
+stay in WM for autonomous navigation. Nodes on a
+planned path could have small weights and may be
+identified for transfer to LTM by Heuristic 1, thus
+eliminating the possibility of finding a loop closure
+link or a proximity link with these nodes and cor-
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+5
+Map 1!
+Map 3!
+Map 4!
+Last node!
+Map 2!
+Local map!
+Global map!
+Fig. 3 Illustration of the local map (inner dashed area) and
+the global map (outer dotter area) in multi-session mapping.
+Red nodes are in LTM, while all other nodes are in WM. Loop
+closure links are shown using bidirectional green arrows.
+rectly follow the path. Therefore, Heuristic 2 must
+supersede Heuristic 1 and allow upcoming nodes to
+remain in WM, even if they are old and have a small
+weight.
+The Graph-based SLAM-MM block provides two
+types of maps derived from nodes in WM and LTM:
+– Local map, i.e., the largest connected graph that can
+be created from the last node in WM with nodes
+available in WM only. The local map is used for
+online path planning.
+– Global map, i.e., the largest connected graph that
+can be created from the last node in WM with nodes
+in WM and LTM. It is used for offline path planning.
+Figure 3 uses diamonds to represent initial and end
+nodes for each mapping session. The nodes in LTM are
+shown in red and the others are those in WM. The lo-
+cal map is created using only the nodes in WM that
+are linked to the last node. The graph linking the last
+node with other nodes in WM and LTM represents the
+global map (outer dotted area). If loop closure detec-
+tions are found between nodes of different maps, loop
+closure links can be generated, and the local map can
+span over multiple mapping sessions. Other nodes in
+WM but not included in the local map are unreachable
+from the last node, but they are still used for loop clo-
+sure detections since all nodes in WM (including those
+in Map 2 for instance) are examined.
+The modules presented in Fig. 2 are described as
+follows.
+3.1 Short-Term Memory Module
+Short-Term Memory (STM) is the entry point where
+sensor data are assembled into a node to be added to
+the map. Similarly to (Labbe and Michaud, 2013), the
+role of the STM module is to update node weight based
+on visual similarity. When a node is created, a unique
+time index ID is assigned and its weight is initialized to
+0. The current pose, RBG image, depth image and laser
+scan readings are also memorized in the node. If two
+consecutive nodes have similar images, i.e., the ratio of
+corresponding visual words between the nodes is over a
+specified threshold Y , the weight of the previous node is
+increased by one. If the robot is not moving (i.e., odom-
+etry poses are the same), the new node is deleted. To re-
+duce odometry errors on successive STM nodes, trans-
+formation refinement is done using 2D iterative-closest-
+point (ICP) optimization (Besl and McKay, 1992) on
+the rigid transformation of the neighbor link with the
+previous node and the corresponding laser scans. If the
+ratio of ICP point correspondences between the laser
+scans over the total laser scan size is greater or equal to
+C, the neighbor link’s transformation is updated with
+the correction.
+When the STM size reaches a fixed size limit of S
+nodes, the oldest node in STM is moved to WM. STM
+size is determined based on the velocity of the robot
+and at which rate the nodes are added to the map.
+Images are generally very similar to the newly added
+node, keeping S nodes in STM avoids using them for
+appearance-based loop closure detection once in WM.
+For example, at the same velocity, STM size should
+be larger if the rate at which the nodes are added to
+map increases, in order to keep nodes with consecutive
+similar images in STM. Transferring nodes with images
+very similar with the current node from STM to WM
+too early limits the ability to detect loop closures with
+older nodes in WM.
+3.2 Appearance-based Loop Closure Detection Module
+Appearance-based loop closure detection is based on
+the bag-of-words approach described in (Labbe and
+Michaud, 2013). Briefly, this approach uses a bayesian
+filter to evaluate appearance-based loop closure hy-
+potheses over all previous images in WM. When a loop
+closure hypothesis reaches a pre-defined threshold H, a
+loop closure is detected. Visual words of the nodes are
+used to compute the likelihood required by the filter. In
+this work, the Term Frequency-Inverse Document Fre-
+quency (TF-IDF) approach (Sivic and Zisserman, 2003)
+is used for fast likelihood estimation, and FLANN (Fast
+
+6
+Mathieu Labb´e, Fran¸cois Michaud
+Library for Approximate Nearest Neighbors) incremen-
+tal KD-Trees (Muja and Lowe, 2009) are used to avoid
+rebuilding the vocabulary at each iteration. To keep it
+balanced, the vocabulary is rebuilt only when it doubles
+in size.
+The RGB image, from which the visual words are
+extracted, is registered with a depth image. Using (1),
+for each 2D point (x, y) in the rectified RGB image, a
+3D position Pxyz can be computed using the calibration
+matrix (focal lengths fx and fy, optical centres cx and
+cy) and the depth information d for the corresponding
+pixel in the depth image. The 3D positions of the visual
+words are then known. When a loop closure is detected,
+the rigid transformation between the matching images
+is computed using a RANSAC (RANdom SAmple Con-
+sensus) approach which exploits the 3D visual word cor-
+respondences (Rusu and Cousins, 2011). If a minimum
+of I inliers are found, the transformation is refined us-
+ing the laser scans in the same way as the odometry
+correction in STM using 2D ICP transformation refine-
+ment. If transformation refinement is accepted, then a
+loop closure link is added with the computed transfor-
+mation between the corresponding nodes. The weight
+of the current node is updated by adding the weight
+of the loop closure hypothesis node and the latter is
+reset to 0, so that only one node with a large weight
+represents the same location.
+Pxyz =
+�(x − cx) · d
+fx
+, (y − cy) · d
+fy
+, d
+�T
+(1)
+By doing appearance-based loop closure detection
+this way, setting H high means that there is less chance
+of detecting false positives, but at the cost of detect-
+ing less loop closures (Labbe and Michaud, 2013). For
+SPLAM-MM, H can be set relatively low to detect more
+loop closures because false positives that are geometri-
+cally different will be rejected by the rigid transforma-
+tion computation step (i.e., the 3D visual word corre-
+spondences and 2D ICP transformation refinement).
+3.3 Proximity Detection Module
+Appearance-based loop closure detection is limited by
+the perceptual range of the sensory data used. For in-
+stance, when the robot is revisiting areas in opposite di-
+rection, the RGB-D camera on AZIMUT-3 is not point-
+ing in the same direction compared to when the nodes
+were created, and thus no appearance-based loop clo-
+sures can be detected. This also happens when there
+are not enough visual features under the depth range
+of the RGB-D camera (e.g., white walls or long halls).
+Simply relying on appearance-based loop closure detec-
+tions for map corrections would then limit path plan-
+ning capabilities, and make navigation difficult in such
+conditions. Figure 4a illustrates a situation where the
+robot is in a hall coming back to its starting position
+in reverse direction. Setting a goal at the starting posi-
+tion would make the planner fail because no loop clo-
+sures could be found to correct the odometry, resulting
+in having a wall directly placed on the starting posi-
+tion. One solution would be to have the robot visit the
+nodes of the graph backward so loop closures could be
+detected to correct the map, and ultimately be able
+to reach the starting position. However, it is inefficient
+and unsafe if the robot does not have sensors pointing
+backward. To deal with such situations, the Proximity
+Detection module uses laser rangefinder data to correct
+odometry drift in areas where the camera cannot de-
+tect loop closures. With a field of view of more than
+180◦, the laser scans can be aligned in reverse direc-
+tion, generating proximity links. As laser scans are not
+as discriminative as images, proximity detection is re-
+stricted to nodes of the local map located around the
+estimated position of the robot. Figure 4b illustrates
+the result.
+Figure 5 illustrates how nodes located close to the
+robot are selected by the Proximity Detection module.
+Only nodes in the local map with their pose inside ra-
+dius R centered on the robot are used. Nodes in STM
+are not considered in order to avoid adding useless links
+with nodes close by: this would increase graph optimiza-
+tion time without adding significative improvements of
+the map. The nodes are then segmented into groups
+with nodes connected only by neighbor links. A group
+must have its nearest node from the robot inside a fixed
+radius L defining close-by nodes (with L < R) to be
+considered for proximity detection, to keep the length
+of the resulting proximity links small for path planning.
+Note that Appearance-based Loop Closure Detection
+is done before Proximity Detection, thus if the near-
+est node has already a loop closure with the new node,
+the group is ignored. Proximity detection is then ap-
+plied separately on each group of nodes by doing the
+following steps:
+1. A rigid transformation between the nearest node
+of each group and the new node added to map is
+computed as in Section 3.2, and if it is accepted, a
+proximity link is added between the corresponding
+nodes, and the group of nodes is ignored for step
+2. These links are referred as visual proximity links
+because visual words are used in the transformation
+estimation.
+2. To avoid having to compare multiple nodes with
+very similar laser scans (and thus to save computa-
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+7
+a)!
+b)!
+Fig. 4 Illustration of the role of the Proximity Detection module. On the left are the raw laser scans, the blue dot is the
+starting position, and on the right the corresponding occupancy grid map at 0.05 m resolution (black, light gray and dark
+gray areas are occupied, empty and unknown spaces, respectively). In a), the yellow circle on the right locates the problematic
+situation: after the second traversal, the first nodes of the graph are located exactly over the wall, making it impossible to
+plan a path (red arrow on the right) to return to the starting position. In b), proximity links are detected using only the laser
+scans, and the local map can then be correctly optimized.
+tion), only the more recent node among those in
+the same fixed small radius L (centered on each
+node) is kept along the nodes in a remaining group.
+Then for each group, the laser scans of the nodes
+are merged together using their respective pose. 2D
+ICP transformation refinement is done between the
+merged laser scans and the one of the new node.
+If the transformation is accepted, a new proximity
+link with this transformation is added to the graph
+between the new node and the nearest one in the
+group.
+3.4 Graph Optimization Module
+TORO (Tree-based netwORk Optimizer) (Grisetti
+et al., 2007) is used for graph optimization. When loop
+closure and proximity links are added, the errors de-
+rived from odometry can be propagated to all links,
+thus correcting the local map. This also guarantees that
+nodes belonging to different maps are transformed into
+the same referential when loop closures are found.
+When only one map exists, it is relatively straight-
+forward to use TORO to create a tree because it only
+has one root. However, for multi-session mapping, each
+map has it own root with its own reference frame. When
+loop closures occur between the maps, TORO cannot
+optimize the graph if there are multiple roots. It may
+also be difficult to find a unique root when some of
+the nodes have been transferred in LTM. As a solution,
+our approach takes the root of the tree to be the latest
+a)	
+b)	
+c)	
+d)	
+R
+L
+Fig. 5 Illustration of how proximity detection works. In a),
+the larger dashed circle represents the radius R used to deter-
+mine close-by nodes, and the smaller dashed circle defined by
+L is used to limit the length of the links to be created. The
+empty dots are nodes for which the laser scans are not used,
+either because they are outside the radius R, they are too
+close from each other or they are in STM. In b) and c), nodes
+in the radius R from the two segmented groups of nodes are
+processed for proximity detection. In d), proximity links are
+added (yellow), and after graph optimization, the groups of
+nodes are connected together and the respective laser scans
+are now aligned.
+
+8
+Mathieu Labb´e, Fran¸cois Michaud
+node added to the local map, which is always uniquely
+defined across intra-session and inter-session mapping.
+All other poses in the graph are then optimized using
+the last odometry pose as the referential.
+3.5 Path Planning Modules
+Memory management has a significant effect on how to
+do path planning online using graph-based SLAM, for
+which the map changes almost at each iteration and
+with only the local map accessible while executing the
+plan. This differs from approaches that assume that the
+map is static and/or that all the previously visited loca-
+tions always remain in the map. In this paper, SPLAM-
+MM uses two path planners: a Metrical Path Planner
+(MPP) and a Topological Path Planner (TPP).
+3.5.1 Metrical Path Planning Module
+MPP receives a pose expressed in (x, y, θ) coordinates,
+and uses the local map to plan a trajectory and to make
+the robot move toward the targeted pose while avoid-
+ing obstacles. Our MPP implementation exploits the
+ROS navigation stack (Marder-Eppstein et al., 2010) to
+compute trajectories expressed as a sequence of veloc-
+ity commands (expressed as twists) sent to the robot’s
+Motion Controller module. A global Costmap is used
+to plan a trajectory to a targeted pose. MPP creates
+the global Costmap from an occupancy grid created us-
+ing the assembled laser scans from the latest local map.
+Each time the local map is updated, the occupancy grid
+is re-assembled and the trajectory is re-planned. MPP
+also uses a local Costmap for its Dynamic Window Ap-
+proach (DWA) (Fox et al., 1997) to handle dynamic
+obstacles for collision avoidance. The local Costmap is
+created directly from sensor readings. To create the lo-
+cal Costmap, only using the laser rangefinder for obsta-
+cle detection revealed to be insufficient: while the laser
+range finder can detect most of the obstacles (e.g., walls,
+people, table legs), it is located 40 cm above the floor
+and all obstacles under this height cannot be detected.
+Therefore, the depth image from the RGB-D camera
+is also used to detect these small obstacles and to add
+them to the local Costmap. Figure 6 shows an example
+where combining laser scans and RGB-D data creates a
+more robust and a safer local Costmap for navigation.
+Note that segmentation of the point cloud generated
+from the depth image is required to be able to add or
+clear small dynamic obstacles below the RGB-D cam-
+era. To segment the ground, all points with normal par-
+allel to z-axis (up to an angle Z) are labeled as ground.
+Then, all other points under a maximum height U are
+labeled as obstacles. This method would also make the
+robot capable of operating on uneven terrain.
+3.5.2 Topological Path Planning Module
+When TPP receives a goal identified by a node ID from
+a user (or a high-level module like a task planner, or
+in this paper the Patrol module), the global map is
+provided by the graph-based SLAM-MM module, and
+a topological path is computed to reach this goal. The
+topological path is a sequence of poses, expressed by
+their respective node IDs, to reach the goal. This step
+must be done offline or when the robot is not moving
+because all nodes linked to the current local map should
+be retrieved from LTM to build the global map.
+To choose which nodes to use for navigation, TPP
+computes a path from the current node to the goal node
+using Djikstra algorithm (Dijkstra, 1959). The choice
+of using Dijkstra over A* is to avoid global graph op-
+timization, which is time consuming, to know the dis-
+tance to goal required by A*. Dijkstra can also be com-
+puted directly when fetching the global map from LTM.
+Similar to (Valencia et al., 2013), to avoid losing track
+of the planned path, TPP prefers paths traversed in
+the same direction (e.g., where the camera is facing the
+same direction than on the nodes on the path) over
+shortest paths. This increases localization confidence:
+loop closure detection and visual proximity detection
+are more reliable than proximity detection using only
+laser scans because of their double verification (3D vi-
+sual word correspondences and 2D ICP transformation
+refinement). To embed this preference in Djikstra, the
+search cost is angular-based instead of distance-based,
+i.e., it finds the path with less orientation changes when
+traversing it in the forward direction.
+Then, TPP selects the farthest node on the path
+in the local map and sends its pose to MPP. While
+MPP makes the robot navigate to its targeted pose,
+TPP indicates to the graph-based SLAM-MM mod-
+ule which upcoming nodes on the topological path is
+needed, expressed as a list of node IDs from the lat-
+est node reached on the path to the farthest node in-
+side the radius R (to limit the size of the list). The re-
+quired nodes are identified by the graph-based SLAM-
+MM module with Heuristic 2 either to remain in WM or
+to be retrieved from LTM to extend the local map. The
+maximum number of retrieved nodes per map update is
+limited to M because this operation is time consuming
+as it needs to load nodes from LTM. M is set based on
+the hardware on which LTM is saved and according to
+the maximum velocity of the robot: for instance, if the
+robot is moving at the same speed or less as when it
+traversed the same area the first time, M = 1 would
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+9
+(a)
+(b)
+(c)
+Fig. 6 Example of obstacle detection using the laser rangefinder and the RGB-D camera. The red dots on the chair show
+what is detected using the laser rangefinder data. The cyan area is derived from the obstacle projection on the ground plane
+up to robot’s footprint radius, delimiting where the center of the robot should not enter to avoid collisions. In a), only the
+laser rangefinder data are used and the chair’s wheels are not detected, making unsafe for the robot to plan a path around the
+chair. In b), the point cloud generated from the camera’s depth image is used and the chair’s wheels are detected (shown by
+the orange dots), increasing the cyan area (and consequently the area to avoid colliding with the chair). Illustration c) presents
+a view from the RGB-D camera where the segmented ground is shown in green and the obstacles in orange.
+suffice to retrieve nodes on the path without having to
+slow down to wait for nodes not yet retrieved.
+Extending the local map with nodes of the topo-
+logical path is important for the robot to localize it-
+self using the Appearance-based Loop Closure Detec-
+tion module or using the Proximity Detection module,
+making it able to follow the topological path appro-
+priately. As the robot moves and new local maps are
+created, TPP always looks for the farthest node of the
+topological path that can be reached in the local map
+to update the current pose sent to MPP module. If new
+nodes are retrieved from LTM on the topological path,
+then the farthest pose is sent to MPP. TPP also de-
+tects changes in the local map after graph optimization
+(e.g., when new loop closures are detected): if so, the
+updated position of the current pose is sent to MPP.
+Up to a ratio O of the WM size, nodes identified by
+the planner and located in the radius R from the robot’s
+current position are immunized to be transferred, with
+R being the sensor range.
+Figure 7 presents an example of the interaction be-
+tween MPP and TPP to reach a goal G. While the robot
+is moving, TPP always sends the farthest pose P of the
+node on the topological path (purple links) in the lo-
+cal map. An occupancy grid is assembled with the laser
+scans contained in the nodes of the local map. MPP
+uses this occupancy grid to plan a trajectory (yellow
+arrow) to P. To keep the WM size constant, as nodes
+are retrieved from LTM on the path, older nodes are
+transferred to LTM. To follow the path appropriately,
+proximity links are detected to correct the map as the
+robot moves, otherwise the situation explained by Fig.
+4a would happen.
+TPP iterates by sending poses until the node of the
+goal (under a goal radius D expressed in m) is reached.
+Finally, handling situations where the environment has
+changed too much for proper localization must be taken
+into consideration. If no loop closures and proximity de-
+tections occur when following a path, a temporary link
+is added between the current node and the closest one
+in the path so that the topological path is always linked
+to the current node in the local map. Without this link,
+if previous nodes between the current node and those of
+the topological path are transferred to LTM, the local
+map would be divided and the nodes of the path would
+not be in the local map anymore. This temporary link
+is removed when a new link is added between the cur-
+rent node and the closest one in the path or when the
+goal is reached. If the robot has not reached the cur-
+rent pose set to MPP after F iterations of SPLAM-MM
+(e.g., MPP cannot plan to the requested pose because
+of the presence of a new obstacle or because the robot
+cannot localize itself on the path), TPP chooses another
+pose on the upcoming nodes and sends it to MPP. If all
+the upcoming nodes cannot be reached, TPP fails and
+sends a status message to its connected modules so that
+they can be notified that the goal cannot be reached.
+
+10
+Mathieu Labb´e, Fran¸cois Michaud
+P"
+G"
+(a)
+P"
+G"
+(b)
+P"
+G"
+(c)
+P"
+G"
+(d)
+P"
+G"
+(e)
+P"
+(f)
+Fig. 7 Interaction between TPP and MPP for path planning. The goal is identified by the purple G. The topological path is
+shown with purple links. The dashed yellow arrow is the trajectory computed by MPP to the targeted poses designated by the
+yellow P. Light gray, dark gray and black areas of the occupancy grid represent free, unknown and occupied cells, respectively.
+Blue nodes are in WM, and red nodes are in LTM. Yellow links are proximity links.
+3.6 Patrol Module
+We implemented the Patrol module to generate naviga-
+tion goals, referred to as waypoints so that the robot is
+programmed to continuously patrol an area. The Patrol
+module receives waypoints as inputs and sends them
+successively to TPP. By examining TPP’s status mes-
+sages, Patrol can know when a goal is reached or if TPP
+has failed. Whenever the status indicates that the goal
+is reached or not, the Patrol module sends the next
+waypoint, and restart to the first one once the whole
+list has been processed.
+4 Results
+Table 1 shows the parameters used for the trials1. The
+acquisition time A used is 1 sec (i.e., the map update
+rate is 1 Hz), which set the maximum online time al-
+lowed to process each node added to the map. For
+the trials, T is set to 200 ms to limit CPU usage for
+SPLAM-MM to around 20%, to make sure that higher
+1 In comparison with (Labbe and Michaud, 2013), T =
+Ttime, S = TST M and Y = Tsimilarity.
+frequency modules (acquisition of Sensor Data acquisi-
+tion and MPP) can run at their fixed frequency of 10
+Hz. The robot is relatively moving at the same velocity
+during the trials, and therefore M is fixed to 2 to make
+sure that nodes on a planned path are retrieved fast
+enough to avoid having the robot wait for nodes still in
+LTM. All computations are done onboard on the robot,
+which is equipped with a 2.66 GHz Intel Core i7-620M
+and a 128 GB SSD hard drive (on which the LTM is
+saved).
+To define the area over which the robot had to pa-
+trol, during session 1 we first teleoperated the robot
+and defined four waypoints (WP1 to WP4). There were
+no people in the environment during the teleoperation
+phase. After reaching WP4, the autonomous navigation
+phase is initiated by sending the waypoints to the Pa-
+trol module. Figure 8 illustrates the four waypoints on
+the global map and the first planned trajectory by TPP
+(purple path) from the current position of the robot
+(WP4) to WP1. To come back to WP1, the robot had
+to follow the path in the opposite direction from when
+these nodes were created. Proximity detection made
+it able to follow the path appropriately. To see more
+clearly the effect of proximity links, Fig. 9 shows the
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+11
+Table 1 Parameters used for the trials
+Acquisition time
+A
+1 sec
+ICP correspondence ratio
+C
+0.3
+Radius of the goal area
+D
+0.5 m
+TPP iterations before failure
+F
+10
+Loop closure hypothesis threshold
+H
+0.11
+Minimum RANSAC visual word inliers
+I
+5
+Close nodes radius
+L
+0.5 m
+Maximum retrieved close nodes
+M
+2
+Heuristics 2 close-by nodes ratio
+O
+0.25
+Laser scan range
+R
+4 m
+STM size
+S
+20
+Time limit
+T
+200 ms
+Maximum obstacle height
+U
+0.4 m
+Similarity threshold
+Y
+0.3
+Ground segmentation maximum angle
+Z
+0.1 rad
+WP4	
+WP3	
+WP2	
+WP1	
+Battery Charger	
+Fig. 8 Waypoints WP1 to WP4 identified on the global map.
+The purple path is the first path planned by TPP from the
+WP4 to WP1.
+maps after reaching WP1 with and without graph op-
+timization. Navigation would not have been possible
+without proximity links: the local map would have look
+like the map in (b) without the yellow links because no
+appearance-based similarities would have been found
+with nodes from the map on the planned path. When
+reaching WP1, the Patrol module sends the next way-
+point (WP2), making the robot continue patrolling.
+Every 45 minutes or so of operation, the robot was
+manually shutdown and moved to the battery charger
+near WP1. Once recharged, a new session of SPLAM-
+MM was initiated, creating a new node in STM with
+odometry reset, while preserving the nodes in WM
+and LTM. As the robot was initialized in the area of
+WP1 for each session, loop closures were found, con-
+WP1!
+WP1!
+WP2!
+WP2!
+WP3!
+WP3!
+WP4!
+WP4!
+(a)
+WP1!
+WP1!
+WP2!
+WP2!
+WP3!
+WP3!
+WP4!
+WP4!
+(b)
+Fig. 9 Global maps, optimized and not optimized, after
+reaching WP1. Yellow and red links are proximity and loop
+closure links, respectively.
+necting and optimizing the new map with nodes cre-
+ated from previous sessions, and allowing the Patrol
+module to provide waypoints as navigation goals to pa-
+trol the area. Overall, 11 indoor mapping sessions were
+conducted, for a total distance of 10.5 km lasting 7.5
+hours of operation spent over two weeks. The robot did
+111 patrolling cycles (i.e., traversing from WP1 through
+WP2, WP3, WP4 and coming back to WP1). The ses-
+sions were conducted during office hours, with people
+walking by. A total of 139 people were encountered by
+the robot while patrolling. Figure 10 illustrates the dy-
+namic conditions and some of the obstacles that the
+robot had to deal with during the trials.
+The main goal of the trials is to see how SPLAM is
+influenced by memory management over long-term op-
+eration, only having the local map for online process-
+ing. This can be illustrated by looking at the influences
+of memory management on SPLAM, interactions be-
+tween TPP and MPP, and the influences of LTM on
+TPP. As the robot is continuously adding new nodes,
+the trials also demonstrate how SPLAM-MM works in
+an unbounded environment.
+4.1 Influences of MM on SPLAM
+Figure 11 shows a typical navigation result when reach-
+ing the time limit T, thus limiting the size of the local
+map used for online navigation. This example shows
+the path planned between WP4 and WP1 after 4.7
+hours of operation. The local maps used for online plan-
+ning, localization and mapping are shown for different
+time steps along the trajectory. At t = 17031 sec, the
+planned path had 67 nodes and was 33 m long. It took
+1.3 sec to be generated by TPP and to have the first
+pose on the path sent to MPP. The laser scan range R
+is delimiting the upcoming nodes on the path provided
+by TPP. As the robot navigates in the environment,
+the farthest available pose in the local map on the path
+(end of the cyan line) is sent from TPP to MPP. Up-
+
+12
+Mathieu Labb´e, Fran¸cois Michaud
+a)!
+b)!
+c)!
+d)!
+e)!
+Fig. 10 Events that occurred during the trials: a) open and closed doors between traversals; b) camera exposure that led to
+the extraction of different visual features, making it difficult to find loop closures; c) someone opening a door while the robot
+is navigating; d) people walking around or blocking the robot; e) featureless images on which loop closure detection cannot
+work.
+t = 17060 sec!
+t = 17053 sec!
+t = 17031 sec!
+t = 17068 sec!
+t = 17075 sec!
+t = 17081 sec!
+t = 17108 sec!
+t = 17095 sec!
+WP4!
+WP4!
+WP4!
+WP4!
+WP4!
+WP4!
+WP4!
+WP1!
+WP1!
+WP1!
+WP1!
+WP1!
+WP1!
+WP1!
+WP1!
+Fig. 11 Example of the effect of memory management when travelling from WP4 to WP1 after 4.7 hours of operation. The
+path planned is shown in purple. The small colored icon represents the robot position at each time step. The dotted circle
+around the robot position illustrates the laser scan range R. The cyan lines represent the upcoming nodes on the planned path.
+coming nodes, if they are not in WM, are retrieved to
+make the robot able to localize itself (though loop clo-
+sures and proximity detections) on the path. Looking
+at how the local map changes in these snapshots, notice
+how starting from t = 17075 sec, the initial portion of
+the path is transferred in LTM to keep the size of the
+WM relatively constant. At t = 17108 sec, the robot
+reached WP1.
+Figure 12 compares the images between each way-
+point and the final position of the robot at the way-
+points. The robot successfully reached the waypoints
+(within D as the goal radius) 445 out of 446 times. For
+WP2, WP3 and WP4, the robot always came from be-
+hind the waypoint, and as soon the robot reached the
+waypoint within a D radius, TPP detected that the goal
+was reached. This explains why all the poses are behind
+the waypoints but inside the goal radius D. Similarly,
+for WP1, the robot came from behind from a slightly
+different direction. Spurious poses on the right part of
+the circle are those where there was an obstacle that
+caused the robot to avoid it, making it reach the way-
+point from a different direction. The one time the robot
+failed to reach a waypoint is because someone blocked
+the robot for a long time, making TPP failed after F at-
+
+SOHTESTHTELong-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+13
+tempts of reaching the upcoming nodes: a failure status
+message was then sent to the Patrol module to provide
+the next waypoint. The person left soon after the next
+waypoint was sent, and the robot reached the new way-
+point provided.
+Figure 13 illustrates the evolution of the number
+of nodes in WM and online processing time over the 11
+mapping sessions. Processing time includes all SPLAM-
+MM modules except MPP which was running concur-
+rently on a separate process (its processing time is only
+dependent of the local map size). As explained in Sec-
+tion 3.5.2, TPP occurs offline and only when a new
+goal is received from the Patrol module, and is exam-
+ined in Section 4.3. Fig. 13a illustrates that the number
+of nodes in WM and the local map was identical until T
+sec was reached. After that, nodes were transferred to
+LTM to limit the WM size for online processing, which
+is satisfied as shown by Fig. 13b. Processing time also
+remained well under the acquisition time A.
+4.2 TPP-MPP Interactions
+To illustrate with a concrete example of the situation
+described in Fig. 7, Fig. 14 presents an example of con-
+secutive poses sent by TPP to MPP while nodes from
+LTM are retrieved for the planned path. The red ar-
+row shows the pose of the farthest node on the path
+(the direction of the arrow shows the orientation of
+the pose). The red line represents the trajectory com-
+puted by MPP from the current position of the robot
+to its targeted pose, combined with obstacle avoidance.
+The blue lines represent the local map. In Fig. 14a,
+the targeted pose is on a node traversed backward (as
+shown by the arrow pointing backward). Between a)
+and b), the local map was updated with nodes loaded
+from LTM of the topological path. The targeted pose
+was updated farther on the path and at the same time,
+the occupancy grid was extended to previously mapped
+areas and MPP recomputed its trajectory. The robot
+could then move farther toward its goal and the nodes
+retrieved were used for proximity detection to correctly
+follow the planned path.
+To also illustrate the importance of obstacle detec-
+tion described in Fig. 6, Fig. 15 presents an example
+where an unexpected obstacle was encountered: as the
+laser rangefinder is 0.4 m above the ground, the forklift
+could only be detected using the RGB-D camera. MPP
+planned a slightly different path (orange) that the one
+planned by TPP (pink) to avoid the obstacle.
+4.3 Influences of LTM on TPP
+Although Fig. 13 demonstrates that SPLAM-MM is
+able to satisfy online constraints on a map increasing
+linearly in size (i.e., not bounded to a maximum size of
+environment), memory used by LTM and consequently
+TPP planning time increase linearly. For example, at
+the end of experiment, LTM contains 24002 nodes and
+113368 links. All raw sensor data in the nodes were
+also saved in the LTM’s database (for debugging and
+visualization purposes), including RGB image (JPEG
+format) and depth image (PNG format) of each node.
+The final database took 6.7 GB of hard drive space.
+With as many links at the end of the experiment, TPP
+required 2.4 sec to compute a plan to the next waypoint.
+In term of memory usage and planning time, LTM must
+be somewhat limited over time when revisiting the same
+areas.
+As a solution to limit LTM memory growth, nodes
+from STM can be merged when moved to WM if they
+have loop closure and/or visual proximity links. We
+studied this possibility by adding a graph reduction al-
+gorithm to STM, to remove the node from the graph
+and to add its neighbor links to the corresponding old
+node(s). Algorithm 1 summarizes the approach used to
+maintain the graph at the same size (same number of
+removed links and nodes than added) if there are many
+successive nodes with loop closure or visual proxim-
+ity links. If two nodes of a same location do not have
+similar images (i.e., they don’t have loop closure or vi-
+sual proximity links), they will not be merged, thus still
+keeping a variety of different images representing the
+same location. To make sure nodes to be merged are
+still in WM (to avoid to modify the LTM), nodes hav-
+ing a link to a node in STM are identified as nodes that
+must stay in WM (similarly to Heuristic 2). Figure 16
+shows how links are merged between the node moved to
+WM and its corresponding node(s) linked by loop clo-
+sure link. In a), the purple node has two loop closure
+links. On graph reduction, its two neighbor links (blue)
+are merged with the loop closure links (red) by multi-
+plying the corresponding transformations together, cre-
+ating merged neighbor links (orange). In this case, the
+same number of links are added than those removed but
+one node is removed. In b), the green node has only one
+neighbor link (with the cyan node), then the loop clo-
+sure link is only merged with it, creating only one link
+and four are removed. Merged neighbor links are ig-
+nored to be merged again to limit the number of links.
+In c), the cyan node does not have any loop closure and
+no graph reduction is done.
+To test this idea, data from the 11 sessions were
+processed again to test the influences of the graph re-
+
+14
+Mathieu Labb´e, Fran¸cois Michaud
+ID=167	
+ID = 266	
+ID = 417	
+a)	
+b)	
+c)	
+WP2	
+WP3	
+d)	
+WP4	
+ID = 26514	
+ID = 6414	
+ID = 22016	
+ID = 9896	
+ID = 19	
+−2
+−1.8
+−1.6
+−1.4
+−1.2
+−1
+−0.8
+−0.6
+−0.4
+−0.2
+−2.2
+−2
+−1.8
+−1.6
+−1.4
+−1.2
+−1
+−0.8
+−0.6
+−0.4
+wp1
+2.2
+2.4
+2.6
+2.8
+3
+3.2
+3.4
+3.6
+3.8
+4
+−8.4
+−8.2
+−8
+−7.8
+−7.6
+−7.4
+−7.2
+−7
+−6.8
+−6.6
+wp2
+15.4
+15.6
+15.8
+16
+16.2
+16.4
+16.6
+16.8
+17
+17.2
+12.2
+12.4
+12.6
+12.8
+13
+13.2
+13.4
+13.6
+13.8
+14
+wp3
+15.4
+15.6
+15.8
+16
+16.2
+16.4
+16.6
+16.8
+17
+17.2
+−4.2
+−4
+−3.8
+−3.6
+−3.4
+−3.2
+−3
+−2.8
+−2.6
+−2.4
+wp4
+WP1	
+Images	
+Laser scans	
+Fig. 12 Comparison of the corresponding images between the waypoint (left image) and at the last pose reached on one of
+the planned path (right image) for the waypoints. The top view grid shows the laser scan readings and referentials of the
+waypoint’s nodes (at the origin of the grid) and the final node. The zoomed portions represent the final poses of the robot
+(represented by blue dots), for all paths planned for each waypoint. The circle represents the goal radius D, and the grid’s
+cells used for visualization have a width of 1 m.
+0
+0.5
+1
+1.5
+2
+2.5
+3
+x 10
+4
+0
+50
+100
+150
+200
+250
+300
+350
+400
+450
+500
+Node indexes
+Nodes
+ 
+ 
+WM
+Local map
+(a) Number of nodes in WM and in the local map.
+0
+0.5
+1
+1.5
+2
+2.5
+3
+x 10
+4
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+Time (s)
+Node indexes
+(b) Processing time (the horizontal line represents T = 0.2
+sec).
+Fig. 13 Memory size and total processing time over the 11 mapping sessions.
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+15
+Goal
+(a)
+Goal
+(b)
+Fig. 14 Example of poses sent by TPP to MPP while nodes
+from LTM are retrieved for the planned path. The goal of the
+path is somewhere outside these images in the direction shown
+by Goal. The bottom left images shows the actual RGB image
+from the RGB-D camera. The blue lines are nodes and links
+of the local map. The red line is the computed trajectory from
+MPP using the local map’s occupancy grid from its current
+pose (red arrow). The RGB point cloud and the occupancy
+grid are created using RGB-D images and laser scans stored
+in nodes from the local map, respectively. In a), the robot is
+following the red trajectory. In b), some nodes are retrieved
+from LTM and a new trajectory is computed to move further
+on the path toward the goal.
+Algorithm 1 Graph Reduction
+1: o ← node moved to WM
+2: m ← loop closure and visual proximity links of o
+3: if m is not empty then
+4:
+n ← neighbor links of o
+5:
+for all m in m do
+6:
+om ← node pointed by m
+7:
+for all n in n do
+8:
+on ← node pointed by n
+9:
+t ← m−1·n
+10:
+Add t to om
+11:
+Add t−1 to on
+12:
+end for
+13:
+end for
+14:
+Remove o from the graph
+15: end if
+duction approach using real data acquired by the robot.
+Note that even though graph reduction was validated
+offline, we carefully monitored the experiment manually
+to make sure that the robot could still localize itself cor-
+rectly on the planned paths.
+Figure 17 shows a comparison of the final global
+map without and with graph reduction. The zones with
+Fig. 15 Example where MPP plans a slightly different path
+(orange) than the one provided by TPP (pink). The yellow
+dot is the current position of the robot and the lower right
+image is the corresponding RGB image.
+STM	
+WM	
+Graph Reduction	
+STM to WM	
+WM	
+STM	
+a)	
+b)	
+c)	
+Fig. 16 Three examples illustrating how the graph reduc-
+tion algorithm works. Blue, red and orange links represent
+neighbor, loop closure and merged neighbor links, respec-
+tively. Black links and white nodes are those removed using
+graph reduction. The left column shows the rightmost node
+(the oldest) of STM moved to WM. Then on the right column,
+this node is removed if it has a loop closure link.
+less blue links indicate that there were many nodes
+merged. The zones with more blue links are where nodes
+were not merged, because of a lack of features or be-
+cause of obstacles: the robot was not able to localize
+itself perfectly on the paths every time, thus adding
+new nodes to the map.
+Figure 18 illustrates TPP planning time correspond-
+ing to LTM size with and without graph reduction. As
+the LTM became larger, TPP planning time increased:
+with graph reduction, TPP planning time was reduced
+by 89% for the last path planned (272 ms instead of 2.4
+
+16
+Mathieu Labb´e, Fran¸cois Michaud
+a)!
+b)!
+Fig. 17 Comparison between the global maps a) without
+graph reduction (24002 nodes and 113368 links); b) with
+graph reduction (6059 nodes and 18255 links).
+sec). Figure 19 illustrates hard drive usage with and
+without graph reduction. Extrapolating linearly mem-
+ory usage with a 100 Gb hard drive, the robot could
+navigate online approximately 110 hours without graph
+reduction before filling up the hard drive. When debug-
+ging data (not used for navigation) are not recorded in
+the database, this estimate would increase to approx-
+imately 33 days (800 hours). This means that if the
+robot is always visiting new locations at a mean velocity
+of 1.4 km/h (as in this experiment), it could travel up
+to 1120 km to map environments online. When graph
+reduction is used, debugging data are not saved and
+having the robot always revisiting the same areas like
+in this experiment, it could do SPLAM continuously for
+about 130 days before reaching the hard drive capacity.
+5 Discussion
+In terms of processing time, results show that SPLAM-
+MM is able to satisfy online processing requirements in-
+dependently of the size of the environment, by transfer-
+ring in LTM portions of the map which then cannot be
+used for loop closure detection, proximity detection and
+graph optimization. Results show also that path fol-
+lowing is still possible in such conditions by incremen-
+tally retrieving locations on the planned path. Thus, as
+shown in Section 4.3, the current hardware limitation
+of the system for long-term continuous SPLAM is hard
+drive capacity, not computation power.
+0
+0.5
+1
+1.5
+2
+2.5
+3
+x 10
+4
+0
+500
+1000
+1500
+2000
+2500
+Time (ms)
+Node indexes
+ 
+ 
+Graph size
+0
+0.5
+1
+1.5
+2
+2.5
+x 10
+4
+Graph size (nodes)
+0
+1000
+2000
+3000
+4000
+0
+100
+200
+300
+Time (ms)
+Node indexes
+Fig. 18 Comparison of TPP planning time and LTM size,
+with (blue) and without (red) graph reduction. The peaks in
+the zoomed section show more precisely when a planning is
+done (when a waypoint is reached).
+0
+1
+2
+3
+4
+5
+6
+7
+8
+0
+1000
+2000
+3000
+4000
+5000
+6000
+7000
+Time (h)
+Hard drive usage (MB)
+ 
+ 
+Raw data discarded
+Fig. 19 Comparison of hard drive usage with (blue) and
+without (red) graph reduction. The dashed curves represents
+results without saving in database the debugging data (i.e.,
+raw RGB and depth images).
+To successfully follow a path, results demonstrate
+the importance of adding loop closure and/or proxim-
+ity links with nodes on the planned path to localize the
+robot in the map. In our trials, the robot navigated in-
+door where static structures (e.g., walls) were most of
+the time visible using the laser rangefinder. However, in
+large empty spaces where the laser rangefinder would
+not be able to perceive nearby structures, it would be
+difficult for the robot to follow a path if appearance-
+based loop closure detection and visual proximity de-
+tection do not occur. A laser rangefinder with larger
+perceptual range or a 3D LIDAR sensor like the Velo-
+dyne could be used to increase perceptual range. For
+a lower cost solution, using a camera facing backward
+could be useful to allow the robot to detect similari-
+ties in images when traversing a path in opposite direc-
+tion (Carrera et al., 2011). Without adding new sensors,
+TPP could also stop sending new poses when no loop
+closure links or proximity links occur for a while. If no
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+17
+loop closures were found over the next few meters, it
+would be possible to wait for the robot to rotate at
+this location so that it can look backward, increasing
+its chance to detect a loop closure to correct its po-
+sition on the planned path and then generate a new
+pose. A similar recovery approach is presented in (Mil-
+ford and Wyeth, 2010), where an exploration phase is
+triggered to re-localize the robot when failing to follow
+the planned path. Also, to be more robust to dynamic
+environments where there are cyclic changes over time,
+TPP could select nodes that match better the current
+time of the day rather than the most recent ones, to in-
+crease localization success as in (Krajn´ık et al., 2016).
+In comparison with large empty environments, those
+in which a lot of dynamic changes occur (e.g., navigat-
+ing through a crowd) would also make simultaneous
+planning and localization more difficult. For instance,
+mapping the area in session 1 without people walk-
+ing by helped the robot acquire the static structures
+of the environment since they were not hidden by peo-
+ple. These static structures facilitate localization when
+the robot comes back to these areas later one. If these
+static structures were previously occluded, they would
+be added to the map as the robot comes back to these
+areas (obviously if people are no longer in the robot’s
+field of view). If people partially occlude the robot’s
+sensors over a long distance, localization would still be
+possible but would occur less frequently.
+For online multi-session mapping with our memory
+management approach, the worst case is when all nodes
+of a previous map are transferred to LTM before a loop
+closure is detected (Labbe and Michaud, 2013). This
+results in definitely ignoring the previous map and dis-
+abling at the same time the ability to plan paths to
+a location in it. To avoid this problem, an additional
+heuristic could be to keep in WM at least one discrim-
+inative node for each map. However, if the number of
+mapping sessions becomes very high (e.g., thousands of
+sessions), these nodes would definitely have to be trans-
+ferred in LTM to satisfy online processing requirements.
+A strategy that makes the robot explore potential paths
+to link maps together would then be useful, and maps
+that could not be linked would eventually be unretriev-
+able.
+In the trials conducted, no invalid loop closures were
+detected, avoiding to corrupt the map with erroneous
+loop closure links. If this happens, graph optimization
+approaches such as (Latif et al., 2013; Sunderhauf and
+Protzel, 2012; Lee et al., 2013) deal with possible invalid
+matches, and could be used to increase robustness of
+SPLAM-MM. However, these approaches assume that
+the whole global map is available online, which is not
+the case here. They could be still used offline at the end
+of a session.
+As shown by Fig. 15, MPP in SPLAM-MM allows
+the robot to find an alternative path to reach the tar-
+geted pose when possible. However, if the alternative
+path is outside the local map, re-planning with TPP is
+required. Some paths may be also blocked temporary or
+permanently by some dynamic or new static obstacles.
+An approach similar to (Konolige et al., 2011) could be
+used to identify some links as blocked so that TPP can-
+not plan a path using them. The Patrol module could
+also manage waypoints that can and cannot be reached.
+Finally, the graph reduction approach can reduce
+significantly the number of nodes and links saved in
+LTM to reduce TPP planning time. However, because
+of dynamic events or the lack of features (e.g., Fig.
+10e), new nodes and links will inevitably be added to
+LTM over time when revisiting the same areas. As an
+improvement, nodes with featureless image could be
+merged through a maximum density threshold like in
+(Milford and Wyeth, 2010), as they cannot be used for
+loop closure detection. After applying graph reduction
+on the experimental data, there are still 3068 featureless
+nodes of 6059 nodes in the global graph, which would
+reduce by about 50% the remaining graph. However,
+even by limiting the rate at which the LTM grows, a
+continuous SLAM approach in unbounded dynamic en-
+vironments will always add new data over time. A com-
+plementary strategy would be to definitely forget some
+parts of the global map, at the cost of not being able
+to return to some locations.
+6 Conclusion
+By limiting the nodes of the map available online in
+WM for loop closure detection, proximity detection and
+graph optimization, results presented in this paper sug-
+gest that the proposed graph-based SPLAM-MM ap-
+proach is able to meet online processing requirements
+needed for simultaneous mapping, localizing and plan-
+ning in multi-session conditions. SPLAM-MM is tightly
+based on appearance-based loop closure detection, al-
+lowing it to naturally deal with the initial state prob-
+lem of multi-session mapping. To successfully localize
+on a planned path through areas previously transferred
+in LTM, memory management allows SPLAM-MM to
+deal with the necessity of retrieving upcoming nodes on
+the path in WM. Our code is open source and available
+at http://introlab.github.io/rtabmap.
+In future works, more robust failure recovery ap-
+proaches will be examined to test SPLAM-MM in dy-
+namic environments where the paths could often be
+blocked (temporally or permanently). We also plan to
+
+18
+Mathieu Labb´e, Fran¸cois Michaud
+study the impact of autonomous coverage and explo-
+ration strategies, especially how it can actively direct
+exploration based on nodes available for online map-
+ping. This could be also useful to conduct longer ex-
+periments at larger scale.
+References
+Atkinson R, Shiffrin R (1968) Human memory: A pro-
+posed system and its control processes. In: Psychol-
+ogy of Learning and Motivation: Advances in Re-
+search and Theory, vol 2, Elsevier, pp 89–195
+Baddeley A (1997) Human Memory: Theory and Prac-
+tice. Psychology Press
+Bay H, Ess A, Tuytelaars T, Gool LV (2008) Speeded
+Up Robust Features (SURF). Computer Vision and
+Image Understanding 110(3):346–359
+Besl PJ, McKay ND (1992) Method for registration of
+3-D shapes. In: Robotics-DL tentative, International
+Society for Optics and Photonics, pp 586–606
+Biber P, Duckett T, et al. (2005) Dynamic maps for
+long-term operation of mobile service robots. In:
+Robotics: Science and Systems, pp 17–24
+Carrera G, Angeli A, Davison AJ (2011) Lightweight
+SLAM and navigation with a multi-camera rig. In:
+European Conference on Mobile Robots, pp 77–82
+Churchill W, Newman P (2012) Practice makes per-
+fect? Managing and leveraging visual experiences for
+lifelong navigation. In: Proc. IEEE Int. Conf. on
+Robotics and Automation, pp 4525–4532
+Dijkstra EW (1959) A note on two problems in connex-
+ion with graphs. Numerische Mathematik 1(1):269–
+271
+Ferland F, Clavien L, Fr´emy J, Letourneau D, Michaud
+F, Lauria M (2010) Teleoperation of AZIMUT-3, an
+omnidirectional non-holonomic platform with steer-
+able wheels. In: Proc. IEEE/RSJ Int. Conf. on Intel-
+ligent Robots and Systems, pp 2515–2516
+Folkesson J, Christensen HI (2007) Closing the loop
+with graphical SLAM. IEEE Trans on Robotics
+23(4):731–41
+Fox D, Burgard W, Thrun S (1997) The dynamic win-
+dow approach to collision avoidance. IEEE Robotics
+& Automation Magazine 4(1):23–33
+Garcia-Fidalgo E, Ortiz A (2015) Vision-based topo-
+logical mapping and localization methods: A survey.
+Robotics and Autonomous Systems 64:1 – 20
+Glover AJ, Maddern WP, Milford MJ, Wyeth GF
+(2010) FAB-MAP + RatSLAM: Appearance-based
+SLAM for multiple times of day. In: Proc. IEEE Int.
+Conf. on Robotics and Automation, pp 3507–3512
+Grisetti G, Grzonka S, Stachniss C, Pfaff P, Burgard
+W (2007) Efficient estimation of accurate maximum
+likelihood maps in 3D. In: Proc. IEEE/RSJ Int. Conf.
+on Intelligent Robots and Systems, pp 3472–3478
+Grisetti G, K¨ummerle R, Stachniss C, Burgard W
+(2010) A tutorial on graph-based SLAM. IEEE Intel-
+ligent Transportation Systems Magazine 2(4):31–43
+Ho KL, Newman P (2006) Loop closure detection in
+SLAM by combining visual and spatial appearance.
+Robotics and Autonomous Systems 54(9):740–749
+Johannsson H, Kaess M, Fallon M, Leonard J (2013)
+Temporally scalable visual SLAM using a reduced
+pose graph. In: Proc. IEEE Int. Conf. on Robotics
+and Automation, pp 54–61
+Kim B, Kaess M, Fletcher L, Leonard J, Bachrach A,
+Roy N, Teller S (2010) Multiple relative pose graphs
+for robust cooperative mapping. In: Proc. IEEE Int.
+Conf. on Robotics and Automation, pp 3185–3192
+Konolige K, Bowman J (2009) Towards lifelong visual
+maps. In: Proc. IEEE/RSJ Int. Conf. on Intelligent
+Robots and Systems, pp 1156–1163
+Konolige K, Marder-Eppstein E, Marthi B (2011) Nav-
+igation in hybrid metric-topological maps. In: Proc.
+IEEE Int. Conf. on Robotics and Automation, pp
+3041–3047
+Krajn´ık T, Fentanes JP, Hanheide M, Duckett T
+(2016) Persistent localization and life-long mapping
+in changing environments using the frequency map
+enhancement. In: Proc. IEEE/RSJ Int. Conf. on In-
+telligent Robots and Systems, pp 4558–4563
+Kummerle R, Grisetti G, Strasdat H, Konolige K, Bur-
+gard W (2011) g2o: A general framework for graph
+optimization. In: Proc. IEEE Int. Conf. on Robotics
+and Automation, pp 3607–3613
+Labbe M, Michaud F (2013) Appearance-based loop
+closure detection for online large-scale and long-term
+operation. IEEE Trans on Robotics 29(3):734–745
+Labbe M, Michaud F (2014) Online global loop closure
+detection for large-scale multi-session graph-gased
+SLAM. In: Proc. IEEE/RSJ Int. Conf. on Intelligent
+Robots and Systems, pp 2661–2666
+Latif Y, Cadena C, Neira J (2013) Robust loop closing
+over time for pose graph SLAM. Int J of Robotics
+Research 32(14):1611—1626
+Lee GH, Fraundorfer F, Pollefeys M (2013) Ro-
+bust
+pose-graph
+loop-closures
+with
+expectation-
+maximization. In: Proc. IEEE/RSJ Int. Conf. on In-
+telligent Robots and Systems, pp 556–563
+Marder-Eppstein E, Berger E, Foote T, Gerkey B,
+Konolige K (2010) The Office Marathon: Robust nav-
+igation in an indoor office environment. In: Proc.
+IEEE Int. Conf. on Robotics and Automation, pp
+300–307
+McDonald J, Kaess M, Cadena C, Neira J, Leonard J
+(2012) Real-time 6-DOF multi-session visual SLAM
+
+Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management
+19
+over large scale environments. Robotics and Au-
+tonomous Systems 61(10):1144–58
+Milford M, Wyeth G (2010) Persistent navigation and
+mapping using a biologically inspired SLAM system.
+Int J of Robotics Research 29(9):1131–53
+Muja M, Lowe DG (2009) Fast approximate nearest
+neighbors with automatic algorithm configuration.
+In: Proc. Int. Conf. on Computer Vision Theory and
+Application, pp 331–340
+Pirker K, Ruther M, Bischof H (2011) CD SLAM –
+Continuous localization and mapping in a dynamic
+world. In: Proc. IEEE/RSJ Int. Conf. on Intelligent
+Robots and Systems, pp 3990–3997
+Rusu RB, Cousins S (2011) 3D is here: Point Cloud
+Library (PCL). In: Proc. IEEE Int. Conf. on Robotics
+and Automation, Shanghai, China, pp 1–4
+Sivic J, Zisserman A (2003) Video Google: A text re-
+trieval approach to object matching in videos. In:
+Proc. 9th Int. Conf. on Computer Vision, Nice,
+France, pp 1470–1478
+Stachniss C (2009) Robotic Mapping and Exploration,
+vol 55. Springer Science & Business Media
+Sunderhauf N, Protzel P (2012) Towards a robust back-
+end for pose graph SLAM. In: Proc. IEEE Int. Conf.
+on Robotics and Automation, pp 1254–1261
+Thrun S, Burgard W, Fox D (2005) Probabilistic
+Robotics. The MIT Press
+Valencia R, Morta M, Andrade-Cetto J, Porta JM
+(2013) Planning reliable paths with Pose SLAM.
+IEEE Trans on Robotics 29(4):1050–1059
+Walcott-Bryant A, Kaess M, Johannsson H, Leonard
+JJ (2012) Dynamic pose graph SLAM: Long-term
+mapping in low dynamic environments. In: Proc.
+IEEE/RSJ Int. Conf. on Intelligent Robots and Sys-
+tems, pp 1871–1878
+
diff --git a/7dAyT4oBgHgl3EQfQvYd/content/tmp_files/load_file.txt b/7dAyT4oBgHgl3EQfQvYd/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf,len=913
+page_content='This is a post-peer-review, pre-copyedit version of an article published in Autonomous Robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The final authenticated version is available online at: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1007/s10514-017-9682-5  Long-Term Online Multi-Session Graph-Based SPLAM with  Memory Management  Mathieu Labb´e · Fran¸cois Michaud  Abstract For long-term simultaneous planning, local-  ization and mapping (SPLAM), a robot should be able  to continuously update its map according to the dy-  namic changes of the environment and the new areas  explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' With limited onboard computation capabili-  ties, a robot should also be able to limit the size of the  map used for online localization and mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This pa-  per addresses these challenges using a memory manage-  ment mechanism, which identifies locations that should  remain in a Working Memory (WM) for online pro-  cessing from locations that should be transferred to  a Long-Term Memory (LTM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When revisiting previ-  ously mapped areas that are in LTM, the mechanism  can retrieve these locations and place them back in WM  for online SPLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The approach is tested on a robot  equipped with a short-range laser rangefinder and a  RGB-D camera, patrolling autonomously 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 km in  an indoor environment over 11 sessions while having  encountered 139 people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Keywords SLAM · path planning · pose graph ·  multi-session · loop closure detection  1 Introduction  The ability to simultaneously map an environment, lo-  calize itself in it, and plan paths using this information  This work was supported by the Natural Sciences and Engi-  neering Research Council of Canada (NSERC), the Canada  Research Chair program and the Canadian Foundation for  Innovation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Labb´e  E-mail: mathieu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='labbe@usherbrooke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='ca  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Michaud  E-mail: francois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='michaud@usherbrooke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='ca  Interdisciplinary Institute for Technological Innovation (3IT),  Universit´e de Sherbrooke, Sherbrooke, Qu´ebec, Canada  is known as Simultaneous Planning, Localization And  Mapping, or SPLAM (Stachniss, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This task can  be particularly complex when done online on a robot  with limited computing resources in large, unstructured  and dynamic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Since SPLAM can be seen  as an extension of Simultaneous Localization And Map-  ping (SLAM), many approaches exist (Thrun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=',  2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Our interest lies with graph-based SLAM ap-  proaches (Grisetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2010), for which combining  a lightweight topological map over a detailed metrical  map reveals to be more suitable for large-scale mapping  and navigation (Konolige et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Two important challenges in graph-based SPLAM  are :  – Multi-session mapping, also known as the kidnapped  robot problem or the initial state problem: when  turned on, a robot does not know its relative po-  sition to a map previously created, making it im-  possible to plan a path to a previously visited loca-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A solution is to have the robot localize itself  in a previously-built map before initiating mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  This solution has the advantage of always using the  same referential, resulting in only one map is created  across the sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, the robot must start  in a portion already mapped of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Another approach is to initialize a new map with  its own referential on startup, and when a previ-  ously visited location is encountered, a transforma-  tion between the two maps can be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  transformations between the maps can be saved ex-  plicitly with special nodes called anchor nodes (Mc-  Donald et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2010), or implicitly  with links added between each map (Konolige and  Bowman, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Latif et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This process is  referred to as loop closure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Loop closure  detection approaches that are independent of the  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='00050v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='RO]  30 Dec 2022  2  Mathieu Labb´e, Fran¸cois Michaud  robot’s estimated position (Ho and Newman, 2006)  can intrinsically detect if the current location is a  new location or a previously visited one among all  the mapping sessions conducted in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Popular  loop closure detection approaches are appearance-  based (Garcia-Fidalgo and Ortiz, 2015), exploiting  the distinctiveness of images of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The underlying idea is that loop closure detection  is done by comparing all previous images with the  new one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When loop closures are found between the  maps, a global map can be created by combining  the maps from each session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In graph-based SLAM,  graph pose optimization approaches (Folkesson and  Christensen, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Grisetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Kummerle  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Johannsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2013) use these loop  closures to reduce odometry errors inside each map  and in between the maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Long-term mapping in dynamic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Per-  sistent (Milford and Wyeth, 2010), lifelong (Kono-  lige and Bowman, 2009) or continuous (Pirker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=',  2011) are terms generally used to describe SLAM  approaches working in such conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Continu-  ously updating and adding new data to the map in  unbounded or dynamic environments will inevitably  increase the map size over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Online simulta-  neous planning, localization and mapping requires  that new incoming data be processed faster than  the time to acquire them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For example, if data are  acquired at 1 Hz, updating the map should be done  in less than 1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As the map grows, the time re-  quired for loop closure detection and graph opti-  mization increases, and eventually limits the size of  the environment that can be mapped and used on-  line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To address these challenges, we introduce SPLAM-  MM, a graph-based SPLAM with a memory manage-  ment (MM) mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As demonstrated in (Labbe  and Michaud, 2013), memory management can be used  to limit the size of the map so that loop closure detec-  tions are always processed under a fixed time limit, thus  satisfying online requirements for long-term and large-  scale environment mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The idea behind SPLAM-  MM is to limit the number of nodes available for  loop closure detection and graph optimization, keeping  enough observations in the map for successful online  localization and planning while still having the ability  to generate a global representation of the environment  that can adapt to changes over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Section 2 reviews  graph-based SLAM approaches that reduce the size of  the map when revisiting the same environment while  continuously adapting to dynamic changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Section 3  describes the implementation and the operating prin-  ciples associated with the use of memory management  with a graph-based SPLAM approach, which extends  our previous metric-based SLAM approach (Labbe and  Michaud, 2014) with a new planning capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  implementation integrates four algorithms: loop clo-  sure detection (Labbe and Michaud, 2013), graph opti-  mization (Grisetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2007), metrical path planner  (Marder-Eppstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2010) and a custom topological  path planner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Section 4 presents experimental results of  11 SPLAM sessions using the AZIMUT-3 robot in an  indoor environment over 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Section 5 discusses  strengths and limitations of SPLAM-MM, and Section  6 concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  2 Related Work  Lifelong appearance-based SLAM requires dealing with  dynamic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Glover et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2010) present an  appearance-based SLAM approach that had to oper-  ate in different lighting conditions over three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  An interesting observation from their experiments is  that even when revisiting the same locations, the map  still grows: in dynamic environments, the loop closure  detector is sometimes unable to detect loop closures,  duplicating locations in the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A map management  approach is therefore required to limit map size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In  highly dynamic environments, multiple views of the  same location may also be required for proper local-  ization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Churchill and Newman (2012) present a graph-  based SLAM approach where visual experiences of the  same locations are kept in the map, to increase localiza-  tion robustness to dynamic changes caused for instance  by outdoor illumination conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If localization fails  when revisiting an area, new experiences are added to  the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Even if adding new visual experiences to the  map happens less often over time (as the robot explores  the same location), there is no mechanism to limit this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Pirker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2011) present a continuous monocular  SLAM approach where new key frames are added to  the map only when the environment has changed, to  keep its size proportional to the explored space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' But if  the environment changes very often, there is no mech-  anism to limit the number of key frames over the same  physical location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Some  SLAM  approaches  can  handle  dynamic  changes of the environment while limiting the size of  the map for long-term operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Biber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2005)  present a sample-based representation for maps, to han-  dle changes at different timescales, tracking both sta-  tionary and non-stationary elements of the environ-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The idea is to refresh samples stored for each  timescale with new sensor measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Map growth  is then indirectly limited as older memories fade at  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  3  different rates depending on the timescale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Walcott-  Bryant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2012) describe Dynamic Pose-Graph  SLAM (DPG-SLAM), a long-term mapping approach  that detects static and dynamic changes of the environ-  ment through time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To keep consistency of the graph  while reducing its size, nodes that are not observable  anymore are removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Johannsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2013) also re-  move unobservable nodes to limit the size of the map  over time when revisiting the same area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Similar nodes  of the graph are merged together while keeping only the  new loop closure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, the graph size is  not bounded when exploring new areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Krajn´ık et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  (2016) present an occupancy grid approach where each  cell in the map estimates its occupancy value depend-  ing on periodical and cyclic changes occurring in the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This increases localization and navigation  accuracy in dynamic environments compared to static  maps, as the predicted map represents the correct state  of the environment at that time of the day (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', doors  can change to be opened or closed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The maximum  data kept for each cell is bounded by some parameters  (depending on the smallest and longest cyclic periods  that should be detected), thus keeping memory usage  fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, the approach assumes that the navi-  gation phase always occur in the same environment as  the first mapping cycle, without possibility to extend it  afterward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  These problems of lifelong SLAM are also addressed  in some SPLAM approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Milford and Wyeth (2010)  present a solution to limit the size of the map (called  experience map) while revisiting the same area: close  nodes are merged together up to a maximum density  threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This approach has the advantage of mak-  ing the map size independent of the operating time,  but the diversity of the observations on each location is  somewhat lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Konolige et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2011) use a view-based  graph SLAM approach (Konolige and Bowman, 2009)  in a SPLAM context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The approach preserves diversity  of the images referring to the same location so that the  map can handle dynamic changes over time, and forget-  ting images limits the size of the graph over time when  revisiting the same area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, the graph still grows  when visiting new areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Overall, these approaches reduce map size when re-  visiting the same area, while continuously adapting to  dynamic changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This makes them independent or al-  most independent of the operation time of the robot in  these conditions, but they are all limited to a maximum  size of the environment that can be mapped online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  SPLAM-MM approach deals specifically with this lim-  itation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 1 The AZIMUT-3 robot equipped with a URG-04LX  laser range finder and a Xtion PRO LIVE sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3 Memory Management for SPLAM  The underlying representation of SPLAM-MM is a  graph with nodes and links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The nodes contain the fol-  lowing information:  – ID: unique time index of the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Weight: an indication of the importance of the node,  used for memory management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Bag-of-words (BOW): visual words used for loop  closure detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' They are SURF features (Bay  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2008) quantized to an incremental vocabu-  lary based on KD-Trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Sensor data: used to find similarities between nodes  and to construct maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For this paper, our imple-  mentation of SPLAM-MM is using the AZIMUT-3  robot (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2010), equipped with an URG-  04LX laser rangefinder and a Xtion Pro Live RGB-D  camera, as shown by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The sensory data used  are:  – Pose: the position of the robot computed by its  odometry system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the value given by wheel  odometry), expressed in (x, y, θ) coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – RGB image: used to extract visual words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Depth image: used to find 3D position of the vi-  sual words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The depth image is registered with  the RGB image, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', each depth pixel corre-  sponds exactly to the same RGB pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Laser scan: used for loop closure transformations  and odometry refinements, and by the Proximity  Detection module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The links store rigid transformations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', Eucledian  transformation derived from odometry or loop closures)  between nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' There are four types of links:  URG-04LX  Xtion PRO LIVE  AZIMUT-34  Mathieu Labb´e,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Fran¸cois Michaud  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Motion Controller  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Waypoints  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Graph-based SLAM-MM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='WM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='STM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='SPLAM-MM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Graph-based  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='SLAM-MM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Wheel Odometry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Laser Rangefinder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='RGB-D Camera  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Motion Controller  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Topological Path  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Planner (TPP)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Twist  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Pose  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Scan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='RGB-D  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Local Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Upcoming Node IDs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Metrical Path  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Planner (MPP)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Pose  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Goal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Appearance-based Loop  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Closure Detection  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Graph  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Optimization  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='New  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Link(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='New  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Local Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Proximity Detection  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Sensor Data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Sensors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Global Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='LTM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Transferred  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Nodes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Retrieved  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Nodes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Global Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Upcoming Node IDs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Patrol  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Goal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Status  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Waypoints  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Topological Path  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Planner (TPP)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Twist  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Metrical Path  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Planner (MPP)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Pose  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Goal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Patrol  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Goal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Status  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 2 Memory management and control architecture of SPLAM-MM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Neighbor link: created between a new node and the  previous one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Loop closure link: added when a loop closure is de-  tected between the new node and one in the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Proximity link: added when two close nodes are  aligned together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Temporary link: used for path planning purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' It  is used to keep the planned path connected to the  current map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 2 presents a high-level representation of  SPLAM-MM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Basically, it consists of a graph-based  SLAM module with memory management, to which  path planners are added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Memory management involves  the use of a Working Memory (WM) and a Long-Term  Memory (LTM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' WM is where maps, which are graphs  of nodes and links, are processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To satisfy online con-  straints, nodes can be transferred and retrieved from  LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' More specifically, the WM size indirectly depends  on a fixed time limit T: when the time required to up-  date the map (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the time required to execute the pro-  cesses in the Graph-based SLAM-MM block) reaches  T, some nodes of the map are transferred from WM to  LTM, thus keeping WM size nearly constant and pro-  cessing time around T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, when a loop closure is  detected, neighbors in LTM with the loop closure node  can be retrieved from LTM to WM for further loop clo-  sure detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In other words, when a robot revisits  an area which was previously transferred to LTM, it  can incrementally retrieve the area if a least one node  of this area is still in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When some LTM nodes are  retrieved, nodes in WM from other areas in the map  can be transferred to LTM, to limit map size in WM  and therefore keeping processing time around T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Therefore, the choice of which nodes to keep in  WM is key in SPLAM-MM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The objective is to have  enough nodes in WM from each mapping session for  loop closure detections and to keep a maximum num-  ber of nodes in WM for generating a map usable to  follow correctly a planned path, while still satisfying  online processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Two heuristics are used to establish  the compromise between selection of which nodes to  keep in WM and online processing:  – Heuristic 1 is inspired from observations made by  psychologists (Atkinson and Shiffrin, 1968;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Badde-  ley, 1997) that people remember more the areas  where they spent most of their time, compared to  those where they spent less time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In terms of mem-  ory management, this means that the longer the  robot is at a particular location, the larger the  weight of the corresponding node should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Old-  est and less weighted nodes in WM are transferred  to LTM before the others, thus keeping in WM only  the nodes seen for longer periods of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As demon-  strated in (Labbe and Michaud, 2013), this heuristic  reveals to be quite efficient in establishing the com-  promise between search time and space, as driven by  the environment and the experiences of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Heuristic 2 is used to identifies nodes that should  stay in WM for autonomous navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Nodes on a  planned path could have small weights and may be  identified for transfer to LTM by Heuristic 1, thus  eliminating the possibility of finding a loop closure  link or a proximity link with these nodes and cor-  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  5  Map 1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Map 3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Map 4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Last node!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Map 2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Local map!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Global map!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 3 Illustration of the local map (inner dashed area) and  the global map (outer dotter area) in multi-session mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Red nodes are in LTM, while all other nodes are in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Loop  closure links are shown using bidirectional green arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  rectly follow the path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Therefore, Heuristic 2 must  supersede Heuristic 1 and allow upcoming nodes to  remain in WM, even if they are old and have a small  weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The Graph-based SLAM-MM block provides two  types of maps derived from nodes in WM and LTM:  – Local map, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the largest connected graph that can  be created from the last node in WM with nodes  available in WM only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The local map is used for  online path planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  – Global map, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the largest connected graph that  can be created from the last node in WM with nodes  in WM and LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' It is used for offline path planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 3 uses diamonds to represent initial and end  nodes for each mapping session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The nodes in LTM are  shown in red and the others are those in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The lo-  cal map is created using only the nodes in WM that  are linked to the last node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The graph linking the last  node with other nodes in WM and LTM represents the  global map (outer dotted area).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If loop closure detec-  tions are found between nodes of different maps, loop  closure links can be generated, and the local map can  span over multiple mapping sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Other nodes in  WM but not included in the local map are unreachable  from the last node, but they are still used for loop clo-  sure detections since all nodes in WM (including those  in Map 2 for instance) are examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The modules presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 2 are described as  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1 Short-Term Memory Module  Short-Term Memory (STM) is the entry point where  sensor data are assembled into a node to be added to  the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Similarly to (Labbe and Michaud, 2013), the  role of the STM module is to update node weight based  on visual similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When a node is created, a unique  time index ID is assigned and its weight is initialized to  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The current pose, RBG image, depth image and laser  scan readings are also memorized in the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If two  consecutive nodes have similar images, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the ratio of  corresponding visual words between the nodes is over a  specified threshold Y , the weight of the previous node is  increased by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If the robot is not moving (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', odom-  etry poses are the same), the new node is deleted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To re-  duce odometry errors on successive STM nodes, trans-  formation refinement is done using 2D iterative-closest-  point (ICP) optimization (Besl and McKay, 1992) on  the rigid transformation of the neighbor link with the  previous node and the corresponding laser scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If the  ratio of ICP point correspondences between the laser  scans over the total laser scan size is greater or equal to  C, the neighbor link’s transformation is updated with  the correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  When the STM size reaches a fixed size limit of S  nodes, the oldest node in STM is moved to WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' STM  size is determined based on the velocity of the robot  and at which rate the nodes are added to the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Images are generally very similar to the newly added  node, keeping S nodes in STM avoids using them for  appearance-based loop closure detection once in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  For example, at the same velocity, STM size should  be larger if the rate at which the nodes are added to  map increases, in order to keep nodes with consecutive  similar images in STM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Transferring nodes with images  very similar with the current node from STM to WM  too early limits the ability to detect loop closures with  older nodes in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2 Appearance-based Loop Closure Detection Module  Appearance-based loop closure detection is based on  the bag-of-words approach described in (Labbe and  Michaud, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Briefly, this approach uses a bayesian  filter to evaluate appearance-based loop closure hy-  potheses over all previous images in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When a loop  closure hypothesis reaches a pre-defined threshold H, a  loop closure is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Visual words of the nodes are  used to compute the likelihood required by the filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In  this work, the Term Frequency-Inverse Document Fre-  quency (TF-IDF) approach (Sivic and Zisserman, 2003)  is used for fast likelihood estimation, and FLANN (Fast  6  Mathieu Labb´e, Fran¸cois Michaud  Library for Approximate Nearest Neighbors) incremen-  tal KD-Trees (Muja and Lowe, 2009) are used to avoid  rebuilding the vocabulary at each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To keep it  balanced, the vocabulary is rebuilt only when it doubles  in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The RGB image, from which the visual words are  extracted, is registered with a depth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Using (1),  for each 2D point (x, y) in the rectified RGB image, a  3D position Pxyz can be computed using the calibration  matrix (focal lengths fx and fy, optical centres cx and  cy) and the depth information d for the corresponding  pixel in the depth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The 3D positions of the visual  words are then known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When a loop closure is detected,  the rigid transformation between the matching images  is computed using a RANSAC (RANdom SAmple Con-  sensus) approach which exploits the 3D visual word cor-  respondences (Rusu and Cousins, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If a minimum  of I inliers are found, the transformation is refined us-  ing the laser scans in the same way as the odometry  correction in STM using 2D ICP transformation refine-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If transformation refinement is accepted, then a  loop closure link is added with the computed transfor-  mation between the corresponding nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The weight  of the current node is updated by adding the weight  of the loop closure hypothesis node and the latter is  reset to 0, so that only one node with a large weight  represents the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Pxyz =  �(x − cx) · d  fx  , (y − cy) · d  fy  , d  �T  (1)  By doing appearance-based loop closure detection  this way, setting H high means that there is less chance  of detecting false positives, but at the cost of detect-  ing less loop closures (Labbe and Michaud, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For  SPLAM-MM, H can be set relatively low to detect more  loop closures because false positives that are geometri-  cally different will be rejected by the rigid transforma-  tion computation step (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the 3D visual word corre-  spondences and 2D ICP transformation refinement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3 Proximity Detection Module  Appearance-based loop closure detection is limited by  the perceptual range of the sensory data used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For in-  stance, when the robot is revisiting areas in opposite di-  rection, the RGB-D camera on AZIMUT-3 is not point-  ing in the same direction compared to when the nodes  were created, and thus no appearance-based loop clo-  sures can be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This also happens when there  are not enough visual features under the depth range  of the RGB-D camera (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', white walls or long halls).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Simply relying on appearance-based loop closure detec-  tions for map corrections would then limit path plan-  ning capabilities, and make navigation difficult in such  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 4a illustrates a situation where the  robot is in a hall coming back to its starting position  in reverse direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Setting a goal at the starting posi-  tion would make the planner fail because no loop clo-  sures could be found to correct the odometry, resulting  in having a wall directly placed on the starting posi-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' One solution would be to have the robot visit the  nodes of the graph backward so loop closures could be  detected to correct the map, and ultimately be able  to reach the starting position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, it is inefficient  and unsafe if the robot does not have sensors pointing  backward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To deal with such situations, the Proximity  Detection module uses laser rangefinder data to correct  odometry drift in areas where the camera cannot de-  tect loop closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' With a field of view of more than  180◦, the laser scans can be aligned in reverse direc-  tion, generating proximity links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As laser scans are not  as discriminative as images, proximity detection is re-  stricted to nodes of the local map located around the  estimated position of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 4b illustrates  the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 5 illustrates how nodes located close to the  robot are selected by the Proximity Detection module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Only nodes in the local map with their pose inside ra-  dius R centered on the robot are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Nodes in STM  are not considered in order to avoid adding useless links  with nodes close by: this would increase graph optimiza-  tion time without adding significative improvements of  the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The nodes are then segmented into groups  with nodes connected only by neighbor links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A group  must have its nearest node from the robot inside a fixed  radius L defining close-by nodes (with L < R) to be  considered for proximity detection, to keep the length  of the resulting proximity links small for path planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Note that Appearance-based Loop Closure Detection  is done before Proximity Detection, thus if the near-  est node has already a loop closure with the new node,  the group is ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Proximity detection is then ap-  plied separately on each group of nodes by doing the  following steps:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A rigid transformation between the nearest node  of each group and the new node added to map is  computed as in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2, and if it is accepted, a  proximity link is added between the corresponding  nodes, and the group of nodes is ignored for step  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' These links are referred as visual proximity links  because visual words are used in the transformation  estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To avoid having to compare multiple nodes with  very similar laser scans (and thus to save computa-  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  7  a)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  b)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 4 Illustration of the role of the Proximity Detection module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' On the left are the raw laser scans, the blue dot is the  starting position, and on the right the corresponding occupancy grid map at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='05 m resolution (black, light gray and dark  gray areas are occupied, empty and unknown spaces, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In a), the yellow circle on the right locates the problematic  situation: after the second traversal, the first nodes of the graph are located exactly over the wall, making it impossible to  plan a path (red arrow on the right) to return to the starting position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In b), proximity links are detected using only the laser  scans, and the local map can then be correctly optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  tion), only the more recent node among those in  the same fixed small radius L (centered on each  node) is kept along the nodes in a remaining group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Then for each group, the laser scans of the nodes  are merged together using their respective pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 2D  ICP transformation refinement is done between the  merged laser scans and the one of the new node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  If the transformation is accepted, a new proximity  link with this transformation is added to the graph  between the new node and the nearest one in the  group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4 Graph Optimization Module  TORO (Tree-based netwORk Optimizer) (Grisetti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2007) is used for graph optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When loop  closure and proximity links are added, the errors de-  rived from odometry can be propagated to all links,  thus correcting the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This also guarantees that  nodes belonging to different maps are transformed into  the same referential when loop closures are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  When only one map exists, it is relatively straight-  forward to use TORO to create a tree because it only  has one root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, for multi-session mapping, each  map has it own root with its own reference frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When  loop closures occur between the maps, TORO cannot  optimize the graph if there are multiple roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' It may  also be difficult to find a unique root when some of  the nodes have been transferred in LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As a solution,  our approach takes the root of the tree to be the latest  a)  b)  c)  d)  R  L  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 5 Illustration of how proximity detection works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In a),  the larger dashed circle represents the radius R used to deter-  mine close-by nodes, and the smaller dashed circle defined by  L is used to limit the length of the links to be created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  empty dots are nodes for which the laser scans are not used,  either because they are outside the radius R, they are too  close from each other or they are in STM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In b) and c), nodes  in the radius R from the two segmented groups of nodes are  processed for proximity detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In d), proximity links are  added (yellow), and after graph optimization, the groups of  nodes are connected together and the respective laser scans  are now aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  8  Mathieu Labb´e, Fran¸cois Michaud  node added to the local map, which is always uniquely  defined across intra-session and inter-session mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  All other poses in the graph are then optimized using  the last odometry pose as the referential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 Path Planning Modules  Memory management has a significant effect on how to  do path planning online using graph-based SLAM, for  which the map changes almost at each iteration and  with only the local map accessible while executing the  plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This differs from approaches that assume that the  map is static and/or that all the previously visited loca-  tions always remain in the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In this paper, SPLAM-  MM uses two path planners: a Metrical Path Planner  (MPP) and a Topological Path Planner (TPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1 Metrical Path Planning Module  MPP receives a pose expressed in (x, y, θ) coordinates,  and uses the local map to plan a trajectory and to make  the robot move toward the targeted pose while avoid-  ing obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Our MPP implementation exploits the  ROS navigation stack (Marder-Eppstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2010) to  compute trajectories expressed as a sequence of veloc-  ity commands (expressed as twists) sent to the robot’s  Motion Controller module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A global Costmap is used  to plan a trajectory to a targeted pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' MPP creates  the global Costmap from an occupancy grid created us-  ing the assembled laser scans from the latest local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Each time the local map is updated, the occupancy grid  is re-assembled and the trajectory is re-planned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' MPP  also uses a local Costmap for its Dynamic Window Ap-  proach (DWA) (Fox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 1997) to handle dynamic  obstacles for collision avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The local Costmap is  created directly from sensor readings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To create the lo-  cal Costmap, only using the laser rangefinder for obsta-  cle detection revealed to be insufficient: while the laser  range finder can detect most of the obstacles (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', walls,  people, table legs), it is located 40 cm above the floor  and all obstacles under this height cannot be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Therefore, the depth image from the RGB-D camera  is also used to detect these small obstacles and to add  them to the local Costmap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 6 shows an example  where combining laser scans and RGB-D data creates a  more robust and a safer local Costmap for navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Note that segmentation of the point cloud generated  from the depth image is required to be able to add or  clear small dynamic obstacles below the RGB-D cam-  era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To segment the ground, all points with normal par-  allel to z-axis (up to an angle Z) are labeled as ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Then, all other points under a maximum height U are  labeled as obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This method would also make the  robot capable of operating on uneven terrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2 Topological Path Planning Module  When TPP receives a goal identified by a node ID from  a user (or a high-level module like a task planner, or  in this paper the Patrol module), the global map is  provided by the graph-based SLAM-MM module, and  a topological path is computed to reach this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  topological path is a sequence of poses, expressed by  their respective node IDs, to reach the goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This step  must be done offline or when the robot is not moving  because all nodes linked to the current local map should  be retrieved from LTM to build the global map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To choose which nodes to use for navigation, TPP  computes a path from the current node to the goal node  using Djikstra algorithm (Dijkstra, 1959).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The choice  of using Dijkstra over A* is to avoid global graph op-  timization, which is time consuming, to know the dis-  tance to goal required by A*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Dijkstra can also be com-  puted directly when fetching the global map from LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Similar to (Valencia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2013), to avoid losing track  of the planned path, TPP prefers paths traversed in  the same direction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', where the camera is facing the  same direction than on the nodes on the path) over  shortest paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This increases localization confidence:  loop closure detection and visual proximity detection  are more reliable than proximity detection using only  laser scans because of their double verification (3D vi-  sual word correspondences and 2D ICP transformation  refinement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To embed this preference in Djikstra, the  search cost is angular-based instead of distance-based,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', it finds the path with less orientation changes when  traversing it in the forward direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Then, TPP selects the farthest node on the path  in the local map and sends its pose to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' While  MPP makes the robot navigate to its targeted pose,  TPP indicates to the graph-based SLAM-MM mod-  ule which upcoming nodes on the topological path is  needed, expressed as a list of node IDs from the lat-  est node reached on the path to the farthest node in-  side the radius R (to limit the size of the list).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The re-  quired nodes are identified by the graph-based SLAM-  MM module with Heuristic 2 either to remain in WM or  to be retrieved from LTM to extend the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  maximum number of retrieved nodes per map update is  limited to M because this operation is time consuming  as it needs to load nodes from LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' M is set based on  the hardware on which LTM is saved and according to  the maximum velocity of the robot: for instance, if the  robot is moving at the same speed or less as when it  traversed the same area the first time, M = 1 would  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  9  (a)  (b)  (c)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 6 Example of obstacle detection using the laser rangefinder and the RGB-D camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The red dots on the chair show  what is detected using the laser rangefinder data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The cyan area is derived from the obstacle projection on the ground plane  up to robot’s footprint radius, delimiting where the center of the robot should not enter to avoid collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In a), only the  laser rangefinder data are used and the chair’s wheels are not detected, making unsafe for the robot to plan a path around the  chair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In b), the point cloud generated from the camera’s depth image is used and the chair’s wheels are detected (shown by  the orange dots), increasing the cyan area (and consequently the area to avoid colliding with the chair).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Illustration c) presents  a view from the RGB-D camera where the segmented ground is shown in green and the obstacles in orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  suffice to retrieve nodes on the path without having to  slow down to wait for nodes not yet retrieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Extending the local map with nodes of the topo-  logical path is important for the robot to localize it-  self using the Appearance-based Loop Closure Detec-  tion module or using the Proximity Detection module,  making it able to follow the topological path appro-  priately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As the robot moves and new local maps are  created, TPP always looks for the farthest node of the  topological path that can be reached in the local map  to update the current pose sent to MPP module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If new  nodes are retrieved from LTM on the topological path,  then the farthest pose is sent to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' TPP also de-  tects changes in the local map after graph optimization  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', when new loop closures are detected): if so, the  updated position of the current pose is sent to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Up to a ratio O of the WM size, nodes identified by  the planner and located in the radius R from the robot’s  current position are immunized to be transferred, with  R being the sensor range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 7 presents an example of the interaction be-  tween MPP and TPP to reach a goal G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' While the robot  is moving, TPP always sends the farthest pose P of the  node on the topological path (purple links) in the lo-  cal map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' An occupancy grid is assembled with the laser  scans contained in the nodes of the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' MPP  uses this occupancy grid to plan a trajectory (yellow  arrow) to P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To keep the WM size constant, as nodes  are retrieved from LTM on the path, older nodes are  transferred to LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To follow the path appropriately,  proximity links are detected to correct the map as the  robot moves, otherwise the situation explained by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  4a would happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  TPP iterates by sending poses until the node of the  goal (under a goal radius D expressed in m) is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Finally, handling situations where the environment has  changed too much for proper localization must be taken  into consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If no loop closures and proximity de-  tections occur when following a path, a temporary link  is added between the current node and the closest one  in the path so that the topological path is always linked  to the current node in the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Without this link,  if previous nodes between the current node and those of  the topological path are transferred to LTM, the local  map would be divided and the nodes of the path would  not be in the local map anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This temporary link  is removed when a new link is added between the cur-  rent node and the closest one in the path or when the  goal is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If the robot has not reached the cur-  rent pose set to MPP after F iterations of SPLAM-MM  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', MPP cannot plan to the requested pose because  of the presence of a new obstacle or because the robot  cannot localize itself on the path), TPP chooses another  pose on the upcoming nodes and sends it to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If all  the upcoming nodes cannot be reached, TPP fails and  sends a status message to its connected modules so that  they can be notified that the goal cannot be reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  10  Mathieu Labb´e, Fran¸cois Michaud  P"  G"  (a)  P"  G"  (b)  P"  G"  (c)  P"  G"  (d)  P"  G"  (e)  P"  (f)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 7 Interaction between TPP and MPP for path planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The goal is identified by the purple G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The topological path is  shown with purple links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The dashed yellow arrow is the trajectory computed by MPP to the targeted poses designated by the  yellow P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Light gray, dark gray and black areas of the occupancy grid represent free, unknown and occupied cells, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Blue nodes are in WM, and red nodes are in LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Yellow links are proximity links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6 Patrol Module  We implemented the Patrol module to generate naviga-  tion goals, referred to as waypoints so that the robot is  programmed to continuously patrol an area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The Patrol  module receives waypoints as inputs and sends them  successively to TPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' By examining TPP’s status mes-  sages, Patrol can know when a goal is reached or if TPP  has failed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Whenever the status indicates that the goal  is reached or not, the Patrol module sends the next  waypoint, and restart to the first one once the whole  list has been processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  4 Results  Table 1 shows the parameters used for the trials1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  acquisition time A used is 1 sec (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', the map update  rate is 1 Hz), which set the maximum online time al-  lowed to process each node added to the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For  the trials, T is set to 200 ms to limit CPU usage for  SPLAM-MM to around 20%, to make sure that higher  1 In comparison with (Labbe and Michaud, 2013), T =  Ttime, S = TST M and Y = Tsimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  frequency modules (acquisition of Sensor Data acquisi-  tion and MPP) can run at their fixed frequency of 10  Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The robot is relatively moving at the same velocity  during the trials, and therefore M is fixed to 2 to make  sure that nodes on a planned path are retrieved fast  enough to avoid having the robot wait for nodes still in  LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' All computations are done onboard on the robot,  which is equipped with a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='66 GHz Intel Core i7-620M  and a 128 GB SSD hard drive (on which the LTM is  saved).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To define the area over which the robot had to pa-  trol, during session 1 we first teleoperated the robot  and defined four waypoints (WP1 to WP4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' There were  no people in the environment during the teleoperation  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' After reaching WP4, the autonomous navigation  phase is initiated by sending the waypoints to the Pa-  trol module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 8 illustrates the four waypoints on  the global map and the first planned trajectory by TPP  (purple path) from the current position of the robot  (WP4) to WP1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To come back to WP1, the robot had  to follow the path in the opposite direction from when  these nodes were created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Proximity detection made  it able to follow the path appropriately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To see more  clearly the effect of proximity links, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 9 shows the  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  11  Table 1 Parameters used for the trials  Acquisition time  A  1 sec  ICP correspondence ratio  C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3  Radius of the goal area  D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 m  TPP iterations before failure  F  10  Loop closure hypothesis threshold  H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='11  Minimum RANSAC visual word inliers  I  5  Close nodes radius  L  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 m  Maximum retrieved close nodes  M  2  Heuristics 2 close-by nodes ratio  O  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='25  Laser scan range  R  4 m  STM size  S  20  Time limit  T  200 ms  Maximum obstacle height  U  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4 m  Similarity threshold  Y  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3  Ground segmentation maximum angle  Z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1 rad  WP4  WP3  WP2  WP1  Battery Charger  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 8 Waypoints WP1 to WP4 identified on the global map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The purple path is the first path planned by TPP from the  WP4 to WP1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  maps after reaching WP1 with and without graph op-  timization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Navigation would not have been possible  without proximity links: the local map would have look  like the map in (b) without the yellow links because no  appearance-based similarities would have been found  with nodes from the map on the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When  reaching WP1, the Patrol module sends the next way-  point (WP2), making the robot continue patrolling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Every 45 minutes or so of operation, the robot was  manually shutdown and moved to the battery charger  near WP1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Once recharged, a new session of SPLAM-  MM was initiated, creating a new node in STM with  odometry reset, while preserving the nodes in WM  and LTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As the robot was initialized in the area of  WP1 for each session, loop closures were found, con-  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  (a)  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 9 Global maps, optimized and not optimized, after  reaching WP1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Yellow and red links are proximity and loop  closure links, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  necting and optimizing the new map with nodes cre-  ated from previous sessions, and allowing the Patrol  module to provide waypoints as navigation goals to pa-  trol the area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Overall, 11 indoor mapping sessions were  conducted, for a total distance of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5 km lasting 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  hours of operation spent over two weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The robot did  111 patrolling cycles (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', traversing from WP1 through  WP2, WP3, WP4 and coming back to WP1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The ses-  sions were conducted during office hours, with people  walking by.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A total of 139 people were encountered by  the robot while patrolling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 10 illustrates the dy-  namic conditions and some of the obstacles that the  robot had to deal with during the trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The main goal of the trials is to see how SPLAM is  influenced by memory management over long-term op-  eration, only having the local map for online process-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This can be illustrated by looking at the influences  of memory management on SPLAM, interactions be-  tween TPP and MPP, and the influences of LTM on  TPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As the robot is continuously adding new nodes,  the trials also demonstrate how SPLAM-MM works in  an unbounded environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1 Influences of MM on SPLAM  Figure 11 shows a typical navigation result when reach-  ing the time limit T, thus limiting the size of the local  map used for online navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This example shows  the path planned between WP4 and WP1 after 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='7  hours of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The local maps used for online plan-  ning, localization and mapping are shown for different  time steps along the trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' At t = 17031 sec, the  planned path had 67 nodes and was 33 m long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' It took  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3 sec to be generated by TPP and to have the first  pose on the path sent to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The laser scan range R  is delimiting the upcoming nodes on the path provided  by TPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As the robot navigates in the environment,  the farthest available pose in the local map on the path  (end of the cyan line) is sent from TPP to MPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Up-  12  Mathieu Labb´e, Fran¸cois Michaud  a)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  b)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  c)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  d)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  e)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 10 Events that occurred during the trials: a) open and closed doors between traversals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' b) camera exposure that led to  the extraction of different visual features, making it difficult to find loop closures;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' c) someone opening a door while the robot  is navigating;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' d) people walking around or blocking the robot;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' e) featureless images on which loop closure detection cannot  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17060 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17053 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17031 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17068 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17075 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17081 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17108 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  t = 17095 sec!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  WP1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 11 Example of the effect of memory management when travelling from WP4 to WP1 after 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='7 hours of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The  path planned is shown in purple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The small colored icon represents the robot position at each time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The dotted circle  around the robot position illustrates the laser scan range R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The cyan lines represent the upcoming nodes on the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  coming nodes, if they are not in WM, are retrieved to  make the robot able to localize itself (though loop clo-  sures and proximity detections) on the path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Looking  at how the local map changes in these snapshots, notice  how starting from t = 17075 sec, the initial portion of  the path is transferred in LTM to keep the size of the  WM relatively constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' At t = 17108 sec, the robot  reached WP1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 12 compares the images between each way-  point and the final position of the robot at the way-  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The robot successfully reached the waypoints  (within D as the goal radius) 445 out of 446 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For  WP2, WP3 and WP4, the robot always came from be-  hind the waypoint, and as soon the robot reached the  waypoint within a D radius, TPP detected that the goal  was reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This explains why all the poses are behind  the waypoints but inside the goal radius D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Similarly,  for WP1, the robot came from behind from a slightly  different direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Spurious poses on the right part of  the circle are those where there was an obstacle that  caused the robot to avoid it, making it reach the way-  point from a different direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The one time the robot  failed to reach a waypoint is because someone blocked  the robot for a long time, making TPP failed after F at-  SOHTESTHTELong-Term Online Multi-Session Graph-Based SPLAM with Memory Management  13  tempts of reaching the upcoming nodes: a failure status  message was then sent to the Patrol module to provide  the next waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The person left soon after the next  waypoint was sent, and the robot reached the new way-  point provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 13 illustrates the evolution of the number  of nodes in WM and online processing time over the 11  mapping sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Processing time includes all SPLAM-  MM modules except MPP which was running concur-  rently on a separate process (its processing time is only  dependent of the local map size).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As explained in Sec-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2, TPP occurs offline and only when a new  goal is received from the Patrol module, and is exam-  ined in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 13a illustrates that the number  of nodes in WM and the local map was identical until T  sec was reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' After that, nodes were transferred to  LTM to limit the WM size for online processing, which  is satisfied as shown by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 13b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Processing time also  remained well under the acquisition time A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2 TPP-MPP Interactions  To illustrate with a concrete example of the situation  described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 7, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 14 presents an example of con-  secutive poses sent by TPP to MPP while nodes from  LTM are retrieved for the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The red ar-  row shows the pose of the farthest node on the path  (the direction of the arrow shows the orientation of  the pose).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The red line represents the trajectory com-  puted by MPP from the current position of the robot  to its targeted pose, combined with obstacle avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The blue lines represent the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 14a,  the targeted pose is on a node traversed backward (as  shown by the arrow pointing backward).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Between a)  and b), the local map was updated with nodes loaded  from LTM of the topological path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The targeted pose  was updated farther on the path and at the same time,  the occupancy grid was extended to previously mapped  areas and MPP recomputed its trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The robot  could then move farther toward its goal and the nodes  retrieved were used for proximity detection to correctly  follow the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To also illustrate the importance of obstacle detec-  tion described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 6, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 15 presents an example  where an unexpected obstacle was encountered: as the  laser rangefinder is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4 m above the ground, the forklift  could only be detected using the RGB-D camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' MPP  planned a slightly different path (orange) that the one  planned by TPP (pink) to avoid the obstacle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3 Influences of LTM on TPP  Although Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 13 demonstrates that SPLAM-MM is  able to satisfy online constraints on a map increasing  linearly in size (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', not bounded to a maximum size of  environment), memory used by LTM and consequently  TPP planning time increase linearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For example, at  the end of experiment, LTM contains 24002 nodes and  113368 links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' All raw sensor data in the nodes were  also saved in the LTM’s database (for debugging and  visualization purposes), including RGB image (JPEG  format) and depth image (PNG format) of each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  The final database took 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='7 GB of hard drive space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  With as many links at the end of the experiment, TPP  required 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4 sec to compute a plan to the next waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In term of memory usage and planning time, LTM must  be somewhat limited over time when revisiting the same  areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  As a solution to limit LTM memory growth, nodes  from STM can be merged when moved to WM if they  have loop closure and/or visual proximity links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' We  studied this possibility by adding a graph reduction al-  gorithm to STM, to remove the node from the graph  and to add its neighbor links to the corresponding old  node(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Algorithm 1 summarizes the approach used to  maintain the graph at the same size (same number of  removed links and nodes than added) if there are many  successive nodes with loop closure or visual proxim-  ity links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If two nodes of a same location do not have  similar images (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', they don’t have loop closure or vi-  sual proximity links), they will not be merged, thus still  keeping a variety of different images representing the  same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To make sure nodes to be merged are  still in WM (to avoid to modify the LTM), nodes hav-  ing a link to a node in STM are identified as nodes that  must stay in WM (similarly to Heuristic 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 16  shows how links are merged between the node moved to  WM and its corresponding node(s) linked by loop clo-  sure link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In a), the purple node has two loop closure  links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' On graph reduction, its two neighbor links (blue)  are merged with the loop closure links (red) by multi-  plying the corresponding transformations together, cre-  ating merged neighbor links (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In this case, the  same number of links are added than those removed but  one node is removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In b), the green node has only one  neighbor link (with the cyan node), then the loop clo-  sure link is only merged with it, creating only one link  and four are removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Merged neighbor links are ig-  nored to be merged again to limit the number of links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In c), the cyan node does not have any loop closure and  no graph reduction is done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To test this idea, data from the 11 sessions were  processed again to test the influences of the graph re-  14  Mathieu Labb´e, Fran¸cois Michaud  ID=167  ID = 266  ID = 417  a)  b)  c)  WP2  WP3  d)  WP4  ID = 26514  ID = 6414  ID = 22016  ID = 9896  ID = 19  −2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  wp1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  4  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −8  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −7  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  wp2  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  16  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
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+page_content='6  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  17  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  13  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  14  wp3  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  16  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  17  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −4  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  −3  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  wp4  WP1  Images  Laser scans  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 12 Comparison of the corresponding images between the waypoint (left image) and at the last pose reached on one of  the planned path (right image) for the waypoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The top view grid shows the laser scan readings and referentials of the  waypoint’s nodes (at the origin of the grid) and the final node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The zoomed portions represent the final poses of the robot  (represented by blue dots), for all paths planned for each waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The circle represents the goal radius D, and the grid’s  cells used for visualization have a width of 1 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  3  x 10  4  0  50  100  150  200  250  300  350  400  450  500  Node indexes  Nodes  WM  Local map  (a) Number of nodes in WM and in the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  3  x 10  4  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='9  1  Time (s)  Node indexes  (b) Processing time (the horizontal line represents T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='2  sec).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 13 Memory size and total processing time over the 11 mapping sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  15  Goal  (a)  Goal  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 14 Example of poses sent by TPP to MPP while nodes  from LTM are retrieved for the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The goal of the  path is somewhere outside these images in the direction shown  by Goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The bottom left images shows the actual RGB image  from the RGB-D camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The blue lines are nodes and links  of the local map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The red line is the computed trajectory from  MPP using the local map’s occupancy grid from its current  pose (red arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The RGB point cloud and the occupancy  grid are created using RGB-D images and laser scans stored  in nodes from the local map, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In a), the robot is  following the red trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In b), some nodes are retrieved  from LTM and a new trajectory is computed to move further  on the path toward the goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Algorithm 1 Graph Reduction  1: o ← node moved to WM  2: m ← loop closure and visual proximity links of o  3: if m is not empty then  4:  n ← neighbor links of o  5:  for all m in m do  6:  om ← node pointed by m  7:  for all n in n do  8:  on ← node pointed by n  9:  t ← m−1·n  10:  Add t to om  11:  Add t−1 to on  12:  end for  13:  end for  14:  Remove o from the graph  15: end if  duction approach using real data acquired by the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Note that even though graph reduction was validated  offline, we carefully monitored the experiment manually  to make sure that the robot could still localize itself cor-  rectly on the planned paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 17 shows a comparison of the final global  map without and with graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The zones with  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 15 Example where MPP plans a slightly different path  (orange) than the one provided by TPP (pink).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The yellow  dot is the current position of the robot and the lower right  image is the corresponding RGB image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  STM  WM  Graph Reduction  STM to WM  WM  STM  a)  b)  c)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 16 Three examples illustrating how the graph reduc-  tion algorithm works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Blue, red and orange links represent  neighbor, loop closure and merged neighbor links, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Black links and white nodes are those removed using  graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The left column shows the rightmost node  (the oldest) of STM moved to WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Then on the right column,  this node is removed if it has a loop closure link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  less blue links indicate that there were many nodes  merged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The zones with more blue links are where nodes  were not merged, because of a lack of features or be-  cause of obstacles: the robot was not able to localize  itself perfectly on the paths every time, thus adding  new nodes to the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Figure 18 illustrates TPP planning time correspond-  ing to LTM size with and without graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As  the LTM became larger, TPP planning time increased:  with graph reduction, TPP planning time was reduced  by 89% for the last path planned (272 ms instead of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4  16  Mathieu Labb´e, Fran¸cois Michaud  a)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  b)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 17 Comparison between the global maps a) without  graph reduction (24002 nodes and 113368 links);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' b) with  graph reduction (6059 nodes and 18255 links).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  sec).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Figure 19 illustrates hard drive usage with and  without graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Extrapolating linearly mem-  ory usage with a 100 Gb hard drive, the robot could  navigate online approximately 110 hours without graph  reduction before filling up the hard drive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When debug-  ging data (not used for navigation) are not recorded in  the database, this estimate would increase to approx-  imately 33 days (800 hours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This means that if the  robot is always visiting new locations at a mean velocity  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='4 km/h (as in this experiment), it could travel up  to 1120 km to map environments online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' When graph  reduction is used, debugging data are not saved and  having the robot always revisiting the same areas like  in this experiment, it could do SPLAM continuously for  about 130 days before reaching the hard drive capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  5 Discussion  In terms of processing time, results show that SPLAM-  MM is able to satisfy online processing requirements in-  dependently of the size of the environment, by transfer-  ring in LTM portions of the map which then cannot be  used for loop closure detection, proximity detection and  graph optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Results show also that path fol-  lowing is still possible in such conditions by incremen-  tally retrieving locations on the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Thus, as  shown in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='3, the current hardware limitation  of the system for long-term continuous SPLAM is hard  drive capacity, not computation power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  3  x 10  4  0  500  1000  1500  2000  2500  Time (ms)  Node indexes  Graph size  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='5  x 10  4  Graph size (nodes)  0  1000  2000  3000  4000  0  100  200  300  Time (ms)  Node indexes  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 18 Comparison of TPP planning time and LTM size,  with (blue) and without (red) graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The peaks in  the zoomed section show more precisely when a planning is  done (when a waypoint is reached).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  0  1  2  3  4  5  6  7  8  0  1000  2000  3000  4000  5000  6000  7000  Time (h)  Hard drive usage (MB)  Raw data discarded  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 19 Comparison of hard drive usage with (blue) and  without (red) graph reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The dashed curves represents  results without saving in database the debugging data (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=',  raw RGB and depth images).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  To successfully follow a path, results demonstrate  the importance of adding loop closure and/or proxim-  ity links with nodes on the planned path to localize the  robot in the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In our trials, the robot navigated in-  door where static structures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', walls) were most of  the time visible using the laser rangefinder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, in  large empty spaces where the laser rangefinder would  not be able to perceive nearby structures, it would be  difficult for the robot to follow a path if appearance-  based loop closure detection and visual proximity de-  tection do not occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A laser rangefinder with larger  perceptual range or a 3D LIDAR sensor like the Velo-  dyne could be used to increase perceptual range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For  a lower cost solution, using a camera facing backward  could be useful to allow the robot to detect similari-  ties in images when traversing a path in opposite direc-  tion (Carrera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Without adding new sensors,  TPP could also stop sending new poses when no loop  closure links or proximity links occur for a while.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If no  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  17  loop closures were found over the next few meters, it  would be possible to wait for the robot to rotate at  this location so that it can look backward, increasing  its chance to detect a loop closure to correct its po-  sition on the planned path and then generate a new  pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A similar recovery approach is presented in (Mil-  ford and Wyeth, 2010), where an exploration phase is  triggered to re-localize the robot when failing to follow  the planned path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Also, to be more robust to dynamic  environments where there are cyclic changes over time,  TPP could select nodes that match better the current  time of the day rather than the most recent ones, to in-  crease localization success as in (Krajn´ık et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In comparison with large empty environments, those  in which a lot of dynamic changes occur (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', navigat-  ing through a crowd) would also make simultaneous  planning and localization more difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' For instance,  mapping the area in session 1 without people walk-  ing by helped the robot acquire the static structures  of the environment since they were not hidden by peo-  ple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' These static structures facilitate localization when  the robot comes back to these areas later one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If these  static structures were previously occluded, they would  be added to the map as the robot comes back to these  areas (obviously if people are no longer in the robot’s  field of view).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If people partially occlude the robot’s  sensors over a long distance, localization would still be  possible but would occur less frequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  For online multi-session mapping with our memory  management approach, the worst case is when all nodes  of a previous map are transferred to LTM before a loop  closure is detected (Labbe and Michaud, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This  results in definitely ignoring the previous map and dis-  abling at the same time the ability to plan paths to  a location in it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To avoid this problem, an additional  heuristic could be to keep in WM at least one discrim-  inative node for each map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, if the number of  mapping sessions becomes very high (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', thousands of  sessions), these nodes would definitely have to be trans-  ferred in LTM to satisfy online processing requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  A strategy that makes the robot explore potential paths  to link maps together would then be useful, and maps  that could not be linked would eventually be unretriev-  able.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In the trials conducted, no invalid loop closures were  detected, avoiding to corrupt the map with erroneous  loop closure links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' If this happens, graph optimization  approaches such as (Latif et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Sunderhauf and  Protzel, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2013) deal with possible invalid  matches, and could be used to increase robustness of  SPLAM-MM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, these approaches assume that  the whole global map is available online, which is not  the case here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' They could be still used offline at the end  of a session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  As shown by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 15, MPP in SPLAM-MM allows  the robot to find an alternative path to reach the tar-  geted pose when possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, if the alternative  path is outside the local map, re-planning with TPP is  required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Some paths may be also blocked temporary or  permanently by some dynamic or new static obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  An approach similar to (Konolige et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', 2011) could be  used to identify some links as blocked so that TPP can-  not plan a path using them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The Patrol module could  also manage waypoints that can and cannot be reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Finally, the graph reduction approach can reduce  significantly the number of nodes and links saved in  LTM to reduce TPP planning time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However, because  of dynamic events or the lack of features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  10e), new nodes and links will inevitably be added to  LTM over time when revisiting the same areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' As an  improvement, nodes with featureless image could be  merged through a maximum density threshold like in  (Milford and Wyeth, 2010), as they cannot be used for  loop closure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' After applying graph reduction  on the experimental data, there are still 3068 featureless  nodes of 6059 nodes in the global graph, which would  reduce by about 50% the remaining graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' However,  even by limiting the rate at which the LTM grows, a  continuous SLAM approach in unbounded dynamic en-  vironments will always add new data over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' A com-  plementary strategy would be to definitely forget some  parts of the global map, at the cost of not being able  to return to some locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  6 Conclusion  By limiting the nodes of the map available online in  WM for loop closure detection, proximity detection and  graph optimization, results presented in this paper sug-  gest that the proposed graph-based SPLAM-MM ap-  proach is able to meet online processing requirements  needed for simultaneous mapping, localizing and plan-  ning in multi-session conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' SPLAM-MM is tightly  based on appearance-based loop closure detection, al-  lowing it to naturally deal with the initial state prob-  lem of multi-session mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' To successfully localize  on a planned path through areas previously transferred  in LTM, memory management allows SPLAM-MM to  deal with the necessity of retrieving upcoming nodes on  the path in WM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Our code is open source and available  at http://introlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='io/rtabmap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In future works, more robust failure recovery ap-  proaches will be examined to test SPLAM-MM in dy-  namic environments where the paths could often be  blocked (temporally or permanently).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' We also plan to  18  Mathieu Labb´e, Fran¸cois Michaud  study the impact of autonomous coverage and explo-  ration strategies, especially how it can actively direct  exploration based on nodes available for online map-  ping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' This could be also useful to conduct longer ex-  periments at larger scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  References  Atkinson R, Shiffrin R (1968) Human memory: A pro-  posed system and its control processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Psychol-  ogy of Learning and Motivation: Advances in Re-  search and Theory, vol 2, Elsevier, pp 89–195  Baddeley A (1997) Human Memory: Theory and Prac-  tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Psychology Press  Bay H, Ess A, Tuytelaars T, Gool LV (2008) Speeded  Up Robust Features (SURF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Computer Vision and  Image Understanding 110(3):346–359  Besl PJ, McKay ND (1992) Method for registration of  3-D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Robotics-DL tentative, International  Society for Optics and Photonics, pp 586–606  Biber P, Duckett T, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' (2005) Dynamic maps for  long-term operation of mobile service robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In:  Robotics: Science and Systems, pp 17–24  Carrera G, Angeli A, Davison AJ (2011) Lightweight  SLAM and navigation with a multi-camera rig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In:  European Conference on Mobile Robots, pp 77–82  Churchill W, Newman P (2012) Practice makes per-  fect?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Managing and leveraging visual experiences for  lifelong navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on  Robotics and Automation, pp 4525–4532  Dijkstra EW (1959) A note on two problems in connex-  ion with graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Numerische Mathematik 1(1):269–  271  Ferland F, Clavien L, Fr´emy J, Letourneau D, Michaud  F, Lauria M (2010) Teleoperation of AZIMUT-3, an  omnidirectional non-holonomic platform with steer-  able wheels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Intel-  ligent Robots and Systems, pp 2515–2516  Folkesson J, Christensen HI (2007) Closing the loop  with graphical SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Trans on Robotics  23(4):731–41  Fox D, Burgard W, Thrun S (1997) The dynamic win-  dow approach to collision avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Robotics  & Automation Magazine 4(1):23–33  Garcia-Fidalgo E, Ortiz A (2015) Vision-based topo-  logical mapping and localization methods: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Robotics and Autonomous Systems 64:1 – 20  Glover AJ, Maddern WP, Milford MJ, Wyeth GF  (2010) FAB-MAP + RatSLAM: Appearance-based  SLAM for multiple times of day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics and Automation, pp 3507–3512  Grisetti G, Grzonka S, Stachniss C, Pfaff P, Burgard  W (2007) Efficient estimation of accurate maximum  likelihood maps in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  on Intelligent Robots and Systems, pp 3472–3478  Grisetti G, K¨ummerle R, Stachniss C, Burgard W  (2010) A tutorial on graph-based SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Intel-  ligent Transportation Systems Magazine 2(4):31–43  Ho KL, Newman P (2006) Loop closure detection in  SLAM by combining visual and spatial appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Robotics and Autonomous Systems 54(9):740–749  Johannsson H, Kaess M, Fallon M, Leonard J (2013)  Temporally scalable visual SLAM using a reduced  pose graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics  and Automation, pp 54–61  Kim B, Kaess M, Fletcher L, Leonard J, Bachrach A,  Roy N, Teller S (2010) Multiple relative pose graphs  for robust cooperative mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics and Automation, pp 3185–3192  Konolige K, Bowman J (2009) Towards lifelong visual  maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Intelligent  Robots and Systems, pp 1156–1163  Konolige K, Marder-Eppstein E, Marthi B (2011) Nav-  igation in hybrid metric-topological maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics and Automation, pp  3041–3047  Krajn´ık T, Fentanes JP, Hanheide M, Duckett T  (2016) Persistent localization and life-long mapping  in changing environments using the frequency map  enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on In-  telligent Robots and Systems, pp 4558–4563  Kummerle R, Grisetti G, Strasdat H, Konolige K, Bur-  gard W (2011) g2o: A general framework for graph  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics  and Automation, pp 3607–3613  Labbe M, Michaud F (2013) Appearance-based loop  closure detection for online large-scale and long-term  operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Trans on Robotics 29(3):734–745  Labbe M, Michaud F (2014) Online global loop closure  detection for large-scale multi-session graph-gased  SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Intelligent  Robots and Systems, pp 2661–2666  Latif Y, Cadena C, Neira J (2013) Robust loop closing  over time for pose graph SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Int J of Robotics  Research 32(14):1611—1626  Lee GH, Fraundorfer F, Pollefeys M (2013) Ro-  bust  pose-graph  loop-closures  with  expectation-  maximization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on In-  telligent Robots and Systems, pp 556–563  Marder-Eppstein E, Berger E, Foote T, Gerkey B,  Konolige K (2010) The Office Marathon: Robust nav-  igation in an indoor office environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics and Automation, pp  300–307  McDonald J, Kaess M, Cadena C, Neira J, Leonard J  (2012) Real-time 6-DOF multi-session visual SLAM  Long-Term Online Multi-Session Graph-Based SPLAM with Memory Management  19  over large scale environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Robotics and Au-  tonomous Systems 61(10):1144–58  Milford M, Wyeth G (2010) Persistent navigation and  mapping using a biologically inspired SLAM system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  Int J of Robotics Research 29(9):1131–53  Muja M, Lowe DG (2009) Fast approximate nearest  neighbors with automatic algorithm configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Computer Vision Theory and  Application, pp 331–340  Pirker K, Ruther M, Bischof H (2011) CD SLAM –  Continuous localization and mapping in a dynamic  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Intelligent  Robots and Systems, pp 3990–3997  Rusu RB, Cousins S (2011) 3D is here: Point Cloud  Library (PCL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Robotics  and Automation, Shanghai, China, pp 1–4  Sivic J, Zisserman A (2003) Video Google: A text re-  trieval approach to object matching in videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In:  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' 9th Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Computer Vision, Nice,  France, pp 1470–1478  Stachniss C (2009) Robotic Mapping and Exploration,  vol 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Springer Science & Business Media  Sunderhauf N, Protzel P (2012) Towards a robust back-  end for pose graph SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  on Robotics and Automation, pp 1254–1261  Thrun S, Burgard W, Fox D (2005) Probabilistic  Robotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' The MIT Press  Valencia R, Morta M, Andrade-Cetto J, Porta JM  (2013) Planning reliable paths with Pose SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  IEEE Trans on Robotics 29(4):1050–1059  Walcott-Bryant A, Kaess M, Johannsson H, Leonard  JJ (2012) Dynamic pose graph SLAM: Long-term  mapping in low dynamic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content='  IEEE/RSJ Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
+page_content=' on Intelligent Robots and Sys-  tems, pp 1871–1878' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dAyT4oBgHgl3EQfQvYd/content/2301.00050v1.pdf'}
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+Cursed Sequential Equilibrium∗
+Meng-Jhang Fong†
+Po-Hsuan Lin‡
+Thomas R. Palfrey§
+January 31, 2023
+Abstract
+This paper develops a framework to extend the strategic form analysis of cursed
+equilibrium (CE) developed by Eyster and Rabin (2005) to multi-stage games. The
+approach uses behavioral strategies rather than normal form mixed strategies, and
+imposes sequential rationality.
+We define cursed sequential equilibrium (CSE) and
+compare it to sequential equilibrium and standard normal-form CE. We provide a
+general characterization of CSE and establish its properties. We apply CSE to five
+applications in economics and political science. These applications illustrate a wide
+range of differences between CSE and Bayesian Nash equilibrium or CE: in signaling
+games; games with preplay communication; reputation building; sequential voting;
+and the dirty faces game where higher order beliefs play a key role. A common theme
+in several of these applications is showing how and why CSE implies systematically
+different behavior than Bayesian Nash equilibrium in dynamic games of incomplete
+information with private values, while CE coincides with Bayesian Nash equilibrium
+for such games.
+JEL Classification Numbers: C72, D83
+Keywords: Multi-stage Games, Private Information, Cursed Equilibrium, Learning
+∗Grants from the National Science Foundation (SES-0617820) and the Gordon and Betty Moore Foun-
+dation (1158) supported this research. We are especially grateful to Shengwu Li and Shani Cohen for recent
+correspondence that helped to clarify the differences between the CSE and SCE approaches to the gener-
+alization of cursed equilibrium for dynamic games. We thank participants of the Caltech Proseminar and
+Colin Camerer for comments and also thank Matthew Rabin for earlier discussions on the subject during his
+visit at Caltech as a Moore Distinguished Scholar.
+†Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125
+USA. mjfong@caltech.edu
+‡Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125
+USA. plin@caltech.edu
+§Corresponding Author: Division of the Humanities and Social Sciences, California Institute of Technol-
+ogy, Pasadena, California 91125 USA. trp@hss.caltech.edu. Fax: +16263958967 Phone: +16263954088
+arXiv:2301.11971v1  [econ.TH]  27 Jan 2023
+
+1
+Introduction
+Cursed equilibrium (CE) proposed by Eyster and Rabin (2005) is a leading behavioral equi-
+librium concept that was developed to explain the “winner’s curse” and related anomalies
+in applied game theory. The basic idea behind CE is that individuals do not fully take
+account of the dependence of other players’ strategic actions on private information. Cursed
+behavior of this sort has been detected in a variety of contexts. Capen et al. (1971) first
+noted that in oil-lease auctions, “the winner tends to be the bidder who most overestimates
+the reserves potential” (Capen et al. (1971), p. 641). Since then, this observation of overbid-
+ding relative to the Bayesian equilibrium benchmark, which can result in large losses for the
+winning bidder, has been widely documented in laboratory auction experiments (Bazerman
+and Samuelson, 1983; Kagel and Levin, 1986; Kagel et al., 1989; Forsythe et al., 1989; Dyer
+et al., 1989; Lind and Plott, 1991; Kagel and Levin, 2009; Ivanov et al., 2010; Camerer et al.,
+2016). In addition, the neglect of the connection between the opponents’ actions and private
+information is also found in non-auction environments, such as bilateral bargaining games
+(Samuelson and Bazerman, 1985; Holt and Sherman, 1994; Carrillo and Palfrey, 2009, 2011),
+zero-sum betting games with asymmetric information (Rogers et al., 2009; Søvik, 2009), and
+voting and jury decisions (Guarnaschelli et al., 2000).
+While CE provides a tractable alternative to Bayesian Nash equilibrium and can explain
+some anomalous behavior in games with a winner’s-curse structure, a significant limitation is
+that it is only developed as a strategic form concept for simultaneous-move Bayesian games.
+Thus, when applying the standard CE to dynamic games, the CE analysis is carried out on
+the strategic form representation of the game, implying that CE cannot distinguish behavior
+across dynamic games that differ in their timing of moves but have the same strategic form.
+That is, players are assumed to choose type-dependent contingent strategies simultaneously
+and not update their beliefs as the history of play unfolds. A further limitation implied
+by the strategic form approach is that CE and standard Bayesian Nash equilibrium make
+identical predictions in games with a private-values information structure (Eyster and Rabin
+(2005), Proposition 2). In this paper we extend the CE in a simple and natural way to
+multi-stage games of incomplete information. We call the new equilibrium concept Cursed
+Sequential Equilibrium (CSE).
+In Section 2, we present the framework and our extension of cursed equilibrium to dy-
+namic games.
+We consider the framework of multi-stage games with observed actions,
+introduced by Fudenberg and Tirole (1991b), where players’ private information is repre-
+sented by types, with the assumption that the set of available actions is independent of their
+types at each public history. Our new solution concept is in the same spirit of the cursed
+1
+
+equilibrium—in our model, at each stage, players will (partially) neglect the dependence of
+the other players’ behavioral strategies on their types, by placing some weight on the incor-
+rect belief that all types adopt the average behavioral strategy. Specifically, at each public
+history, this corresponds to the average distribution of actions given the current belief about
+others’ types at that stage. Therefore, as players update their beliefs about others’ private
+information via Bayes’ rule, but with incorrect beliefs about the other players’ behavioral
+strategies, in later stages this can lead them to have incorrect beliefs about the other players’
+average distribution of actions.
+Following Eyster and Rabin (2005)’s notion of cursedness, we parameterize the model by
+a single parameter χ ∈ [0, 1] which captures the degree of cursedness and define fully cursed
+(χ = 1) CSE analogously to fully cursed (χ = 1) CE. Recall that in a fully cursed (χ = 1) CE,
+each type of each player chooses a best reply to expected (cursed) equilibrium distribution
+of other players’ actions, averaged over the type-conditional strategies of the other players,
+with this average distribution calculated using the prior belief on types. Loosely speaking,
+a player best responds to the average CE strategy of the others. In a χ-CE, players are
+only partially cursed, in the sense that each player best responds to a χ-weighted linear
+combination of the average χ-CE strategy of the others and the true (type-dependent) χ-CE
+strategy of the others.
+The extension of this definition to multi-stage games with observed actions is different
+from χ-CE in two essential ways: (1) the game is analyzed with behavioral strategies; and
+(2) we impose sequential rationality and Bayesian updating. In a fully cursed (χ = 1) CSE,
+(1) implies at every stage t and each public history at t, each type of each player i chooses a
+best reply to the expected (cursed) equilibrium distribution of other players’ stage-t actions,
+averaged over the type-conditional stage-t behavioral strategies of other players, with this
+average distribution calculated using i’s current belief about types at stage t. That is, player
+i best responds to the average stage-t CSE strategy of others. Moreover, (2) requires that
+each player’s belief at each public history is derived by Bayes’ rule wherever possible, and
+best replies are with respect to the continuation values computed by using the fully cursed
+beliefs about the behavioral strategies of the other players in current and future stages.
+A χ-CSE, for χ < 1, is then defined in analogously to χ-CE, except for using a χ-weighted
+linear combination of the average χ-CSE behavioral strategies of others and the true (type-
+dependent) χ-CSE behavioral strategies of others. Thus, similar to the fully cursed CE, in
+a fully cursed (χ = 1) CSE, each player believes other players’ actions at each history are
+independent of their private information. On the other hand, χ = 0 corresponds to the
+standard sequential equilibrium where players have correct perceptions about other players’
+2
+
+behavioral strategies and are able to make correct Bayesian inferences.1
+After defining the equilibrium concept, in Section 3 we explore some general properties of
+the model. We first prove the existence of a cursed sequential equilibrium in Proposition 1.
+Intuitively speaking, CSE mirrors the standard sequential equilibrium. The only difference is
+that players have incorrect beliefs about the other players’ behavioral strategies at each stage
+since they fail to fully account for the correlation between others’ actions and types at every
+history. We prove in Proposition 2 that the set of CSE is upper hemi-continuous with respect
+to χ. Consequently, every limit point of a sequence of χ-CSE points as χ converges to 0 is a
+sequential equilibrium. This result bridges our behavioral solution concept with the standard
+equilibrium theory. Finally, we also show in Proposition 4 that χ-CSE is equivalent to χ-CE
+for one-stage games, demonstrating the connection between the two behavioral solutions.
+In multi-stage games, cursed beliefs about behavioral strategies will distort the evolution
+of a player’s beliefs about the other players’ types. As shown in Proposition 3, a direct
+consequence of the distortion is that in χ-CSE players tend to update their beliefs about
+others’ types too passively. That is, there is some persistence in beliefs in the sense that
+at each stage t, each χ-cursed player’s belief about any type profile is at least χ times the
+belief about that type profile at stage t − 1. Among other things, this implies that if the
+prior belief about the types is full support and χ > 0, the full support property will persist
+at all histories, and players will (possibly incorrectly) believe every profile of others’ types is
+possible at every history.
+This dampened updating property plays an important role in our framework. Not only
+does it contribute to the difference between CSE and the standard CE through the updating
+process, but it also implies additional restrictions on off-path beliefs. The effect of dampened
+updating is starkly illustrated in the pooling equilibria of signaling games where every type
+of sender behaves the same everywhere. In this case, Proposition 5 shows if an assessment
+associated with a pooling equilibrium is a χ-CSE, then it also a χ′-CSE for all χ′ ≤ χ, but it
+is not necessarily a pooling equilibrium for all χ′ > χ. This contrasts with one of the main
+results about CE, that if a pooling equilibrium is a χ-CE for some χ, then it is a χ′-CE for
+all χ′ ∈ [0, 1] (Eyster and Rabin (2005), Proposition 3).
+This suggests that perhaps the dampened updating property is an equilibrium selection
+device that eliminates some pooling equilibrium, but actually this is not a general property.
+As we demonstrate later, the χ-CE and χ-CSE sets are non-overlapping, which we illustrate
+1For the off-path histories, similar to the idea of Kreps and Wilson (1982), we impose the χ-consistency
+requirement (see Definition 2) so the assessment is approachable by a sequence of totally mixed behavioral
+strategies. The only difference is that players’ beliefs are incorrectly updated by assuming others play the
+χ-cursed behavioral strategies. Hence, in our approach if χ = 0, a CSE is a sequential equilibrium.
+3
+
+with a variety of applications. The intuition is that in CSE, players generally do not have
+correct beliefs about the opponents’ average behavioral strategies. The pooling equilibrium
+is just a special case where players have correct beliefs.
+In Section 4 we explore the implications of cursed sequential equilibrium with five ap-
+plications in economics and political science. Section 4.1 analyzes the χ-CSE of signaling
+games. Besides studying the theoretical properties of pooling χ-CSE, we also analyze two
+simple signaling games that were studied in a laboratory experiment (Brandts and Holt,
+1993). We show how varying the degree of cursedness can change the set of χ-CSE in these
+two signaling games in ways that are consistent with the reported experimental findings.
+Next, we turn to the exploration of how sequentially cursed reasoning can influence strategic
+communication. To this end, we analyze the χ-CSE for a public goods game with communi-
+cation (Palfrey and Rosenthal, 1991; Palfrey et al., 2017) in Section 4.2, finding that χ-CSE
+predicts there will be less effective communication when players are more cursed.
+Next, in Section 4.3 we apply χ-CSE to the centipede game studied experimentally by
+McKelvey and Palfrey (1992) where one of the players believes the other player might be
+an “altruistic” player who always passes. This is a simple reputation-building game, where
+selfish types can gain by imitating altruistic types in early stages of the game. The public
+goods application and the centipede game are both private-values environments, so these
+two applications clearly demonstrate how CSE departs from CE and the Bayesian Nash
+equilibrium, and shows the interplay between sequentially cursed reasoning and the learning
+of types in private-value models.
+In strategic voting applications, conditioning on “pivotality”—the event where your vote
+determines the final outcome—plays a crucial role in understanding equilibrium voting be-
+havior. To illustrate how cursedness distorts the pivotal reasoning, in Section 4.4 we study
+the three-voter two-stage agenda voting game introduced by Ordeshook and Palfrey (1988).
+Since this is a private value game, the predictions of the χ-CE and the Bayesian Nash equilib-
+rium coincide for all χ. That is, cursed equilibrium predicts no matter how cursed the voters
+are, they are able to correctly perform pivotal reasoning. On the contrary, our CSE predicts
+that cursedness will make the voters less likely to vote strategically (predicted by CE and
+BNE). This is consistent with the empirical evidence about the prevalence of sincere voting
+over sequential agendas when inexperienced voters have incomplete information about other
+voters’ preferences (Levine and Plott, 1977; Plott and Levine, 1978; Eckel and Holt, 1989).
+Finally, in Section 4.5 we study the relationship between cursedness and epistemic rea-
+soning by considering the two-person dirty faces game previously studied by Weber (2001)
+and Bayer and Chan (2007). In this game, χ-CSE predicts cursed players are, to some extent,
+4
+
+playing a “coordination” game where they coordinate on a specific learning speed about their
+face types. Therefore, from the perspective of CSE, the non-equilibrium behavior observed
+in experiments can be interpreted as possibly due to a coordination failure resulting from
+cognitive limitations.
+The cursed sequential equilibrium extends the concept of cursed equilibrium from static
+Bayesian games to multi-stage games with observed actions. This generalization preserves
+the spirit of the original cursed equilibrium in a simple and tractable way, and provides
+additional insights about the effect of cursedness in dynamic games. A contemporaneous
+working paper by Cohen and Li (2022) is closely related to our paper. Their paper adopts a
+different approach from ours, based on the coarsening of information sets, to define sequential
+cursed equilibrium for extensive form games with perfect recall. A two-parameter model of
+partial cursedness is developed, and a series of examples demonstrate that for plausible
+parameter values the model is consistent with some experimental findings related to the
+failure of subjects to fully take account of unobserved hypothetical events, whereas behavior
+is “more rational” if subjects make decisions after directly observing such events. At a more
+conceptual level, our paper is related to several other behavioral solution concepts developed
+for dynamic games, such as the agent quantal response equilibrium (AQRE) (McKelvey
+and Palfrey, 1998), the dynamic cognitive hierarchy theory (DCH) (Lin and Palfrey, 2022;
+Lin, 2022), and the analogy-based expectation equilibrium (ABEE) (Jehiel, 2005; Jehiel and
+Koessler, 2008), all of which modify the requirements of sequential equilibrium in different
+ways than cursed sequential equilibrium.
+2
+The Model
+Since CSE is a solution concept for dynamic games of incomplete information, in this pa-
+per we will focus on the framework of multistage games with observed actions (Fudenberg
+and Tirole, 1991b). Section 2.1 defines the formal structure of multi-stage games with ob-
+served actions, followed by Section 2.2, where the χ-cursed sequential equilibrium is formally
+developed.
+2.1
+Multi-Stage Games with Observed Actions
+Let N = {1, . . . , n} be a finite set of players. Each player i ∈ N has a type θi drawn from
+a finite set Θi. Let θ ∈ Θ ≡ ×n
+i=1Θi be the type profile and θ−i ∈ Θ−i ≡ ×j̸=iΘj be the
+type profile without player i. All players share a common (full support) prior distribution
+F(·) : Θ → (0, 1). Therefore, for every player i, the belief of other players’ types conditional
+5
+
+on his own type is
+F(θ−i|θi) =
+F(θ−i, θi)
+�
+θ′
+−i∈Θ−i F(θ′
+−i, θi).
+At the beginning of the game, players observe their own types, but not the other players’
+types. That is, each player’s type is his own private information.
+The game is played in stages t = 1, 2, . . . , T. In each stage, players simultaneously choose
+actions, which will be revealed at the end of the stage. The feasible set of actions can vary
+with histories, so games with alternating moves are also included. Let Ht−1 be the set of
+all possible histories at stage t, where H0 = {h∅} and HT is the set of terminal histories.
+Let H = ∪T
+t=0Ht be the set of all possible histories of the game, and H\HT be the set of
+non-terminal histories.
+For every player i, the available information at stage t is in Θi × Ht−1. Therefore, player
+i’s information sets can be specified as Ii ∈ Qi = {(h, θ) : h ∈ H\HT, θi ∈ Θi}. For the sake
+of simplicity, we assume that, at each history, the feasible set of actions for every player is
+independent of their type and use Ai(ht−1) to denote the feasible set of actions for player
+i at history ht−1. Let Ai = ×h∈H\HT Ai(h) denote player i’s feasible actions in all histories
+of the game and A = A1 × · · · × An. In addition, we assume Ai is finite for all i ∈ N and
+|Ai(h)| ≥ 1 for all i ∈ N and any h ∈ H\HT.
+A behavioral strategy for player i is a function σi : Qi → ∆(Ai) satisfying σi(ht−1, θi) ∈
+∆(Ai(ht−1)). Furthermore, we use σi(at
+i|ht−1, θi) to denote the probability player i chooses
+at
+i ∈ Ai(ht−1). We use at = (at
+1, . . . , at
+n) ∈ ×n
+i=1Ai(ht−1) ≡ A(ht−1) to denote the action
+profile at stage t and at
+−i to denote the action profile at stage t without player i. If at is
+the action profile realized at stage t, then ht = (ht−1, at). Finally, each player i has a payoff
+function ui : HT × Θ → R, and we let u = (u1, . . . , un) be the profile of payoff functions. A
+multi-stage game with observed actions, Γ, is defined by the tuple Γ = ⟨T, A, N, H, Θ, F, u⟩.
+2.2
+Cursed Sequential Equilibrium
+In a multi-stage game with observed actions, a solution is defined by an “assessment,” which
+consists of a (behavioral) strategy profile σ, and a belief system µ. Since action profiles will
+be revealed to all players at the end of each stage, the belief system specifies, for each player,
+a conditional distribution over the set of type profiles conditional on each history. Consider
+an assessment (µ, σ). Following the spirit of the cursed equilibrium, for player i at stage t,
+6
+
+we define the average behavioral strategy profile of the other players as:
+¯σ−i(at
+−i|ht−1, θi) =
+�
+θ−i∈Θ−i
+µi(θ−i|ht−1, θi)σ−i(at
+−i|ht−1, θ−i)
+for any i ∈ N, θi ∈ Θi and ht−1 ∈ Ht−1.
+In CSE, players have incorrect perceptions about other players’ behavioral strategies.
+Instead of thinking they are using σ−i, a χ-cursed2 type θi player i would believe the other
+players are using a χ-weighted average of the average behavioral strategy and the true
+behavioral strategy:3
+σχ
+−i(at
+−i|ht−1, θ−i, θi) = χ¯σ−i(at
+−i|ht−1, θi) + (1 − χ)σ−i(at
+−i|ht−1, θ−i).
+The beliefs of player i about θ−i are updated in the χ-CSE via Bayes’ rule, whenever
+possible, assuming other players are using the χ-cursed behavioral strategy rather than the
+true behavioral strategy. We call this updating rule the χ-cursed Bayes’ rule. Specifically, an
+assessment satisfies the χ-cursed Bayes’ rule if the belief system is derived from the Bayes’
+rule while perceiving others are using σχ
+−i rather than σ−i.
+Definition 1. (µ, σ) satisfies χ-cursed Bayes’ rule if the following rule is applied to update
+the posterior beliefs whenever �
+θ′
+−i∈Θ−i µi(θ′
+−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ′
+−i, θi) > 0:
+µi(θ−i|ht, θi) =
+µi(θ−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ−i, θi)
+�
+θ′
+−i∈Θ−i µi(θ′
+−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ′
+−i, θi).
+Let Σ0 be the set of totally mixed behavioral strategy profiles, and let Ψχ be the set of
+assessments (µ, σ) such that σ ∈ Σ0 and µ is derived from σ using χ-cursed Bayes’ rule.4
+Lemma 1 below shows that another interpretation of the χ-cursed Bayes’ rule is that players
+have correct perceptions about σ−i but are unable to make perfect Bayesian inference when
+updating beliefs. From this perspective, player i’s cursed belief is simply a linear combination
+of player i’s cursed belief at the beginning of that stage (with χ weight) and the Bayesian
+posterior belief (with 1−χ weight). Because σ is totally mixed, there are no off-path histories.
+2We assume throughout the paper that all players are equally cursed, so there is no i subscript on χ. The
+framework is easily extended to allow for heterogeneous degrees of cursedness.
+3If χ = 0, players have correct beliefs about the other players’ behavioral strategies at every stage.
+4In the following, we will use µχ(·) to denote the belief system derived under χ-cursed Bayes’ Rule. Also,
+note that both σχ
+−i and µχ are induced by σ; that is, σχ
+−i(·) = σχ
+−i[σ](·) and µχ(·) = µχ[σ](·). For the ease
+of exposition, we drop [σ] when it does not cause confusion.
+7
+
+Lemma 1. For any (µ, σ) ∈ Ψχ, i ∈ N, ht = (ht−1, at) ∈ H\HT and θ ∈ Θ,
+µi(θ−i|ht, θi) = χµi(θ−i|ht−1, θi) + (1 − χ)
+�
+µi(θ−i|ht−1, θi)σ−i(at
+−i|ht−1, θ−i)
+�
+θ′
+−i µi(θ′
+−i|ht−1, θi)σ−i(at
+−i|ht−1, θ′
+−i)
+�
+Proof. See Appendix A.
+This is analogous to Lemma 1 of Eyster and Rabin (2005). Another insight provided
+by Lemma 1 is that even if player types are independently drawn, i.e., F(θ) = Πn
+i=1Fi(θi),
+players’ cursed beliefs about other players’ types are generally not independent across players.
+That is, in general, µi(θ−i|ht, θi) ̸= Πj̸=iµij(θj|ht, θi). The belief system will preserve the
+independence only when the players are either fully rational (χ = 0) or fully cursed (χ = 1).
+Finally, we place a consistency restriction, analogous to consistent assessments in sequen-
+tial equilibrium, on how χ-cursed beliefs are updated off the equilibrium path, i.e., when
+�
+θ′
+−i∈Θ−i
+µi(θ′
+−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ′
+−i, θi) = 0.
+An assessment satisfies χ-consistency if it is in the closure of Ψχ.
+Definition 2. (µ, σ) satisfies χ-consistency if there is a sequence of assessments {(µk, σk)} ⊆
+Ψχ such that limk→∞(µk, σk) = (µ, σ).
+For any i ∈ N, χ ∈ [0, 1], σ, and θ ∈ Θ, let ρχ
+i (hT|ht, θ, σχ
+−i, σi) be player i’s perceived
+conditional realization probability of terminal history hT ∈ HT at history ht ∈ H\HT if the
+type profile is θ and player i uses the behavioral strategy σi whereas perceives other players’
+using the cursed behavioral strategy σχ
+−i. At every non-terminal history ht, a χ-cursed player
+in χ-CSE will use χ-cursed Bayes’ rule (Definition 1) to derive the posterior belief about the
+other players’ types. Accordingly, a type θi player i’s conditional expected payoff at history
+ht is given by:
+Eui(σ|ht, θi) =
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µi(θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i, σi)ui(hT, θi, θ−i).
+Definition 3. An assessment (µ∗, σ∗) is a χ-cursed sequential equilibrium if it satisfies χ-
+consistency and σ∗
+i (ht, θi) maximizes Eui(σ∗|ht, θi) for all i, θi, ht ∈ H\HT.
+8
+
+3
+General Properties of χ-CSE
+In this section, we characterize some general theoretical properties of χ-CSE. The first result
+is the existence of the χ-CSE. The definition of χ-CSE mirrors the definition of the sequential
+equilibrium by Kreps and Wilson (1982)—the only difference is that players in χ-CSE update
+their beliefs by χ-cursed Bayes’ rule and best respond to χ-cursed (behavioral) strategies.
+Therefore, one can prove the existence of χ-CSE in a similar way as in the standard argument
+of the existence of sequential equilibrium.
+Proposition 1. For any χ ∈ [0, 1] and any finite multi-stage game with observed actions,
+there is at least one χ-CSE.
+Proof. We briefly sketch the proof here, and the details can be found in Appendix A.
+Fix any χ ∈ [0, 1]. For any i ∈ N and any information set Ii = (ht−1, θi), player i has
+to choose every action at
+i ∈ Ai(ht−1) with probability at least ϵ. Since there are no off-path
+histories, the belief system is uniquely pinned down by χ-cursed Bayes’ rule and a χ-CSE
+exists in this ϵ-constrained game. We denote this χ-CSE as (µϵ, σϵ). By compactness, there
+is a converging sub-sequence of assessments such that (µϵ, σϵ) → (µ∗, σ∗) as ϵ → 0, which is
+a χ-CSE, as desired.
+Let Φ(χ) be the correspondence that maps χ ∈ [0, 1] to the set of χ-CSE. Proposition 1
+guarantees Φ(χ) is non-empty for any χ ∈ [0, 1]. Because χ-cursed Bayes’ rule changes con-
+tinuously in χ, we can further prove in Proposition 2 that Φ(χ) is an upper hemi-continuous
+correspondence.
+Proposition 2. Φ(χ) is upper hemi-continuous with respect to χ.
+Proof. The proof follows a standard argument. See Appendix A for details.
+As shown in Corollary 1, a direct consequence of upper hemi-continuity is that every
+limit point of a sequence of χ-CSE when χ → 0 is a sequential equilibrium. This result
+bridges our behavioral equilibrium concept with standard equilibrium theory.
+Corollary 1. Every limit point of a sequence of χ-CSE with χ converging to 0 is a sequential
+equilibrium.
+Proof. By Proposition 2, we know Φ(χ) is upper hemi-continuous at 0. Consider of a se-
+quence of χ-CSE. As χ → 0, the limit point remains a CSE, which is a sequential equilibrium
+at χ = 0. This completes the proof.
+9
+
+Finally, by a similar argument to Kreps and Wilson (1982), for any χ ∈ [0, 1], χ-CSE is
+also upper hemi-continuous with respect to payoffs. In other words, our χ-CSE preserves
+the continuity property of sequential equilibrium.
+The next result is the characterization of a necessary condition for χ-CSE. As seen
+from Lemma 1, players update their beliefs more passively in χ-CSE than in the stan-
+dard equilibrium—they put χ-weight on their beliefs formed in previous stage. To formalize
+this, we define the χ-dampened updating property in Definition 4. An assessment satisfies
+this property if at any non-terminal history, the belief puts at least χ weight on the belief
+in previous stage—both on and off the equilibrium path. In Proposition 3, we show that
+χ-consistency implies the χ-dampened updating property.
+Definition 4. An assessment (µ, σ) satisfies the χ-dampened updating property if for any
+i ∈ N, θ ∈ Θ and ht = (ht−1, at) ∈ H\HT,
+µi(θ−i|ht, θi) ≥ χµi(θ−i|ht−1, θi).
+Proposition 3. χ-consistency implies χ-dampened updating for any χ ∈ [0, 1].
+Proof. See Appendix A.
+It follows that if assessment (µ, σ) satisfies the χ-dampened updating property, then for
+any player i, any history ht and any type profile θ, player i’s belief about θ−i is bounded by
+χµi(θ−i|ht−1, θi) ≤ µi(θ−i|ht, θi) ≤ 1 − χ
+�
+θ′
+−i̸=θ−i
+µi(θ′
+−i|ht−1, θi).
+One can see from this condition that when χ increases, the feasible range of µi(θ−i|ht, θi)
+shrinks, and the restriction on the belief system becomes more stringent. Moreover, if the
+history ht is an off-path history of (µ, σ), then this condition characterizes the feasible set of
+off-path beliefs, which shrinks as χ increases.
+An important implication of this observation is that Φ(χ) is not lower hemi-continuous
+with respect to χ. The intuition is that for some χ-CSE that contains off-path histories, the
+off-path beliefs to support the equilibrium might not be χ-consistent for sufficiently large χ.
+In this case, the χ-CSE is not attainable by a sequence of χk-CSE where χk converges to χ
+from above, causing the lack of lower hemi-continuity.5
+Lastly, another implication of χ-dampened updating property is that for each player i,
+history ht and type profile θ, the belief µi(θ−i|ht, θi) has a lower bound that is independent
+5An example is provided in Section 4.1.
+10
+
+of the strategy profile. The lower bound is characterized in Corollary 2. This result implies
+that when χ > 0, F(θ−i|θi) > 0 implies µi(θ−i|ht, θi) > 0 for all ht, so that if prior beliefs are
+bounded away from zero, beliefs are always bounded away from 0 as well. In other words,
+when χ > 0, because of the χ-dampened updating, beliefs will always have full support even
+if at off-path histories.
+Corollary 2. For any χ-consistent assessment (µ, σ), i ∈ N, θ ∈ Θ and ht ∈ H\HT,
+µi(θ−i|ht, θi) ≥ χtF(θ−i|θi)
+Proof. See Appendix A.
+If the game has only one stage, then the dampened updating property has no effect, in
+which case χ-CSE and χ-CE are equivalent solution concepts. This is formally stated and
+proved in Proposition 4.
+Proposition 4. For any one-stage game and for any χ, χ-CSE and χ-CE are equivalent.
+Proof. For any one-stage game, the only public history is the initial history h∅. Thus, in any
+χ-CSE, for each player i ∈ N and type profile θ ∈ Θ, player i’s belief about other players’
+types at this history is
+µi(θ−i|h∅, θi) = F(θ−i|θi).
+Since the game has only one stage, the outcome is simply a1 = (a1
+1, . . . , a1
+n), the action profile
+at stage 1. Moreover, given any behavioral strategy profile σ, player i believes a1 will be the
+outcome with probability
+σi(a1
+i |h∅, θi) ×
+�
+χ¯σ−i(a1
+−i|h∅, θi) + (1 − χ)σ−i(a1
+−i|h∅, θ−i)
+�
+.
+Therefore, if σ is the behavioral strategy profile of a χ-CSE in an one-stage game, then for
+each player i, type θi ∈ Θi and each a1
+i ∈ Ai(h∅) such that σi(a1
+i |h∅, θi) > 0,
+a1
+i ∈ argmax
+a1′
+i ∈Ai(h∅)
+�
+θ−i∈Θ−i
+F(θ−i|θi) ×
+�
+�
+�
+�
+a1
+−i∈A−i(h∅)
+�
+χ¯σ−i(a1
+−i|h∅, θi) + (1 − χ)σ−i(a1
+−i|h∅, θ−i)
+�
+�
+�
+� ui(a1′
+i , a1
+−i, θi, θ−i),
+which coincides with the maximization problem of χ-CE. This completes the proof.
+11
+
+From the proof of Proposition 4, one can see that in one-stage games players have correct
+perceptions about the average strategy of others.
+Therefore, the maximization problem
+of χ-CSE coincides with the problem of χ-CE. For general multi-stage games, because of
+the χ-dampened updating property, players will update beliefs incorrectly and thus their
+perceptions about other players’ future moves can also be distorted.
+4
+Applications
+In this section, we will explore χ-CSE in five applications of multi-stage games with observed
+actions, in order to illustrate the range of effects it can have and to show how it is different
+from the χ-CE and sequential equilibrium.
+Our first application is the sender-receiver signaling game, which is practically the sim-
+plest possible multi-stage game. From our analysis, we will see both the theoretical and
+empirical implications of our χ-CSE.
+4.1
+Pooling Equilibria in Signaling Games
+We first make a general observation about pooling equilibria in multi-stage games. Player
+j follows a pooling strategy if for every non-terminal history, ht, all types of player j take
+the same action at+1
+j
+∈ Aj(ht). Conceptually, since every type of player j takes the same
+action, players other than j cannot make any inference about j’s type from j’s actions. A
+pooling χ-CSE is a χ-CSE where every player follows a pooling strategy. Hence, every player
+has correct beliefs about any other player’s future move because every type of every player
+chooses the same action.
+Since in any pooling χ-CSE, players can correctly anticipate other players’ future moves
+no matter how cursed they are, one may naturally conjecture that a pooling χ-CSE is also a
+χ′-CSE for any χ′ ∈ [0, 1]. As shown by Eyster and Rabin (2005), this is true for one-stage
+Bayesian games: if a pooling strategy profile is a χ-cursed equilibrium, then it is also a
+χ′-cursed equilibrium for any χ′ ∈ [0, 1]. Surprisingly, this result does not extend to multi-
+stage games. Proposition 5 shows if a pooling behavioral strategy profile is a χ-CSE, then it
+remains a χ′-CSE only for χ′ ≤ χ, which is a weaker result than Eyster and Rabin (2005).
+This result is driven by the χ-dampened updating property which restricts the set of
+off-path beliefs. As discussed above, when χ gets larger, the set of feasible off-path beliefs
+shrinks, eliminating some pooling χ-CSE.
+Proposition 5. A pooling χ-CSE is a χ′-CSE for χ′ ≤ χ.
+12
+
+Proof. See Appendix B.
+The proof strategy is similar to the one in Eyster and Rabin (2005) Proposition 3. Given
+a χ-CSE behavioral strategy profile, we can separate the histories into on-path and off-path
+histories. For on-path histories in a pooling equilibrium, since all types of players make the
+same decisions, players cannot make any inference about other players’ types. Therefore,
+for on-path histories, their beliefs are the prior beliefs, which are independent of χ. On the
+other hand, for off-path histories, as shown in Proposition 3, a necessary condition for χ-CSE
+is that the belief system has to satisfy the χ-dampened updating property. When χ gets
+larger, this requirement becomes more stringent, and hence some pooling χ-CSE may break
+down.
+Example 1 is a signaling game where the sender has only two types and two messages, and
+the receiver has only two actions. This example demonstrates the implication of Proposition
+5 and shows the lack of lower hemi-continuity; i.e., it is possible for a pooling behavioral
+strategy profile to be a χ-CSE, but not a χ′-CSE for χ′ > χ.
+Example 1.
+The sender has two possible types drawn from the set Θ = {θ1, θ2} with
+Pr(θ1) = 1/4. The receiver does not have any private information. After the sender’s type
+is drawn, the sender observes his type and decides to send a message m ∈ {A, B}, or any
+mixture between the two. After that, the receiver decides between action a ∈ {L, R} or any
+mixture between the two, and the game ends. The game tree is illustrated in Figure 1.
+2, 2
+L
+−1, 4
+R
+A
+4, −1
+L
+1, 0
+R
+B
+θ1
+[ 1
+4]
+2, 1
+L
+−1, 0
+R
+A
+4, −2
+L
+1, 0
+R
+B
+θ2
+[ 3
+4]
+Nature
+1
+1
+2
+2
+Figure 1: Game Tree for Example 1
+If we solve for the χ-CE of the game (or the sequential equilibria), we find that there
+are two pooling equilibria for every value of χ. In the first pooling χ-CE, both sender types
+choose A; the receiver chooses L in response to A and R at the off-path history B. In
+13
+
+the second pooling χ-CE, both sender types pool at B and the receiver chooses R at both
+histories. By Proposition 3 of Eyster and Rabin (2005), these two equilibria are in fact
+pooling χ-CE for all χ ∈ [0, 1]. The intuition is that in a pooling χ-CE, players are not
+able to make any inference about other players’ types from their actions because the average
+normal form strategy is the same as the type-conditional normal form strategy. Therefore,
+their beliefs are independent of χ, and hence a pooling χ-CE will still be an equilibrium for
+any χ ∈ [0, 1].
+However, as summarized in Claim 1 below, the χ-CSE imposes stronger restrictions than
+χ-CE in this example, in the sense that when χ is sufficiently large, the second pooling equi-
+librium cannot be supported as a χ-CSE. The key reason is that when the game is analyzed
+in its normal form, the χ-dampened updating property shown in Proposition 3 does not have
+any bite, allowing both pooling equilibria to be supported as a χ-CE for any value of χ. Yet,
+in the χ-CSE analysis, the additional restriction of χ-dampened updating property eliminates
+some extreme off-path beliefs, and hence, eliminates the second pooling χ-CSE equilibrium
+for sufficiently large χ. For simplicity, we use a four-tuple [(m(θ1), m(θ2)); (a(A), a(B))] to
+denote a behavioral strategy profile.
+Claim 1. In this example, there are two pure pooling χ-CSE, which are:
+1. [(A, A); (L, R)] is a pooling χ-CSE for any χ ∈ [0, 1].
+2. [(B, B); (R, R)] with µ2(θ1|A) ∈
+� 1
+3, 1 − 3
+4χ
+�
+is a pooling χ-CSE if and only if χ ≤ 8/9.
+Proof. See Appendix B.
+From previous discussion, we know in general, the sets of χ-CSE and χ-CE are non-
+overlapping because of the nature of sequential distortion of beliefs in χ-CSE. Yet, a pooling
+χ-CSE is an exception. In a pooling χ-CSE, players can correctly anticipate others’ future
+moves, so a pooling χ-CSE will mechanically be a pooling χ-CE. In cases such as this, we
+can find that χ-CSE ia a refinement of χ-CE.
+Lastly, we can observe from this example that the χ-CSE correspondence Φ(χ) is not
+lower hemi-continuous with respect to χ. To see this, we consider a sequence of {χk} where
+χk = 8
+9 + 1
+9k for k ≥ 1. From the analysis of Claim 1, we know [(B, B); (R, R)] ̸∈ Φ(χk) for
+any k ≥ 1. However, in the limit where χk → 8/9, [(B, B); (R, R)] with µ2(θ1|A) = 1/3 is
+indeed a CSE. That is, [(B, B); (R, R)] is not approachable by this sequence of χk-CSE.
+Remark 1. Φ(χ) is not lower hemi-continuous with respect to χ.
+14
+
+45, 30
+30, 30
+C
+15, 0
+0, 0
+D
+30, 15
+50, 35
+E
+I
+30, 90
+45, 90
+C
+0, 15
+15, 15
+D
+45, 15
+100, 30
+E
+S
+θ1
+[ 1
+2]
+30, 30
+30, 30
+C
+0, 45
+30, 45
+D
+30, 15
+30, 0
+E
+I
+45, 0
+45, 0
+C
+15, 30
+0, 30
+D
+30, 15
+0, 15
+E
+S
+θ2
+[ 1
+2]
+�BH 3
+BH 4
+�
+Nature
+1
+1
+2
+2
+Figure 2: Game Tree for BH 3 and BH 4 in Brandts and Holt (1993)
+Example 2. Here we analyze two signaling games that were studied experimentally by
+Brandts and Holt (1993) (BH 3 and BH 4) and show that χ-CSE can help explain some
+of their findings. In both Game BH 3 and Game BH 4, the sender has two possible types
+{θ1, θ2} which are equally likely. There are two messages m ∈ {I, S} available to the sender.6
+After seeing the message, the receiver chooses an action from a ∈ {C, D, E}. The game tree
+and payoffs for both games are summarized in Figure 2.
+In both games, there are two pooling sequential equilibria. In the first equilibrium, both
+sender types send message I, and the receiver will choose C in response to I and choose
+D in response to S. In the second equilibrium, both sender types send message S, and the
+receiver will choose D in response to I while choose C in response to S. Both are sequential
+equilibria, in both games, but only the first equilibrium where the sender sends I satisfies
+the intuitive criterion proposed by Cho and Kreps (1987).
+Since the equilibrium structure is similar in both games, the sequential equilibrium and
+the intuitive criterion predict the behavior should be the same in both games. However, this
+prediction is strikingly rejected by the data. Brandts and Holt (1993) report that in the
+later rounds of the experiment, almost all type θ1 senders send I in Game BH 3 (97 %), and
+yet all type θ1 senders send S in Game BH 4 (100%). In contrast, type θ2 senders behave
+similarly in both games—46.2% and 44.1% of type θ2 senders send I in Games BH 3 and
+BH 4, respectively. Qualitatively speaking, the empirical pattern reported by Brandts and
+Holt (1993) is that sender type θ1 is more likely to send I in Game BH 3 than Game BH 4
+6I stands for “Intuitive” and S stands for “Sequential but not intuitive”, corresponding to the two pooling
+sequential equilibria of the two games.
+15
+
+while sender type θ2’s behavior is insensitive to the change of games.
+To explain this finding, Brandts and Holt (1993) propose a descriptive story based on
+naive receivers. A naive receiver will think both sender types are equally likely, regardless of
+which message is observed. This naive reasoning will lead the receiver to choose C in both
+games. Given this naive response, a type θ1 sender has an incentive to send I in Game BH
+3 and choose S in Game BH 4. (Brandts and Holt (1993), p. 284 – 285)
+In fact, their story of naive reasoning echoes the logic of χ-CSE. When the receiver is
+fully cursed (or naive), he will ignore the correlation between the sender’s action and type,
+causing him to not update the belief about the sender’s type. Proposition 6 characterizes
+the set of χ-CSE of both games. Following the notation in Example 1, we use a four-tuple
+[(m(θ1), m(θ2)); (a(I), a(S))] to denote a behavioral strategy profile.
+Proposition 6. The set of χ-CSE of Game BH 3 and BH 4 are characterized as below.
+• In Game BH 3, there are three pure χ-CSE:
+1. [(I, I); (C, D)] is a pooling χ-CSE if and only if χ ≤ 4/7.
+2. [(S, S); (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.
+3. [(I, S); (C, C)] is a separating χ-CSE if and only if χ ≥ 4/7.
+• In Game BH 4, there are three pure χ-CSE:
+1. [(I, I); (C, D)] is a pooling χ-CSE if and only if χ ≤ 4/7.
+2. [(S, S); (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.
+3. [(S, S); (C, C)] is a pooling χ-CSE for any χ ∈ [0, 1].
+Proof. See Appendix B.
+As noted earlier for Example 1, by Proposition 3 of Eyster and Rabin (2005), pooling
+equilibria (1) and (2) in games BH 3 and BH 4 survive as χ-CE for all χ ∈ [0, 1]. Hence,
+Proposition 6 implies that χ-CSE refines the χ-CE pooling equilibria for larger values of χ.
+Moreover, χ-CSE actually eliminates all pooling equilibria in BH 3 if χ > 2/3. Proposition
+6 also suggests that for any χ ∈ [0, 1], sender type θ2 will behave similarly in both games,
+which is qualitatively consistent with the empirical pattern. In addition, χ-CSE predicts that
+a highly cursed (χ > 2/3) type θ1 sender will send different messages in different games—
+highly cursed type θ1 senders will send I and S in Games BH 3 and BH 4, respectively. This
+is consistent with the empirical data.
+16
+
+4.2
+A Public Goods Game with Communication
+Our second application is a threshold public goods game with private information and pre-
+play communication, variations of which have been studied in laboratory experiments (Pal-
+frey and Rosenthal, 1991; Palfrey et al., 2017). Here we consider the “unanimity” case where
+there are N players and the threshold is also N.
+Each player i has a private cost parameter ci, which is independently drawn from a
+uniform distribution on [0, K] where K > 1. After each player’s ci is drawn, each player ob-
+serves their own cost, but not the others’ costs. Therefore, ci is player i’s private information
+and corresponds to θi in the general formulation.7 The game consists of two stages. After
+the profile of cost parameters is drawn, the game will proceed to stage 1 where each player
+simultaneously broadcasts a public message mi ∈ {0, 1} without any cost or commitment.
+After all players observe the message profile from this first stage, the game proceeds to stage
+2 which is a unanimity threshold public goods game. Player i has to pay the cost ci if he
+contributes, but the public good will be provided only if all players contribute. If the public
+good is provided, each player receives a payoff of 1 − ci.
+If there is no communication stage, the unique Bayesian Nash equilibrium is that no
+player contributes, which is also the unique χ-CE for any χ ∈ [0, 1]. In contrast, with the
+communication stage, there exists an efficient sequential equilibrium where each player i
+sends mi = 1 if and only if ci ≤ 1 and contributes if and only if all players send 1 in the
+first stage.8 Since this is a private value game, the standard cursed equilibrium has no bite,
+and this efficient sequential equilibrium is also a χ-CE for all values of χ, by Proposition 2
+of Eyster and Rabin (2005). In the following, we demonstrate that the prediction of χ-CSE
+is different from CE (and sequential equilibrium).
+To analyze the χ-CSE, consider a collection of “cutoff” costs, {Cχ
+c , Cχ
+0 , Cχ
+1 , . . . , Cχ
+N}. In
+the communication stage, each player communicates the message mi = 1 if and only if
+ci ≤ Cχ
+c . In the second stage, if there are exactly 0 ≤ k ≤ N players sending mi = 1 in the
+first stage, then such a player would contribute in the second stage if and only if ci ≤ Cχ
+k .
+A χ-CSE is a collection of these cost cutoffs such that the associated strategies are a χ-CSE
+for the public goods game with communication. The most efficient sequential equilibrium
+identified above for χ = 0 corresponds to cutoffs with C0
+0 = C0
+1 = · · · = C0
+N−1 = 0 and
+C0
+c = C0
+N = 1.
+7This application has a continuum of types.
+The framework of analysis developed for finite types is
+applied in the obvious way.
+8One can think of the first stage as a poll, where players are asked the following question: “Are you
+willing to contribute if everyone else says they are willing to contribute?”. The message mi = 1 corresponds
+to a “yes” answer and the message mi = 0 corresponds to a “no” answer.
+17
+
+There are in fact multiple equilibria in this game with communication.
+In order to
+demonstrate how the cursed belief can distort players’ behavior, here we will focus on the
+χ-CSE that is similar to the most efficient sequential equilibrium identified above, where
+Cχ
+0 = Cχ
+1 = · · · = Cχ
+N−1 = 0 and Cχ
+c = Cχ
+N. The resulting χ-CSE is given in Proposition 7.
+Proposition 7. In the public goods game with communication, there is a χ-CSE where
+1. Cχ
+0 = Cχ
+1 = · · · = Cχ
+N−1 = 0, and
+2. there is a unique C∗(N, K, χ) ≤ 1 s.t. Cχ
+c = Cχ
+N = C∗(N, K, χ) that solves:
+C∗(N, K, χ) − χ
+�C∗(N, K, χ)
+K
+�N−1
+= 1 − χ.
+Proof. See Appendix B.
+To provide some intuition, we sketch the proof by analyzing the two-person game, where
+the χ-CSE is characterized by four cutoffs {Cχ
+c , Cχ
+0 , Cχ
+1 , Cχ
+2 }, with Cχ
+0 = Cχ
+1 = 0 and Cχ
+c =
+Cχ
+2 . If players use the strategy that they would send message 1 if the cost is less than Cχ
+c ,
+then by Lemma 1, at the history where both players send 1, player i’s cursed posterior belief
+density would be
+µχ
+i (c−i|{1, 1}) =
+�
+�
+�
+χ ·
+� 1
+K
+�
++ (1 − χ) ·
+�
+1
+Cχ
+c
+�
+if c−i ≤ Cχ
+c
+χ ·
+� 1
+K
+�
+if c−i > Cχ
+c .
+Notice that cursedness leads a player to put some probability weight on a type that is
+not compatible with the history. Namely, for χ-cursed players, when seeing another player
+sending 1, they still believe the other player might have c−i > Cχ
+c . When χ converges to
+1, the belief simply collapses to the prior belief as fully cursed players never update their
+beliefs. On the other hand, when χ converges to 0, the belief converges to 1/Cχ
+c , which is
+the correct Bayesian inference.
+Given this cursed belief density, the optimal cost cutoff to contribute, Cχ
+2 , solves
+Cχ
+2 =
+� Cχ
+2
+0
+µχ
+i (c−i|{1, 1})dc−i.
+Finally, at the first stage cutoff equilibrium, the Cχ
+c type of player would be indifferent
+18
+
+between sending 1 and 0 at the first stage. Therefore, Cχ
+c satisfies
+0 =
+�Cχ
+c
+K
+� �
+−Cχ
+c +
+� Cχ
+2
+0
+µχ
+i (c−i|{1, 1})dc−i
+�
+.
+After substituting Cχ
+c = Cχ
+2 and solving, we obtain the χ-CSE:
+Cχ
+c = Cχ
+2 = K − Kχ
+K − χ .
+From this expression, one can see that the cutoff Cχ
+c (as well as Cχ
+2 ) is decreasing in χ and
+K. When χ → 0, Cχ
+c converges to 1, which is the cutoff of the sequential equilibrium. On
+the other hand, when χ → 1, Cχ
+c converges to 0, so there is no possibility for communication
+when players are fully cursed. Similarly, when K → 1, Cχ
+c converges to 1, which is the cutoff
+of the sequential equilibrium, while limK→∞ Cχ
+c = 1 − χ.
+These comparative statics results with respect to χ and K are not just a special property
+of the N = 2 case, but hold for all N > 1.
+Furthermore, there is a similar effect of
+increasing N that results in a lower cutoff (less effective communication). These properties
+of C∗(N, K, χ) are summarized in Corollary 3.
+Corollary 3. The efficient χ-CSE predicts the following comparative statics for all N ≥ 2
+and K > 1:
+1. C∗(N, K, 0) = 1 and C∗(N, K, 1) = 0.
+2. C∗(N, K, χ) is strictly decreasing in N, K, and χ for any χ ∈ (0, 1).
+3. For all χ ∈ [0, 1], limN→∞ C∗(N, K, χ) = limK→∞ C∗(N, K, χ) = 1 − χ.
+Proof. See Appendix B.
+These properties are illustrated in Figure 3. The left panel illustrates the equilibrium
+condition for C∗ in a graph where the horizontal axis is C ∈ [0, K]. We can rewrite the
+characterization of C∗(N, K, χ) in Proposition 7 as a solution for C to the following equation:
+1 − C
+χ
+= 1 −
+� C
+K
+�N−1
+.
+The left panel displays the LHS of this equation, 1−C
+χ , as the downward sloping line that
+connects the points (0, 1
+χ) and (1, 0). The RHS is displayed for N = 2 and N = 3 by the two
+curves that connect the points (0, 1) and (K, 0). The equilibrium, C∗(N, K, χ), is given by
+19
+
+0.0
+C * (3, K, )            
+      C * (2, K, )
+    1.0
+K
+C
+0.0
+1.0
+1
+1
+(C
+K )
+N
+1
+1
+C
+-CSE Equilibrium Condition (K = 1.5,  = 0.5)
+N = 2
+N = 3
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+C*(N, K, )
+-CSE Cutoffs for Different N (K = 1.5)
+N = 2
+N = 3
+N = 
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+C*(N, K, )
+-CSE Cutoffs for Different K (N = 2)
+K = 1.25
+K = 1.5
+K = 
+Figure 3: (Left) Illustration of the χ-CSE equilibrium condition when K = 1.5 and χ = 0.5.
+(Middle) The χ-CSE cutoff C∗(N, K, χ) for N = 2, 3 and for N → ∞ when K = 1.5. (Right)
+The χ-CSE cutoff C∗(N, K, χ) for K = 1.25, 1.5 and for K → ∞ when N = 2.
+the (unique) intersection of the LHS and RHS curves. It is easy to see from this graph that
+C∗(N, K, χ) is strictly decreasing in N, K, and χ. When N increases, the RHS increases for
+all C ∈ (0, K), resulting in an intersection at a lower value of C. When K increases, again
+the RHS increases for all C ∈ (0, K), and also the intercept of the RHS on the horizontal axis
+increases, leading to a similar effect; and when χ increases, the intercept of the LHS on the
+horizontal axis decreases, resulting in an intersection at a lower value of C. In addition, when
+N grows without bound, the RHS approaches a constant function equal to 1 for C < K,
+resulting in a limiting intersection at C∗(∞, K, χ) = 1 − χ. This is illustrated in the middle
+panel of Figure 3, which graphs C∗(2, 1.5, ·), C∗(3, 1.5, ·), and C∗(∞, 1.5, ·). A similar effect
+occurs for K → ∞, illustrated in the right panel of Figure 3, which displays C∗(2, 1.25, ·),
+C∗(2, 1.5, ·), and C∗(2, ∞, ·).
+An interesting takeaway of this analysis is that in the public goods game with communi-
+cation, cursedness limits information transmission: χ-CSE predicts when players are more
+cursed (higher χ), it will be harder for them to effectively communicate in the first stage
+for efficient coordination in the second stage. Moreover, Corollary 3 shows that this χ-CSE
+varies systematically with all three parameters of the model: N, K, and χ.
+In contrast,
+in the standard χ-CE, players best respond to the average type-contingent strategy rather
+than the average behavioral strategy. Since it is a private value game, players do not care
+about the distribution of types, only the distribution of actions. Thus, the prediction of
+standard CE coincides with the equilibrium prediction for all values of N, K, and χ. This
+seems behaviorally implausible and is also suggestive of an experimental design that varies
+20
+
+the two parameters N and K, since the qualitative effects of changing these parameters are
+identified.
+4.3
+Reputation Building: The Centipede Game with Altruists
+T1
+T2
+T3
+T4
+P4
+P3
+P2
+P1
+1
+1
+1
+2
+2
+4, 1
+2, 8
+16, 4
+8, 32
+64, 16
+Figure 4: Four-stage Centipede Game
+In order to further demonstrate the difference between χ-CE and χ-CSE, in this section
+we consider a variation of the centipede game with private information, as analyzed in
+McKelvey and Palfrey (1992) and Kreps (1990). This game is an illustration of reputation-
+building, where a selfish player imitates an altruistic type in order to develop a reputation
+for passing, which in turn entices the opponent to pass and leads to higher payoffs.
+There are two players and four stages, and the game tree is shown in Figure 4. In stage
+one, player one can choose either Take (T1) or Pass (P1). If she chooses action T1, the
+game ends and the payoffs to players one and two are 4 and 1, respectively. If she chooses
+the action P1, the game continues and player two has a choice between take (T2) and pass
+(P2). If he chooses T2, the game ends and the payoffs to players one and two are 2 and
+8, respectively. If he chooses P2, the game continues to the third stage where player one
+chooses between T3 and P3. Similar to the previous stages, if she chooses T3, the payoffs
+to players one and two are 16 and 4, respectively. If she chooses P3, the game proceeds to
+the last stage where player two chooses between T4 and P4. If player two chooses T4 the
+payoffs are 8 and 32, respectively. If player two alternatively chooses P4, the payoffs are 64
+and 16, respectively.
+There are two types of player one, selfish and altruistic. Selfish players are assumed to
+have a utility function that is linear in their own payoff. Altruistic players are assumed to
+have a utility function that is linear in the sum of the two payoffs. For the sake of simplicity,
+we assume that player two has only one type, selfish. The common knowledge probability
+that player one is altruistic is α. Player one knows her own type, but player two does not.
+Therefore, player one’s type is her private information. In the following, we will focus on the
+21
+
+interesting case where α ≤ 1/7.9
+Because this is a game of incomplete information with private values, the standard χ-CE
+is equivalent to the Bayesian Nash equilibrium of the game for all χ ∈ [0, 1], and yields
+the same take probabilities as the Bayesian equilibrium. Since altruistic player one wants
+to maximize the sum of the payoffs, it is optimal for her to always pass. The equilibrium
+behavior is summarized in Claim 2.
+Claim 2. In the Bayesian Nash equilibrium, selfish player one will choose P1 with probability
+6α
+1−α and choose T3 with probability 1; player two will choose P2 with probability 1
+7 and choose
+T4 with probability 1.
+Proof. See Appendix B.
+It is useful to see exactly why, in this example (and more generally) the standard χ-CE
+is the same as the perfect Bayesian equilibrium. In particular, why it is not the case that
+cursed beliefs will change player two’s updating process after observing P1 at stage one.
+Belief updating is not a property of the standard χ-CE as the analysis is in the strategic
+form, and thus is solved as a BNE of the game in the reduced normal form.10
+Table 1
+summarizes the payoff matrices in the reduced normal form of centipede game for selfish and
+altruistic type.
+Table 1: Reduced Normal Form Centipede Game Payoff Matrix
+selfish (1 − α)
+T2
+P2T4
+P2P4
+altruistic (α)
+T2
+P2T4
+P2P4
+T1
+4, 1
+4, 1
+4, 1
+T1
+5, 1
+5, 1
+5, 1
+P1T3
+2, 8
+16, 4
+16, 4
+P1T3
+10, 8
+20, 4
+20, 4
+P1P3
+2, 8
+8, 32
+64, 16
+P1P3
+10, 8
+40, 32
+80, 16
+It is easily verified that at the Bayesian Nash equilibrium, selfish player one would choose
+T1 with probability (1 − 7α)/(1 − α) and choose P1T3 with probability 6α/(1 − α), while
+player two would choose T2 with probability 6/7.
+To solve the standard χ-CE, let selfish player one choose T1 with probability p and P1T3
+with probability 1−p. Let player two choose T2 with probability q and P2T4 with probability
+1 − q. Notice that for player two, P2P4 is a dominated strategy and given this, it is also
+sub-optimal for selfish player one to choose P1P3. In this case, selfish player one would choose
+9If α > 1
+7, player two always chooses P2 in the second stage since the probability of encountering altruistic
+player one is sufficiently high. Selfish player one would thus chooses P1 in the first stage and choose T3 in
+the third stage.
+10The analysis is similar for the unreduced normal form.
+22
+
+T1 if and only if
+4 ≥ 2q + 16(1 − q) ⇐⇒ q ≥ 6/7,
+implying that selfish player one’s best response correspondence in the standard cursed anal-
+ysis coincides with the Bayesian Nash equilibrium analysis. On the other hand, to solve for
+player two’s best responses we need to first solve for the perceived strategy. When player
+two is χ-cursed, he would think that player one is using σχ
+1 (a|θ) where a ∈ {T1, P1T3, P1P3}
+and θ ∈ {selfish, altruistic}. Player one’s true strategy is given in Table 2.
+Table 2: Player 1’s True Strategy
+player one’s type
+σ1(a|θ)
+selfish
+altruistic
+T1
+p
+0
+P1T3
+1 − p
+0
+P1P3
+0
+1
+In this case, player one’s average strategy is simply:
+¯σ1(T1) = (1 − α)p, ¯σ1(P1T3) = (1 − α)(1 − p), ¯σ1(P1P3) = α.
+By definition, σχ
+1 (a|θ) = χ¯σ1(a) + (1 − χ)σ1(a|s) and hence we can find that σχ
+1 (a|θ) is given
+in Table 3.
+Table 3: Cursed Perception of Player 1’s Strategy
+player one’s type
+σχ
+1 (a|θ)
+selfish
+altruistic
+T1
+p(1 − χα)
+pχ(1 − α)
+P1T3
+(1 − p)(1 − χα)
+(1 − p)χ(1 − α)
+P1P3
+χα
+1 − χ + χα
+From player two’s perspective, given any action profile, player two’s expected payoff is
+not affected by whether player one is selfish or altruistic. Hence, player two only cares about
+the marginal distribution of player one’s actions. In this case, χ-cursed player two believes
+player one will choose a ∈ {T1, P1T3, P1P3} with probability ¯σ1(a). Therefore, it is optimal
+for player two to choose T2 if and only if
+¯σ1(T1) + 8 [1 − ¯σ1(T1)] ≥ ¯σ1(T1) + 4¯σ1(P1T3) + 32¯σ1(P1P3) ⇐⇒ p ≤ 1 − 7α
+1 − α ,
+23
+
+implying player two’s best responses in the standard cursed analysis also coincides with the
+Nash best responses. As a result, one concludes that standard χ-CE would make exactly the
+same prediction as the Bayesian Nash equilibrium regardless how cursed the players are.
+In contrast, the χ-CSE will exhibit distortions to the conditional beliefs of player two,
+given that player one has passed, because player two incorrectly takes into account how
+player one’s choice to pass depended on player one’s private information. In particular, it
+is harder to build a reputation, since a selfish type will have to imitate altruists in such a
+way that the true posterior on altruistic type conditional on a pass is higher than in the
+perfect Bayesian equilibrium, because the updating by player two about player one’s type is
+dampened relative to this true posterior due to cursedness. This distorted belief updating
+will result in less passing by player one compared to the Bayesian equilibrium. Formally,
+the χ-CSE is described in Proposition 8.
+Proposition 8. In the χ-CSE, selfish player one will choose P1 with probability qχ
+1 and
+choose T3 with probability 1; player two will choose P2 with probability qχ
+2 and choose T4
+with probability 1 where
+qχ
+1 =
+�
+�
+�
+�
+�
+�
+7α−7αχ
+1−7αχ − α
+� �
+(1 − α)
+if χ ≤
+6
+7(1−α)
+0
+if χ >
+6
+7(1−α)
+and,
+qχ
+2 =
+�
+�
+�
+1/7
+if χ ≤
+6
+7(1−α)
+0
+if χ >
+6
+7(1−α).
+Proof. See Appendix B.
+In order to see how the cursedness affects the equilibrium behavior, here we focus on the
+case of χ ≤
+6
+7(1−α) where selfish player one and player two will both mix at stage one and
+two. Given selfish player one chooses P1 with probability qχ
+1 , by Lemma 1, we know when
+the game reaches stage two, player two’s belief about player one being altruistic becomes
+µχ = χα + (1 − χ)
+�
+α
+α + (1 − α)qχ
+1
+�
+.
+Here we see that when χ is larger, player two will update his belief more slowly. Therefore,
+in order to maintain indifference at the mixed equilibrium, selfish player one has to pass
+with lower probability so that P1 is a more informative signal to player two. As a result,
+to make player two indifferent between T2 and P2, the following condition must hold at the
+24
+
+equilibrium:
+µχ = 1
+7 ⇐⇒ qχ
+1 =
+�7α − 7αχ
+1 − 7αχ − α
+� �
+(1 − α).
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.40
+Probability of Choosing P1
+Probability of P1 Predicted by -CSE and -CE
+-CSE
+-CE / PBE
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.40
+Probability of Choosing P2
+Probability of P2 Predicted by -CSE and -CE
+-CSE
+-CE / PBE
+Figure 5: χ-CSE of the centipede game with altruistic players (α = 0.05)
+To conclude this section, in Figure 5, we plot the probabilities of choosing P1 and P2 at
+χ-CSE when there is a five percent chance that player one is an altruist (i.e., α = 0.05). From
+our analysis above, we can find that both the standard equilibrium theory and χ-CE predict
+selfish player one chooses P1 with probability and player two chooses P2 with probability
+0.14. Moreover, these probabilities are independent of χ. However, χ-CSE predicts when
+players are more cursed, selfish player one is less likely to choose P1. When players are
+sufficiently cursed (χ ≥ 0.91), selfish player one and player two will never pass—i.e., behave
+as if there were no altruistic players.
+4.4
+Sequential Voting over Binary Agendas
+In this section, we apply the concept of χ-CSE to the model of strategic binary amendment
+voting with incomplete information studied by Ordeshook and Palfrey (1988). Let N =
+{1, 2, 3} denote the set of voters. These three voters will vote over three possible alternatives
+in X = {a, b, c}. Voting takes place in a two-stage agenda. In the first stage, voters vote
+between a and b. In the second stage, voters vote between c and the majority rule winner of
+the first stage. The majority rule winner of the second stage is the outcome.
+25
+
+Each voter i has three possible private-value types where Θ ∈ {θ1, θ2, θ3} is the set of
+possible types. Each voter’s type is independently drawn from a common prior distribution
+of types, p. In other words, the probability of a voter being type θk is pk. Each voter’s type
+is their own private information. Each voter has the same type-dependent payoff function,
+which is denoted by u(x|θ) for any x ∈ X and θ ∈ Θ. We summarize the payoff function
+with the following table.
+x
+u(x|θ)
+a
+b
+c
+θ1
+1
+v
+0
+θ
+θ2
+0
+1
+v
+θ3
+v
+0
+1
+Notice that v ∈ (0, 1) is a parameter that measures the intensity of the second ranked
+outcome relative to the top ranked outcome. This intensity parameter, v, is assumed to be
+the same for all types of all voters. Because this is a game of private values, the standard
+χ-CE and the Bayesian Nash equilibrium coincide.
+We use a1
+i (θ) to denote type θ voter i’s action at stage 1. As is standard in majority
+voting games we will focus on the analysis of symmetric pure-strategy equilibria where voters
+do not use weakly dominated strategies. In other words, we will consider at
+i(·) = at
+j(·) for all
+i, j ∈ N, and will drop the subscript.
+In this PBE (and χ-CE) all voters will vote sincerely in equilibrium except for type θ1
+voters at stage 1. To see this, first note that voting insincerely in the last stage is dominated
+and thus eliminated, so all types of voters vote for their preferred alternative on the last
+ballot. Second, voting sincerely in both stages is a dominant strategy for a type θ2 voter,
+who prefers any lottery between b and c to either a or c. Third, voting sincerely in both
+stages is also dominant for a type θ3 voter in the sense that, in the event that neither of the
+other two voters are type θ3, then any lottery between a and c is better than a vote between
+b and c since b (i.e., type θ3’s least preferred alternative) will win.11
+The PBE (and χ-CE) prediction about a type θ1 voter’s strategy at stage 1 is summarized
+in the following claim.
+Claim 3. The symmetric (undominated pure) PBE strategy for type θ1 voters in the first
+stage can be characterized as follows.
+1. a1(θ1) = b is a PBE strategy if and only if v ≥
+p1
+p1+p2.
+11When there is another type θ3 voter, the first ballot does not matter since their most preferred alternative
+c will always win in the second stage.
+26
+
+2. a1(θ1) = a is a PBE strategy if and only if v ≤
+p1
+p1+p3.
+Proof. See Ordeshook and Palfrey (1988).
+Claim 3 shows that, if v is relatively large, only type θ1 voting sophisticatedly for b instead
+of sincerely for a can be supported by a PBE. Conditional on being pivotal, voting for b in
+the first stage guarantees an outcome of b and thus guarantees getting v, while voting for a
+leads to a lottery between a and c. As a result, when v is sufficiently high, a type θ1 voter
+will have an incentive to strategically vote for b to avoid the risk of having c elected in the
+last stage.
+The analysis of a cursed sequential equilibrium is different from the standard cursed
+equilibrium in strategic form because the cursedness affects belief updating over the stages
+of the game, and players anticipate future play of the game. Because of the dynamics and
+the anticipation of future cursed behavior, such cursed behavior at later stages of a game
+can feedback and affect strategic behavior earlier in the game.
+In the context of the two-stage binary amendment strategic voting model, cursed behavior
+and belief updating mean that voters in the first stage use the expected cursed beliefs in
+the second stage to compute the continuation values in the two continuation games of the
+second stage, either a vote between a and c or a vote between b and c. Because they have
+a cursed understanding about the relationship between types and voting in the first stage,
+this affects their predictions about which alternative wins in the second stage, conditional
+on which alternative wins in the first stage.
+It is noteworthy that, given any χ ∈ [0, 1], all voters will still vote sincerely in χ-CSE
+except for type θ1 voters at stage 1. As implied by Proposition 4, a voter in the last stage
+would act as if solving a maximization problem of χ-CE but under an (incorrectly) updated
+belief. Therefore, we can follow the same arguments as solving for the undominated Bayesian
+equilibrium and conclude that type θ2 and θ3 voters as well as type θ1 voters at stage 2 will
+vote sincerely under a χ-CSE.
+Proposition 9 establishes that the set of parameters v and p that can support a χ-CSE
+in which type θ1 voters vote sophisticatedly for b shrinks as χ increases.
+Proposition 9. If a1(θ1) = b can be supported by a symmetric χ-CSE, then it can also be
+supported by a symmetric χ′-CSE for all χ′ ≤ χ.
+Proof. See Appendix B.
+The intuition behind strategic voting over agendas mainly comes from the information
+content of hypothetical pivotal events. However, a cursed voter does not (fully) take such
+27
+
+information into consideration, and thus becomes overly optimistic about his favorite alter-
+native a being elected in the second stage. Therefore, a type θ1 voter has a stronger incentive
+to deviate from sophisticated voting to sincere voting in stage 1 as χ increases.
+Interestingly, the set of v and p that can support a χ-CSE in which type θ1 voters vote
+sincerely for a does not necessarily expand as the level of cursedness becomes higher, as
+characterized in Proposition 10.
+Proposition 10. Given p and v ∈ (0, 1), there exists ˜χ(p, v) such that
+1. If v >
+p1
+p1+p3, then a1(θ1) = a is a χ-CSE strategy if and only if χ ≥ ˜χ(p, v);
+2. If v <
+p1
+p1+p3, then a1(θ1) = a is a χ-CSE strategy if and only if χ ≤ ˜χ(p, v).
+Proof. See Appendix B.
+Thus, Proposition 10 shows that, when χ is sufficiently large, there are some values of
+(v, p) that cannot support sincere voting for type θ1 voters under PBE (and χ-CE) but can
+support it under χ-CSE. Alternatively, there also exist some values of (v, p) that can support
+sincere voting under PBE but fail to support it under χ-CSE when χ is large.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p3
+Sophisticated Voting -CSE when v = 0.7
+ = 0
+ = 0.5
+ = 1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p3
+Sincere Voting -CSE when v = 0.7
+ = 0
+ = 0.5
+ = 1
+Figure 6: χ-CSE for Sophisticated (left) and Sincere (right) Voting When v = 0.7
+To illustrate this, Figure 6 plots the set of p (fixing v = 0.7) that can support a χ-CSE
+for type θ1 voters at stage 1 to vote sophisticatedly for b and sincerely for a. The left panel
+of Figure 6 shows that a sophisticated voting χ-CSE becomes harder to be supported as χ
+28
+
+increases, as indicated by Proposition 9. For example, when p ≡ (p1, p2, p3) = (0.6, 0.3, 0.1),
+type θ1 voters will not vote for second preferred alternative b if χ > 0.18.
+On the other hand, the right panel of Figure 6 shows that, while type θ1 voters who
+sincerely vote for a at stage 1 cannot be supported under PBE when p3 is large, they may
+emerge in a χ-CSE with sufficiently high χ. Also note that when p2 is large, sincere voting
+by type θ1 voters is no longer a χ-CSE with high χ. In such a sincere voting equilibrium, a
+fully rational type θ1 voter knows there will be only one type θ2 voter among the other two
+voters when being pivotal. As a result, whether to sincerely vote for a is determined by the
+ratio of p1 to p3. When p3 is large, sincere voting at stage 1 will likely lead to zero payoff
+for type θ1 voters and thus cannot be a PBE strategy. However, cursed type θ1 voters will
+take the possibility of having two type θ2 voters into account since they are not correctly
+conditioning on pivotality. As a result, when p2 is large, sincere voting at stage 1 will likely
+lead to zero payoff for type θ1 voters, and thus cannot be a χ-CSE strategy with high χ,
+while voting sophisticatedly for b can likely secure a payoff of v.
+4.5
+The Dirty Faces Game
+The dirty faces game was first described by Littlewood (1953) to study the relationship be-
+tween common knowledge and behavior.12 There are several different variants of this game,
+but here we focus on a simplified version, the two-person dirty faces game, which was theo-
+retically analyzed by Fudenberg and Tirole (1991a) and Lin (2022) and was experimentally
+studied by Weber (2001) and Bayer and Chan (2007).
+Let N = {1, 2} be the set of players. For each i ∈ N, let xi ∈ {O, X} represent whether
+player i has a clean face (O) or a dirty face (X). Each player’s face type is independently and
+identically determined by a commonly known probability p = Pr(xi = X) = 1 − Pr(xi = O).
+Once the face types are drawn, each player i can observe the other player’s face x−i but not
+their own face.13 If there is at least one player with a dirty face, a public announcement of
+this fact is broadcast to both players at the beginning of the game. Let ω ∈ {0, 1} denote
+whether there is an announcement or not. If there is an announcement (ω = 1), all players
+are informed there is at least one dirty face but not the identities. When ω = 0, it is common
+knowledge to both players that their faces are clean and the game becomes trivial. Hence,
+in the following, we will focus only on the interesting case where ω = 1.
+12The dirty faces game has also been reframed as the “cheating wives puzzle” (Gamow and Stern, 1958),
+the “cheating husbands puzzle” (Moses et al., 1986), the “muddy children puzzle” (Barwise, 1981) and
+(Halpern and Moses, 1990), and the “red hat puzzle” (Hardin and Taylor, 2008).
+13To fit into the framework, each player’s “type” (their own private information) can be specified as “other
+players’ faces.” That is, θi = x−i.
+29
+
+There are a finite number of T ≥ 2 stages. In each stage, each player i simultaneously
+chooses si ∈ {U, D}. The game ends as soon as either player (or both) chooses D, or at the
+end of stage T in case neither player has chosen D. Actions are revealed at the end of each
+stage. Payoffs depend on own face types and action. If a player chooses D, he will get α > 0
+if he has a dirty face while receive −1 if he has a clean face. We assume that
+pα − (1 − p) < 0 ⇐⇒ 0 < ¯α ≡
+α
+(1 − p)(1 + α) < 1,
+(1)
+where pα − (1 − p) is the expected payoff of D when the belief of having a dirty face is
+p. Thus, Assumption (1) guarantees it is strictly dominated to choose D at stage 1 when
+observing a dirty face. In other words, players will be rewarded when correctly inferring the
+dirty face but penalized when wrongly claiming the dirty face.
+The payoffs are discounted with a common discount factor δ ∈ (0, 1). To summarize,
+conditional on reaching stage t, each player’s payoff function (which depends on their own
+face and action) can be written as:
+ui(si|t, xi = X) =
+�
+�
+�
+δt−1α
+if si = D
+0
+if si = U
+and
+ui(si|t, xi = O) =
+�
+�
+�
+−δt−1
+if si = D
+0
+if si = U.
+Therefore, a two-person dirty faces game is defined by a tuple ⟨p, T, α, δ⟩.
+Since the game ends as soon as some player chooses D, the information sets of the game
+can be specified by the face type the player observes and the stage number. Thus a behavioral
+strategy can be represented as:
+σ : {O, X} × {1, . . . , T} → [0, 1],
+which is a mapping from information sets to the probability of choosing D, where {O, X}
+corresponds to a player’s observation of the other player’s face.
+There is a unique Nash equilibrium. When observing a clean face, a player would im-
+mediately know his face is dirty. Hence, it is strictly dominant to choose D at stage 1 in
+this case. On the other hand, when observing a dirty face, because of Assumption (1), it is
+optimal for the player to choose U at stage 1. However, if the game proceeds to stage 2, the
+player would know his face is dirty because the other player would have chosen D at stage 1 if
+his face were clean and the game would not have reached stage 2. This result is independent
+of the payoffs, the timing, the discount factor, and the (prior) probability of having a dirty
+face. The only assumption for this argument is common knowledge of rationality.
+30
+
+Alternatively, when players are “cursed,” they are not able to make perfect inferences
+from the other player’s actions. Specifically, since a cursed player has incorrect perceptions
+about the relationship between the other player’s actions and their private information after
+seeing the other player choose U in stage 1, a cursed player does not believe they have a dirty
+face for sure. At the extreme when χ = 1, fully cursed players never update their beliefs.
+In the following, we will compare the predictions of the standard χ-CE and the χ-CSE. A
+surprising result is that there is always a unique χ-CE, but there can be multiple χ-CSE.
+For the sake of simplicity, we will focus on the characterization of pure strategy equi-
+librium in the following analysis. Since the game ends when some player chooses D, we
+can equivalently characterize a stopping strategy as a mapping from the observed face type
+to a stage in {1, 2, . . . , T, T + 1} where T + 1 corresponds to the strategy of never stop-
+ping. Furthermore, both χ-CE and χ-CSE will be symmetric because if players were to stop
+at different stages, least one of the players would have a profitable deviation. Finally, we
+use ˆσχ(x−i) and ˜σχ(x−i) to denote the equilibrium stopping strategies of χ-CE and χ-CSE,
+respectively.
+We characterize the χ-CE in Proposition 11. Since χ-CE is defined for simultaneous
+move Bayesian games, to solve for the χ-CE, we need to look at the corresponding normal
+form where players simultaneously choose {1, 2, . . . , T, T + 1} given the observed face type.
+Proposition 11. The χ-cursed equilibrium can be characterized as follows.
+1. If χ > ¯α, the only χ-CE is that both players choose:
+ˆσχ(O) = 1
+and
+ˆσχ(X) = T + 1.
+2. If χ < ¯α, the only χ-CE is that both players choosing
+ˆσχ(O) = 1
+and
+ˆσχ(X) = 2.
+Proof. See Appendix B.
+Proposition 11 shows that χ-CE makes an extreme prediction—when observing a dirty
+face, players would either choose D at stage 2 (the equilibrium prediction) or never choose
+D. Moreover, the prediction of χ-CE is unique for χ ̸= ¯α. As characterized in the next
+Proposition 12, for extreme values of χ, the prediction of χ-CSE coincides with χ-CE. But
+for intermediate values of χ, there can be multiple χ-CSE.
+Proposition 12. The pure strategy χ-CSE can be characterized as follows.
+31
+
+1. ˜σχ(O) = 1 for all χ ∈ [0, 1].
+2. Both players choosing ˜σχ(X) = T + 1 is a χ-CSE if and only if χ ≥ ¯α
+1
+T +1.
+3. Both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if χ ≤ ¯α.
+4. For any 3 ≤ t ≤ T, both players choosing ˜σχ(X) = t is a χ-CSE if and only if
+�1 − κ(χ)
+1 − p
+�
+1
+t−2
+≤ χ ≤ ¯α
+1
+t−1
+where
+κ(χ) ≡ [(1 + α)(1 + δχ) − αδ] −
+�
+[(1 + α)(1 + δχ) − αδ]2 − 4δχ(1 + α)
+2δχ(1 + α)
+.
+Proof. See Appendix B.
+Illustrative Example
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0
+1
+2
+3
+4
+5
+6
+-CE Stopping Periods (When Observing a Dirty Face)
+-CE of Two-Person Dirty Faces Games
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0
+1
+2
+3
+4
+5
+6
+-CSE Stopping Periods (When Observing a Dirty Face)
+-CSE of Two-Person Dirty Faces Games
+Figure 7: χ-CE vs. χ-CSE When (α, δ, p, T) =
+� 1
+4, 4
+5, 2
+3, 5
+�
+In order to illustrate the sharp contrast between the predictions of χ-CE and χ-CSE,
+here we consider an illustrative example where α = 1/4, δ = 4/5, p = 2/3 and the horizon
+of the game is T = 5. As characterized by Proposition 11, χ-CE predicts players will choose
+ˆσχ(X) = 2 if χ ≤ ¯α = 0.6; otherwise, they will choose ˆσχ(X) = 6, i.e., they never choose
+32
+
+D when observing a dirty face. As demonstrated in the left panel of Figure 7, χ-CE is
+(generically) unique and it predicts players will either behave extremely sophisticated or
+unresponsive to the other player’s action at all.
+In contrast, as characterized by Proposition 12, there can be multiple χ-CSE. As shown
+in the right panel of Figure 7, when χ ≤ ¯α = 0.6, both players stopping at stage 2 is still
+an equilibrium, but it is not unique except for very low values of χ. For 0.168 ≤ χ ≤ 0.505,
+both players stopping at stage 3 is also a χ-CSE, and for 0.505 ≤ χ ≤ 0.6, there are three
+pure strategy χ-CSE where both players stop at stage 2, 3, or 4, respectively.
+The existence of multiple χ-CSE in which both players stop at t > 2 highlights a player’s
+learning process in a multi-stage game, which does not happen in strategic form cursed
+equilibrium. In the strategic form, a player has no opportunity to learn about the other
+player’s type in middle stages. Thus, when level of cursedness is not low enough to support
+a χ-CE with stopping at stage 2, both players would never stop. However, in a χ-CSE of
+the multi-stage game, a cursed player would still learn about his own face being dirty as
+the game proceeds, even though he might not be confident enough to choose D at stage 2.
+If χ is not too large, the expected payoff of choosing D would eventually become positive
+at some stage before the last stage T.14 For some intermediate values of χ, there might
+be multiple stopping stages which yield positive expected payoffs. In this case, the dirty
+faces game becomes a special type of coordination games where both players coordinate on
+stopping strategies, resulting in the existence of multiple χ-CSE.15
+5
+Concluding Remarks
+In this paper, we formally developed Cursed Sequential Equilibrium, which extends the
+strategic form cursed equilibrium (Eyster and Rabin, 2005) to multi-stage games, and il-
+lustrated the new equilibrium concept with a series of applications. While the standard
+CE has no bite in private value games, we show that cursed beliefs can actually have
+significant consequences for dynamic private value games. In the private value games we
+consider, our cursed sequential equilibrium predicts (1) under-contribution caused by under-
+communication in the public goods game with communication, (2) low passing rate in the
+presence of altruistic players in the centipede game, and (3) less sophisticated voting in the
+14The upper bound of the inequality in Proposition 12 characterizes the stages at which stopping yields
+positive expected payoffs.
+15Note that players with low levels of cursedness would not coordinate on stopping at late stages since the
+discount factor shrinks the informative value of waiting (i.e., both choosing U). This result is characterized
+by the lower bound of the inequality in Proposition 12.
+33
+
+sequential two-stage binary agenda game. We also illustrate the distinction between CE and
+CSE in some non-private value games. In simple signaling games, χ-CSE implies refinements
+of pooling equilibria that are not captured by traditional belief-based refinements (or χ-CE),
+and are qualitatively consistent with some experimental evidence. Lastly, we examine the
+dirty face game, showing that the CSE further expands the set of equilibrium and predicts
+stopping in middle stages of the game. We summarize our findings from these applications
+in Table 4.
+Table 4: Summary of Findings in Section 4
+Private-Value
+Game
+χ-CE vs. BNE
+χ-CSE vs. χ-CE
+Signaling Games with
+Pooling Equilibrium
+No
+̸=
+χ-CSE ⊂ χ-CE
+Public Goods Game
+with Communication
+Yes
+=
+̸=
+Centipede Game
+with Altruists
+Yes
+=
+̸=
+Sequential Voting
+Game
+Yes
+=
+̸=
+Dirty Faces Game
+No
+̸=
+̸=
+The applications we consider are only a small sample of the possible dynamic games where
+CSE could be usefully applied. One prominent class of problems where it would be interesting
+to study the dynamic effects of cursedness is social learning. For example, in the standard
+information cascade model of Bikhchandani et al. (1992), we conjecture that the effect would
+be to delay the formation of an information cascade because players will partially neglect
+the information content of prior decision makers. Laboratory experiments report evidence
+that subjects underweight the information contained in prior actions relative to their own
+signal (Goeree et al., 2007). A related class of problems involves information aggregation
+through sequential voting and bandwagon effects (Callander, 2007; Ali et al., 2008; Ali and
+Kartik, 2012). A natural conjecture is that CSE will impede information transmission in
+committees and juries as later voters will under-appreciate the information content of the
+decisions by early voters. This would dampen bandwagon effects. The centipede example
+34
+
+we studied suggests than CSE might have broader implications for behavior in reputation-
+building games, such as the finitely repeated prisoner’s dilemma or entry deterrence games
+such as the chain store paradox.
+As a final remark, our analysis of applications of χ-CSE suggests some interesting exper-
+iments. For instance, χ-CSE predicts in the public goods game with communication, when
+either N or K increases, pre-play communication will be less effective, while the prediction
+of sequential equilibrium and χ-CE is independent of N and K. In other words, in an exper-
+iment where N and K are manipulated, a significant treatment effect in this direction would
+provide evidence supporting χ-CSE. Also, χ-CSE makes qualitatively testable predictions
+in the sequential voting games and the dirty faces games, which have not been extensively
+studied in laboratory experiments. In the sequential voting game, it would be interesting to
+test how sensitive strategic (vs. sincere) voting behavior is to preference intensity (v) and
+the type distribution. In the dirty faces game, it would be interesting to design an exper-
+iment to identify the extent to which deviations from sequential equilibrium are related to
+the coordination problem that arises in χ-CSE.
+35
+
+References
+Ali, N., J. K. Goeree, N. Kartik, and T. R. Palfrey (2008): “Information Aggre-
+gation in Standing and Ad Hoc Committees,” American Economic Review, 98, 181–186.
+Ali, N. and N. Kartik (2012): “Herding with Collective Preferences,” Economic Theory,
+51, 601–626.
+Barwise, J. (1981): “Scenes and other situations,” Journal of Philosophy, 78, 369–397.
+Bayer, R. C. and M. Chan (2007): “The dirty faces game revisited,” Tech. rep., Univer-
+sity of Adelaide, School of Economics.
+Bazerman, M. H. and W. F. Samuelson (1983): “I won the auction but don’t want
+the prize,” Journal of Conflict Resolution, 27, 618–634.
+Bikhchandani, S., D. Hirshleifer, and I. Welch (1992): “A theory of fads, fashion,
+custom, and cultural change as informational cascades,” Journal of Political Economy,
+100, 992–1026.
+Brandts, J. and C. A. Holt (1993): “Adjustment patterns and equilibrium selection in
+experimental signaling games,” International Journal of Game Theory, 22, 279–302.
+Callander, S. (2007): “Bandwagons and Momentum in Sequential Voting,” Review of
+Economic Studies, 74, 653–684.
+Camerer, C. F., S. Nunnari, and T. R. Palfrey (2016): “Quantal Response and
+Non-equilibrium Beliefs Explain Overbidding in Maximum Value Auctions,” Games and
+Economic Behavior, 98, 243–263.
+Capen, E. C., R. V. Clapp, and W. M. Campbell (1971): “Competitive bidding in
+high-risk situations,” Journal of Petroleum Technology, 23, 641–653.
+Carrillo, J. and T. R. Palfrey (2009): “The Compromise Game: Two-Sided Adverse
+Selection in the Laboratory,” American Economic Journal: Microeconomics, 1, 151–181.
+Carrillo, J. D. and T. R. Palfrey (2011): “No trade,” Games and Economic Behavior,
+71, 66–87.
+Cho, I.-K. and D. M. Kreps (1987): “Signaling games and stable equilibria,” Quarterly
+Journal of Economics, 102, 179–221.
+Cohen,
+S.
+and
+S.
+Li (2022):
+“Sequential Cursed Equilibrium,”
+arXiv preprint
+arXiv:2212.06025.
+Dyer, D., J. H. Kagel, and D. Levin (1989): “A comparison of naive and experienced
+bidders in common value offer auctions: A laboratory analysis,” Economic Journal, 99,
+108–115.
+36
+
+Eckel, C. C. and C. A. Holt (1989): “Strategic Voting in Agenda Controlled Committee
+Experiments,” American Economic Review, 79, 763–773.
+Eyster, E. and M. Rabin (2005): “Cursed equilibrium,” Econometrica, 73, 1623–1672.
+Forsythe, R. E., R. M. Isaac, and T. R. Palfrey (1989): “Theories and Tests of
+Blind Bidding in Sealed-bid Auctions,” Rand Journal of Economics, 20, 214–238.
+Fudenberg, D. and J. Tirole (1991a): Game theory, MIT press.
+——— (1991b): “Perfect Bayesian equilibrium and sequential equilibrium,” Journal of Eco-
+nomic Theory, 53, 236–260.
+Gamow, G. and M. Stern (1958): “Forty unfaithful wives,” Puzzle Math, 20–23.
+Goeree, J. K., T. R. Palfrey, B. W. Rogers, and R. D. McKelvey (2007): “Self-
+correcting information cascades,” Review of Economic Studies, 74, 733–762.
+Guarnaschelli, S., R. D. McKelvey, and T. R. Palfrey (2000): “An experimental
+study of jury decision rules,” American Political Science Review, 94, 407–423.
+Halpern, J. Y. and Y. Moses (1990): “Knowledge and common knowledge in a dis-
+tributed environment,” Journal of the ACM (JACM), 37, 549–587.
+Hardin, C. S. and A. D. Taylor (2008): “An introduction to infinite hat problems,”
+The Mathematical Intelligencer, 30, 20–25.
+Holt, C. A. and R. Sherman (1994): “The loser’s curse,” American Economic Review,
+84, 642–652.
+Ivanov, A., D. Levin, and M. Niederle (2010): “Can Relaxation of Beliefs Rationalize
+the Winner’s Curse,” Econometrica, 78, 1435–1452.
+Jehiel, P. (2005): “Analogy-based expectation equilibrium,” Journal of Economic Theory,
+123, 81–104.
+Jehiel, P. and F. Koessler (2008): “Revisiting games of incomplete information with
+analogy-based expectations,” Games and Economic Behavior, 62, 533–557.
+Kagel, J. H. and D. Levin (1986): “The winner’s curse and public information in com-
+mon value auctions,” American Economic Review, 894–920.
+——— (2009): “Common value auctions and the winner’s curse,” in Common Value Auctions
+and the Winner’s Curse, Princeton University Press.
+Kagel, J. H., D. Levin, R. C. Battalio, and D. J. Meyer (1989): “First-price
+common value auctions: bidder behavior and the “Winner’s Curse”,” Economic Inquiry,
+27, 241–258.
+Kreps, D. M. (1990): A course in microeconomic theory, Princeton university press.
+37
+
+Kreps, D. M. and R. Wilson (1982): “Sequential Equilibria,” Econometrica, 50, 863–
+894.
+Levine, M. E. and C. R. Plott (1977): “Agenda influence and its implications,” Virginia
+Law Review, 561–604.
+Lin, P.-H. (2022): “Cognitive Hierarchies in Multi-Stage Games of Incomplete Informa-
+tion,” arXiv preprint arXiv:2208.11190.
+Lin, P.-H. and T. R. Palfrey (2022): “Cognitive Hierarchies in Extensive Form Games,”
+Caltech Social Science Working Paper.
+Lind, B. and C. R. Plott (1991): “The winner’s curse: experiments with buyers and
+with sellers,” American Economic Review, 81, 335–346.
+Littlewood, J. E. (1953): A Mathematician’s Miscellany, London, England: Meuthen &
+Co. Ltd.
+McKelvey, R. D. and T. R. Palfrey (1992): “An experimental study of the centipede
+game,” Econometrica, 803–836.
+——— (1998): “Quantal response equilibria for extensive form games,” Experimental Eco-
+nomics, 1, 9–41.
+Moses, Y., D. Dolev, and J. Y. Halpern (1986): “Cheating husbands and other
+stories: a case study of knowledge, action, and communication,” Distributed Computing,
+1, 167–176.
+Ordeshook, P. C. and T. R. Palfrey (1988): “Agendas, strategic voting, and signaling
+with incomplete information,” American Journal of Political Science, 441–466.
+Palfrey, T. R. and H. Rosenthal (1991): “Testing for effects of cheap talk in a public
+goods game with private information,” Games and Economic Behavior, 3, 183–220.
+Palfrey, T. R., H. Rosenthal, and N. Roy (2017): “How Cheap Talk Enhances
+Efficiency in Threshold Public Goods Games,” Games and Economic Behavior, 101, 234–
+259.
+Plott, C. R. and M. E. Levine (1978): “A Model of Agenda Influence on Committee
+Decisions,” American Economic Review, 68, 146–160.
+Rogers, B. W., T. R. Palfrey, and C. F. Camerer (2009): “Heterogeneous quantal
+response equilibrium and cognitive hierarchies,” Journal of Economic Theory, 144, 1440–
+1467.
+Samuelson, W. F. and M. H. Bazerman (1985): “Negotiation under the winner’s
+curse,” Research in experimental economics, 3, 105–138.
+Søvik, Y. (2009): “Strength of dominance and depths of reasoning—An experimental
+study,” Journal of Economic Behavior & Organization, 70, 196–205.
+38
+
+Weber, R. A. (2001): “Behavior and learning in the “dirty faces” game,” Experimental
+Economics, 4, 229–242.
+39
+
+A
+Omitted Proofs of Section 2 and 3
+Proof of Lemma 1
+By definition 1, for any (µ, σ) ∈ Ψχ, any history ht−1, any player i and any type profile
+θ = (θi, θ−i),
+�
+θ′
+−i
+µi(θ′
+−i|ht−1, θi)[χ¯σ−i(at
+−i|ht−1, θi) + (1 − χ)σ−i(at
+−i|ht−1, θ′
+−i)]
+= χ
+�
+��
+θ′
+−i
+µi(θ′
+−i|ht−1, θi)
+�
+�
+�
+��
+�
+=1
+¯σ−i(at
+−i|ht−1, θi) + (1 − χ)
+�
+��
+θ′
+−i
+µi(θ′
+−i|ht−1, θi)σ−i(at
+−i|ht−1, θ′
+−i)
+�
+�
+�
+��
+�
+=¯σ−i(at
+−i|ht−1,θi)
+= ¯σ−i(at
+−i|ht−1, θi).
+Therefore, since (µ, σ) ∈ Ψχ, with some rearrangement, it follows that
+µi(θ−i|ht, θi) =
+µi(θ−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ−i, θi)
+�
+θ′
+−i∈Θ−i µi(θ′
+−i|ht−1, θi)σχ
+−i(at
+−i|ht−1, θ′
+−i, θi)
+= µi(θ−i|ht−1, θi)[χ¯σ−i(at
+−i|ht−1, θi) + (1 − χ)σ−i(at
+−i|ht−1, θ−i)]
+¯σ−i(at
+−i|ht−1, θi)
+= χµi(θ−i|ht−1, θi) + (1 − χ)
+�
+µi(θ−i|ht−1, θi)σ−i(at
+−i|ht−1, θ−i)
+�
+θ′
+−i µi(θ′
+−i|ht−1, θi)σ−i(at
+−i|ht−1, θ′
+−i)
+�
+.
+This completes the proof. ■
+Proof of Proposition 1
+The proof is similar to the proof for sequential equilibrium and proceeds in three steps. First,
+for any finite multi-stage games with observed actions, Γ, we construct an ϵ-perturbed game
+Γϵ that is identical to Γ but every player in every information set has to play any available
+action with probability at least ϵ. Second, we defined a cursed best-response correspondence
+for Γϵ and prove that the correspondence has a fixed point by Kakutani’s fixed point theorem.
+Finally, in step 3, we use a sequence of fixed points in perturbed games, with ϵ converging
+to 0, where the limit of this sequence is a χ-CSE.
+Step 1:
+Let Γϵ be a game identical to Γ but for each player i ∈ N, player i must play any available
+action in every information set Ii = (θi, ht) with probability at least ϵ where ϵ <
+1
+�n
+j=1 |Aj|.
+Let Σϵ = ×n
+j=1Σϵ
+j be set of feasible behavioral strategy profiles for players in the perturbed
+game Γϵ. For any behavioral strategy profile σ ∈ Σϵ, let µχ(·) ≡ (µχ
+i (·))n
+i=1 be the belief
+system induced by σ via χ-cursed Bayes’ rule. That is, for each player i ∈ N, information
+40
+
+set Ii = (θi, ht) where ht = (ht−1, at) and type profile θ−i ∈ Θ−i,
+µχ
+i (θ−i|ht, θi) = χµχ
+i (θ−i|ht−1, θi) +
+(1 − χ)
+�
+µχ
+i (θ−i|ht−1, θi)σ−i(at
+−i|ht−1, θ−i)
+�
+θ′
+−i∈Θ−i µχ
+i (θ′
+−i|ht−1, θi)σ−i(at
+−i|ht−1, θ′
+−i)
+�
+.
+Notice that the χ-cursed Bayes’ rule is only defined on the framework of multi-stage games
+with observed actions. As σ is fully mixed, the belief system is uniquely pinned down.
+Finally, let Bϵ : Σϵ ⇒ Σϵ be the cursed best response correspondence which maps any
+behavioral strategy profile σ ∈ Σϵ to the set of ϵ-constrained behavioral strategy profiles
+˜σ ∈ Σϵ that are best replies given the belief system µχ(·).
+Step 2:
+Next, fix any 0 < ϵ <
+1
+�n
+j=1 |Aj| and show that Bϵ has a fixed point by Kakutani’s fixed
+point theorem. We check the conditions of the theorem:
+1. It is straightforward that Σϵ is compact and convex.
+2. For any σ ∈ Σϵ, as µχ(·) is uniquely pinned down by χ-cursed Bayes’ rule, it is straight-
+forward that Bϵ(σ) is non-empty and convex.
+3. To verify that Bϵ has a closed graph, take any sequence of ϵ-constrained behavioral
+strategy profiles {σk}∞
+k=1 ⊆ Σϵ such that σk → σ ∈ Σϵ as k → ∞, and any sequence
+{˜σk}∞
+k=1 such that ˜σk ∈ Bϵ(σk) for any k and ˜σk → ˜σ. We want to prove that ˜σ ∈ Bϵ(σ).
+Fix any player i ∈ N and information set Ii = (θi, ht). For any σ ∈ Σϵ, recall that
+σχ
+−i(·) is player i’s χ-cursed perceived behavioral strategies of other players induced by
+σ. Specifically, for any type profile θ ∈ Θ, non-terminal history ht−1 and action profile
+at
+−i ∈ A−i(ht−1),
+σχ
+−i(at
+−i|ht−1, θ−i, θi) = χ¯σ−i(at
+−i|ht−1, θi) + (1 − χ)σ−i(at
+−i|ht−1, θ−i).
+Additionally, recall that ρχ
+i (·) is player i’s belief about the terminal nodes (conditional
+on the history and type profile), which is also induced by σ. Since µχ(·) is continuous
+in σ we have thaat σχ
+−i(·) and ρχ
+i (·) are also continuous in σ.
+We further define
+Sk
+Ii ≡
+�
+σ′
+i ∈ Σϵ
+i : σ′
+i( · |Ii) = ˜σk
+i ( · |Ii)
+�
+,
+SIi ≡ {σ′
+i ∈ Σϵ
+i : σ′
+i( · |Ii) = ˜σi( · |Ii)} .
+Since ˜σk ∈ Bϵ(σk), for any σ′
+i ∈ Σϵ
+i, we can obtain that
+41
+
+max
+σ′′
+i ∈Sk
+Ii
+�
+�
+�
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µχ
+i [σk](θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i[σk], σ′′
+i )ui(hT, θi, θ−i)
+�
+�
+�
+≥
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µχ
+i [σk](θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i[σk], σ′
+i)ui(hT, θi, θ−i).
+By continuity, as we take limits on both sides, we can obtain that
+max
+σ′′
+i ∈SIi
+�
+�
+�
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µχ
+i [σ](θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i[σ], σ′′
+i )ui(hT, θi, θ−i)
+�
+�
+�
+≥
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µχ
+i [σ](θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i[σ], σ′
+i)ui(hT, θi, θ−i).
+Therefore, ˜σ ∈ Bϵ(σ).
+By Kakutani’s fixed point theorem, Bϵ has a fixed point.
+Step 3:
+For any ϵ, let σϵ be a fixed point of Bϵ and µϵ be the belief system induced by σϵ via
+χ-cursed Bayes’ rule. We combine these two components and let (µϵ, σϵ) be the induced
+assessment. We now consider a sequence of ϵ → 0, where {(µϵ, σϵ)} is the corresponding
+sequence of assessments.
+By compactness and the finiteness of Γ, the Bolzano-Weierstrass theorem guarantees
+the existence of a convergent subsequence of the assessments. As ϵ → 0, let (µϵ, σϵ) →
+(µ∗, σ∗). By construction, the limit assessment (µ∗, σ∗) satisfies χ-consistency and sequential
+rationality. Hence, (µ∗, σ∗) is a χ-CSE. ■
+Proof of Proposition 2
+To prove Φ(χ) is upper hemi-continuous in χ, consider any sequence of {χk}∞
+k=1 such that
+χk → χ∗ ∈ [0, 1], and any sequence of CSE, {(µk, σk)}, such that (µk, σk) ∈ Φ(χk) for all
+k. Let (µ∗, σ∗) be the limit assessment, i.e., (µk, σk) → (µ∗, σ∗). We need to show that
+(µ∗, σ∗) ∈ Φ(χ∗).
+To simplify notation, for any player i ∈ N, any information set Ii = (ht, θi), any σ′
+i ∈ Σi,
+and any σ ∈ Σ, the expected payoff under the belief system µχ(·) induced by σ is denoted
+as:
+Eµχ[σ]
+�
+ui(σ′
+i, σ−i|ht, θi)
+�
+≡
+�
+θ−i∈Θ−i
+�
+hT ∈HT
+µχ
+i (θ−i|ht, θi)ρχ
+i (hT|ht, θ, σχ
+−i, σ′
+i)ui(hT, θi, θ−i).
+Suppose (µ∗, σ∗) ̸∈ Φ(χ∗). Then there exists some player i ∈ N, some information set
+42
+
+Ii = (ht, θi), some σ′
+i ∈ Σi, and some ϵ > 0 such that
+Eµχ∗[σ∗]
+�
+ui(σ′
+i, σ∗
+−i|ht, θi)
+�
+− Eµχ∗[σ∗]
+�
+ui(σ∗
+i , σ∗
+−i|ht, θi)
+�
+> ϵ.
+(A)
+Since µχ(·) is continuous in χ, it follows that for any strategy profile σ, σχ
+−i(·) and ρχ
+i (·) are
+both continuous in χ. As a result, there exists a sufficiently large M1 such that for every
+k ≥ M1,
+����Eµχk[σk]
+�
+ui(σk
+i , σk
+−i|ht, θi)
+�
+− Eµχ∗[σ∗]
+�
+ui(σ∗
+i , σ∗
+−i|ht, θi)
+� ���� < ϵ
+3.
+(B)
+Similarly, there exists a sufficiently large M2 such that for every k ≥ M2,
+����Eµχk[σk]
+�
+ui(σ′
+i, σk
+−i|ht, θi)
+�
+− Eµχ∗[σ∗]
+�
+ui(σ′
+i, σ∗
+−i|ht, θi)
+� ���� < ϵ
+3.
+(C)
+Therefore, for any k ≥ max{M1, M2}, inequalities (A), (B) and (C) imply:
+Eµχk[σk]
+�
+ui(σ′
+i, σk
+−i|ht, θi)
+�
+− Eµχk[σk]
+�
+ui(σk
+i , σk
+−i|ht, θi)
+�
+> ϵ
+3,
+implying that σ′
+i is a profitable deviation for player i at information set Ii = (ht, θi), which
+contradicts (µk, σk) ∈ Φ(χk). Therefore, (µ∗, σ∗) ∈ Φ(χ∗), as desired. ■
+Proof of Proposition 3
+Fix any χ ∈ [0, 1] and let (µ, σ) be a χ-consistent assessment.
+We prove the result by
+contradiction. Suppose (µ, σ) does not satisfy χ-dampened updating property. Then there
+exists i ∈ N, ˜θ ∈ Θ and a non-terminal history ht such that
+µi(θ−i|ht, ˜θi) < χµi(θ−i|ht−1, ˜θi).
+Since (µ, σ) is χ-consistent, there exists a sequence {(µk, σk)} ⊆ Ψχ such that (µk, σk) →
+(µ, σ) as k → ∞. By Lemma 1, we know for this i, ˜θ and ht,
+µk
+i (˜θ−i|ht, ˜θi) =χµk
+i (˜θ−i|ht−1, ˜θi) + (1 − χ)
+�
+µk
+i (˜θ−i|ht−1, ˜θi)σk
+−i(at
+−i|ht−1, ˜θ−i)
+�
+θ′
+−i µk
+i (θ′
+−i|ht−1, ˜θi)σk
+−i(at
+−i|ht−1, θ′
+−i)
+�
+≥χµk
+i (˜θ−i|ht−1, ˜θi).
+As we take the limit k → ∞ on both sides, we can obtain that
+µi(˜θ−i|ht, ˜θi) = lim
+k→∞ µk
+i (˜θ−i|ht, ˜θi) ≥ lim
+k→∞ χµk
+i (˜θ−i|ht−1, ˜θi) = χµi(˜θ−i|ht−1, ˜θi),
+which yields a contradiction. ■
+43
+
+Proof of Corollary 2
+We prove the statement by induction on t. For t = 1, by Proposition 3,
+µi(θ−i|h1, θi) ≥ χµi(θ−i|h∅, θi) = χF(θ−i|θi).
+Next, suppose there is t′ such that the statement holds for all 1 ≤ t ≤ t′ − 1. At stage t′, by
+Proposition 3 and the induction hypothesis, we can find that
+µi(θ−i|ht′, θi) ≥ χµi(θ−i|ht′−1, θi) ≥ χ
+�
+χt′−1F(θ−i|θi)
+�
+= χt′F(θ−i|θi).
+This completes the proof. ■
+44
+
+B
+Omitted Proofs of Section 4
+4.1 Pooling Equilibria in Signaling Games
+Proof of Proposition 5
+Let the assessment (µ, σ) be a pooling χ-CSE. We want to show that for any χ′ ≤ χ, the
+assessment (µ, σ) is also a χ′-CSE. Consider any non-terminal history ht−1, any player i, any
+at
+i ∈ Ai(ht−1) and any θ ∈ Θ. We can first observe that
+¯σ−i(at
+−i|ht−1, θi) =
+�
+θ′
+−i
+µi(θ′
+−i|ht−1, θi)σ−i(at
+−i|ht−1, θ′
+−i)
+= σ−i(at
+−i|ht−1, θ−i)
+�
+��
+θ′
+−i
+µi(θ′
+−i|ht−1, θi)
+�
+�
+= σ−i(at
+−i|ht−1, θ−i)
+where the second equality holds because σ is a pooling behavioral strategy profile, so σ−i is
+independent of other players’ types. For this pooling χ-CSE, let Gσ be the set of on-path
+histories and ˜Gσ be the set of off-path histories. We can first show that for every h ∈ Gσ,
+i ∈ N and θ ∈ Θ,
+µi(θ−i|h, θi) = F(θ−i|θi).
+This can be shown by induction on t. For t = 1, any h1 = (h∅, a1) and any θ ∈ Θ, by Lemma
+1, we can obtain that
+µi(θ−i|h1, θi) =χµi(θ−i|h∅, θi) + (1 − χ)
+�µi(θ−i|h∅, θi)σ−i(a1
+−i|h∅, θ−i)
+¯σ−i(a1
+−i|h∅, θi)
+�
+=χF(θ−i|θi) + (1 − χ)F(θ−i|θi)
+�σ−i(a1
+−i|h∅, θ−i)
+¯σ−i(a1
+−i|h∅, θi)
+�
+�
+��
+�
+=1
+=F(θ−i|θi).
+Now, suppose there is t′ such that the statement holds for 1 ≤ t ≤ t′ − 1. At stage t′ and
+ht′ = (ht′−1, at′) ∈ Gσ, by Lemma 1 and the induction hypothesis, we can again obtain that
+the posterior belief is the prior belief
+µi(θ−i|ht′, θi) =χµi(θ−i|ht′−1, θi) + (1 − χ)
+�
+µi(θ−i|ht′−1, θi)σ−i(at′
+−i|ht′−1, θ−i)
+¯σ−i(at′
+−i|ht′−1, θi)
+�
+=χF(θ−i|θi) + (1 − χ)F(θ−i|θi)
+�
+σ−i(at′
+−i|ht′−1, θ−i)
+¯σ−i(at′
+−i|ht′−1, θi)
+�
+�
+��
+�
+=1
+=F(θ−i|θi).
+45
+
+Therefore, we have shown that players will not update their beliefs at every on-path informa-
+tion set, so the belief system is independent of χ. Finally, for any off-path history ht ∈ ˜Gσ,
+by Proposition 3, we can find that the belief system satisfies for any θ ∈ Θ,
+µi(θ−i|ht, θi) ≥ χµi(θ−i|ht−1, θi) ≥ χ′µi(θ−i|ht−1, θi),
+implying that when χ′ ≤ χ, µ will still satisfy the dampened updating property. Therefore,
+(µ, σ) remains a χ′-CSE. This completes the proof. ■
+Proof of Claim 1
+First observe that after player 1 chooses B, it is strictly optimal for player 2 to choose R
+for all beliefs µ2(θ1|B), and after player 1 chooses A, it is optimal for player 2 to choose L
+if and only if
+2µ2(θ1|A) + [1 − µ2(θ1|A)] ≥ 4µ2(θ1|A) ⇐⇒ µ2(θ1|A) ≤ 1/3.
+Equilibrium 1.
+If both types of player 1 choose A, then µ2(θ1|A) = 1/4, so it is optimal for player 2 to
+choose L. Given a(A) = L and a(B) = R, it is optimal for both types of player 1 to choose
+A as 2 > 1. Hence m(θ1) = m(θ2) = A, a(A) = L and a(B) = R is a pooling χ-CSE for any
+χ ∈ [0, 1].
+Equilibrium 2.
+In order to support m(θ1) = m(θ2) = B to be an equilibrium, player 2 has to choose R at
+the off-path information set A, which is optimal if and onlly if µ2(θ1|A) ≥ 1/3. In addition,
+by Proposition 3, we know in a χ-CSE, the belief system satisfies
+µ2(θ2|A) ≥ 3
+4χ ⇐⇒ µ2(θ1|A) ≤ 1 − 3
+4χ.
+Therefore, the belief system has to satisfy that µ2(θ1|A) ∈
+� 1
+3, 1 − 3
+4χ
+�
+, which requires χ ≤
+8/9.
+Finally, it is straightforward to verify that for any µ ∈
+� 1
+3, 1 − 3
+4χ
+�
+, µ2(θ1|A) = µ satisfies
+χ-consistency. Suppose type θ1 player 1 chooses A with probability p and type θ2 player 1
+chooses A with probability q where p, q ∈ (0, 1). Given this behavioral strategy profile for
+player 1, by Lemma 1, we have:
+µ2(θ1|A) = 1
+4χ + (1 − χ)
+�
+p
+p + 3q
+�
+.
+In other words, as long as (p, q) satisfies
+q =
+�4 − 4µ − 3χ
+12 − 3χ
+�
+p,
+46
+
+we can find that µ2(θ1|A) = µ. Therefore, if {(pk, qk)} → (0, 0) such that
+qk =
+�4 − 4µ − 3χ
+12 − 3χ
+�
+pk,
+then µk
+2(θ1|A) = µ for all k. Hence, limk→∞ µk
+2(θ1|A) = µ, suggesting that µ2(θ1|A) = µ is
+indeed χ-consistent. This completes the proof. ■
+Proof of Proposition 6
+Here we provide a characterization of χ-CSE of Game 1 and Game 2. For the analysis of
+both games, we denote µI ≡ µ2(θ1|m = I) and µS ≡ µ2(θ1|m = S).
+Analysis of Game BH 3.
+At information set S, given µS, the expected payoffs of C, D, E are 90µS, 30 − 15µS and
+15, respectively. Therefore, for any µS, E is never a best response. Moreover, C is the best
+response if and only if 90µS ≥ 30 − 15µS or µS ≥ 2/7. Similarly, at information set I, given
+µI, the expected payoffs of C, D, E are 30, 45 − 45µI and 15, respectively. Therefore, E is
+strictly dominated, and C is the best response if and only if 30 ≥ 45 − 45µI or µI ≥ 1/3.
+Now we consider four cases.
+Case 1 [m(θ1) = I, m(θ2) = S]:
+By Lemma 1, µI = 1 − χ/2 and µS = χ/2. Moreover, since µI = 1 − χ/2 ≥ 1/2 for any
+χ, player 2 will choose C at information set I. To support this equilibrium, player 2 has to
+choose C at information set S. In other words, [(I, S); (C, C)] is separating χ-CSE if and
+only if µS ≥ 2/7 or χ ≥ 4/7.
+Case 2 [m(θ1) = S, m(θ2) = I]:
+By Lemma 1, µI = χ/2 and µS = 1 − χ/2. Because µS ≥ 1 − χ/2 ≥ 1/2, it is optimal
+for player 2 to choose C at information set S. To support this as an equilibrium, player 2
+has to choose D at information set I. Yet, in this case, type θ2 player 1 will deviate to S.
+Therefore, this profile cannot be supported as an equilibrium.
+Case 3 [m(θ1) = I, m(θ2) = I]:
+Since player 1 follows a pooling strategy, player 2 will not update his belief at information
+set I, i.e., µI = 1/2. χ-dampened updating property implies χ/2 ≤ µS ≤ 1 − χ/2. Since
+µI > 1/3, player 2 will choose C at information set I. To support this profile to be an
+equilibrium, player 2 has to choose D at information set S, and hence, it must be the case
+that µS ≤ 2/7. Coupled with the requirement from χ-dampened updating, the off-path
+belief has to satisfy χ/2 ≤ µS ≤ 2/7. That is, [(I, I); (C, D)] is pooling χ-CSE if and only if
+χ/2 ≤ 2/7 or χ ≤ 4/7.
+Case 4 [m(θ1) = S, m(θ2) = S]:
+Similar to the previous case, since player 1 follows a pooling strategy, player 2 will not
+update his belief at information set S, i.e., µS = 1/2.
+Also, the χ-dampened updating
+47
+
+property suggests χ/2 ≤ µI ≤ 1 − χ/2. Because µS > 2/7, it is optimal for player 2 to
+choose C at information set S. To support this as an equilibrium, player 2 has to choose D
+at information set I. Therefore, it must be that µI ≤ 1/3. Combined with the requirement
+of χ-dampened updating, the off-path belief has to satisfy χ/2 ≤ µI ≤ 1/3. As a result,
+[(S, S); (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.
+Analysis of Game BH 4.
+At information set I, given µI, the expected payoffs of C, D, E are 30, 45 − 45µI and
+35µI. Hence, D is the best response if and only if µI ≤ 1/3 while E is the best response
+if µI ≥ 6/7. For 1/3 ≤ µI ≤ 6/7, C is the best response. On the other hand, since player
+2’s payoffs at information set S are the same as in Game 1, player 2 will adopt the same
+decision rule—player 2 will choose C if and only if µS ≥ 2/7, and choose D if and only if
+µS ≤ 2/7. Now, we consider the following four cases.
+Case 1 [m(θ1) = I, m(θ2) = S]:
+In this case, by Lemma 1, µI = 1 − χ/2 and µS = χ/2. To support this profile to be an
+equilibrium, player 2 has to choose E and C at information set I and S, respectively. To
+make it profitable for player 2 to choose E at information set I, it must be that:
+µI = 1 − χ/2 ≥ 6/7 ⇐⇒ χ ≤ 2/7.
+On the other hand, player 2 will choose C at information set S if and only if χ/2 ≥ 2/7 or
+χ ≥ 4/7, which is not compatible with the previous inequality. Therefore, this profile cannot
+be supported as an equilibrium.
+Case 2 [m(θ1) = S, m(θ2) = I]:
+In this case, by Lemma 1, µI = χ/2 and µS = 1−χ/2. To support this as an equilibrium,
+player 2 has to choose D at both information sets. Yet, µS = 1 − χ/2 > 2/7, implying that
+it is not a best reply for player 2 to choose D at information set S. Hence this profile also
+cannot be supported as an equilibrium.
+Case 3 [m(θ1) = I, m(θ2) = I]:
+Since player 1 follows a pooling strategy, player 2 will not update his belief at information
+set I, i.e., µI = 1/2. The χ-dampened updating property implies χ/2 ≤ µS ≤ 1 − χ/2.
+Because 1/3 < µI = 1/2 < 6/7, player 2 will choose C at information set I. To support
+this profile as an equilibrium, player 2 has to choose D at information set S, and hence, it
+must be the case that µS ≤ 2/7. Coupled with the requirement of χ-dampened updating,
+the off-path belief has to satisfy χ/2 ≤ µS ≤ 2/7. That is, [(I, I); (C, D)] is pooling χ-CSE
+if and only if χ/2 ≤ 2/7 or χ ≤ 4/7.
+Case 4 [m(θ1) = S, m(θ2) = S]:
+Similar to the previous case, since player 1 follows a pooling strategy, player 2 will not
+update his belief at information set S, i.e., µS = 1/2.
+Also, the χ-dampened updating
+property implies χ/2 ≤ µI ≤ 1 − χ/2. Because µS > 2/7, it is optimal for player 2 to choose
+48
+
+C at information set S. To support this as an equilibrium, player 2 can choose either C or
+D at information set I.
+Case 4.1: To make it a best reply for player 2 to choose D at information set I, it must
+be that µI ≤ 1/3. Combined with the requirement from χ-dampened updating, the off-path
+belief has to satisfy χ/2 ≤ µI ≤ 1/3. As a result, [(S, S); (D, C)] is a pooling χ-CSE if and
+only if χ ≤ 2/3.
+Case 4.2: To make it a best reply for player 2 to choose C at information set S, it must
+be that 1/3 ≤ µI ≤ 6/7. Combined with the requirement from χ-dampened updating, the
+off-path belief has to satisfy
+max
+�1
+2χ, 1
+3
+�
+≤ µI ≤ min
+�6
+7, 1 − 1
+2χ
+�
+.
+For any χ ∈ [0, 1], one can find µI that satisfies both inequalities. Hence [(S, S); (C, C)] is a
+pooling χ-CSE for any χ.
+This completes the analysis of Game 1 and Game 2. ■
+4.2
+A Public Goods Game with Communication
+Proof of Proposition 7
+To prove this set of cost cutoffs form a χ-CSE, we need to show that there is no profitable
+deviation for any type at any subgame. First, at the second stage where there are exactly
+0 ≤ k ≤ N − 1 players sending 1 in the first stage, since no players will contribute, setting
+Cχ
+k = 0 is indeed a best response. At the subgame where all N players send 1 in the first
+stage, we use µχ
+i (c−i|N) to denote player i’s cursed belief density. By Lemma 1, the cursed
+belief about all other players having a cost lower than c is simply:
+F χ(c) ≡
+�
+{cj≤c, ∀j̸=i}
+µχ
+i (c′
+−i|N)dc′
+−i
+=
+�
+χ (c/K)N−1 + (1 − χ) (c/Cχ
+c )N−1
+if c ≤ Cχ
+c
+1 − χ + χ (c/Cχ
+c )N−1
+if c > Cχ
+c ,
+and Cχ
+N is the solution of the fixed point problem of Cχ
+N = F χ(Cχ
+N).
+Moreover, in equilibrium, Cχ
+c type of players would be indifferent between sending 1 and
+0 in the communication stage. Thus, given Cχ
+N, Cχ
+c is the solution of the following equation
+0 =
+�Cχ
+c
+K
+�N−1
+[−Cχ
+c + F χ(Cχ
+N)] .
+As a result, we obtain that in equilibrium, Cχ
+c = Cχ
+N = F χ(Cχ
+N) ≤ 1 and denote this cost
+49
+
+cutoff by C∗(N, K, χ). Substituting it into F χ(c), gives:
+C∗(N, K, χ) − χ
+�C∗(N, K, χ)
+K
+�N−1
+= 1 − χ.
+In the following, we show that for any N ≥ 2 and χ, the cutoff C∗(N, K, χ) is unique.
+Case 1: When N = 2, the cutoff C∗(2, K, χ) is the unique solution of the linear equation
+C∗(2, K, χ) − χ
+�C∗(2, K, χ)
+K
+�
+= 1 − χ ⇐⇒ C∗(2, K, χ) = K − Kχ
+K − χ .
+Case 2: For N ≥ 3, we define the function h(y) : [0, 1] → R where
+h(y) = y − χ
+� y
+K
+�N−1
+− (1 − χ).
+It suffices to show that h(y) has a unique root in [0, 1]. When χ = 0, h(y) = y − 1 which has
+a unique root at y = 1. In the following, we will focus on the case where χ > 0. Since h(y)
+is continuous, h(0) = −(1 − χ) < 0 and h(1) = χ
+�
+1 − (1/K)N−1�
+> 0, there exists a root
+y∗ ∈ (0, 1) by the intermediate value theorem. Moreover, as we take the second derivative,
+we can find that for any y ∈ (0, 1),
+h′′(y) = −
+�
+χ
+KN−1
+�
+(N − 1)(N − 2)yN−3 < 0,
+implying that h(y) is strictly concave in [0, 1]. Furthermore, h(0) < 0 and h(1) > 0, so the
+root is unique, as illustrated in the left panel of Figure 3. This completes the proof. ■
+Proof of Corollary 3
+By Proposition 7, we know the cutoff C∗(N, K, χ) ≤ 1 and it satisfies
+C∗(N, K, χ) − χ
+�C∗(N, K, χ)
+K
+�N−1
+= 1 − χ.
+Therefore, when χ = 0, the condition becomes C∗(N, K, 0) = 1. In addition, when χ = 1,
+the condition becomes
+C∗(N, K, 1) −
+�C∗(N, K, 1)
+K
+�N−1
+= 0,
+implying C∗(N, K, 1) = 0.
+For χ ∈ (0, 1), to prove C∗(N, K, χ) is strictly decreasing in N, K and χ, we consider a
+function g(y; N, K, χ) : (0, 1) → R where g(y; N, K, χ) = y − χ[y/K]N−1. For any y ∈ (0, 1)
+and fix any K and χ, we can observe that when N ≥ 2,
+g(y; N + 1, K) − g(y; N, K) = −χ
+� y
+K
+�N
++ χ
+� y
+K
+�N−1
+> 0,
+50
+
+so g(·; N, K, χ) is strictly increasing in N.
+Therefore, the cutoff C∗(N, K, χ) is strictly
+decreasing in N. Similarly, for any y ∈ (0, 1) and fix any N and χ, observe that when
+K > 1,
+∂g
+∂K = χ(N − 1)
+�yN−1
+KN
+�
+> 0,
+which implies that cutoff C∗(N, K, χ) is also strictly decreasing in K. For the comparative
+statics of χ, we can rearrange the equilibrium condition where
+1 − C∗(N, K, χ)
+χ
+= 1 −
+�C∗(N, K, χ)
+K
+�N−1
+.
+Since LHS is strictly decreasing in χ, the equilibrium cutoff is also strictly decreasing in χ.
+Finally, taking the limit on both sides of the equilibrium condition, we obtain:
+lim
+N→∞ C∗(N, K, χ) = lim
+K→∞ C∗(N, K, χ) = 1 − χ.
+This completes the proof. ■
+4.3
+The Centipede Game with Altruistic Types
+Proof of Claim 2
+By backward induction, we know selfish player two will choose T4 for sure. Given that
+player two will choose T4 at stage four, it is optimal for selfish player one to choose T3.
+Now, suppose selfish player one will choose P1 with probability q1 and player two will choose
+P2 with probability q2. Given this behavioral strategy profile, player two’s belief about the
+other player being altruistic at stage two is:
+µ =
+α
+α + (1 − α)q1
+.
+In this case, it is optimal for selfish player two to pass if and only if
+32µ + 4(1 − µ) ≥ 8 ⇐⇒ µ ≥ 1
+7.
+At the equilibrium, selfish player two is indifferent between T2 and P2. If not, say 32µ +
+4(1 − µ) > 8, player two will choose P2. Given that player two will choose P2, it is optimal
+for selfish player one to choose P1, which makes µ = α and α > 1/7. However, we know
+α ≤ 1/7 which yields a contradiction. On the other hand, if 32µ + 4(1 − µ) < 8, then it is
+optimal for player two to choose T2 at stage two. As a result, selfish player one would choose
+T1 at stage one, causing µ = 1. In this case, player two would deviate to choose P2, which
+again yields a contradiction. To summarize, in equilibrium, player two has to be indifferent
+between T2 and P2, i.e., µ = 1/7. As we rearrange the equality, we can obtain that
+α
+α + (1 − α)q∗
+1
+= 1
+7 ⇐⇒ q∗
+1 =
+6α
+1 − α.
+51
+
+Finally, since the equilibrium requires selfish player one to mix at stage one, selfish player
+one has to be indifferent between P1 and T1. Therefore,
+4 = 16q∗
+2 + 2(1 − q∗
+2) ⇐⇒ q∗
+2 = 1
+7.
+This completes the proof. ■
+Proof of Proposition 8
+By backward induction, we know selfish player two will choose T4 for sure. Given this, it is
+optimal for selfish player one to choose T3. Now, suppose selfish player one will choose P1
+with probability q1 and player two will choose P2 with probability q2. Given this behavioral
+strategy profile, by Lemma 1, player two’s cursed belief about the other player being altruistic
+at stage 2 is:
+µχ = χα + (1 − χ)
+�
+α
+α + (1 − α)q1
+�
+.
+In this case, it is optimal for player two to pass if and only if
+32µχ + 4(1 − µχ) ≥ 8 ⇐⇒ µχ ≥ 1
+7.
+We can first show that in equilibrium, it must be that µχ ≤ 1/7. If not, then it is strictly
+optimal for player two to choose P2. Therefore, it is optimal for selfish player one to choose
+P1 and hence µχ = α ≤ 1/7, which yields a contradiction. In the following, we separate the
+discussion into two cases.
+Case 1: χ ≤
+6
+7(1−α)
+In this case, we argue that player two is indifferent between P2 and T2. If not, then
+32µχ +4(1−µχ) < 8 and it is strictly optimal for player two to choose T2. This would cause
+selfish player one to choose T1 and hence µχ = 1 − (1 − α)χ. This yields a contradiction
+because
+µχ = 1 − (1 − α)χ < 1
+7 ⇐⇒ χ >
+6
+7(1 − α).
+Therefore, in this case, player two is indifferent between T2 and P2 and thus,
+µχ = 1
+7 ⇐⇒ χα + (1 − χ)
+�
+α
+α + (1 − α)qχ
+1
+�
+= 1
+7
+⇐⇒ χ +
+1 − χ
+α + (1 − α)qχ
+1
+= 1
+7α
+⇐⇒ α + (1 − α)qχ
+1 = (1 − χ)
+� � 1
+7α − χ
+�
+⇐⇒ qχ
+1 =
+�7α − 7αχ
+1 − 7αχ − α
+� �
+(1 − α).
+52
+
+Since the equilibrium requires selfish player one to mix at stage 1, selfish player one has to
+be indifferent between P1 and T1. Therefore,
+4 = 16qχ
+2 + 2(1 − qχ
+2 ) ⇐⇒ qχ
+2 = 1
+7.
+Case 2: χ >
+6
+7(1−α)
+In this case, we know for any qχ
+1 ∈ [0, 1],
+µχ = χα + (1 − χ)
+�
+α
+α + (1 − α)qχ
+1
+�
+≤ 1 − (1 − α)χ < 1
+7,
+implying that it is strictly optimal for player two to choose T2, and hence it is strictly
+optimal for selfish player one to choose T1 at stage 1. This completes the proof. ■
+4.4
+Sequential Voting over Binary Agendas
+Proof of Proposition 9
+Assuming that a1(θ1) = b and all other types of voters as well as type θ1 at stage 2 vote
+sincerely, voter i’s χ-cursed belief in the second stage upon observing a1
+−i = (a, b) is
+µχ
+i (θ−i|a1
+−i = (a, b)) =
+�
+�
+�
+�
+�
+p1p3χ +
+p1
+p1+p2(1 − χ)
+if θ−i = (θ3, θ1)
+p2p3χ +
+p2
+p1+p2(1 − χ)
+if θ−i = (θ3, θ2)
+pkplχ
+otherwise.
+As mentioned in Section 4.4, a voter would act as if he perceives the other voters’ (be-
+havioral) strategies correctly in the last stage. However, misunderstanding the link between
+the other voters’ types and actions would distort a voter’s belief updating process. In other
+words, a voter would perceive the strategies correctly but form beliefs incorrectly. As a
+result, the continuation value of the a vs c subgame to a type θ1 voter is simply the voter’s
+χ-cursed belief, conditional on being pivotal, about there being at least one type θ1 voter
+among his opponents. Similarly, the continuation value of the b vs c subgame is equal to the
+voter’s conditional χ-cursed belief about there being at least one type θ1 or θ2 voter among
+his opponents multiplied by v. Therefore, the continuation values to a type θ1 voter in the
+two possible subgames of the second stage are (let ˜p2 ≡
+p1
+p1+p2):
+a vs c :
+χ
+�
+1 − (1 − p1)2�
++ (1 − χ)˜p2
+b vs c :
+�
+1 − p2
+3χ
+�
+v
+It is thus optimal for a type θ1 voter to vote for b in the first stage if
+χ
+�
+1 − (1 − p1)2�
++ (1 − χ)˜p2 ≤
+�
+1 − p2
+3χ
+�
+v
+⇐⇒ [2p1 − p2
+1 − ˜p2 + p2
+3v]χ ≤ v − ˜p2
+(2)
+53
+
+Notice that the statement would automatically hold when χ = 0. In the following, we
+want to show that given v and p, if condition (2) holds for some χ ∈ (0, 1], then it will hold
+for all χ′ ≤ χ. As χ > 0, we can rewrite condition (2) as
+2p1 − p2
+1 − ˜p2 + p2
+3v ≤ v − ˜p2
+χ
+.
+(2’)
+Case 1: v − ˜p2 < 0.
+In this case, we want to show that voting b in the first stage is never optimal for type θ1
+voter. That is, we want to show condition (2’) never holds for v < ˜p2. To see this, we can
+first observe that the RHS is strictly increasing in χ. Therefore, it suffices to show
+2p1 − p2
+1 − ˜p2 + p2
+3v > v − ˜p2.
+This is true because
+2p1 − p2
+1 − ˜p2 + p2
+3v − (v − ˜p2) = 2p1 − p2
+1 − (1 − p2
+3)v
+> 2p1 − p2
+1 − (1 + p3)p1 = p1p2 ≥ 0
+where the second inequality holds as v <
+p1
+p1+p2.
+Case 2: v − ˜p2 ≥ 0.
+Since the RHS of condition (2’) is greater or equal to 0, it will weakly increase as χ
+decreases. Thus, if condition (2’) holds for some χ ∈ (0, 1], it will also hold for all χ′ ≤ χ.
+This completes the proof. ■
+Proof of Proposition 10
+Assuming that all voters vote sincerely in both stages, voter i’s χ-cursed belief in the second
+stage upon observing a1
+−i = (a, b) is
+µχ
+i (θ−i|a1
+−i = (a, b)) =
+�
+�
+�
+�
+�
+p1p2χ +
+p1
+p1+p3(1 − χ)
+if θ−i = (θ1, θ2)
+p2p3χ +
+p3
+p1+p3(1 − χ)
+if θ−i = (θ3, θ2)
+pkplχ
+otherwise.
+Similar to the proof of Proposition 9, the continuation values to a type θ1 voter in the
+two possible subgames of the second stage are (let ˜p3 ≡
+p1
+p1+p3):
+a vs c :
+χ
+�
+1 − (1 − p1)2�
++ (1 − χ)˜p3
+b vs c :
+�
+1 − p2
+3χ
+�
+v
+54
+
+Thus, it is optimal for a type θ1 voter to vote for a in the first stage if
+χ
+�
+1 − (1 − p1)2�
++ (1 − χ)˜p3 ≥
+�
+1 − p2
+3χ
+�
+v
+⇐⇒ χ
+�
+2p1 − p2
+1 − ˜p3 + p2
+3v
+�
+≥ v − ˜p3.
+(3)
+Case 1: v − ˜p3 > 0.
+In this case, we want to show that given p and v, there exists ˜χ such that condition (3)
+holds if and only if χ ≥ ˜χ. Let τ ≡ 2p1 − p2
+1 − ˜p3 + p2
+3v. If τ > 0, then condition (3) holds
+if and only if χ ≥ ˜χ ≡ v−˜p3
+τ . On the other hand, if τ ≤ 0, condition (3) will not hold for all
+χ ∈ [0, 1] and hence we can set ˜χ = 2.
+Case 2: v − ˜p3 ≤ 0.
+In this case, we want to show that given p and v, there exists ˜χ such that condition (3)
+holds if and only if χ ≤ ˜χ. If τ < 0, then condition (3) holds if and only if χ ≤ v−˜p3
+τ
+where
+the RHS is greater or equal to 0. On the other hand, if τ ≥ 0, then condition (3) will hold
+for any χ ∈ [0, 1] and hence we can again set ˜χ = 2. This completes the proof. ■
+4.5
+The Dirty Faces Game
+Proof of Proposition 11
+When observing a clean face, a player will know that he has a dirty face immediately.
+Therefore, choosing 1 (i.e., choosing D at stage 1) when observing a clean face is a strictly
+dominant strategy. In other words, for any χ ∈ [0, 1], ˆσχ(O) = 1.
+The analysis of the case where the player observes a dirty face is separated into two cases.
+Case 1: χ > ¯α
+In this case, we show that ˆσχ(X) = T + 1 is the only χ-CE. If not, suppose ˆσχ(X) = t
+where t ≤ T can be supported as a χ-CE. We can first notice that ˆσχ(X) = 1 cannot be
+supported as a χ-CE because it is strictly dominated to choose 1 when observing a dirty
+face. For 2 ≤ t ≤ T, given the other player −i chooses ˆσχ(X) = t, we can find player −i’s
+average strategy is
+¯σ−i(j) =
+�
+�
+�
+�
+�
+1 − p
+if
+j = 1
+p
+if
+j = t
+0
+if
+j ̸= 1, t.
+55
+
+Therefore, the other player −i’s χ-cursed strategy is:
+σχ
+−i(j|xi = O) =
+�
+�
+�
+�
+�
+χ(1 − p) + (1 − χ)
+if
+j = 1
+χp
+if
+j = t
+0
+if
+j ̸= 1, t,
+and
+σχ
+−i(j|xi = X) =
+�
+�
+�
+�
+�
+χ(1 − p)
+if
+j = 1
+χp + (1 − χ)
+if
+j = t
+0
+if
+j ̸= 1, t.
+In this case, given (player i perceives that) player −i chooses the χ-cursed strategy, player
+i’s expected payoff to choose 2 ≤ j ≤ t when observing a dirty face is:
+(1 − p)
+�
+−δj−1χp
+�
++ p
+�
+δj−1α [χp + (1 − χ)]
+�
+= pδj−1 [α − χ(1 + α)(1 − p)]
+�
+��
+�
+<0 ⇐⇒ χ>¯α
+< 0.
+Hence, given the other player chooses t when observing a dirty face, it is strictly dominated
+to choose any j ≤ t. Therefore, the only χ-CE is ˆσχ(X) = T + 1.
+Case 2: χ < ¯α
+In this case, we want to show that ˆσχ(X) = 2 is the only χ-CE. If not, suppose ˆσ(X) = t
+for some t ≥ 3 can be supported as a χ-CE. We can again notice that since when observing
+a dirty face, it is strictly dominated to choose 1, 1 is never a best response. Given player
+−i chooses ˆσχ(X) = t, by the same calculation as in Case 1, the expected payoff to choose
+2 ≤ j ≤ t is:
+pδj−1 [α − χ(1 + α)(1 − p)]
+�
+��
+�
+>0 ⇐⇒ χ<¯α
+> 0,
+which is decreasing in j. Therefore, the best response to ˆσχ(X) = t is to choose 2 when
+observing a dirty face. As a result, the only χ-CE in this case is ˆσχ(X) = 2. This completes
+the proof. ■
+Proof of Proposition 12
+When observing a clean face, the player would know that his face is dirty. Thus, choosing
+D at stage 1 is a strictly dominant strategy, and ˜σχ(O) = 1 for all χ ∈ [0, 1]. On the other
+hand, the analysis for the case where the player observes a dirty face consists of several steps.
+Step 1: Assume that both players choosing D at some stage ¯t. We claim that at stage
+t ≤ ¯t, the cursed belief µχ(X|t, X) = 1 − (1 − p)χt−1. We can prove this by induction on t.
+At stage t = 1, the belief about having a dirty face is simply the prior belief p. Hence this
+establishes the base case. Now suppose the statement holds for any stage 1 ≤ t ≤ t′ (and
+56
+
+t′ < ¯t). At stage t′ + 1, by Lemma 1,
+µχ(X|t′ + 1, X) = χµχ(X|t′, X) + (1 − χ)
+= χ
+�
+1 − (1 − p)χt′−1�
++ (1 − χ)
+= 1 − (1 − p)χt′
+where the second equality holds by the induction hypothesis. This proves the claim.
+Step 2: Given the cursed belief computed in the previous step, the expected payoff to choose
+D at stage t is:
+µχ(X|t, X)α − [1 − µχ(X|t, X)] =
+�
+1 − (1 − p)χt−1�
+α −
+�
+(1 − p)χt−1�
+= α − (1 − p)(1 + α)χt−1,
+which is increasing in t. Notice that at the first stage, the expected payoff is α−(1−p)(1+α) <
+0 by Assumption (1), so choosing U at stage 1 is strictly dominated. Furthermore, the player
+would choose U at every stage when observing a dirty face if and only if
+µχ(X|T, X)α − [1 − µχ(X|T, X)] ≤ 0 ⇐⇒ α − (1 − p)(1 + α)χT−1 ≤ 0
+⇐⇒ χ ≥ ¯α
+1
+T +1.
+As a result, both players choosing ˜σχ(X) = T + 1 is a χ-CSE if and only if χ ≥ ¯α
+1
+T +1.
+Step 3: In this step, we show both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if
+χ ≤ ¯α. We can notice that given the other player chooses D at stage 2, the player would
+know stage 2 would be the last stage regardless of his face type. Therefore, it is optimal to
+choose D at stage 2 as long as the expected payoff of D at stage 2 is positive. Consequently,
+both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if
+µχ(X|2, X)α − [1 − µχ(X|2, X)] ≥ 0 ⇐⇒ α − (1 − p)(1 + α)χ
+⇐⇒ χ ≤ ¯α.
+Step 4: Given the other player chooses ˜σχ(X) > t, as the game reaches stage t, the belief
+about the other player choosing U at stage t is:
+µχ(X|t, X)
+�
+��
+�
+prob. of dirty
+[χµχ(X|t, X) + (1 − χ)]
++ [1 − µχ(X|t, X)]
+�
+��
+�
+prob. of clean
+[χµχ(X|t, X)] = µχ(X|t, X).
+Furthermore, we denote the expected payoff of choosing D at stage t as
+E [uχ(D|t, X)] ≡ µχ(X|t, X)α − (1 − µχ(X|t, X)) .
+57
+
+In the following, we claim that for any stage 2 ≤ t ≤ T − 2, given the other player will stop
+at some stage later than stage t + 2 or never stop, if it is optimal to choose U at stage t + 1,
+then it is also optimal for you to choose U at stage t. That is,
+E [uχ(D|t + 1, X)] < δµχ(X|t + 1, X)E [uχ(D|t + 2, X)]
+=⇒ E [uχ(D|t, X)] < δµχ(X|t, X)E [uχ(D|t + 1, X)] .
+To prove this claim, first observe that
+E [uχ(D|t + 1, X)] < δµχ(X|t + 1, X)E [uχ(D|t + 2, X)]
+⇐⇒ (1 + α)µχ(X|t + 1, X) − 1 < δµχ(X|t + 1, X) [(1 + α)µχ(X|t + 2, X) − 1] .
+After rearrangement, the inequality is equivalent to
+δχ [µχ(X|t + 1, X)]2 +
+�
+δ(1 − χ) −
+δ
+1 + α − 1
+�
+µχ(X|t + 1, X) +
+1
+1 + α > 0.
+Consider a function F : [0, 1] → R where
+F(y) = δχy2 +
+�
+δ(1 − χ) −
+δ
+1 + α − 1
+�
+y +
+1
+1 + α.
+Since µχ(X|j, X) = 1 − (1 − p)χj−1 is increasing in j, it suffices to complete the proof of
+the claim by showing there exists a unique y∗ ∈ (0, 1) such that F is single-crossing on [0, 1]
+where F(y∗) = 0, F(y) < 0 for all y > y∗, and F(y) > 0 for all y < y∗. Because F is
+continuous and
+• F(0) =
+1
+1+α > 0,
+• F(1) = δχ +
+�
+δ(1 − χ) −
+δ
+1+α − 1
+�
++
+1
+1+α = − α(1−δ)
+1+α
+< 0.
+By intermediate value theorem, there exists a y∗ ∈ (0, 1) such that F(y∗) = 0. Moreover,
+y∗ is the unique root of F on [0, 1] because F is a strictly convex parabola and F(1) < 0.
+This establishes the claim.
+Step 5: For any 3 ≤ t ≤ T, in this step, we find the conditions to support both players
+choosing ˜σχ(X) = t as a χ-CSE. We can first notice that both players choosing ˜σχ(X) = t
+is a χ-CSE if and only if
+1. E [uχ(D|t, X)] ≥ 0
+2. E [uχ(D|t − 1, X)] ≤ δµχ(X|t − 1, X)E [uχ(D|t, X)].
+Condition 1 is necessary because if it fails, then it is better for the player to choose U
+at stage t and get at least 0. Condition 2 is also necessary because if the condition doesn’t
+hold, it would be profitable for the player to choose D before stage t. Furthermore, these
+58
+
+two conditions are jointly sufficient to support ˜σχ(X) = t as a χ-CSE by the same argument
+as step 3.
+From condition 1, we can obtain that
+E [uχ(D|t, X)] ≥ 0 ⇐⇒ (1 + α)µχ(X|t, X) − 1 ≥ 0
+⇐⇒ 1 − (1 − p)χt−1 ≥
+1
+1 + α ⇐⇒ χ ≤ ¯α
+1
+t−1.
+In addition, by the calculation of step 4, we know
+E [uχ(D|t − 1, X)] ≤ δµχ(X|t − 1, X)E [uχ(D|t, X)] ⇐⇒ F (µχ(X|t − 1, X)) ≥ 0,
+which is equivalent to
+µχ(X|t − 1, X) ≤
+�
+1 +
+δ
+1+α − δ(1 − χ)
+�
+−
+��
+1 +
+δ
+1+α − δ(1 − χ)
+�2 − 4δχ
+�
+1
+1+α
+�
+2δχ
+= [(1 + α)(1 + δχ) − αδ] −
+�
+[(1 + α)(1 + δχ) − αδ]2 − 4δχ(1 + α)
+2δχ(1 + α)
+≡ κ(χ).
+Therefore, condition 2 holds if and only if
+1 − (1 − p)χt−2 ≤ κ(χ) ⇐⇒ χ ≥
+�1 − κ(χ)
+1 − p
+�
+1
+t−2
+.
+In summary, both players choosing ˜σχ(X) = t is a χ-CSE if and only if
+�1 − κ(χ)
+1 − p
+�
+1
+t−2
+≤ χ ≤ ¯α
+1
+t−1.
+This completes the proof. ■
+59
+
diff --git a/89FLT4oBgHgl3EQfBi6R/content/tmp_files/load_file.txt b/89FLT4oBgHgl3EQfBi6R/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..28feff30988f2548c3d90786ed0b05502c68e1a9
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+++ b/89FLT4oBgHgl3EQfBi6R/content/tmp_files/load_file.txt
@@ -0,0 +1,1503 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf,len=1502
+page_content='Cursed Sequential Equilibrium∗  Meng-Jhang Fong†  Po-Hsuan Lin‡  Thomas R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey§  January 31, 2023  Abstract  This paper develops a framework to extend the strategic form analysis of cursed  equilibrium (CE) developed by Eyster and Rabin (2005) to multi-stage games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The  approach uses behavioral strategies rather than normal form mixed strategies, and  imposes sequential rationality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We define cursed sequential equilibrium (CSE) and  compare it to sequential equilibrium and standard normal-form CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We provide a  general characterization of CSE and establish its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We apply CSE to five  applications in economics and political science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' These applications illustrate a wide  range of differences between CSE and Bayesian Nash equilibrium or CE: in signaling  games;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' games with preplay communication;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' reputation building;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' sequential voting;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  and the dirty faces game where higher order beliefs play a key role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A common theme  in several of these applications is showing how and why CSE implies systematically  different behavior than Bayesian Nash equilibrium in dynamic games of incomplete  information with private values, while CE coincides with Bayesian Nash equilibrium  for such games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  JEL Classification Numbers: C72, D83  Keywords: Multi-stage Games, Private Information, Cursed Equilibrium, Learning  ∗Grants from the National Science Foundation (SES-0617820) and the Gordon and Betty Moore Foun-  dation (1158) supported this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We are especially grateful to Shengwu Li and Shani Cohen for recent  correspondence that helped to clarify the differences between the CSE and SCE approaches to the gener-  alization of cursed equilibrium for dynamic games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We thank participants of the Caltech Proseminar and  Colin Camerer for comments and also thank Matthew Rabin for earlier discussions on the subject during his  visit at Caltech as a Moore Distinguished Scholar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  †Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125  USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' mjfong@caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='edu  ‡Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125  USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' plin@caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='edu  §Corresponding Author: Division of the Humanities and Social Sciences, California Institute of Technol-  ogy, Pasadena, California 91125 USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' trp@hss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Fax: +16263958967 Phone: +16263954088  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='11971v1  [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='TH]  27 Jan 2023  1  Introduction  Cursed equilibrium (CE) proposed by Eyster and Rabin (2005) is a leading behavioral equi-  librium concept that was developed to explain the “winner’s curse” and related anomalies  in applied game theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The basic idea behind CE is that individuals do not fully take  account of the dependence of other players’ strategic actions on private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Cursed  behavior of this sort has been detected in a variety of contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Capen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1971) first  noted that in oil-lease auctions, “the winner tends to be the bidder who most overestimates  the reserves potential” (Capen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1971), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 641).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since then, this observation of overbid-  ding relative to the Bayesian equilibrium benchmark, which can result in large losses for the  winning bidder, has been widely documented in laboratory auction experiments (Bazerman  and Samuelson, 1983;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kagel and Levin, 1986;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kagel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Forsythe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Dyer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Lind and Plott, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kagel and Levin, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Ivanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Camerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=',  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition, the neglect of the connection between the opponents’ actions and private  information is also found in non-auction environments, such as bilateral bargaining games  (Samuelson and Bazerman, 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Holt and Sherman, 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Carrillo and Palfrey, 2009, 2011),  zero-sum betting games with asymmetric information (Rogers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Søvik, 2009), and  voting and jury decisions (Guarnaschelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  While CE provides a tractable alternative to Bayesian Nash equilibrium and can explain  some anomalous behavior in games with a winner’s-curse structure, a significant limitation is  that it is only developed as a strategic form concept for simultaneous-move Bayesian games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Thus, when applying the standard CE to dynamic games, the CE analysis is carried out on  the strategic form representation of the game, implying that CE cannot distinguish behavior  across dynamic games that differ in their timing of moves but have the same strategic form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  That is, players are assumed to choose type-dependent contingent strategies simultaneously  and not update their beliefs as the history of play unfolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A further limitation implied  by the strategic form approach is that CE and standard Bayesian Nash equilibrium make  identical predictions in games with a private-values information structure (Eyster and Rabin  (2005), Proposition 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this paper we extend the CE in a simple and natural way to  multi-stage games of incomplete information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We call the new equilibrium concept Cursed  Sequential Equilibrium (CSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In Section 2, we present the framework and our extension of cursed equilibrium to dy-  namic games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We consider the framework of multi-stage games with observed actions,  introduced by Fudenberg and Tirole (1991b), where players’ private information is repre-  sented by types, with the assumption that the set of available actions is independent of their  types at each public history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Our new solution concept is in the same spirit of the cursed  1  equilibrium—in our model, at each stage, players will (partially) neglect the dependence of  the other players’ behavioral strategies on their types, by placing some weight on the incor-  rect belief that all types adopt the average behavioral strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Specifically, at each public  history, this corresponds to the average distribution of actions given the current belief about  others’ types at that stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, as players update their beliefs about others’ private  information via Bayes’ rule, but with incorrect beliefs about the other players’ behavioral  strategies, in later stages this can lead them to have incorrect beliefs about the other players’  average distribution of actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Following Eyster and Rabin (2005)’s notion of cursedness, we parameterize the model by  a single parameter χ ∈ [0, 1] which captures the degree of cursedness and define fully cursed  (χ = 1) CSE analogously to fully cursed (χ = 1) CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Recall that in a fully cursed (χ = 1) CE,  each type of each player chooses a best reply to expected (cursed) equilibrium distribution  of other players’ actions, averaged over the type-conditional strategies of the other players,  with this average distribution calculated using the prior belief on types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Loosely speaking,  a player best responds to the average CE strategy of the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In a χ-CE, players are  only partially cursed, in the sense that each player best responds to a χ-weighted linear  combination of the average χ-CE strategy of the others and the true (type-dependent) χ-CE  strategy of the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The extension of this definition to multi-stage games with observed actions is different  from χ-CE in two essential ways: (1) the game is analyzed with behavioral strategies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and  (2) we impose sequential rationality and Bayesian updating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In a fully cursed (χ = 1) CSE,  (1) implies at every stage t and each public history at t, each type of each player i chooses a  best reply to the expected (cursed) equilibrium distribution of other players’ stage-t actions,  averaged over the type-conditional stage-t behavioral strategies of other players, with this  average distribution calculated using i’s current belief about types at stage t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, player  i best responds to the average stage-t CSE strategy of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, (2) requires that  each player’s belief at each public history is derived by Bayes’ rule wherever possible, and  best replies are with respect to the continuation values computed by using the fully cursed  beliefs about the behavioral strategies of the other players in current and future stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  A χ-CSE, for χ < 1, is then defined in analogously to χ-CE, except for using a χ-weighted  linear combination of the average χ-CSE behavioral strategies of others and the true (type-  dependent) χ-CSE behavioral strategies of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, similar to the fully cursed CE, in  a fully cursed (χ = 1) CSE, each player believes other players’ actions at each history are  independent of their private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, χ = 0 corresponds to the  standard sequential equilibrium where players have correct perceptions about other players’  2  behavioral strategies and are able to make correct Bayesian inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1  After defining the equilibrium concept, in Section 3 we explore some general properties of  the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We first prove the existence of a cursed sequential equilibrium in Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Intuitively speaking, CSE mirrors the standard sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The only difference is  that players have incorrect beliefs about the other players’ behavioral strategies at each stage  since they fail to fully account for the correlation between others’ actions and types at every  history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We prove in Proposition 2 that the set of CSE is upper hemi-continuous with respect  to χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Consequently, every limit point of a sequence of χ-CSE points as χ converges to 0 is a  sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This result bridges our behavioral solution concept with the standard  equilibrium theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Finally, we also show in Proposition 4 that χ-CSE is equivalent to χ-CE  for one-stage games, demonstrating the connection between the two behavioral solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In multi-stage games, cursed beliefs about behavioral strategies will distort the evolution  of a player’s beliefs about the other players’ types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As shown in Proposition 3, a direct  consequence of the distortion is that in χ-CSE players tend to update their beliefs about  others’ types too passively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, there is some persistence in beliefs in the sense that  at each stage t, each χ-cursed player’s belief about any type profile is at least χ times the  belief about that type profile at stage t − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Among other things, this implies that if the  prior belief about the types is full support and χ > 0, the full support property will persist  at all histories, and players will (possibly incorrectly) believe every profile of others’ types is  possible at every history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This dampened updating property plays an important role in our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Not only  does it contribute to the difference between CSE and the standard CE through the updating  process, but it also implies additional restrictions on off-path beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The effect of dampened  updating is starkly illustrated in the pooling equilibria of signaling games where every type  of sender behaves the same everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this case, Proposition 5 shows if an assessment  associated with a pooling equilibrium is a χ-CSE, then it also a χ′-CSE for all χ′ ≤ χ, but it  is not necessarily a pooling equilibrium for all χ′ > χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This contrasts with one of the main  results about CE, that if a pooling equilibrium is a χ-CE for some χ, then it is a χ′-CE for  all χ′ ∈ [0, 1] (Eyster and Rabin (2005), Proposition 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This suggests that perhaps the dampened updating property is an equilibrium selection  device that eliminates some pooling equilibrium, but actually this is not a general property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As we demonstrate later, the χ-CE and χ-CSE sets are non-overlapping, which we illustrate  1For the off-path histories, similar to the idea of Kreps and Wilson (1982), we impose the χ-consistency  requirement (see Definition 2) so the assessment is approachable by a sequence of totally mixed behavioral  strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The only difference is that players’ beliefs are incorrectly updated by assuming others play the  χ-cursed behavioral strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, in our approach if χ = 0, a CSE is a sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3  with a variety of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The intuition is that in CSE, players generally do not have  correct beliefs about the opponents’ average behavioral strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The pooling equilibrium  is just a special case where players have correct beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In Section 4 we explore the implications of cursed sequential equilibrium with five ap-  plications in economics and political science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1 analyzes the χ-CSE of signaling  games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Besides studying the theoretical properties of pooling χ-CSE, we also analyze two  simple signaling games that were studied in a laboratory experiment (Brandts and Holt,  1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We show how varying the degree of cursedness can change the set of χ-CSE in these  two signaling games in ways that are consistent with the reported experimental findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Next, we turn to the exploration of how sequentially cursed reasoning can influence strategic  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To this end, we analyze the χ-CSE for a public goods game with communi-  cation (Palfrey and Rosenthal, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2017) in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2, finding that χ-CSE  predicts there will be less effective communication when players are more cursed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Next, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='3 we apply χ-CSE to the centipede game studied experimentally by  McKelvey and Palfrey (1992) where one of the players believes the other player might be  an “altruistic” player who always passes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This is a simple reputation-building game, where  selfish types can gain by imitating altruistic types in early stages of the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The public  goods application and the centipede game are both private-values environments, so these  two applications clearly demonstrate how CSE departs from CE and the Bayesian Nash  equilibrium, and shows the interplay between sequentially cursed reasoning and the learning  of types in private-value models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In strategic voting applications, conditioning on “pivotality”—the event where your vote  determines the final outcome—plays a crucial role in understanding equilibrium voting be-  havior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To illustrate how cursedness distorts the pivotal reasoning, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4 we study  the three-voter two-stage agenda voting game introduced by Ordeshook and Palfrey (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since this is a private value game, the predictions of the χ-CE and the Bayesian Nash equilib-  rium coincide for all χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, cursed equilibrium predicts no matter how cursed the voters  are, they are able to correctly perform pivotal reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the contrary, our CSE predicts  that cursedness will make the voters less likely to vote strategically (predicted by CE and  BNE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This is consistent with the empirical evidence about the prevalence of sincere voting  over sequential agendas when inexperienced voters have incomplete information about other  voters’ preferences (Levine and Plott, 1977;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Plott and Levine, 1978;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Eckel and Holt, 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5 we study the relationship between cursedness and epistemic rea-  soning by considering the two-person dirty faces game previously studied by Weber (2001)  and Bayer and Chan (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this game, χ-CSE predicts cursed players are, to some extent,  4  playing a “coordination” game where they coordinate on a specific learning speed about their  face types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, from the perspective of CSE, the non-equilibrium behavior observed  in experiments can be interpreted as possibly due to a coordination failure resulting from  cognitive limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The cursed sequential equilibrium extends the concept of cursed equilibrium from static  Bayesian games to multi-stage games with observed actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This generalization preserves  the spirit of the original cursed equilibrium in a simple and tractable way, and provides  additional insights about the effect of cursedness in dynamic games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A contemporaneous  working paper by Cohen and Li (2022) is closely related to our paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Their paper adopts a  different approach from ours, based on the coarsening of information sets, to define sequential  cursed equilibrium for extensive form games with perfect recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A two-parameter model of  partial cursedness is developed, and a series of examples demonstrate that for plausible  parameter values the model is consistent with some experimental findings related to the  failure of subjects to fully take account of unobserved hypothetical events, whereas behavior  is “more rational” if subjects make decisions after directly observing such events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At a more  conceptual level, our paper is related to several other behavioral solution concepts developed  for dynamic games, such as the agent quantal response equilibrium (AQRE) (McKelvey  and Palfrey, 1998), the dynamic cognitive hierarchy theory (DCH) (Lin and Palfrey, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Lin, 2022), and the analogy-based expectation equilibrium (ABEE) (Jehiel, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Jehiel and  Koessler, 2008), all of which modify the requirements of sequential equilibrium in different  ways than cursed sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2  The Model  Since CSE is a solution concept for dynamic games of incomplete information, in this pa-  per we will focus on the framework of multistage games with observed actions (Fudenberg  and Tirole, 1991b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1 defines the formal structure of multi-stage games with ob-  served actions, followed by Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2, where the χ-cursed sequential equilibrium is formally  developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1  Multi-Stage Games with Observed Actions  Let N = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , n} be a finite set of players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Each player i ∈ N has a type θi drawn from  a finite set Θi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let θ ∈ Θ ≡ ×n  i=1Θi be the type profile and θ−i ∈ Θ−i ≡ ×j̸=iΘj be the  type profile without player i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' All players share a common (full support) prior distribution  F(·) : Θ → (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, for every player i, the belief of other players’ types conditional  5  on his own type is  F(θ−i|θi) =  F(θ−i, θi)  �  θ′  −i∈Θ−i F(θ′  −i, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  At the beginning of the game, players observe their own types, but not the other players’  types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, each player’s type is his own private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The game is played in stages t = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In each stage, players simultaneously choose  actions, which will be revealed at the end of the stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The feasible set of actions can vary  with histories, so games with alternating moves are also included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let Ht−1 be the set of  all possible histories at stage t, where H0 = {h∅} and HT is the set of terminal histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Let H = ∪T  t=0Ht be the set of all possible histories of the game, and H\\HT be the set of  non-terminal histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  For every player i, the available information at stage t is in Θi × Ht−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, player  i’s information sets can be specified as Ii ∈ Qi = {(h, θ) : h ∈ H\\HT, θi ∈ Θi}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For the sake  of simplicity, we assume that, at each history, the feasible set of actions for every player is  independent of their type and use Ai(ht−1) to denote the feasible set of actions for player  i at history ht−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let Ai = ×h∈H\\HT Ai(h) denote player i’s feasible actions in all histories  of the game and A = A1 × · · · × An.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition, we assume Ai is finite for all i ∈ N and  |Ai(h)| ≥ 1 for all i ∈ N and any h ∈ H\\HT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  A behavioral strategy for player i is a function σi : Qi → ∆(Ai) satisfying σi(ht−1, θi) ∈  ∆(Ai(ht−1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Furthermore, we use σi(at  i|ht−1, θi) to denote the probability player i chooses  at  i ∈ Ai(ht−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We use at = (at  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , at  n) ∈ ×n  i=1Ai(ht−1) ≡ A(ht−1) to denote the action  profile at stage t and at  −i to denote the action profile at stage t without player i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If at is  the action profile realized at stage t, then ht = (ht−1, at).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Finally, each player i has a payoff  function ui : HT × Θ → R, and we let u = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , un) be the profile of payoff functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A  multi-stage game with observed actions, Γ, is defined by the tuple Γ = ⟨T, A, N, H, Θ, F, u⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  Cursed Sequential Equilibrium  In a multi-stage game with observed actions, a solution is defined by an “assessment,” which  consists of a (behavioral) strategy profile σ, and a belief system µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since action profiles will  be revealed to all players at the end of each stage, the belief system specifies, for each player,  a conditional distribution over the set of type profiles conditional on each history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Consider  an assessment (µ, σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Following the spirit of the cursed equilibrium, for player i at stage t,  6  we define the average behavioral strategy profile of the other players as:  ¯σ−i(at  −i|ht−1, θi) =  �  θ−i∈Θ−i  µi(θ−i|ht−1, θi)σ−i(at  −i|ht−1, θ−i)  for any i ∈ N, θi ∈ Θi and ht−1 ∈ Ht−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In CSE, players have incorrect perceptions about other players’ behavioral strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Instead of thinking they are using σ−i, a χ-cursed2 type θi player i would believe the other  players are using a χ-weighted average of the average behavioral strategy and the true  behavioral strategy:3  σχ  −i(at  −i|ht−1, θ−i, θi) = χ¯σ−i(at  −i|ht−1, θi) + (1 − χ)σ−i(at  −i|ht−1, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The beliefs of player i about θ−i are updated in the χ-CSE via Bayes’ rule, whenever  possible, assuming other players are using the χ-cursed behavioral strategy rather than the  true behavioral strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We call this updating rule the χ-cursed Bayes’ rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Specifically, an  assessment satisfies the χ-cursed Bayes’ rule if the belief system is derived from the Bayes’  rule while perceiving others are using σχ  −i rather than σ−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (µ, σ) satisfies χ-cursed Bayes’ rule if the following rule is applied to update  the posterior beliefs whenever �  θ′  −i∈Θ−i µi(θ′  −i|ht−1, θi)σχ  −i(at  −i|ht−1, θ′  −i, θi) > 0:  µi(θ−i|ht, θi) =  µi(θ−i|ht−1, θi)σχ  −i(at  −i|ht−1, θ−i, θi)  �  θ′  −i∈Θ−i µi(θ′  −i|ht−1, θi)σχ  −i(at  −i|ht−1, θ′  −i, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Let Σ0 be the set of totally mixed behavioral strategy profiles, and let Ψχ be the set of  assessments (µ, σ) such that σ ∈ Σ0 and µ is derived from σ using χ-cursed Bayes’ rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  Lemma 1 below shows that another interpretation of the χ-cursed Bayes’ rule is that players  have correct perceptions about σ−i but are unable to make perfect Bayesian inference when  updating beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' From this perspective, player i’s cursed belief is simply a linear combination  of player i’s cursed belief at the beginning of that stage (with χ weight) and the Bayesian  posterior belief (with 1−χ weight).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because σ is totally mixed, there are no off-path histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2We assume throughout the paper that all players are equally cursed, so there is no i subscript on χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The  framework is easily extended to allow for heterogeneous degrees of cursedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3If χ = 0, players have correct beliefs about the other players’ behavioral strategies at every stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4In the following, we will use µχ(·) to denote the belief system derived under χ-cursed Bayes’ Rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Also,  note that both σχ  −i and µχ are induced by σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' that is, σχ  −i(·) = σχ  −i[σ](·) and µχ(·) = µχ[σ](·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For the ease  of exposition, we drop [σ] when it does not cause confusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  7  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any (µ, σ) ∈ Ψχ, i ∈ N, ht = (ht−1, at) ∈ H\\HT and θ ∈ Θ,  µi(θ−i|ht, θi) = χµi(θ−i|ht−1, θi) + (1 − χ)  �  µi(θ−i|ht−1, θi)σ−i(at  −i|ht−1, θ−i)  �  θ′  −i µi(θ′  −i|ht−1, θi)σ−i(at  −i|ht−1, θ′  −i)  �  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This is analogous to Lemma 1 of Eyster and Rabin (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Another insight provided  by Lemma 1 is that even if player types are independently drawn, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', F(θ) = Πn  i=1Fi(θi),  players’ cursed beliefs about other players’ types are generally not independent across players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  That is, in general, µi(θ−i|ht, θi) ̸= Πj̸=iµij(θj|ht, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The belief system will preserve the  independence only when the players are either fully rational (χ = 0) or fully cursed (χ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, we place a consistency restriction, analogous to consistent assessments in sequen-  tial equilibrium, on how χ-cursed beliefs are updated off the equilibrium path, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', when  �  θ′  −i∈Θ−i  µi(θ′  −i|ht−1, θi)σχ  −i(at  −i|ht−1, θ′  −i, θi) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  An assessment satisfies χ-consistency if it is in the closure of Ψχ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (µ, σ) satisfies χ-consistency if there is a sequence of assessments {(µk, σk)} ⊆  Ψχ such that limk→∞(µk, σk) = (µ, σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  For any i ∈ N, χ ∈ [0, 1], σ, and θ ∈ Θ, let ρχ  i (hT|ht, θ, σχ  −i, σi) be player i’s perceived  conditional realization probability of terminal history hT ∈ HT at history ht ∈ H\\HT if the  type profile is θ and player i uses the behavioral strategy σi whereas perceives other players’  using the cursed behavioral strategy σχ  −i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At every non-terminal history ht, a χ-cursed player  in χ-CSE will use χ-cursed Bayes’ rule (Definition 1) to derive the posterior belief about the  other players’ types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Accordingly, a type θi player i’s conditional expected payoff at history  ht is given by:  Eui(σ|ht, θi) =  �  θ−i∈Θ−i  �  hT ∈HT  µi(θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i, σi)ui(hT, θi, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' An assessment (µ∗, σ∗) is a χ-cursed sequential equilibrium if it satisfies χ-  consistency and σ∗  i (ht, θi) maximizes Eui(σ∗|ht, θi) for all i, θi, ht ∈ H\\HT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  8  3  General Properties of χ-CSE  In this section, we characterize some general theoretical properties of χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The first result  is the existence of the χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The definition of χ-CSE mirrors the definition of the sequential  equilibrium by Kreps and Wilson (1982)—the only difference is that players in χ-CSE update  their beliefs by χ-cursed Bayes’ rule and best respond to χ-cursed (behavioral) strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, one can prove the existence of χ-CSE in a similar way as in the standard argument  of the existence of sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any χ ∈ [0, 1] and any finite multi-stage game with observed actions,  there is at least one χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We briefly sketch the proof here, and the details can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Fix any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any i ∈ N and any information set Ii = (ht−1, θi), player i has  to choose every action at  i ∈ Ai(ht−1) with probability at least ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since there are no off-path  histories, the belief system is uniquely pinned down by χ-cursed Bayes’ rule and a χ-CSE  exists in this ϵ-constrained game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We denote this χ-CSE as (µϵ, σϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By compactness, there  is a converging sub-sequence of assessments such that (µϵ, σϵ) → (µ∗, σ∗) as ϵ → 0, which is  a χ-CSE, as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Let Φ(χ) be the correspondence that maps χ ∈ [0, 1] to the set of χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Proposition 1  guarantees Φ(χ) is non-empty for any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because χ-cursed Bayes’ rule changes con-  tinuously in χ, we can further prove in Proposition 2 that Φ(χ) is an upper hemi-continuous  correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Φ(χ) is upper hemi-continuous with respect to χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The proof follows a standard argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix A for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As shown in Corollary 1, a direct consequence of upper hemi-continuity is that every  limit point of a sequence of χ-CSE when χ → 0 is a sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This result  bridges our behavioral equilibrium concept with standard equilibrium theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Every limit point of a sequence of χ-CSE with χ converging to 0 is a sequential  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By Proposition 2, we know Φ(χ) is upper hemi-continuous at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Consider of a se-  quence of χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As χ → 0, the limit point remains a CSE, which is a sequential equilibrium  at χ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  9  Finally, by a similar argument to Kreps and Wilson (1982), for any χ ∈ [0, 1], χ-CSE is  also upper hemi-continuous with respect to payoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, our χ-CSE preserves  the continuity property of sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The next result is the characterization of a necessary condition for χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As seen  from Lemma 1, players update their beliefs more passively in χ-CSE than in the stan-  dard equilibrium—they put χ-weight on their beliefs formed in previous stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To formalize  this, we define the χ-dampened updating property in Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' An assessment satisfies  this property if at any non-terminal history, the belief puts at least χ weight on the belief  in previous stage—both on and off the equilibrium path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In Proposition 3, we show that  χ-consistency implies the χ-dampened updating property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' An assessment (µ, σ) satisfies the χ-dampened updating property if for any  i ∈ N, θ ∈ Θ and ht = (ht−1, at) ∈ H\\HT,  µi(θ−i|ht, θi) ≥ χµi(θ−i|ht−1, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' χ-consistency implies χ-dampened updating for any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  It follows that if assessment (µ, σ) satisfies the χ-dampened updating property, then for  any player i, any history ht and any type profile θ, player i’s belief about θ−i is bounded by  χµi(θ−i|ht−1, θi) ≤ µi(θ−i|ht, θi) ≤ 1 − χ  �  θ′  −i̸=θ−i  µi(θ′  −i|ht−1, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  One can see from this condition that when χ increases, the feasible range of µi(θ−i|ht, θi)  shrinks, and the restriction on the belief system becomes more stringent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, if the  history ht is an off-path history of (µ, σ), then this condition characterizes the feasible set of  off-path beliefs, which shrinks as χ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  An important implication of this observation is that Φ(χ) is not lower hemi-continuous  with respect to χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The intuition is that for some χ-CSE that contains off-path histories, the  off-path beliefs to support the equilibrium might not be χ-consistent for sufficiently large χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, the χ-CSE is not attainable by a sequence of χk-CSE where χk converges to χ  from above, causing the lack of lower hemi-continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  Lastly, another implication of χ-dampened updating property is that for each player i,  history ht and type profile θ, the belief µi(θ−i|ht, θi) has a lower bound that is independent  5An example is provided in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  10  of the strategy profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The lower bound is characterized in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This result implies  that when χ > 0, F(θ−i|θi) > 0 implies µi(θ−i|ht, θi) > 0 for all ht, so that if prior beliefs are  bounded away from zero, beliefs are always bounded away from 0 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words,  when χ > 0, because of the χ-dampened updating, beliefs will always have full support even  if at off-path histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any χ-consistent assessment (µ, σ), i ∈ N, θ ∈ Θ and ht ∈ H\\HT,  µi(θ−i|ht, θi) ≥ χtF(θ−i|θi)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  If the game has only one stage, then the dampened updating property has no effect, in  which case χ-CSE and χ-CE are equivalent solution concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This is formally stated and  proved in Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any one-stage game and for any χ, χ-CSE and χ-CE are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any one-stage game, the only public history is the initial history h∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, in any  χ-CSE, for each player i ∈ N and type profile θ ∈ Θ, player i’s belief about other players’  types at this history is  µi(θ−i|h∅, θi) = F(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since the game has only one stage, the outcome is simply a1 = (a1  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , a1  n), the action profile  at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, given any behavioral strategy profile σ, player i believes a1 will be the  outcome with probability  σi(a1  i |h∅, θi) ×  �  χ¯σ−i(a1  −i|h∅, θi) + (1 − χ)σ−i(a1  −i|h∅, θ−i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, if σ is the behavioral strategy profile of a χ-CSE in an one-stage game, then for  each player i, type θi ∈ Θi and each a1  i ∈ Ai(h∅) such that σi(a1  i |h∅, θi) > 0,  a1  i ∈ argmax  a1′  i ∈Ai(h∅)  �  θ−i∈Θ−i  F(θ−i|θi) ×  �  �  �  �  a1  −i∈A−i(h∅)  �  χ¯σ−i(a1  −i|h∅, θi) + (1 − χ)σ−i(a1  −i|h∅, θ−i)  �  �  �  � ui(a1′  i , a1  −i, θi, θ−i),  which coincides with the maximization problem of χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  11  From the proof of Proposition 4, one can see that in one-stage games players have correct  perceptions about the average strategy of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, the maximization problem  of χ-CSE coincides with the problem of χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For general multi-stage games, because of  the χ-dampened updating property, players will update beliefs incorrectly and thus their  perceptions about other players’ future moves can also be distorted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4  Applications  In this section, we will explore χ-CSE in five applications of multi-stage games with observed  actions, in order to illustrate the range of effects it can have and to show how it is different  from the χ-CE and sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Our first application is the sender-receiver signaling game, which is practically the sim-  plest possible multi-stage game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' From our analysis, we will see both the theoretical and  empirical implications of our χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1  Pooling Equilibria in Signaling Games  We first make a general observation about pooling equilibria in multi-stage games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Player  j follows a pooling strategy if for every non-terminal history, ht, all types of player j take  the same action at+1  j  ∈ Aj(ht).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Conceptually, since every type of player j takes the same  action, players other than j cannot make any inference about j’s type from j’s actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A  pooling χ-CSE is a χ-CSE where every player follows a pooling strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, every player  has correct beliefs about any other player’s future move because every type of every player  chooses the same action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since in any pooling χ-CSE, players can correctly anticipate other players’ future moves  no matter how cursed they are, one may naturally conjecture that a pooling χ-CSE is also a  χ′-CSE for any χ′ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As shown by Eyster and Rabin (2005), this is true for one-stage  Bayesian games: if a pooling strategy profile is a χ-cursed equilibrium, then it is also a  χ′-cursed equilibrium for any χ′ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Surprisingly, this result does not extend to multi-  stage games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Proposition 5 shows if a pooling behavioral strategy profile is a χ-CSE, then it  remains a χ′-CSE only for χ′ ≤ χ, which is a weaker result than Eyster and Rabin (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This result is driven by the χ-dampened updating property which restricts the set of  off-path beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As discussed above, when χ gets larger, the set of feasible off-path beliefs  shrinks, eliminating some pooling χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A pooling χ-CSE is a χ′-CSE for χ′ ≤ χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  12  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The proof strategy is similar to the one in Eyster and Rabin (2005) Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given  a χ-CSE behavioral strategy profile, we can separate the histories into on-path and off-path  histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For on-path histories in a pooling equilibrium, since all types of players make the  same decisions, players cannot make any inference about other players’ types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  for on-path histories, their beliefs are the prior beliefs, which are independent of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the  other hand, for off-path histories, as shown in Proposition 3, a necessary condition for χ-CSE  is that the belief system has to satisfy the χ-dampened updating property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When χ gets  larger, this requirement becomes more stringent, and hence some pooling χ-CSE may break  down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Example 1 is a signaling game where the sender has only two types and two messages, and  the receiver has only two actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This example demonstrates the implication of Proposition  5 and shows the lack of lower hemi-continuity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', it is possible for a pooling behavioral  strategy profile to be a χ-CSE, but not a χ′-CSE for χ′ > χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The sender has two possible types drawn from the set Θ = {θ1, θ2} with  Pr(θ1) = 1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The receiver does not have any private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' After the sender’s type  is drawn, the sender observes his type and decides to send a message m ∈ {A, B}, or any  mixture between the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' After that, the receiver decides between action a ∈ {L, R} or any  mixture between the two, and the game ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The game tree is illustrated in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2, 2  L  −1, 4  R  A  4, −1  L  1, 0  R  B  θ1  [ 1  4]  2, 1  L  −1, 0  R  A  4, −2  L  1, 0  R  B  θ2  [ 3  4]  Nature  1  1  2  2  Figure 1: Game Tree for Example 1  If we solve for the χ-CE of the game (or the sequential equilibria), we find that there  are two pooling equilibria for every value of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the first pooling χ-CE, both sender types  choose A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' the receiver chooses L in response to A and R at the off-path history B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In  13  the second pooling χ-CE, both sender types pool at B and the receiver chooses R at both  histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By Proposition 3 of Eyster and Rabin (2005), these two equilibria are in fact  pooling χ-CE for all χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The intuition is that in a pooling χ-CE, players are not  able to make any inference about other players’ types from their actions because the average  normal form strategy is the same as the type-conditional normal form strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  their beliefs are independent of χ, and hence a pooling χ-CE will still be an equilibrium for  any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  However, as summarized in Claim 1 below, the χ-CSE imposes stronger restrictions than  χ-CE in this example, in the sense that when χ is sufficiently large, the second pooling equi-  librium cannot be supported as a χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The key reason is that when the game is analyzed  in its normal form, the χ-dampened updating property shown in Proposition 3 does not have  any bite, allowing both pooling equilibria to be supported as a χ-CE for any value of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Yet,  in the χ-CSE analysis, the additional restriction of χ-dampened updating property eliminates  some extreme off-path beliefs, and hence, eliminates the second pooling χ-CSE equilibrium  for sufficiently large χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For simplicity, we use a four-tuple [(m(θ1), m(θ2));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (a(A), a(B))] to  denote a behavioral strategy profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Claim 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this example, there are two pure pooling χ-CSE, which are:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(A, A);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (L, R)] is a pooling χ-CSE for any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(B, B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (R, R)] with µ2(θ1|A) ∈  � 1  3, 1 − 3  4χ  �  is a pooling χ-CSE if and only if χ ≤ 8/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  From previous discussion, we know in general, the sets of χ-CSE and χ-CE are non-  overlapping because of the nature of sequential distortion of beliefs in χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Yet, a pooling  χ-CSE is an exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In a pooling χ-CSE, players can correctly anticipate others’ future  moves, so a pooling χ-CSE will mechanically be a pooling χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In cases such as this, we  can find that χ-CSE ia a refinement of χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Lastly, we can observe from this example that the χ-CSE correspondence Φ(χ) is not  lower hemi-continuous with respect to χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To see this, we consider a sequence of {χk} where  χk = 8  9 + 1  9k for k ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' From the analysis of Claim 1, we know [(B, B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (R, R)] ̸∈ Φ(χk) for  any k ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, in the limit where χk → 8/9, [(B, B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (R, R)] with µ2(θ1|A) = 1/3 is  indeed a CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, [(B, B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (R, R)] is not approachable by this sequence of χk-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Φ(χ) is not lower hemi-continuous with respect to χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  14  45, 30  30, 30  C  15, 0  0, 0  D  30, 15  50, 35  E  I  30, 90  45, 90  C  0, 15  15, 15  D  45, 15  100, 30  E  S  θ1  [ 1  2]  30, 30  30, 30  C  0, 45  30, 45  D  30, 15  30, 0  E  I  45, 0  45, 0  C  15, 30  0, 30  D  30, 15  0, 15  E  S  θ2  [ 1  2]  �BH 3  BH 4  �  Nature  1  1  2  2  Figure 2: Game Tree for BH 3 and BH 4 in Brandts and Holt (1993)  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Here we analyze two signaling games that were studied experimentally by  Brandts and Holt (1993) (BH 3 and BH 4) and show that χ-CSE can help explain some  of their findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In both Game BH 3 and Game BH 4, the sender has two possible types  {θ1, θ2} which are equally likely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' There are two messages m ∈ {I, S} available to the sender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  After seeing the message, the receiver chooses an action from a ∈ {C, D, E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The game tree  and payoffs for both games are summarized in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In both games, there are two pooling sequential equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the first equilibrium, both  sender types send message I, and the receiver will choose C in response to I and choose  D in response to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the second equilibrium, both sender types send message S, and the  receiver will choose D in response to I while choose C in response to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Both are sequential  equilibria, in both games, but only the first equilibrium where the sender sends I satisfies  the intuitive criterion proposed by Cho and Kreps (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since the equilibrium structure is similar in both games, the sequential equilibrium and  the intuitive criterion predict the behavior should be the same in both games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, this  prediction is strikingly rejected by the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Brandts and Holt (1993) report that in the  later rounds of the experiment, almost all type θ1 senders send I in Game BH 3 (97 %), and  yet all type θ1 senders send S in Game BH 4 (100%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In contrast, type θ2 senders behave  similarly in both games—46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2% and 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1% of type θ2 senders send I in Games BH 3 and  BH 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Qualitatively speaking, the empirical pattern reported by Brandts and  Holt (1993) is that sender type θ1 is more likely to send I in Game BH 3 than Game BH 4  6I stands for “Intuitive” and S stands for “Sequential but not intuitive”, corresponding to the two pooling  sequential equilibria of the two games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  15  while sender type θ2’s behavior is insensitive to the change of games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To explain this finding, Brandts and Holt (1993) propose a descriptive story based on  naive receivers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A naive receiver will think both sender types are equally likely, regardless of  which message is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This naive reasoning will lead the receiver to choose C in both  games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given this naive response, a type θ1 sender has an incentive to send I in Game BH  3 and choose S in Game BH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (Brandts and Holt (1993), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 284 – 285)  In fact, their story of naive reasoning echoes the logic of χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When the receiver is  fully cursed (or naive), he will ignore the correlation between the sender’s action and type,  causing him to not update the belief about the sender’s type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Proposition 6 characterizes  the set of χ-CSE of both games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Following the notation in Example 1, we use a four-tuple  [(m(θ1), m(θ2));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (a(I), a(S))] to denote a behavioral strategy profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The set of χ-CSE of Game BH 3 and BH 4 are characterized as below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In Game BH 3, there are three pure χ-CSE:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(I, I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, D)] is a pooling χ-CSE if and only if χ ≤ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(I, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, C)] is a separating χ-CSE if and only if χ ≥ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In Game BH 4, there are three pure χ-CSE:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(I, I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, D)] is a pooling χ-CSE if and only if χ ≤ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, C)] is a pooling χ-CSE for any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As noted earlier for Example 1, by Proposition 3 of Eyster and Rabin (2005), pooling  equilibria (1) and (2) in games BH 3 and BH 4 survive as χ-CE for all χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence,  Proposition 6 implies that χ-CSE refines the χ-CE pooling equilibria for larger values of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Moreover, χ-CSE actually eliminates all pooling equilibria in BH 3 if χ > 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Proposition  6 also suggests that for any χ ∈ [0, 1], sender type θ2 will behave similarly in both games,  which is qualitatively consistent with the empirical pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition, χ-CSE predicts that  a highly cursed (χ > 2/3) type θ1 sender will send different messages in different games—  highly cursed type θ1 senders will send I and S in Games BH 3 and BH 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This  is consistent with the empirical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  16  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  A Public Goods Game with Communication  Our second application is a threshold public goods game with private information and pre-  play communication, variations of which have been studied in laboratory experiments (Pal-  frey and Rosenthal, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Here we consider the “unanimity” case where  there are N players and the threshold is also N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Each player i has a private cost parameter ci, which is independently drawn from a  uniform distribution on [0, K] where K > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' After each player’s ci is drawn, each player ob-  serves their own cost, but not the others’ costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, ci is player i’s private information  and corresponds to θi in the general formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='7 The game consists of two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' After  the profile of cost parameters is drawn, the game will proceed to stage 1 where each player  simultaneously broadcasts a public message mi ∈ {0, 1} without any cost or commitment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  After all players observe the message profile from this first stage, the game proceeds to stage  2 which is a unanimity threshold public goods game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Player i has to pay the cost ci if he  contributes, but the public good will be provided only if all players contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If the public  good is provided, each player receives a payoff of 1 − ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  If there is no communication stage, the unique Bayesian Nash equilibrium is that no  player contributes, which is also the unique χ-CE for any χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In contrast, with the  communication stage, there exists an efficient sequential equilibrium where each player i  sends mi = 1 if and only if ci ≤ 1 and contributes if and only if all players send 1 in the  first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8 Since this is a private value game, the standard cursed equilibrium has no bite,  and this efficient sequential equilibrium is also a χ-CE for all values of χ, by Proposition 2  of Eyster and Rabin (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the following, we demonstrate that the prediction of χ-CSE  is different from CE (and sequential equilibrium).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To analyze the χ-CSE, consider a collection of “cutoff” costs, {Cχ  c , Cχ  0 , Cχ  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , Cχ  N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In  the communication stage, each player communicates the message mi = 1 if and only if  ci ≤ Cχ  c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the second stage, if there are exactly 0 ≤ k ≤ N players sending mi = 1 in the  first stage, then such a player would contribute in the second stage if and only if ci ≤ Cχ  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  A χ-CSE is a collection of these cost cutoffs such that the associated strategies are a χ-CSE  for the public goods game with communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The most efficient sequential equilibrium  identified above for χ = 0 corresponds to cutoffs with C0  0 = C0  1 = · · · = C0  N−1 = 0 and  C0  c = C0  N = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  7This application has a continuum of types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The framework of analysis developed for finite types is  applied in the obvious way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  8One can think of the first stage as a poll, where players are asked the following question: “Are you  willing to contribute if everyone else says they are willing to contribute?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The message mi = 1 corresponds  to a “yes” answer and the message mi = 0 corresponds to a “no” answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  17  There are in fact multiple equilibria in this game with communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In order to  demonstrate how the cursed belief can distort players’ behavior, here we will focus on the  χ-CSE that is similar to the most efficient sequential equilibrium identified above, where  Cχ  0 = Cχ  1 = · · · = Cχ  N−1 = 0 and Cχ  c = Cχ  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The resulting χ-CSE is given in Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the public goods game with communication, there is a χ-CSE where  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Cχ  0 = Cχ  1 = · · · = Cχ  N−1 = 0, and  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' there is a unique C∗(N, K, χ) ≤ 1 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Cχ  c = Cχ  N = C∗(N, K, χ) that solves:  C∗(N, K, χ) − χ  �C∗(N, K, χ)  K  �N−1  = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To provide some intuition, we sketch the proof by analyzing the two-person game, where  the χ-CSE is characterized by four cutoffs {Cχ  c , Cχ  0 , Cχ  1 , Cχ  2 }, with Cχ  0 = Cχ  1 = 0 and Cχ  c =  Cχ  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If players use the strategy that they would send message 1 if the cost is less than Cχ  c ,  then by Lemma 1, at the history where both players send 1, player i’s cursed posterior belief  density would be  µχ  i (c−i|{1, 1}) =  �  �  �  χ ·  � 1  K  �  + (1 − χ) ·  �  1  Cχ  c  �  if c−i ≤ Cχ  c  χ ·  � 1  K  �  if c−i > Cχ  c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Notice that cursedness leads a player to put some probability weight on a type that is  not compatible with the history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Namely, for χ-cursed players, when seeing another player  sending 1, they still believe the other player might have c−i > Cχ  c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When χ converges to  1, the belief simply collapses to the prior belief as fully cursed players never update their  beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, when χ converges to 0, the belief converges to 1/Cχ  c , which is  the correct Bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Given this cursed belief density, the optimal cost cutoff to contribute, Cχ  2 , solves  Cχ  2 =  � Cχ  2  0  µχ  i (c−i|{1, 1})dc−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, at the first stage cutoff equilibrium, the Cχ  c type of player would be indifferent  18  between sending 1 and 0 at the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, Cχ  c satisfies  0 =  �Cχ  c  K  � �  −Cχ  c +  � Cχ  2  0  µχ  i (c−i|{1, 1})dc−i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  After substituting Cχ  c = Cχ  2 and solving, we obtain the χ-CSE:  Cχ  c = Cχ  2 = K − Kχ  K − χ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  From this expression, one can see that the cutoff Cχ  c (as well as Cχ  2 ) is decreasing in χ and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When χ → 0, Cχ  c converges to 1, which is the cutoff of the sequential equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On  the other hand, when χ → 1, Cχ  c converges to 0, so there is no possibility for communication  when players are fully cursed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Similarly, when K → 1, Cχ  c converges to 1, which is the cutoff  of the sequential equilibrium, while limK→∞ Cχ  c = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  These comparative statics results with respect to χ and K are not just a special property  of the N = 2 case, but hold for all N > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Furthermore, there is a similar effect of  increasing N that results in a lower cutoff (less effective communication).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' These properties  of C∗(N, K, χ) are summarized in Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The efficient χ-CSE predicts the following comparative statics for all N ≥ 2  and K > 1:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C∗(N, K, 0) = 1 and C∗(N, K, 1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C∗(N, K, χ) is strictly decreasing in N, K, and χ for any χ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For all χ ∈ [0, 1], limN→∞ C∗(N, K, χ) = limK→∞ C∗(N, K, χ) = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  These properties are illustrated in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The left panel illustrates the equilibrium  condition for C∗ in a graph where the horizontal axis is C ∈ [0, K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can rewrite the  characterization of C∗(N, K, χ) in Proposition 7 as a solution for C to the following equation:  1 − C  χ  = 1 −  � C  K  �N−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The left panel displays the LHS of this equation, 1−C  χ , as the downward sloping line that  connects the points (0, 1  χ) and (1, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The RHS is displayed for N = 2 and N = 3 by the two  curves that connect the points (0, 1) and (K, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The equilibrium, C∗(N, K, χ), is given by  19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  C * (3, K, )  C * (2, K, )  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  K  C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  1  1  (C  K )  N  1  1  C  CSE Equilibrium Condition (K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5,  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5)  N = 2  N = 3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  C*(N, K, )  CSE Cutoffs for Different N (K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5)  N = 2  N = 3  N =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  C*(N, K, )  CSE Cutoffs for Different K (N = 2)  K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='25  K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  K =  Figure 3: (Left) Illustration of the χ-CSE equilibrium condition when K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5 and χ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (Middle) The χ-CSE cutoff C∗(N, K, χ) for N = 2, 3 and for N → ∞ when K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (Right)  The χ-CSE cutoff C∗(N, K, χ) for K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='25, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5 and for K → ∞ when N = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  the (unique) intersection of the LHS and RHS curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' It is easy to see from this graph that  C∗(N, K, χ) is strictly decreasing in N, K, and χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When N increases, the RHS increases for  all C ∈ (0, K), resulting in an intersection at a lower value of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When K increases, again  the RHS increases for all C ∈ (0, K), and also the intercept of the RHS on the horizontal axis  increases, leading to a similar effect;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and when χ increases, the intercept of the LHS on the  horizontal axis decreases, resulting in an intersection at a lower value of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition, when  N grows without bound, the RHS approaches a constant function equal to 1 for C < K,  resulting in a limiting intersection at C∗(∞, K, χ) = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This is illustrated in the middle  panel of Figure 3, which graphs C∗(2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5, ·), C∗(3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5, ·), and C∗(∞, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5, ·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A similar effect  occurs for K → ∞, illustrated in the right panel of Figure 3, which displays C∗(2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='25, ·),  C∗(2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5, ·), and C∗(2, ∞, ·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  An interesting takeaway of this analysis is that in the public goods game with communi-  cation, cursedness limits information transmission: χ-CSE predicts when players are more  cursed (higher χ), it will be harder for them to effectively communicate in the first stage  for efficient coordination in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, Corollary 3 shows that this χ-CSE  varies systematically with all three parameters of the model: N, K, and χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In contrast,  in the standard χ-CE, players best respond to the average type-contingent strategy rather  than the average behavioral strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since it is a private value game, players do not care  about the distribution of types, only the distribution of actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, the prediction of  standard CE coincides with the equilibrium prediction for all values of N, K, and χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This  seems behaviorally implausible and is also suggestive of an experimental design that varies  20  the two parameters N and K, since the qualitative effects of changing these parameters are  identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='3  Reputation Building: The Centipede Game with Altruists  T1  T2  T3  T4  P4  P3  P2  P1  1  1  1  2  2  4, 1  2, 8  16, 4  8, 32  64, 16  Figure 4: Four-stage Centipede Game  In order to further demonstrate the difference between χ-CE and χ-CSE, in this section  we consider a variation of the centipede game with private information, as analyzed in  McKelvey and Palfrey (1992) and Kreps (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This game is an illustration of reputation-  building, where a selfish player imitates an altruistic type in order to develop a reputation  for passing, which in turn entices the opponent to pass and leads to higher payoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  There are two players and four stages, and the game tree is shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In stage  one, player one can choose either Take (T1) or Pass (P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If she chooses action T1, the  game ends and the payoffs to players one and two are 4 and 1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If she chooses  the action P1, the game continues and player two has a choice between take (T2) and pass  (P2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If he chooses T2, the game ends and the payoffs to players one and two are 2 and  8, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If he chooses P2, the game continues to the third stage where player one  chooses between T3 and P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Similar to the previous stages, if she chooses T3, the payoffs  to players one and two are 16 and 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If she chooses P3, the game proceeds to  the last stage where player two chooses between T4 and P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If player two chooses T4 the  payoffs are 8 and 32, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If player two alternatively chooses P4, the payoffs are 64  and 16, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  There are two types of player one, selfish and altruistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Selfish players are assumed to  have a utility function that is linear in their own payoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Altruistic players are assumed to  have a utility function that is linear in the sum of the two payoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For the sake of simplicity,  we assume that player two has only one type, selfish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The common knowledge probability  that player one is altruistic is α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Player one knows her own type, but player two does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, player one’s type is her private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the following, we will focus on the  21  interesting case where α ≤ 1/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='9  Because this is a game of incomplete information with private values, the standard χ-CE  is equivalent to the Bayesian Nash equilibrium of the game for all χ ∈ [0, 1], and yields  the same take probabilities as the Bayesian equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since altruistic player one wants  to maximize the sum of the payoffs, it is optimal for her to always pass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The equilibrium  behavior is summarized in Claim 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Claim 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the Bayesian Nash equilibrium, selfish player one will choose P1 with probability  6α  1−α and choose T3 with probability 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' player two will choose P2 with probability 1  7 and choose  T4 with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  It is useful to see exactly why, in this example (and more generally) the standard χ-CE  is the same as the perfect Bayesian equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In particular, why it is not the case that  cursed beliefs will change player two’s updating process after observing P1 at stage one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Belief updating is not a property of the standard χ-CE as the analysis is in the strategic  form, and thus is solved as a BNE of the game in the reduced normal form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='10  Table 1  summarizes the payoff matrices in the reduced normal form of centipede game for selfish and  altruistic type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Table 1: Reduced Normal Form Centipede Game Payoff Matrix  selfish (1 − α)  T2  P2T4  P2P4  altruistic (α)  T2  P2T4  P2P4  T1  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  T1  5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 1  P1T3  2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 8  16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 4  16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 4  P1T3  10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 8  20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 4  20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 4  P1P3  2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 8  8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 32  64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 16  P1P3  10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 8  40,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 32  80,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' 16  It is easily verified that at the Bayesian Nash equilibrium,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' selfish player one would choose  T1 with probability (1 − 7α)/(1 − α) and choose P1T3 with probability 6α/(1 − α),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' while  player two would choose T2 with probability 6/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To solve the standard χ-CE, let selfish player one choose T1 with probability p and P1T3  with probability 1−p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let player two choose T2 with probability q and P2T4 with probability  1 − q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Notice that for player two, P2P4 is a dominated strategy and given this, it is also  sub-optimal for selfish player one to choose P1P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this case, selfish player one would choose  9If α > 1  7, player two always chooses P2 in the second stage since the probability of encountering altruistic  player one is sufficiently high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Selfish player one would thus chooses P1 in the first stage and choose T3 in  the third stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  10The analysis is similar for the unreduced normal form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  22  T1 if and only if  4 ≥ 2q + 16(1 − q) ⇐⇒ q ≥ 6/7,  implying that selfish player one’s best response correspondence in the standard cursed anal-  ysis coincides with the Bayesian Nash equilibrium analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, to solve for  player two’s best responses we need to first solve for the perceived strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When player  two is χ-cursed, he would think that player one is using σχ  1 (a|θ) where a ∈ {T1, P1T3, P1P3}  and θ ∈ {selfish, altruistic}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Player one’s true strategy is given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Table 2: Player 1’s True Strategy  player one’s type  σ1(a|θ)  selfish  altruistic  T1  p  0  P1T3  1 − p  0  P1P3  0  1  In this case, player one’s average strategy is simply:  ¯σ1(T1) = (1 − α)p, ¯σ1(P1T3) = (1 − α)(1 − p), ¯σ1(P1P3) = α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  By definition, σχ  1 (a|θ) = χ¯σ1(a) + (1 − χ)σ1(a|s) and hence we can find that σχ  1 (a|θ) is given  in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Table 3: Cursed Perception of Player 1’s Strategy  player one’s type  σχ  1 (a|θ)  selfish  altruistic  T1  p(1 − χα)  pχ(1 − α)  P1T3  (1 − p)(1 − χα)  (1 − p)χ(1 − α)  P1P3  χα  1 − χ + χα  From player two’s perspective, given any action profile, player two’s expected payoff is  not affected by whether player one is selfish or altruistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, player two only cares about  the marginal distribution of player one’s actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this case, χ-cursed player two believes  player one will choose a ∈ {T1, P1T3, P1P3} with probability ¯σ1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, it is optimal  for player two to choose T2 if and only if  ¯σ1(T1) + 8 [1 − ¯σ1(T1)] ≥ ¯σ1(T1) + 4¯σ1(P1T3) + 32¯σ1(P1P3) ⇐⇒ p ≤ 1 − 7α  1 − α ,  23  implying player two’s best responses in the standard cursed analysis also coincides with the  Nash best responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, one concludes that standard χ-CE would make exactly the  same prediction as the Bayesian Nash equilibrium regardless how cursed the players are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In contrast, the χ-CSE will exhibit distortions to the conditional beliefs of player two,  given that player one has passed, because player two incorrectly takes into account how  player one’s choice to pass depended on player one’s private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In particular, it  is harder to build a reputation, since a selfish type will have to imitate altruists in such a  way that the true posterior on altruistic type conditional on a pass is higher than in the  perfect Bayesian equilibrium, because the updating by player two about player one’s type is  dampened relative to this true posterior due to cursedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This distorted belief updating  will result in less passing by player one compared to the Bayesian equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Formally,  the χ-CSE is described in Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the χ-CSE, selfish player one will choose P1 with probability qχ  1 and  choose T3 with probability 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' player two will choose P2 with probability qχ  2 and choose T4  with probability 1 where  qχ  1 =  �  �  �  �  �  �  7α−7αχ  1−7αχ − α  � �  (1 − α)  if χ ≤  6  7(1−α)  0  if χ >  6  7(1−α)  and,  qχ  2 =  �  �  �  1/7  if χ ≤  6  7(1−α)  0  if χ >  6  7(1−α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In order to see how the cursedness affects the equilibrium behavior, here we focus on the  case of χ ≤  6  7(1−α) where selfish player one and player two will both mix at stage one and  two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given selfish player one chooses P1 with probability qχ  1 , by Lemma 1, we know when  the game reaches stage two, player two’s belief about player one being altruistic becomes  µχ = χα + (1 − χ)  �  α  α + (1 − α)qχ  1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Here we see that when χ is larger, player two will update his belief more slowly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  in order to maintain indifference at the mixed equilibrium, selfish player one has to pass  with lower probability so that P1 is a more informative signal to player two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result,  to make player two indifferent between T2 and P2, the following condition must hold at the  24  equilibrium:  µχ = 1  7 ⇐⇒ qχ  1 =  �7α − 7αχ  1 − 7αχ − α  � �  (1 − α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='40  Probability of Choosing P1  Probability of P1 Predicted by -CSE and -CE  CSE  CE / PBE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='40  Probability of Choosing P2  Probability of P2 Predicted by -CSE and -CE  CSE  CE / PBE  Figure 5: χ-CSE of the centipede game with altruistic players (α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='05)  To conclude this section, in Figure 5, we plot the probabilities of choosing P1 and P2 at  χ-CSE when there is a five percent chance that player one is an altruist (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' From  our analysis above, we can find that both the standard equilibrium theory and χ-CE predict  selfish player one chooses P1 with probability and player two chooses P2 with probability  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, these probabilities are independent of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, χ-CSE predicts when  players are more cursed, selfish player one is less likely to choose P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When players are  sufficiently cursed (χ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='91), selfish player one and player two will never pass—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', behave  as if there were no altruistic players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  Sequential Voting over Binary Agendas  In this section, we apply the concept of χ-CSE to the model of strategic binary amendment  voting with incomplete information studied by Ordeshook and Palfrey (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let N =  {1, 2, 3} denote the set of voters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' These three voters will vote over three possible alternatives  in X = {a, b, c}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Voting takes place in a two-stage agenda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the first stage, voters vote  between a and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the second stage, voters vote between c and the majority rule winner of  the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The majority rule winner of the second stage is the outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  25  Each voter i has three possible private-value types where Θ ∈ {θ1, θ2, θ3} is the set of  possible types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Each voter’s type is independently drawn from a common prior distribution  of types, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, the probability of a voter being type θk is pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Each voter’s type  is their own private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Each voter has the same type-dependent payoff function,  which is denoted by u(x|θ) for any x ∈ X and θ ∈ Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We summarize the payoff function  with the following table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  x  u(x|θ)  a  b  c  θ1  1  v  0  θ  θ2  0  1  v  θ3  v  0  1  Notice that v ∈ (0, 1) is a parameter that measures the intensity of the second ranked  outcome relative to the top ranked outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This intensity parameter, v, is assumed to be  the same for all types of all voters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because this is a game of private values, the standard  χ-CE and the Bayesian Nash equilibrium coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We use a1  i (θ) to denote type θ voter i’s action at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As is standard in majority  voting games we will focus on the analysis of symmetric pure-strategy equilibria where voters  do not use weakly dominated strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, we will consider at  i(·) = at  j(·) for all  i, j ∈ N, and will drop the subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this PBE (and χ-CE) all voters will vote sincerely in equilibrium except for type θ1  voters at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To see this, first note that voting insincerely in the last stage is dominated  and thus eliminated, so all types of voters vote for their preferred alternative on the last  ballot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Second, voting sincerely in both stages is a dominant strategy for a type θ2 voter,  who prefers any lottery between b and c to either a or c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Third, voting sincerely in both  stages is also dominant for a type θ3 voter in the sense that, in the event that neither of the  other two voters are type θ3, then any lottery between a and c is better than a vote between  b and c since b (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', type θ3’s least preferred alternative) will win.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='11  The PBE (and χ-CE) prediction about a type θ1 voter’s strategy at stage 1 is summarized  in the following claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Claim 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The symmetric (undominated pure) PBE strategy for type θ1 voters in the first  stage can be characterized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' a1(θ1) = b is a PBE strategy if and only if v ≥  p1  p1+p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  11When there is another type θ3 voter, the first ballot does not matter since their most preferred alternative  c will always win in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  26  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' a1(θ1) = a is a PBE strategy if and only if v ≤  p1  p1+p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Ordeshook and Palfrey (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Claim 3 shows that, if v is relatively large, only type θ1 voting sophisticatedly for b instead  of sincerely for a can be supported by a PBE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Conditional on being pivotal, voting for b in  the first stage guarantees an outcome of b and thus guarantees getting v, while voting for a  leads to a lottery between a and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, when v is sufficiently high, a type θ1 voter  will have an incentive to strategically vote for b to avoid the risk of having c elected in the  last stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The analysis of a cursed sequential equilibrium is different from the standard cursed  equilibrium in strategic form because the cursedness affects belief updating over the stages  of the game, and players anticipate future play of the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because of the dynamics and  the anticipation of future cursed behavior, such cursed behavior at later stages of a game  can feedback and affect strategic behavior earlier in the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In the context of the two-stage binary amendment strategic voting model, cursed behavior  and belief updating mean that voters in the first stage use the expected cursed beliefs in  the second stage to compute the continuation values in the two continuation games of the  second stage, either a vote between a and c or a vote between b and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because they have  a cursed understanding about the relationship between types and voting in the first stage,  this affects their predictions about which alternative wins in the second stage, conditional  on which alternative wins in the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  It is noteworthy that, given any χ ∈ [0, 1], all voters will still vote sincerely in χ-CSE  except for type θ1 voters at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As implied by Proposition 4, a voter in the last stage  would act as if solving a maximization problem of χ-CE but under an (incorrectly) updated  belief.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, we can follow the same arguments as solving for the undominated Bayesian  equilibrium and conclude that type θ2 and θ3 voters as well as type θ1 voters at stage 2 will  vote sincerely under a χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 9 establishes that the set of parameters v and p that can support a χ-CSE  in which type θ1 voters vote sophisticatedly for b shrinks as χ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If a1(θ1) = b can be supported by a symmetric χ-CSE, then it can also be  supported by a symmetric χ′-CSE for all χ′ ≤ χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The intuition behind strategic voting over agendas mainly comes from the information  content of hypothetical pivotal events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, a cursed voter does not (fully) take such  27  information into consideration, and thus becomes overly optimistic about his favorite alter-  native a being elected in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, a type θ1 voter has a stronger incentive  to deviate from sophisticated voting to sincere voting in stage 1 as χ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Interestingly, the set of v and p that can support a χ-CSE in which type θ1 voters vote  sincerely for a does not necessarily expand as the level of cursedness becomes higher, as  characterized in Proposition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given p and v ∈ (0, 1), there exists ˜χ(p, v) such that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If v >  p1  p1+p3, then a1(θ1) = a is a χ-CSE strategy if and only if χ ≥ ˜χ(p, v);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If v <  p1  p1+p3, then a1(θ1) = a is a χ-CSE strategy if and only if χ ≤ ˜χ(p, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Thus, Proposition 10 shows that, when χ is sufficiently large, there are some values of  (v, p) that cannot support sincere voting for type θ1 voters under PBE (and χ-CE) but can  support it under χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Alternatively, there also exist some values of (v, p) that can support  sincere voting under PBE but fail to support it under χ-CSE when χ is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  p1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  p3  Sophisticated Voting -CSE when v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='7  = 0  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  = 1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  p1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  p3  Sincere Voting -CSE when v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='7  = 0  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  = 1  Figure 6: χ-CSE for Sophisticated (left) and Sincere (right) Voting When v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='7  To illustrate this, Figure 6 plots the set of p (fixing v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='7) that can support a χ-CSE  for type θ1 voters at stage 1 to vote sophisticatedly for b and sincerely for a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The left panel  of Figure 6 shows that a sophisticated voting χ-CSE becomes harder to be supported as χ  28  increases, as indicated by Proposition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For example, when p ≡ (p1, p2, p3) = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1),  type θ1 voters will not vote for second preferred alternative b if χ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  On the other hand, the right panel of Figure 6 shows that, while type θ1 voters who  sincerely vote for a at stage 1 cannot be supported under PBE when p3 is large, they may  emerge in a χ-CSE with sufficiently high χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Also note that when p2 is large, sincere voting  by type θ1 voters is no longer a χ-CSE with high χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In such a sincere voting equilibrium, a  fully rational type θ1 voter knows there will be only one type θ2 voter among the other two  voters when being pivotal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, whether to sincerely vote for a is determined by the  ratio of p1 to p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When p3 is large, sincere voting at stage 1 will likely lead to zero payoff  for type θ1 voters and thus cannot be a PBE strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, cursed type θ1 voters will  take the possibility of having two type θ2 voters into account since they are not correctly  conditioning on pivotality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, when p2 is large, sincere voting at stage 1 will likely  lead to zero payoff for type θ1 voters, and thus cannot be a χ-CSE strategy with high χ,  while voting sophisticatedly for b can likely secure a payoff of v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  The Dirty Faces Game  The dirty faces game was first described by Littlewood (1953) to study the relationship be-  tween common knowledge and behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='12 There are several different variants of this game,  but here we focus on a simplified version, the two-person dirty faces game, which was theo-  retically analyzed by Fudenberg and Tirole (1991a) and Lin (2022) and was experimentally  studied by Weber (2001) and Bayer and Chan (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Let N = {1, 2} be the set of players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For each i ∈ N, let xi ∈ {O, X} represent whether  player i has a clean face (O) or a dirty face (X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Each player’s face type is independently and  identically determined by a commonly known probability p = Pr(xi = X) = 1 − Pr(xi = O).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Once the face types are drawn, each player i can observe the other player’s face x−i but not  their own face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='13 If there is at least one player with a dirty face, a public announcement of  this fact is broadcast to both players at the beginning of the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let ω ∈ {0, 1} denote  whether there is an announcement or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If there is an announcement (ω = 1), all players  are informed there is at least one dirty face but not the identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When ω = 0, it is common  knowledge to both players that their faces are clean and the game becomes trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence,  in the following, we will focus only on the interesting case where ω = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  12The dirty faces game has also been reframed as the “cheating wives puzzle” (Gamow and Stern, 1958),  the “cheating husbands puzzle” (Moses et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 1986), the “muddy children puzzle” (Barwise, 1981) and  (Halpern and Moses, 1990), and the “red hat puzzle” (Hardin and Taylor, 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  13To fit into the framework, each player’s “type” (their own private information) can be specified as “other  players’ faces.” That is, θi = x−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  29  There are a finite number of T ≥ 2 stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In each stage, each player i simultaneously  chooses si ∈ {U, D}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The game ends as soon as either player (or both) chooses D, or at the  end of stage T in case neither player has chosen D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Actions are revealed at the end of each  stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Payoffs depend on own face types and action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If a player chooses D, he will get α > 0  if he has a dirty face while receive −1 if he has a clean face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We assume that  pα − (1 − p) < 0 ⇐⇒ 0 < ¯α ≡  α  (1 − p)(1 + α) < 1,  (1)  where pα − (1 − p) is the expected payoff of D when the belief of having a dirty face is  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, Assumption (1) guarantees it is strictly dominated to choose D at stage 1 when  observing a dirty face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, players will be rewarded when correctly inferring the  dirty face but penalized when wrongly claiming the dirty face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The payoffs are discounted with a common discount factor δ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To summarize,  conditional on reaching stage t, each player’s payoff function (which depends on their own  face and action) can be written as:  ui(si|t, xi = X) =  �  �  �  δt−1α  if si = D  0  if si = U  and  ui(si|t, xi = O) =  �  �  �  −δt−1  if si = D  0  if si = U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, a two-person dirty faces game is defined by a tuple ⟨p, T, α, δ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since the game ends as soon as some player chooses D, the information sets of the game  can be specified by the face type the player observes and the stage number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus a behavioral  strategy can be represented as:  σ : {O, X} × {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , T} → [0, 1],  which is a mapping from information sets to the probability of choosing D, where {O, X}  corresponds to a player’s observation of the other player’s face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  There is a unique Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When observing a clean face, a player would im-  mediately know his face is dirty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, it is strictly dominant to choose D at stage 1 in  this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, when observing a dirty face, because of Assumption (1), it is  optimal for the player to choose U at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, if the game proceeds to stage 2, the  player would know his face is dirty because the other player would have chosen D at stage 1 if  his face were clean and the game would not have reached stage 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This result is independent  of the payoffs, the timing, the discount factor, and the (prior) probability of having a dirty  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The only assumption for this argument is common knowledge of rationality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  30  Alternatively, when players are “cursed,” they are not able to make perfect inferences  from the other player’s actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Specifically, since a cursed player has incorrect perceptions  about the relationship between the other player’s actions and their private information after  seeing the other player choose U in stage 1, a cursed player does not believe they have a dirty  face for sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At the extreme when χ = 1, fully cursed players never update their beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In the following, we will compare the predictions of the standard χ-CE and the χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A  surprising result is that there is always a unique χ-CE, but there can be multiple χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  For the sake of simplicity, we will focus on the characterization of pure strategy equi-  librium in the following analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since the game ends when some player chooses D, we  can equivalently characterize a stopping strategy as a mapping from the observed face type  to a stage in {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , T, T + 1} where T + 1 corresponds to the strategy of never stop-  ping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Furthermore, both χ-CE and χ-CSE will be symmetric because if players were to stop  at different stages, least one of the players would have a profitable deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Finally, we  use ˆσχ(x−i) and ˜σχ(x−i) to denote the equilibrium stopping strategies of χ-CE and χ-CSE,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We characterize the χ-CE in Proposition 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since χ-CE is defined for simultaneous  move Bayesian games, to solve for the χ-CE, we need to look at the corresponding normal  form where players simultaneously choose {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' , T, T + 1} given the observed face type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The χ-cursed equilibrium can be characterized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If χ > ¯α, the only χ-CE is that both players choose:  ˆσχ(O) = 1  and  ˆσχ(X) = T + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If χ < ¯α, the only χ-CE is that both players choosing  ˆσχ(O) = 1  and  ˆσχ(X) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 11 shows that χ-CE makes an extreme prediction—when observing a dirty  face, players would either choose D at stage 2 (the equilibrium prediction) or never choose  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, the prediction of χ-CE is unique for χ ̸= ¯α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As characterized in the next  Proposition 12, for extreme values of χ, the prediction of χ-CSE coincides with χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' But  for intermediate values of χ, there can be multiple χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proposition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The pure strategy χ-CSE can be characterized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ˜σχ(O) = 1 for all χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Both players choosing ˜σχ(X) = T + 1 is a χ-CSE if and only if χ ≥ ¯α  1  T +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if χ ≤ ¯α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any 3 ≤ t ≤ T, both players choosing ˜σχ(X) = t is a χ-CSE if and only if  �1 − κ(χ)  1 − p  �  1  t−2  ≤ χ ≤ ¯α  1  t−1  where  κ(χ) ≡ [(1 + α)(1 + δχ) − αδ] −  �  [(1 + α)(1 + δχ) − αδ]2 − 4δχ(1 + α)  2δχ(1 + α)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Illustrative Example  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0  1  2  3  4  5  6  CE Stopping Periods (When Observing a Dirty Face)  CE of Two-Person Dirty Faces Games  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='0  0  1  2  3  4  5  6  CSE Stopping Periods (When Observing a Dirty Face)  CSE of Two-Person Dirty Faces Games  Figure 7: χ-CE vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' χ-CSE When (α, δ, p, T) =  � 1  4, 4  5, 2  3, 5  �  In order to illustrate the sharp contrast between the predictions of χ-CE and χ-CSE,  here we consider an illustrative example where α = 1/4, δ = 4/5, p = 2/3 and the horizon  of the game is T = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As characterized by Proposition 11, χ-CE predicts players will choose  ˆσχ(X) = 2 if χ ≤ ¯α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' otherwise, they will choose ˆσχ(X) = 6, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', they never choose  32  D when observing a dirty face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As demonstrated in the left panel of Figure 7, χ-CE is  (generically) unique and it predicts players will either behave extremely sophisticated or  unresponsive to the other player’s action at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In contrast, as characterized by Proposition 12, there can be multiple χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As shown  in the right panel of Figure 7, when χ ≤ ¯α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6, both players stopping at stage 2 is still  an equilibrium, but it is not unique except for very low values of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='168 ≤ χ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='505,  both players stopping at stage 3 is also a χ-CSE, and for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='505 ≤ χ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='6, there are three  pure strategy χ-CSE where both players stop at stage 2, 3, or 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The existence of multiple χ-CSE in which both players stop at t > 2 highlights a player’s  learning process in a multi-stage game, which does not happen in strategic form cursed  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the strategic form, a player has no opportunity to learn about the other  player’s type in middle stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, when level of cursedness is not low enough to support  a χ-CE with stopping at stage 2, both players would never stop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, in a χ-CSE of  the multi-stage game, a cursed player would still learn about his own face being dirty as  the game proceeds, even though he might not be confident enough to choose D at stage 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  If χ is not too large, the expected payoff of choosing D would eventually become positive  at some stage before the last stage T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='14 For some intermediate values of χ, there might  be multiple stopping stages which yield positive expected payoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this case, the dirty  faces game becomes a special type of coordination games where both players coordinate on  stopping strategies, resulting in the existence of multiple χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='15  5  Concluding Remarks  In this paper, we formally developed Cursed Sequential Equilibrium, which extends the  strategic form cursed equilibrium (Eyster and Rabin, 2005) to multi-stage games, and il-  lustrated the new equilibrium concept with a series of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' While the standard  CE has no bite in private value games, we show that cursed beliefs can actually have  significant consequences for dynamic private value games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the private value games we  consider, our cursed sequential equilibrium predicts (1) under-contribution caused by under-  communication in the public goods game with communication, (2) low passing rate in the  presence of altruistic players in the centipede game, and (3) less sophisticated voting in the  14The upper bound of the inequality in Proposition 12 characterizes the stages at which stopping yields  positive expected payoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  15Note that players with low levels of cursedness would not coordinate on stopping at late stages since the  discount factor shrinks the informative value of waiting (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', both choosing U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This result is characterized  by the lower bound of the inequality in Proposition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  33  sequential two-stage binary agenda game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We also illustrate the distinction between CE and  CSE in some non-private value games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In simple signaling games, χ-CSE implies refinements  of pooling equilibria that are not captured by traditional belief-based refinements (or χ-CE),  and are qualitatively consistent with some experimental evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Lastly, we examine the  dirty face game, showing that the CSE further expands the set of equilibrium and predicts  stopping in middle stages of the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We summarize our findings from these applications  in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Table 4: Summary of Findings in Section 4  Private-Value  Game  χ-CE vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' BNE  χ-CSE vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' χ-CE  Signaling Games with  Pooling Equilibrium  No  ̸=  χ-CSE ⊂ χ-CE  Public Goods Game  with Communication  Yes  =  ̸=  Centipede Game  with Altruists  Yes  =  ̸=  Sequential Voting  Game  Yes  =  ̸=  Dirty Faces Game  No  ̸=  ̸=  The applications we consider are only a small sample of the possible dynamic games where  CSE could be usefully applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' One prominent class of problems where it would be interesting  to study the dynamic effects of cursedness is social learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For example, in the standard  information cascade model of Bikhchandani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1992), we conjecture that the effect would  be to delay the formation of an information cascade because players will partially neglect  the information content of prior decision makers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Laboratory experiments report evidence  that subjects underweight the information contained in prior actions relative to their own  signal (Goeree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A related class of problems involves information aggregation  through sequential voting and bandwagon effects (Callander, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Ali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Ali and  Kartik, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A natural conjecture is that CSE will impede information transmission in  committees and juries as later voters will under-appreciate the information content of the  decisions by early voters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This would dampen bandwagon effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The centipede example  34  we studied suggests than CSE might have broader implications for behavior in reputation-  building games, such as the finitely repeated prisoner’s dilemma or entry deterrence games  such as the chain store paradox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As a final remark, our analysis of applications of χ-CSE suggests some interesting exper-  iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For instance, χ-CSE predicts in the public goods game with communication, when  either N or K increases, pre-play communication will be less effective, while the prediction  of sequential equilibrium and χ-CE is independent of N and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, in an exper-  iment where N and K are manipulated, a significant treatment effect in this direction would  provide evidence supporting χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Also, χ-CSE makes qualitatively testable predictions  in the sequential voting games and the dirty faces games, which have not been extensively  studied in laboratory experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the sequential voting game, it would be interesting to  test how sensitive strategic (vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' sincere) voting behavior is to preference intensity (v) and  the type distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the dirty faces game, it would be interesting to design an exper-  iment to identify the extent to which deviations from sequential equilibrium are related to  the coordination problem that arises in χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  35  References  Ali, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Goeree, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kartik, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2008): “Information Aggre-  gation in Standing and Ad Hoc Committees,” American Economic Review, 98, 181–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Ali, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kartik (2012): “Herding with Collective Preferences,” Economic Theory,  51, 601–626.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Barwise, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1981): “Scenes and other situations,” Journal of Philosophy, 78, 369–397.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Bayer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Chan (2007): “The dirty faces game revisited,” Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', Univer-  sity of Adelaide, School of Economics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Bazerman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Samuelson (1983): “I won the auction but don’t want  the prize,” Journal of Conflict Resolution, 27, 618–634.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Bikhchandani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hirshleifer, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Welch (1992): “A theory of fads, fashion,  custom, and cultural change as informational cascades,” Journal of Political Economy,  100, 992–1026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Brandts, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Holt (1993): “Adjustment patterns and equilibrium selection in  experimental signaling games,” International Journal of Game Theory, 22, 279–302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Callander, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (2007): “Bandwagons and Momentum in Sequential Voting,” Review of  Economic Studies, 74, 653–684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Camerer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Nunnari, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2016): “Quantal Response and  Non-equilibrium Beliefs Explain Overbidding in Maximum Value Auctions,” Games and  Economic Behavior, 98, 243–263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Capen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Clapp, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Campbell (1971): “Competitive bidding in  high-risk situations,” Journal of Petroleum Technology, 23, 641–653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Carrillo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2009): “The Compromise Game: Two-Sided Adverse  Selection in the Laboratory,” American Economic Journal: Microeconomics, 1, 151–181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Carrillo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2011): “No trade,” Games and Economic Behavior,  71, 66–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Cho, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kreps (1987): “Signaling games and stable equilibria,” Quarterly  Journal of Economics, 102, 179–221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Cohen,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Li (2022):  “Sequential Cursed Equilibrium,”  arXiv preprint  arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='06025.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Dyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Kagel, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Levin (1989): “A comparison of naive and experienced  bidders in common value offer auctions: A laboratory analysis,” Economic Journal, 99,  108–115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  36  Eckel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Holt (1989): “Strategic Voting in Agenda Controlled Committee  Experiments,” American Economic Review, 79, 763–773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Eyster, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Rabin (2005): “Cursed equilibrium,” Econometrica, 73, 1623–1672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Forsythe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Isaac, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (1989): “Theories and Tests of  Blind Bidding in Sealed-bid Auctions,” Rand Journal of Economics, 20, 214–238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Fudenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Tirole (1991a): Game theory, MIT press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  ——— (1991b): “Perfect Bayesian equilibrium and sequential equilibrium,” Journal of Eco-  nomic Theory, 53, 236–260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Gamow, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Stern (1958): “Forty unfaithful wives,” Puzzle Math, 20–23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Goeree, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Rogers, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' McKelvey (2007): “Self-  correcting information cascades,” Review of Economic Studies, 74, 733–762.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Guarnaschelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' McKelvey, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2000): “An experimental  study of jury decision rules,” American Political Science Review, 94, 407–423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Halpern, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moses (1990): “Knowledge and common knowledge in a dis-  tributed environment,” Journal of the ACM (JACM), 37, 549–587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Hardin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Taylor (2008): “An introduction to infinite hat problems,”  The Mathematical Intelligencer, 30, 20–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Holt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Sherman (1994): “The loser’s curse,” American Economic Review,  84, 642–652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Ivanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Levin, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Niederle (2010): “Can Relaxation of Beliefs Rationalize  the Winner’s Curse,” Econometrica, 78, 1435–1452.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Jehiel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (2005): “Analogy-based expectation equilibrium,” Journal of Economic Theory,  123, 81–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Jehiel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Koessler (2008): “Revisiting games of incomplete information with  analogy-based expectations,” Games and Economic Behavior, 62, 533–557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Kagel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Levin (1986): “The winner’s curse and public information in com-  mon value auctions,” American Economic Review, 894–920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  ——— (2009): “Common value auctions and the winner’s curse,” in Common Value Auctions  and the Winner’s Curse, Princeton University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Kagel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Levin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Battalio, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Meyer (1989): “First-price  common value auctions: bidder behavior and the “Winner’s Curse”,” Economic Inquiry,  27, 241–258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Kreps, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1990): A course in microeconomic theory, Princeton university press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  37  Kreps, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Wilson (1982): “Sequential Equilibria,” Econometrica, 50, 863–  894.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Levine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Plott (1977): “Agenda influence and its implications,” Virginia  Law Review, 561–604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (2022): “Cognitive Hierarchies in Multi-Stage Games of Incomplete Informa-  tion,” arXiv preprint arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='11190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (2022): “Cognitive Hierarchies in Extensive Form Games,”  Caltech Social Science Working Paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Lind, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Plott (1991): “The winner’s curse: experiments with buyers and  with sellers,” American Economic Review, 81, 335–346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Littlewood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (1953): A Mathematician’s Miscellany, London, England: Meuthen &  Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  McKelvey, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (1992): “An experimental study of the centipede  game,” Econometrica, 803–836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  ——— (1998): “Quantal response equilibria for extensive form games,” Experimental Eco-  nomics, 1, 9–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Moses, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Dolev, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Halpern (1986): “Cheating husbands and other  stories: a case study of knowledge, action, and communication,” Distributed Computing,  1, 167–176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Ordeshook, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey (1988): “Agendas, strategic voting, and signaling  with incomplete information,” American Journal of Political Science, 441–466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Palfrey, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Rosenthal (1991): “Testing for effects of cheap talk in a public  goods game with private information,” Games and Economic Behavior, 3, 183–220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Palfrey, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Rosenthal, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Roy (2017): “How Cheap Talk Enhances  Efficiency in Threshold Public Goods Games,” Games and Economic Behavior, 101, 234–  259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Plott, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Levine (1978): “A Model of Agenda Influence on Committee  Decisions,” American Economic Review, 68, 146–160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Rogers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Palfrey, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Camerer (2009): “Heterogeneous quantal  response equilibrium and cognitive hierarchies,” Journal of Economic Theory, 144, 1440–  1467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Samuelson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Bazerman (1985): “Negotiation under the winner’s  curse,” Research in experimental economics, 3, 105–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Søvik, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (2009): “Strength of dominance and depths of reasoning—An experimental  study,” Journal of Economic Behavior & Organization, 70, 196–205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  38  Weber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (2001): “Behavior and learning in the “dirty faces” game,” Experimental  Economics, 4, 229–242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  39  A  Omitted Proofs of Section 2 and 3  Proof of Lemma 1  By definition 1, for any (µ, σ) ∈ Ψχ, any history ht−1, any player i and any type profile  θ = (θi, θ−i),  �  θ′  −i  µi(θ′  −i|ht−1, θi)[χ¯σ−i(at  −i|ht−1, θi) + (1 − χ)σ−i(at  −i|ht−1, θ′  −i)]  = χ  �  ��  θ′  −i  µi(θ′  −i|ht−1, θi)  �  �  �  ��  �  =1  ¯σ−i(at  −i|ht−1, θi) + (1 − χ)  �  ��  θ′  −i  µi(θ′  −i|ht−1, θi)σ−i(at  −i|ht−1, θ′  −i)  �  �  �  ��  �  =¯σ−i(at  −i|ht−1,θi)  = ¯σ−i(at  −i|ht−1, θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, since (µ, σ) ∈ Ψχ, with some rearrangement, it follows that  µi(θ−i|ht, θi) =  µi(θ−i|ht−1, θi)σχ  −i(at  −i|ht−1, θ−i, θi)  �  θ′  −i∈Θ−i µi(θ′  −i|ht−1, θi)σχ  −i(at  −i|ht−1, θ′  −i, θi)  = µi(θ−i|ht−1, θi)[χ¯σ−i(at  −i|ht−1, θi) + (1 − χ)σ−i(at  −i|ht−1, θ−i)]  ¯σ−i(at  −i|ht−1, θi)  = χµi(θ−i|ht−1, θi) + (1 − χ)  �  µi(θ−i|ht−1, θi)σ−i(at  −i|ht−1, θ−i)  �  θ′  −i µi(θ′  −i|ht−1, θi)σ−i(at  −i|ht−1, θ′  −i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 1  The proof is similar to the proof for sequential equilibrium and proceeds in three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' First,  for any finite multi-stage games with observed actions, Γ, we construct an ϵ-perturbed game  Γϵ that is identical to Γ but every player in every information set has to play any available  action with probability at least ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Second, we defined a cursed best-response correspondence  for Γϵ and prove that the correspondence has a fixed point by Kakutani’s fixed point theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, in step 3, we use a sequence of fixed points in perturbed games, with ϵ converging  to 0, where the limit of this sequence is a χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 1:  Let Γϵ be a game identical to Γ but for each player i ∈ N, player i must play any available  action in every information set Ii = (θi, ht) with probability at least ϵ where ϵ <  1  �n  j=1 |Aj|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Let Σϵ = ×n  j=1Σϵ  j be set of feasible behavioral strategy profiles for players in the perturbed  game Γϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any behavioral strategy profile σ ∈ Σϵ, let µχ(·) ≡ (µχ  i (·))n  i=1 be the belief  system induced by σ via χ-cursed Bayes’ rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, for each player i ∈ N, information  40  set Ii = (θi, ht) where ht = (ht−1, at) and type profile θ−i ∈ Θ−i,  µχ  i (θ−i|ht, θi) = χµχ  i (θ−i|ht−1, θi) +  (1 − χ)  �  µχ  i (θ−i|ht−1, θi)σ−i(at  −i|ht−1, θ−i)  �  θ′  −i∈Θ−i µχ  i (θ′  −i|ht−1, θi)σ−i(at  −i|ht−1, θ′  −i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Notice that the χ-cursed Bayes’ rule is only defined on the framework of multi-stage games  with observed actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As σ is fully mixed, the belief system is uniquely pinned down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, let Bϵ : Σϵ ⇒ Σϵ be the cursed best response correspondence which maps any  behavioral strategy profile σ ∈ Σϵ to the set of ϵ-constrained behavioral strategy profiles  ˜σ ∈ Σϵ that are best replies given the belief system µχ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 2:  Next, fix any 0 < ϵ <  1  �n  j=1 |Aj| and show that Bϵ has a fixed point by Kakutani’s fixed  point theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We check the conditions of the theorem:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' It is straightforward that Σϵ is compact and convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any σ ∈ Σϵ, as µχ(·) is uniquely pinned down by χ-cursed Bayes’ rule, it is straight-  forward that Bϵ(σ) is non-empty and convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To verify that Bϵ has a closed graph, take any sequence of ϵ-constrained behavioral  strategy profiles {σk}∞  k=1 ⊆ Σϵ such that σk → σ ∈ Σϵ as k → ∞, and any sequence  {˜σk}∞  k=1 such that ˜σk ∈ Bϵ(σk) for any k and ˜σk → ˜σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We want to prove that ˜σ ∈ Bϵ(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Fix any player i ∈ N and information set Ii = (θi, ht).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any σ ∈ Σϵ, recall that  σχ  −i(·) is player i’s χ-cursed perceived behavioral strategies of other players induced by  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Specifically, for any type profile θ ∈ Θ, non-terminal history ht−1 and action profile  at  −i ∈ A−i(ht−1),  σχ  −i(at  −i|ht−1, θ−i, θi) = χ¯σ−i(at  −i|ht−1, θi) + (1 − χ)σ−i(at  −i|ht−1, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Additionally, recall that ρχ  i (·) is player i’s belief about the terminal nodes (conditional  on the history and type profile), which is also induced by σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since µχ(·) is continuous  in σ we have thaat σχ  −i(·) and ρχ  i (·) are also continuous in σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We further define  Sk  Ii ≡  �  σ′  i ∈ Σϵ  i : σ′  i( · |Ii) = ˜σk  i ( · |Ii)  �  ,  SIi ≡ {σ′  i ∈ Σϵ  i : σ′  i( · |Ii) = ˜σi( · |Ii)} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since ˜σk ∈ Bϵ(σk), for any σ′  i ∈ Σϵ  i, we can obtain that  41  max  σ′′  i ∈Sk  Ii  �  �  �  �  θ−i∈Θ−i  �  hT ∈HT  µχ  i [σk](θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i[σk], σ′′  i )ui(hT, θi, θ−i)  �  �  �  ≥  �  θ−i∈Θ−i  �  hT ∈HT  µχ  i [σk](θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i[σk], σ′  i)ui(hT, θi, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  By continuity, as we take limits on both sides, we can obtain that  max  σ′′  i ∈SIi  �  �  �  �  θ−i∈Θ−i  �  hT ∈HT  µχ  i [σ](θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i[σ], σ′′  i )ui(hT, θi, θ−i)  �  �  �  ≥  �  θ−i∈Θ−i  �  hT ∈HT  µχ  i [σ](θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i[σ], σ′  i)ui(hT, θi, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, ˜σ ∈ Bϵ(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  By Kakutani’s fixed point theorem, Bϵ has a fixed point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 3:  For any ϵ, let σϵ be a fixed point of Bϵ and µϵ be the belief system induced by σϵ via  χ-cursed Bayes’ rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We combine these two components and let (µϵ, σϵ) be the induced  assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We now consider a sequence of ϵ → 0, where {(µϵ, σϵ)} is the corresponding  sequence of assessments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  By compactness and the finiteness of Γ, the Bolzano-Weierstrass theorem guarantees  the existence of a convergent subsequence of the assessments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As ϵ → 0, let (µϵ, σϵ) →  (µ∗, σ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By construction, the limit assessment (µ∗, σ∗) satisfies χ-consistency and sequential  rationality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, (µ∗, σ∗) is a χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 2  To prove Φ(χ) is upper hemi-continuous in χ, consider any sequence of {χk}∞  k=1 such that  χk → χ∗ ∈ [0, 1], and any sequence of CSE, {(µk, σk)}, such that (µk, σk) ∈ Φ(χk) for all  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let (µ∗, σ∗) be the limit assessment, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', (µk, σk) → (µ∗, σ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We need to show that  (µ∗, σ∗) ∈ Φ(χ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To simplify notation, for any player i ∈ N, any information set Ii = (ht, θi), any σ′  i ∈ Σi,  and any σ ∈ Σ, the expected payoff under the belief system µχ(·) induced by σ is denoted  as:  Eµχ[σ]  �  ui(σ′  i, σ−i|ht, θi)  �  ≡  �  θ−i∈Θ−i  �  hT ∈HT  µχ  i (θ−i|ht, θi)ρχ  i (hT|ht, θ, σχ  −i, σ′  i)ui(hT, θi, θ−i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Suppose (µ∗, σ∗) ̸∈ Φ(χ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Then there exists some player i ∈ N, some information set  42  Ii = (ht, θi), some σ′  i ∈ Σi, and some ϵ > 0 such that  Eµχ∗[σ∗]  �  ui(σ′  i, σ∗  −i|ht, θi)  �  − Eµχ∗[σ∗]  �  ui(σ∗  i , σ∗  −i|ht, θi)  �  > ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (A)  Since µχ(·) is continuous in χ, it follows that for any strategy profile σ, σχ  −i(·) and ρχ  i (·) are  both continuous in χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, there exists a sufficiently large M1 such that for every  k ≥ M1,  ����Eµχk[σk]  �  ui(σk  i , σk  −i|ht, θi)  �  − Eµχ∗[σ∗]  �  ui(σ∗  i , σ∗  −i|ht, θi)  � ���� < ϵ  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (B)  Similarly, there exists a sufficiently large M2 such that for every k ≥ M2,  ����Eµχk[σk]  �  ui(σ′  i, σk  −i|ht, θi)  �  − Eµχ∗[σ∗]  �  ui(σ′  i, σ∗  −i|ht, θi)  � ���� < ϵ  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (C)  Therefore, for any k ≥ max{M1, M2}, inequalities (A), (B) and (C) imply:  Eµχk[σk]  �  ui(σ′  i, σk  −i|ht, θi)  �  − Eµχk[σk]  �  ui(σk  i , σk  −i|ht, θi)  �  > ϵ  3,  implying that σ′  i is a profitable deviation for player i at information set Ii = (ht, θi), which  contradicts (µk, σk) ∈ Φ(χk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, (µ∗, σ∗) ∈ Φ(χ∗), as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 3  Fix any χ ∈ [0, 1] and let (µ, σ) be a χ-consistent assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We prove the result by  contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Suppose (µ, σ) does not satisfy χ-dampened updating property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Then there  exists i ∈ N, ˜θ ∈ Θ and a non-terminal history ht such that  µi(θ−i|ht, ˜θi) < χµi(θ−i|ht−1, ˜θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since (µ, σ) is χ-consistent, there exists a sequence {(µk, σk)} ⊆ Ψχ such that (µk, σk) →  (µ, σ) as k → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By Lemma 1, we know for this i, ˜θ and ht,  µk  i (˜θ−i|ht, ˜θi) =χµk  i (˜θ−i|ht−1, ˜θi) + (1 − χ)  �  µk  i (˜θ−i|ht−1, ˜θi)σk  −i(at  −i|ht−1, ˜θ−i)  �  θ′  −i µk  i (θ′  −i|ht−1, ˜θi)σk  −i(at  −i|ht−1, θ′  −i)  �  ≥χµk  i (˜θ−i|ht−1, ˜θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As we take the limit k → ∞ on both sides, we can obtain that  µi(˜θ−i|ht, ˜θi) = lim  k→∞ µk  i (˜θ−i|ht, ˜θi) ≥ lim  k→∞ χµk  i (˜θ−i|ht−1, ˜θi) = χµi(˜θ−i|ht−1, ˜θi),  which yields a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  43  Proof of Corollary 2  We prove the statement by induction on t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For t = 1, by Proposition 3,  µi(θ−i|h1, θi) ≥ χµi(θ−i|h∅, θi) = χF(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Next, suppose there is t′ such that the statement holds for all 1 ≤ t ≤ t′ − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At stage t′, by  Proposition 3 and the induction hypothesis, we can find that  µi(θ−i|ht′, θi) ≥ χµi(θ−i|ht′−1, θi) ≥ χ  �  χt′−1F(θ−i|θi)  �  = χt′F(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  44  B  Omitted Proofs of Section 4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1 Pooling Equilibria in Signaling Games  Proof of Proposition 5  Let the assessment (µ, σ) be a pooling χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We want to show that for any χ′ ≤ χ, the  assessment (µ, σ) is also a χ′-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Consider any non-terminal history ht−1, any player i, any  at  i ∈ Ai(ht−1) and any θ ∈ Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can first observe that  ¯σ−i(at  −i|ht−1, θi) =  �  θ′  −i  µi(θ′  −i|ht−1, θi)σ−i(at  −i|ht−1, θ′  −i)  = σ−i(at  −i|ht−1, θ−i)  �  ��  θ′  −i  µi(θ′  −i|ht−1, θi)  �  �  = σ−i(at  −i|ht−1, θ−i)  where the second equality holds because σ is a pooling behavioral strategy profile, so σ−i is  independent of other players’ types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For this pooling χ-CSE, let Gσ be the set of on-path  histories and ˜Gσ be the set of off-path histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can first show that for every h ∈ Gσ,  i ∈ N and θ ∈ Θ,  µi(θ−i|h, θi) = F(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This can be shown by induction on t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For t = 1, any h1 = (h∅, a1) and any θ ∈ Θ, by Lemma  1, we can obtain that  µi(θ−i|h1, θi) =χµi(θ−i|h∅, θi) + (1 − χ)  �µi(θ−i|h∅, θi)σ−i(a1  −i|h∅, θ−i)  ¯σ−i(a1  −i|h∅, θi)  �  =χF(θ−i|θi) + (1 − χ)F(θ−i|θi)  �σ−i(a1  −i|h∅, θ−i)  ¯σ−i(a1  −i|h∅, θi)  �  �  ��  �  =1  =F(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Now, suppose there is t′ such that the statement holds for 1 ≤ t ≤ t′ − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At stage t′ and  ht′ = (ht′−1, at′) ∈ Gσ, by Lemma 1 and the induction hypothesis, we can again obtain that  the posterior belief is the prior belief  µi(θ−i|ht′, θi) =χµi(θ−i|ht′−1, θi) + (1 − χ)  �  µi(θ−i|ht′−1, θi)σ−i(at′  −i|ht′−1, θ−i)  ¯σ−i(at′  −i|ht′−1, θi)  �  =χF(θ−i|θi) + (1 − χ)F(θ−i|θi)  �  σ−i(at′  −i|ht′−1, θ−i)  ¯σ−i(at′  −i|ht′−1, θi)  �  �  ��  �  =1  =F(θ−i|θi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  45  Therefore, we have shown that players will not update their beliefs at every on-path informa-  tion set, so the belief system is independent of χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Finally, for any off-path history ht ∈ ˜Gσ,  by Proposition 3, we can find that the belief system satisfies for any θ ∈ Θ,  µi(θ−i|ht, θi) ≥ χµi(θ−i|ht−1, θi) ≥ χ′µi(θ−i|ht−1, θi),  implying that when χ′ ≤ χ, µ will still satisfy the dampened updating property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  (µ, σ) remains a χ′-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Claim 1  First observe that after player 1 chooses B, it is strictly optimal for player 2 to choose R  for all beliefs µ2(θ1|B), and after player 1 chooses A, it is optimal for player 2 to choose L  if and only if  2µ2(θ1|A) + [1 − µ2(θ1|A)] ≥ 4µ2(θ1|A) ⇐⇒ µ2(θ1|A) ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Equilibrium 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  If both types of player 1 choose A, then µ2(θ1|A) = 1/4, so it is optimal for player 2 to  choose L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given a(A) = L and a(B) = R, it is optimal for both types of player 1 to choose  A as 2 > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence m(θ1) = m(θ2) = A, a(A) = L and a(B) = R is a pooling χ-CSE for any  χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Equilibrium 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In order to support m(θ1) = m(θ2) = B to be an equilibrium, player 2 has to choose R at  the off-path information set A, which is optimal if and onlly if µ2(θ1|A) ≥ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition,  by Proposition 3, we know in a χ-CSE, the belief system satisfies  µ2(θ2|A) ≥ 3  4χ ⇐⇒ µ2(θ1|A) ≤ 1 − 3  4χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, the belief system has to satisfy that µ2(θ1|A) ∈  � 1  3, 1 − 3  4χ  �  , which requires χ ≤  8/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, it is straightforward to verify that for any µ ∈  � 1  3, 1 − 3  4χ  �  , µ2(θ1|A) = µ satisfies  χ-consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Suppose type θ1 player 1 chooses A with probability p and type θ2 player 1  chooses A with probability q where p, q ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given this behavioral strategy profile for  player 1, by Lemma 1, we have:  µ2(θ1|A) = 1  4χ + (1 − χ)  �  p  p + 3q  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In other words, as long as (p, q) satisfies  q =  �4 − 4µ − 3χ  12 − 3χ  �  p,  46  we can find that µ2(θ1|A) = µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, if {(pk, qk)} → (0, 0) such that  qk =  �4 − 4µ − 3χ  12 − 3χ  �  pk,  then µk  2(θ1|A) = µ for all k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, limk→∞ µk  2(θ1|A) = µ, suggesting that µ2(θ1|A) = µ is  indeed χ-consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 6  Here we provide a characterization of χ-CSE of Game 1 and Game 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For the analysis of  both games, we denote µI ≡ µ2(θ1|m = I) and µS ≡ µ2(θ1|m = S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Analysis of Game BH 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  At information set S, given µS, the expected payoffs of C, D, E are 90µS, 30 − 15µS and  15, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, for any µS, E is never a best response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, C is the best  response if and only if 90µS ≥ 30 − 15µS or µS ≥ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Similarly, at information set I, given  µI, the expected payoffs of C, D, E are 30, 45 − 45µI and 15, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, E is  strictly dominated, and C is the best response if and only if 30 ≥ 45 − 45µI or µI ≥ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Now we consider four cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 1 [m(θ1) = I, m(θ2) = S]:  By Lemma 1, µI = 1 − χ/2 and µS = χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, since µI = 1 − χ/2 ≥ 1/2 for any  χ, player 2 will choose C at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this equilibrium, player 2 has to  choose C at information set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, [(I, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, C)] is separating χ-CSE if and  only if µS ≥ 2/7 or χ ≥ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2 [m(θ1) = S, m(θ2) = I]:  By Lemma 1, µI = χ/2 and µS = 1 − χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because µS ≥ 1 − χ/2 ≥ 1/2, it is optimal  for player 2 to choose C at information set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this as an equilibrium, player 2  has to choose D at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Yet, in this case, type θ2 player 1 will deviate to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, this profile cannot be supported as an equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 3 [m(θ1) = I, m(θ2) = I]:  Since player 1 follows a pooling strategy, player 2 will not update his belief at information  set I, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', µI = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' χ-dampened updating property implies χ/2 ≤ µS ≤ 1 − χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since  µI > 1/3, player 2 will choose C at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this profile to be an  equilibrium, player 2 has to choose D at information set S, and hence, it must be the case  that µS ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Coupled with the requirement from χ-dampened updating, the off-path  belief has to satisfy χ/2 ≤ µS ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, [(I, I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, D)] is pooling χ-CSE if and only if  χ/2 ≤ 2/7 or χ ≤ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 4 [m(θ1) = S, m(θ2) = S]:  Similar to the previous case, since player 1 follows a pooling strategy, player 2 will not  update his belief at information set S, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', µS = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Also, the χ-dampened updating  47  property suggests χ/2 ≤ µI ≤ 1 − χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because µS > 2/7, it is optimal for player 2 to  choose C at information set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this as an equilibrium, player 2 has to choose D  at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, it must be that µI ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Combined with the requirement  of χ-dampened updating, the off-path belief has to satisfy χ/2 ≤ µI ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result,  [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (D, C)] is a pooling χ-CSE if and only if χ ≤ 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Analysis of Game BH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  At information set I, given µI, the expected payoffs of C, D, E are 30, 45 − 45µI and  35µI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence, D is the best response if and only if µI ≤ 1/3 while E is the best response  if µI ≥ 6/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For 1/3 ≤ µI ≤ 6/7, C is the best response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, since player  2’s payoffs at information set S are the same as in Game 1, player 2 will adopt the same  decision rule—player 2 will choose C if and only if µS ≥ 2/7, and choose D if and only if  µS ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Now, we consider the following four cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 1 [m(θ1) = I, m(θ2) = S]:  In this case, by Lemma 1, µI = 1 − χ/2 and µS = χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this profile to be an  equilibrium, player 2 has to choose E and C at information set I and S, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To  make it profitable for player 2 to choose E at information set I, it must be that:  µI = 1 − χ/2 ≥ 6/7 ⇐⇒ χ ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  On the other hand, player 2 will choose C at information set S if and only if χ/2 ≥ 2/7 or  χ ≥ 4/7, which is not compatible with the previous inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, this profile cannot  be supported as an equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2 [m(θ1) = S, m(θ2) = I]:  In this case, by Lemma 1, µI = χ/2 and µS = 1−χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this as an equilibrium,  player 2 has to choose D at both information sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Yet, µS = 1 − χ/2 > 2/7, implying that  it is not a best reply for player 2 to choose D at information set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence this profile also  cannot be supported as an equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 3 [m(θ1) = I, m(θ2) = I]:  Since player 1 follows a pooling strategy, player 2 will not update his belief at information  set I, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', µI = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' The χ-dampened updating property implies χ/2 ≤ µS ≤ 1 − χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Because 1/3 < µI = 1/2 < 6/7, player 2 will choose C at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support  this profile as an equilibrium, player 2 has to choose D at information set S, and hence, it  must be the case that µS ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Coupled with the requirement of χ-dampened updating,  the off-path belief has to satisfy χ/2 ≤ µS ≤ 2/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, [(I, I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, D)] is pooling χ-CSE  if and only if χ/2 ≤ 2/7 or χ ≤ 4/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 4 [m(θ1) = S, m(θ2) = S]:  Similar to the previous case, since player 1 follows a pooling strategy, player 2 will not  update his belief at information set S, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', µS = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Also, the χ-dampened updating  property implies χ/2 ≤ µI ≤ 1 − χ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because µS > 2/7, it is optimal for player 2 to choose  48  C at information set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To support this as an equilibrium, player 2 can choose either C or  D at information set I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='1: To make it a best reply for player 2 to choose D at information set I, it must  be that µI ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Combined with the requirement from χ-dampened updating, the off-path  belief has to satisfy χ/2 ≤ µI ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (D, C)] is a pooling χ-CSE if and  only if χ ≤ 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2: To make it a best reply for player 2 to choose C at information set S, it must  be that 1/3 ≤ µI ≤ 6/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Combined with the requirement from χ-dampened updating, the  off-path belief has to satisfy  max  �1  2χ, 1  3  �  ≤ µI ≤ min  �6  7, 1 − 1  2χ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  For any χ ∈ [0, 1], one can find µI that satisfies both inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence [(S, S);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' (C, C)] is a  pooling χ-CSE for any χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the analysis of Game 1 and Game 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='2  A Public Goods Game with Communication  Proof of Proposition 7  To prove this set of cost cutoffs form a χ-CSE, we need to show that there is no profitable  deviation for any type at any subgame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' First, at the second stage where there are exactly  0 ≤ k ≤ N − 1 players sending 1 in the first stage, since no players will contribute, setting  Cχ  k = 0 is indeed a best response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At the subgame where all N players send 1 in the first  stage, we use µχ  i (c−i|N) to denote player i’s cursed belief density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' By Lemma 1, the cursed  belief about all other players having a cost lower than c is simply:  F χ(c) ≡  �  {cj≤c, ∀j̸=i}  µχ  i (c′  −i|N)dc′  −i  =  �  χ (c/K)N−1 + (1 − χ) (c/Cχ  c )N−1  if c ≤ Cχ  c  1 − χ + χ (c/Cχ  c )N−1  if c > Cχ  c ,  and Cχ  N is the solution of the fixed point problem of Cχ  N = F χ(Cχ  N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Moreover, in equilibrium, Cχ  c type of players would be indifferent between sending 1 and  0 in the communication stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, given Cχ  N, Cχ  c is the solution of the following equation  0 =  �Cχ  c  K  �N−1  [−Cχ  c + F χ(Cχ  N)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As a result, we obtain that in equilibrium, Cχ  c = Cχ  N = F χ(Cχ  N) ≤ 1 and denote this cost  49  cutoff by C∗(N, K, χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Substituting it into F χ(c), gives:  C∗(N, K, χ) − χ  �C∗(N, K, χ)  K  �N−1  = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In the following, we show that for any N ≥ 2 and χ, the cutoff C∗(N, K, χ) is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 1: When N = 2, the cutoff C∗(2, K, χ) is the unique solution of the linear equation  C∗(2, K, χ) − χ  �C∗(2, K, χ)  K  �  = 1 − χ ⇐⇒ C∗(2, K, χ) = K − Kχ  K − χ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2: For N ≥ 3, we define the function h(y) : [0, 1] → R where  h(y) = y − χ  � y  K  �N−1  − (1 − χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  It suffices to show that h(y) has a unique root in [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' When χ = 0, h(y) = y − 1 which has  a unique root at y = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the following, we will focus on the case where χ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Since h(y)  is continuous, h(0) = −(1 − χ) < 0 and h(1) = χ  �  1 − (1/K)N−1�  > 0, there exists a root  y∗ ∈ (0, 1) by the intermediate value theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover, as we take the second derivative,  we can find that for any y ∈ (0, 1),  h′′(y) = −  �  χ  KN−1  �  (N − 1)(N − 2)yN−3 < 0,  implying that h(y) is strictly concave in [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Furthermore, h(0) < 0 and h(1) > 0, so the  root is unique, as illustrated in the left panel of Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Corollary 3  By Proposition 7, we know the cutoff C∗(N, K, χ) ≤ 1 and it satisfies  C∗(N, K, χ) − χ  �C∗(N, K, χ)  K  �N−1  = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, when χ = 0, the condition becomes C∗(N, K, 0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In addition, when χ = 1,  the condition becomes  C∗(N, K, 1) −  �C∗(N, K, 1)  K  �N−1  = 0,  implying C∗(N, K, 1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  For χ ∈ (0, 1), to prove C∗(N, K, χ) is strictly decreasing in N, K and χ, we consider a  function g(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' N, K, χ) : (0, 1) → R where g(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' N, K, χ) = y − χ[y/K]N−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For any y ∈ (0, 1)  and fix any K and χ, we can observe that when N ≥ 2,  g(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' N + 1, K) − g(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' N, K) = −χ  � y  K  �N  + χ  � y  K  �N−1  > 0,  50  so g(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' N, K, χ) is strictly increasing in N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, the cutoff C∗(N, K, χ) is strictly  decreasing in N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Similarly, for any y ∈ (0, 1) and fix any N and χ, observe that when  K > 1,  ∂g  ∂K = χ(N − 1)  �yN−1  KN  �  > 0,  which implies that cutoff C∗(N, K, χ) is also strictly decreasing in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For the comparative  statics of χ, we can rearrange the equilibrium condition where  1 − C∗(N, K, χ)  χ  = 1 −  �C∗(N, K, χ)  K  �N−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since LHS is strictly decreasing in χ, the equilibrium cutoff is also strictly decreasing in χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Finally, taking the limit on both sides of the equilibrium condition, we obtain:  lim  N→∞ C∗(N, K, χ) = lim  K→∞ C∗(N, K, χ) = 1 − χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='3  The Centipede Game with Altruistic Types  Proof of Claim 2  By backward induction, we know selfish player two will choose T4 for sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given that  player two will choose T4 at stage four, it is optimal for selfish player one to choose T3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Now, suppose selfish player one will choose P1 with probability q1 and player two will choose  P2 with probability q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given this behavioral strategy profile, player two’s belief about the  other player being altruistic at stage two is:  µ =  α  α + (1 − α)q1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, it is optimal for selfish player two to pass if and only if  32µ + 4(1 − µ) ≥ 8 ⇐⇒ µ ≥ 1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  At the equilibrium, selfish player two is indifferent between T2 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If not, say 32µ +  4(1 − µ) > 8, player two will choose P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given that player two will choose P2, it is optimal  for selfish player one to choose P1, which makes µ = α and α > 1/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, we know  α ≤ 1/7 which yields a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, if 32µ + 4(1 − µ) < 8, then it is  optimal for player two to choose T2 at stage two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, selfish player one would choose  T1 at stage one, causing µ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In this case, player two would deviate to choose P2, which  again yields a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To summarize, in equilibrium, player two has to be indifferent  between T2 and P2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', µ = 1/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As we rearrange the equality, we can obtain that  α  α + (1 − α)q∗  1  = 1  7 ⇐⇒ q∗  1 =  6α  1 − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  51  Finally, since the equilibrium requires selfish player one to mix at stage one, selfish player  one has to be indifferent between P1 and T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  4 = 16q∗  2 + 2(1 − q∗  2) ⇐⇒ q∗  2 = 1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 8  By backward induction, we know selfish player two will choose T4 for sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given this, it is  optimal for selfish player one to choose T3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Now, suppose selfish player one will choose P1  with probability q1 and player two will choose P2 with probability q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given this behavioral  strategy profile, by Lemma 1, player two’s cursed belief about the other player being altruistic  at stage 2 is:  µχ = χα + (1 − χ)  �  α  α + (1 − α)q1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, it is optimal for player two to pass if and only if  32µχ + 4(1 − µχ) ≥ 8 ⇐⇒ µχ ≥ 1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  We can first show that in equilibrium, it must be that µχ ≤ 1/7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If not, then it is strictly  optimal for player two to choose P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, it is optimal for selfish player one to choose  P1 and hence µχ = α ≤ 1/7, which yields a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the following, we separate the  discussion into two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 1: χ ≤  6  7(1−α)  In this case, we argue that player two is indifferent between P2 and T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If not, then  32µχ +4(1−µχ) < 8 and it is strictly optimal for player two to choose T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This would cause  selfish player one to choose T1 and hence µχ = 1 − (1 − α)χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This yields a contradiction  because  µχ = 1 − (1 − α)χ < 1  7 ⇐⇒ χ >  6  7(1 − α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, in this case, player two is indifferent between T2 and P2 and thus,  µχ = 1  7 ⇐⇒ χα + (1 − χ)  �  α  α + (1 − α)qχ  1  �  = 1  7  ⇐⇒ χ +  1 − χ  α + (1 − α)qχ  1  = 1  7α  ⇐⇒ α + (1 − α)qχ  1 = (1 − χ)  � � 1  7α − χ  �  ⇐⇒ qχ  1 =  �7α − 7αχ  1 − 7αχ − α  � �  (1 − α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  52  Since the equilibrium requires selfish player one to mix at stage 1, selfish player one has to  be indifferent between P1 and T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore,  4 = 16qχ  2 + 2(1 − qχ  2 ) ⇐⇒ qχ  2 = 1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2: χ >  6  7(1−α)  In this case, we know for any qχ  1 ∈ [0, 1],  µχ = χα + (1 − χ)  �  α  α + (1 − α)qχ  1  �  ≤ 1 − (1 − α)χ < 1  7,  implying that it is strictly optimal for player two to choose T2, and hence it is strictly  optimal for selfish player one to choose T1 at stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4  Sequential Voting over Binary Agendas  Proof of Proposition 9  Assuming that a1(θ1) = b and all other types of voters as well as type θ1 at stage 2 vote  sincerely, voter i’s χ-cursed belief in the second stage upon observing a1  −i = (a, b) is  µχ  i (θ−i|a1  −i = (a, b)) =  �  �  �  �  �  p1p3χ +  p1  p1+p2(1 − χ)  if θ−i = (θ3, θ1)  p2p3χ +  p2  p1+p2(1 − χ)  if θ−i = (θ3, θ2)  pkplχ  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As mentioned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='4, a voter would act as if he perceives the other voters’ (be-  havioral) strategies correctly in the last stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' However, misunderstanding the link between  the other voters’ types and actions would distort a voter’s belief updating process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other  words, a voter would perceive the strategies correctly but form beliefs incorrectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a  result, the continuation value of the a vs c subgame to a type θ1 voter is simply the voter’s  χ-cursed belief, conditional on being pivotal, about there being at least one type θ1 voter  among his opponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Similarly, the continuation value of the b vs c subgame is equal to the  voter’s conditional χ-cursed belief about there being at least one type θ1 or θ2 voter among  his opponents multiplied by v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, the continuation values to a type θ1 voter in the  two possible subgames of the second stage are (let ˜p2 ≡  p1  p1+p2):  a vs c :  χ  �  1 − (1 − p1)2�  + (1 − χ)˜p2  b vs c :  �  1 − p2  3χ  �  v  It is thus optimal for a type θ1 voter to vote for b in the first stage if  χ  �  1 − (1 − p1)2�  + (1 − χ)˜p2 ≤  �  1 − p2  3χ  �  v  ⇐⇒ [2p1 − p2  1 − ˜p2 + p2  3v]χ ≤ v − ˜p2  (2)  53  Notice that the statement would automatically hold when χ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In the following, we  want to show that given v and p, if condition (2) holds for some χ ∈ (0, 1], then it will hold  for all χ′ ≤ χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As χ > 0, we can rewrite condition (2) as  2p1 − p2  1 − ˜p2 + p2  3v ≤ v − ˜p2  χ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (2’)  Case 1: v − ˜p2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, we want to show that voting b in the first stage is never optimal for type θ1  voter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is, we want to show condition (2’) never holds for v < ˜p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' To see this, we can  first observe that the RHS is strictly increasing in χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, it suffices to show  2p1 − p2  1 − ˜p2 + p2  3v > v − ˜p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This is true because  2p1 − p2  1 − ˜p2 + p2  3v − (v − ˜p2) = 2p1 − p2  1 − (1 − p2  3)v  > 2p1 − p2  1 − (1 + p3)p1 = p1p2 ≥ 0  where the second inequality holds as v <  p1  p1+p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2: v − ˜p2 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since the RHS of condition (2’) is greater or equal to 0, it will weakly increase as χ  decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, if condition (2’) holds for some χ ∈ (0, 1], it will also hold for all χ′ ≤ χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 10  Assuming that all voters vote sincerely in both stages, voter i’s χ-cursed belief in the second  stage upon observing a1  −i = (a, b) is  µχ  i (θ−i|a1  −i = (a, b)) =  �  �  �  �  �  p1p2χ +  p1  p1+p3(1 − χ)  if θ−i = (θ1, θ2)  p2p3χ +  p3  p1+p3(1 − χ)  if θ−i = (θ3, θ2)  pkplχ  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Similar to the proof of Proposition 9, the continuation values to a type θ1 voter in the  two possible subgames of the second stage are (let ˜p3 ≡  p1  p1+p3):  a vs c :  χ  �  1 − (1 − p1)2�  + (1 − χ)˜p3  b vs c :  �  1 − p2  3χ  �  v  54  Thus, it is optimal for a type θ1 voter to vote for a in the first stage if  χ  �  1 − (1 − p1)2�  + (1 − χ)˜p3 ≥  �  1 − p2  3χ  �  v  ⇐⇒ χ  �  2p1 − p2  1 − ˜p3 + p2  3v  �  ≥ v − ˜p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  (3)  Case 1: v − ˜p3 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, we want to show that given p and v, there exists ˜χ such that condition (3)  holds if and only if χ ≥ ˜χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Let τ ≡ 2p1 − p2  1 − ˜p3 + p2  3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If τ > 0, then condition (3) holds  if and only if χ ≥ ˜χ ≡ v−˜p3  τ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, if τ ≤ 0, condition (3) will not hold for all  χ ∈ [0, 1] and hence we can set ˜χ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2: v − ˜p3 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, we want to show that given p and v, there exists ˜χ such that condition (3)  holds if and only if χ ≤ ˜χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If τ < 0, then condition (3) holds if and only if χ ≤ v−˜p3  τ  where  the RHS is greater or equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other hand, if τ ≥ 0, then condition (3) will hold  for any χ ∈ [0, 1] and hence we can again set ˜χ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='5  The Dirty Faces Game  Proof of Proposition 11  When observing a clean face, a player will know that he has a dirty face immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, choosing 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=', choosing D at stage 1) when observing a clean face is a strictly  dominant strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' In other words, for any χ ∈ [0, 1], ˆσχ(O) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  The analysis of the case where the player observes a dirty face is separated into two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 1: χ > ¯α  In this case, we show that ˆσχ(X) = T + 1 is the only χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If not, suppose ˆσχ(X) = t  where t ≤ T can be supported as a χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can first notice that ˆσχ(X) = 1 cannot be  supported as a χ-CE because it is strictly dominated to choose 1 when observing a dirty  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' For 2 ≤ t ≤ T, given the other player −i chooses ˆσχ(X) = t, we can find player −i’s  average strategy is  ¯σ−i(j) =  �  �  �  �  �  1 − p  if  j = 1  p  if  j = t  0  if  j ̸= 1, t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  55  Therefore, the other player −i’s χ-cursed strategy is:  σχ  −i(j|xi = O) =  �  �  �  �  �  χ(1 − p) + (1 − χ)  if  j = 1  χp  if  j = t  0  if  j ̸= 1, t,  and  σχ  −i(j|xi = X) =  �  �  �  �  �  χ(1 − p)  if  j = 1  χp + (1 − χ)  if  j = t  0  if  j ̸= 1, t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In this case, given (player i perceives that) player −i chooses the χ-cursed strategy, player  i’s expected payoff to choose 2 ≤ j ≤ t when observing a dirty face is:  (1 − p)  �  −δj−1χp  �  + p  �  δj−1α [χp + (1 − χ)]  �  = pδj−1 [α − χ(1 + α)(1 − p)]  �  ��  �  <0 ⇐⇒ χ>¯α  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Hence, given the other player chooses t when observing a dirty face, it is strictly dominated  to choose any j ≤ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, the only χ-CE is ˆσχ(X) = T + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Case 2: χ < ¯α  In this case, we want to show that ˆσχ(X) = 2 is the only χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' If not, suppose ˆσ(X) = t  for some t ≥ 3 can be supported as a χ-CE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can again notice that since when observing  a dirty face, it is strictly dominated to choose 1, 1 is never a best response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Given player  −i chooses ˆσχ(X) = t, by the same calculation as in Case 1, the expected payoff to choose  2 ≤ j ≤ t is:  pδj−1 [α − χ(1 + α)(1 − p)]  �  ��  �  >0 ⇐⇒ χ<¯α  > 0,  which is decreasing in j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, the best response to ˆσχ(X) = t is to choose 2 when  observing a dirty face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' As a result, the only χ-CE in this case is ˆσχ(X) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This completes  the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  Proof of Proposition 12  When observing a clean face, the player would know that his face is dirty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Thus, choosing  D at stage 1 is a strictly dominant strategy, and ˜σχ(O) = 1 for all χ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' On the other  hand, the analysis for the case where the player observes a dirty face consists of several steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 1: Assume that both players choosing D at some stage ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We claim that at stage  t ≤ ¯t, the cursed belief µχ(X|t, X) = 1 − (1 − p)χt−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can prove this by induction on t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  At stage t = 1, the belief about having a dirty face is simply the prior belief p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Hence this  establishes the base case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Now suppose the statement holds for any stage 1 ≤ t ≤ t′ (and  56  t′ < ¯t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' At stage t′ + 1, by Lemma 1,  µχ(X|t′ + 1, X) = χµχ(X|t′, X) + (1 − χ)  = χ  �  1 − (1 − p)χt′−1�  + (1 − χ)  = 1 − (1 − p)χt′  where the second equality holds by the induction hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' This proves the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 2: Given the cursed belief computed in the previous step, the expected payoff to choose  D at stage t is:  µχ(X|t, X)α − [1 − µχ(X|t, X)] =  �  1 − (1 − p)χt−1�  α −  �  (1 − p)χt−1�  = α − (1 − p)(1 + α)χt−1,  which is increasing in t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Notice that at the first stage, the expected payoff is α−(1−p)(1+α) <  0 by Assumption (1), so choosing U at stage 1 is strictly dominated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Furthermore, the player  would choose U at every stage when observing a dirty face if and only if  µχ(X|T, X)α − [1 − µχ(X|T, X)] ≤ 0 ⇐⇒ α − (1 − p)(1 + α)χT−1 ≤ 0  ⇐⇒ χ ≥ ¯α  1  T +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  As a result, both players choosing ˜σχ(X) = T + 1 is a χ-CSE if and only if χ ≥ ¯α  1  T +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 3: In this step, we show both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if  χ ≤ ¯α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can notice that given the other player chooses D at stage 2, the player would  know stage 2 would be the last stage regardless of his face type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Therefore, it is optimal to  choose D at stage 2 as long as the expected payoff of D at stage 2 is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Consequently,  both players choosing ˜σχ(X) = 2 is a χ-CSE if and only if  µχ(X|2, X)α − [1 − µχ(X|2, X)] ≥ 0 ⇐⇒ α − (1 − p)(1 + α)χ  ⇐⇒ χ ≤ ¯α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 4: Given the other player chooses ˜σχ(X) > t, as the game reaches stage t, the belief  about the other player choosing U at stage t is:  µχ(X|t, X)  �  ��  �  prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' of dirty  [χµχ(X|t, X) + (1 − χ)]  + [1 − µχ(X|t, X)]  �  ��  �  prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' of clean  [χµχ(X|t, X)] = µχ(X|t, X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Furthermore, we denote the expected payoff of choosing D at stage t as  E [uχ(D|t, X)] ≡ µχ(X|t, X)α − (1 − µχ(X|t, X)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  57  In the following, we claim that for any stage 2 ≤ t ≤ T − 2, given the other player will stop  at some stage later than stage t + 2 or never stop, if it is optimal to choose U at stage t + 1,  then it is also optimal for you to choose U at stage t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' That is,  E [uχ(D|t + 1, X)] < δµχ(X|t + 1, X)E [uχ(D|t + 2, X)]  =⇒ E [uχ(D|t, X)] < δµχ(X|t, X)E [uχ(D|t + 1, X)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  To prove this claim, first observe that  E [uχ(D|t + 1, X)] < δµχ(X|t + 1, X)E [uχ(D|t + 2, X)]  ⇐⇒ (1 + α)µχ(X|t + 1, X) − 1 < δµχ(X|t + 1, X) [(1 + α)µχ(X|t + 2, X) − 1] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  After rearrangement, the inequality is equivalent to  δχ [µχ(X|t + 1, X)]2 +  �  δ(1 − χ) −  δ  1 + α − 1  �  µχ(X|t + 1, X) +  1  1 + α > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Consider a function F : [0, 1] → R where  F(y) = δχy2 +  �  δ(1 − χ) −  δ  1 + α − 1  �  y +  1  1 + α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Since µχ(X|j, X) = 1 − (1 − p)χj−1 is increasing in j, it suffices to complete the proof of  the claim by showing there exists a unique y∗ ∈ (0, 1) such that F is single-crossing on [0, 1]  where F(y∗) = 0, F(y) < 0 for all y > y∗, and F(y) > 0 for all y < y∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Because F is  continuous and  F(0) =  1  1+α > 0,  F(1) = δχ +  �  δ(1 − χ) −  δ  1+α − 1  �  +  1  1+α = − α(1−δ)  1+α  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  By intermediate value theorem, there exists a y∗ ∈ (0, 1) such that F(y∗) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Moreover,  y∗ is the unique root of F on [0, 1] because F is a strictly convex parabola and F(1) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This establishes the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Step 5: For any 3 ≤ t ≤ T, in this step, we find the conditions to support both players  choosing ˜σχ(X) = t as a χ-CSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' We can first notice that both players choosing ˜σχ(X) = t  is a χ-CSE if and only if  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E [uχ(D|t, X)] ≥ 0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' E [uχ(D|t − 1, X)] ≤ δµχ(X|t − 1, X)E [uχ(D|t, X)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Condition 1 is necessary because if it fails, then it is better for the player to choose U  at stage t and get at least 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Condition 2 is also necessary because if the condition doesn’t  hold, it would be profitable for the player to choose D before stage t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' Furthermore, these  58  two conditions are jointly sufficient to support ˜σχ(X) = t as a χ-CSE by the same argument  as step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  From condition 1, we can obtain that  E [uχ(D|t, X)] ≥ 0 ⇐⇒ (1 + α)µχ(X|t, X) − 1 ≥ 0  ⇐⇒ 1 − (1 − p)χt−1 ≥  1  1 + α ⇐⇒ χ ≤ ¯α  1  t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In addition, by the calculation of step 4, we know  E [uχ(D|t − 1, X)] ≤ δµχ(X|t − 1, X)E [uχ(D|t, X)] ⇐⇒ F (µχ(X|t − 1, X)) ≥ 0,  which is equivalent to  µχ(X|t − 1, X) ≤  �  1 +  δ  1+α − δ(1 − χ)  �  −  ��  1 +  δ  1+α − δ(1 − χ)  �2 − 4δχ  �  1  1+α  �  2δχ  = [(1 + α)(1 + δχ) − αδ] −  �  [(1 + α)(1 + δχ) − αδ]2 − 4δχ(1 + α)  2δχ(1 + α)  ≡ κ(χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  Therefore, condition 2 holds if and only if  1 − (1 − p)χt−2 ≤ κ(χ) ⇐⇒ χ ≥  �1 − κ(χ)  1 − p  �  1  t−2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  In summary, both players choosing ˜σχ(X) = t is a χ-CSE if and only if  �1 − κ(χ)  1 − p  �  1  t−2  ≤ χ ≤ ¯α  1  t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
+page_content=' ■  59' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FLT4oBgHgl3EQfBi6R/content/2301.11971v1.pdf'}
diff --git a/8NFLT4oBgHgl3EQfsy_c/content/tmp_files/2301.12149v1.pdf.txt b/8NFLT4oBgHgl3EQfsy_c/content/tmp_files/2301.12149v1.pdf.txt
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+POSTER V2: A simpler and stronger facial expression recognition network
+Jiawei Mao†
+Rui Xu†
+Xuesong Yin*
+Yuanqi Chang
+Binling Nie
+Aibin Huang∗
+School of Media and Design, Hangzhou Dianzi University, Hangzhou, China
+{jiaweima0,211330017,yinxs,yuanqichang,binlingnie,huangaibin}@hdu.edu.cn
+Abstract
+Facial expression recognition (FER) plays an impor-
+tant role in a variety of real-world applications such as
+human-computer interaction.
+POSTER V1 achieves the
+state-of-the-art (SOTA) performance in FER by effectively
+combining facial landmark and image features through
+two-stream pyramid cross-fusion design.
+However, the
+architecture of POSTER V1 is undoubtedly complex.
+It
+causes expensive computational costs. In order to relieve
+the computational pressure of POSTER V1, in this pa-
+per, we propose POSTER V2.
+It improves POSTER V1
+in three directions: cross-fusion, two-stream, and multi-
+scale feature extraction. In cross-fusion, we use window-
+based cross-attention mechanism replacing vanilla cross-
+attention mechanism. We remove the image-to-landmark
+branch in the two-stream design. For multi-scale feature
+extraction, POSTER V2 combines images with landmark’s
+multi-scale features to replace POSTER V1’s pyramid de-
+sign. Extensive experiments on several standard datasets
+show that our POSTER V2 achieves the SOTA FER perfor-
+mance with the minimum computational cost. For exam-
+ple, POSTER V2 reached 92.21% on RAF-DB, 67.49% on
+AffectNet (7 cls) and 63.77% on AffectNet (8 cls), respec-
+tively, using only 8.4G floating point operations (FLOPs)
+and 43.7M parameters (Param). This demonstrates the ef-
+fectiveness of our improvements. The code and models are
+available at https://github.com/Talented-Q/
+POSTER_V2.
+1. Introduction
+With the continuous development of technology and
+the continuous improvement of automation, the need
+for human-computer interaction is becoming increasingly
+strong.
+Facial expression recognition (FER) helps ma-
+chines to understand human emotions from facial expres-
+sions. This makes it as a core task for human-computer in-
+teraction. Besides, with its powerful expression understand-
+*Corresponding author.†Equal contribution.
+Figure 1. POSTER V2 results on RAF-DB. We compare POSTER
+V2 with three variants of POSTER V1 and other FER algorithms.
+The results indicate that POSTER V2 weighs the number of pa-
+rameters and accuracy better than other FER methods on RAF-
+DB.
+ing ability, FER has great potential applications in psychol-
+ogy, intelligent robotics, intelligent surveillance, virtual re-
+ality and synthetic animation. Therefore, research on FER
+is very necessary.
+Due to the increasing attention of FER, it has been
+able to develop rapidly in recent years. Early FER works
+[55, 59, 33, 20] used manual features [6, 34, 23] for the anal-
+ysis of facial expressions. However, FER algorithms based
+on manual features are often only applicable to specific FER
+tasks. When applied to real world scenarios, it is difficult for
+these algorithms to achieve the same results as in the experi-
+mental setting. With the development of deep learning, con-
+volutional neural networks (CNNs) are introduced to FER
+for improving the robustness of the network. Savchenko et
+al. [38] first verified the effectiveness of CNNs such as Mo-
+bileNet [19], EfficientNet [41] and RexNet [15] for FER.
+Zhao et al. proposed an efficient and robust FER network
+EfficientFace [57] for the analysis of facial expressions in
+the wild. Nevertheless, convolution-based FER algorithms
+cannot consider the global information of the image due to
+the limitation of convolutional local receptive field. Influ-
+enced by the vision transformer, Xue et al. [51] designed the
+first transformer-based FER network to model long-range
+arXiv:2301.12149v1  [cs.CV]  28 Jan 2023
+
+93
+POSTER V2
+POSTER V1
+92
+POSTER V1-S
+POSTER V1-T
+★
+Acc
+TransFER
+91
+RAF-DB Top-1 
+90
+DMUE
+89
+VTFF
+88
+87
+40
+45
+50
+55
+60
+65
+70
+75
+80
+Param(M)dependencies for FER. Kim et al. [24] improved the vision
+transformer (ViT) to combine both global and local features
+so that ViT can be adapted to FER task.
+Among many excellent FER works, POSTER V1
+[58] stands out with state-of-the-art (SOTA) performance.
+POSTER V1 mainly solves three key issues of FER at the
+same time: inter-class similarity, intra-class discrepancy
+and scale sensitivity. POSTER V1 cleverly combines facial
+landmark with image features through a network design of
+two-stream pyramidal cross-fusion transformer. With the
+difference and sparsity of landmark, POSTER V1 success-
+fully solves the issue of inter-class similarity and intra-class
+discrepancy in FER. The network design of pyramid archi-
+tecture introduces multi-scale features for POSTER V1 to
+solve the scale sensitivity problem. Along with the solution
+of the three main issues of FER, POSTER V1 shows the
+amazing expression analysis ability.
+Although POSTER V1 works so well on FER, the huge
+number of parameters and expensive computational cost
+brought by its network architecture affects the efficiency
+of FER. To address this issue, we revisit the network de-
+sign of POSTER V1 and improve it to obtain POSTER
+V2. We mainly improve POSTER V1 in three directions:
+two-stream, cross-fusion and multi-scale feature extrac-
+tion.
+POSTER V1 contains two main branches: image-
+to-landmark and landmark-to-image. Landmark-to-image
+branch is essential as the core of POSTER V1 to solve inter-
+class similarity and intra-class discrepancy.
+The image-
+to-landmark branch is only used to provide information to
+landmark that it fails to take into account. This does not
+contribute to solving the three main issues of FER. There-
+fore, in POSTER V2, we remove the image-to-landmark
+branch from the two-stream design. This greatly reduces
+the computational cost on POSTER V1. For cross-fusion,
+we use a window-based cross-attention mechanism instead
+of the vanilla cross-attention mechanism in POSTER V1.
+The window-based cross-attention mechanism not only pro-
+vides linear computational complexity for POSTER V2 but
+also enhances the local modeling capability of the network.
+In addition, POSTER V2 no longer uses an additional pyra-
+mid architecture for multi-scale feature extraction. We per-
+form multi-scale feature extraction directly from the image
+backbone as well as from the facial landmark detector. For
+the extracted multi-scale features, we use a vision trans-
+former network consisting of only two layers of transformer
+modules for integration. Based on the above designs, our
+POSTER V2 becomes a simpler and more powerful facial
+expression recognition network. It achieves SOTA perfor-
+mance on several standard FER datasets with only 8.4G
+floating point operations (FLOPs) and 43.7M parameters
+(Param). Figure 1 demonstrates the superiority of POSTER
+V2.
+Specially, POSTER V2 reached 92.21% on RAF-DB
+[29], 67.49% on AffectNet [32] (7 cls) and 63.77% on Af-
+fecNet (8 cls), respectively. This is better than POSTER
+V1 (RAF-DB with 92.05%, AffectNet (7 cls) with 67.31%
+and AffectNet (8 cls) with 63.34%). And POSTER V2 of-
+fers a smaller Param (43.7M vs. 71.8M) and FLOPs (8.4G
+vs. 15.7G). We hope that our work could contribute to the
+design of future FER models.
+In general, we summarize the contributions of this paper
+as follows:
+1) We design POSTER V2 by modifying POSTER V1
+from three perspectives: two-stream, cross-fusion and
+feature extraction.
+Compared with POSTER V1,
+POSTER V2 is simpler and stronger.
+2) POSTER V2 shows state-of-the-art performance on
+several standard FER datasets such as RAF-DB, Affec-
+Net and CAER-S. This shows the powerful expression
+analysis capability of POSTER V2.
+3) POSTER V2 greatly reduces the FLOPs and Param
+of POSTER V1. Specifically, POSTER V2 reduces
+28.1M of Param and 7.3G of FLOPs. This greatly im-
+proves the computational efficiency of the model.
+2. Related Work
+2.1. Facial Expression Recognition
+The study of FER has become very popular in re-
+cent years as more and more researchers focus on human-
+computer interaction. Zhao et al. [55] used the manual fea-
+ture LBP [34] for the research of FER with good results.
+Zhong et al. [59] proposed a two-stage multitask sparse
+learning framework (MTSL) for the FER task by explor-
+ing some common and specific information among differ-
+ent expressions. Savchenko et al. [38] studied lightweight
+convolutional neural networks for FER task learning and
+verified the effectiveness of CNNs for FER. Sang et al. [37]
+focused on reducing intra-class variation in facial expres-
+sion depth features and introduced a dense convolutional
+network [21] for the FER task. PSR [45] solves the prac-
+tical issues associated with individual wild images in FER
+in terms of pose, orientation and input resolution with its
+super-resolution pyramidal network architecture. Zhang et
+al. [54] proposed an erasing attention consistency method to
+handle the noise-labeled facial expression recognition task
+that is more challenging than the conventional FER.
+With the rise of transformer in the field of computer vi-
+sion, many FER methods combined with transformer have
+emerged. The vision transformer was first used for the study
+of FER by Xue et al. [51] and achieved state-of-the-art per-
+formance. VTFF [31] excels in dealing with facial expres-
+sion recognition tasks in the wild by virtue of its feature fu-
+sion. Huang et al. designed the teacher-student model PID-
+ViT [22] for modeling the probability distribution of frontal
+
+Figure 2. Pipeline of POSTER V1. POSTER V1 mainly contains facial landmark detector, image backbone, cross-fusion transformer
+encoders and pyramid network.
+and multi-pose facial expressions, and solved the problem
+of pose change and occlusion in FER. Zhao et al. [9] com-
+bined global and local attention in order to address the two
+key issues of occlusion and pose change in FER. POSTER
+V1 [58] solves the intra-class discrepancy, inter-class sim-
+ilarity and scale sensitivity issues of FER in the same time
+by integrating image features with facial landmark features
+through two-stream, cross-fusion and pyramid design.
+However, the huge computational cost of POSTER V1
+has prevented researchers from investigating further im-
+provements in FER. To solve this issue, we improved the
+architecture of POSTER V1 and proposed POSTER V2,
+which is simpler and more powerful for FER tasks.
+2.2. Vision Transformer
+Recently vision transformer has been widely used for
+computer vision tasks on large scale datasets with its ex-
+cellent ability to model long distance dependencies.
+Dosovitskiy et al. [8] pioneered the introduction of trans-
+former from the field of natural language processing to com-
+puter vision. Touvron et al. [42] used a teacher-student
+strategy to accelerate the training of transformer by distill-
+ing tokens. Zhou et al. [60] found that the reason why
+the transformer quickly saturates at deeper levels is that
+the attention map becomes increasingly similar as the trans-
+former goes deeper. Based on this observation, they pro-
+posed the Re-attention model to regenerate the attention
+map in order to enhance the diversity among layers at a
+small computational cost. Touvron et al. also designed CaiT
+[43], a deep vision transformer for optimal image classifi-
+cation. To solve the issue that ViT is inferior to traditional
+ResNet [17] on datasets without huge data size, Yuan et al.
+proposed T2T-ViT [52]. Besides, Hassani et al. proposed
+CCT [16] which uses convolution rather than patch em-
+bedding layer for self-attention processing. This introduces
+convolutional inductive bias for the transformer. Chen et
+al. proposed CrossViT [4], which combines image patches
+of different sizes by dual branches to produce stronger im-
+age features. Heo et al. [18] also verified whether pooling
+layers bring advantages to ViT as they do in convolutional
+neural networks (CNNs). Liu et al. [30] reduced the atten-
+tion mechanism from quadratic computational complexity
+to linear by window attention and the design of a shift win-
+dow scheme. Graham et al. grafted CNN with Transformer
+to obtain LeViT [13] with higher accuracy and faster speed.
+Wu et al. have designed a new architecture called convo-
+lutional visual transformer CVT [50], which improves the
+performance and efficiency of ViT by introducing convolu-
+tion into vision transformer to produce the better results of
+both designs. Chen et al. proposed a new architecture with
+a pyramidal structure and a novel region-to-local-attention
+vision transformer, RegionViT [3]. Wang et al. [48] intro-
+duced ViT into a CNN-like pyramid structure for intensive
+prediction tasks such as object detection and semantic seg-
+mentation.
+The architectural design of these vision transformer ef-
+forts inspires our improvements for POSTER V1.
+This
+leads to a better trade-off between accuracy and computa-
+tional complexity in FER with our POSTER V2.
+3. Method
+In this section, we first review the POSTER V1 process.
+We then describe the overall architecture of POSTER V2
+and discuss the specific details of POSTER V2 in three di-
+rections: two-stream, cross-fusion, and multi-scale feature
+extraction.
+3.1. A brief review of POSTER V1
+POSTER V1 contains four main core designs: facial
+landmark detector, image backbone, cross-fusion trans-
+former encoders and pyramid network. Given the input im-
+age X ∈ RH×W ×3, POSTER V1 obtain the image features
+Ximg and landmark features Xlm by facial landmark detec-
+tor and image backbone, respectively.
+The image features Ximg ∈ RN×D as well as the land-
+mark features Xlm ∈ RN×D are mapped into three ma-
+trices respectively: image query matrix Qimg, image key
+matrix Kimg, image value matrix Vimg and landmark query
+
+Cross-fusion
+Transform
+Landmark Feature
+Encoders
+Input Image
+Landmark
+Dector
+Cross-fusion
+Transform
+head
+Encoders
+Concat
+Image
+Backbone
+Cross-fusion
+Transform
+Image Feature
+EncodersFigure 3. The overview of POSTER V2 architecture. LMFi and IMFi denotes facial landmark features and image features at the i-th
+level of POSTER V2 respectively.
+matrix Qlm, landmark key matrix Klm, landmark value ma-
+trix Vlm in the cross-fusion transformer encoder. Specifi-
+cally expressed as:
+Qimg = XimgWq1, Qlm = XlmWq2,
+Kimg = XimgWk1, Klm = XlmWk2,
+Vimg = XimgWv1, Vlm = XlmWv2,
+(1)
+where Wq1, Wq2, Wk1, Wk2, Wv1 and Wv2 ∈ RD×D are
+the mapping matrix.
+The cross-fusion transformer encoder uses the vanilla
+cross-attention mechanism to interact image features and
+landmark features respectively. It is defined as follows:
+Attention(img) = softmax(QlmKT
+img/
+√
+d)Vimg,
+Attention(lm) = softmax(QimgKT
+lm/
+√
+d)Vlm,
+(2)
+where softmax(·) is softmax [1] activation function and
+1
+√
+d is an appropriately normalized scaling factor used to
+prevent the gradient from being too small.
+In summary cross-fusion transformer encoder can be de-
+noted as:
+X’img = Attention(img) + Ximg,
+Ximg o = MLP(Norm(X’img)) + X’img,
+X’lm = Attention(lm) + Xlm,
+Xlm o = MLP(Norm(X’lm)) + X’lm,
+(3)
+where MLP (·) is multi-layer perceptron and Norm (·)
+denotes the normalization operation.
+Finally, POSTER V1 extracts and integrates multi-scale
+features of images and landmarks by the pyramid network
+design. The specific details are shown in Figure 2.
+3.2. Architecture
+Figure 3 shows the pipeline for POSTER V2.
+The
+POSTER V2 keeps the facial landmark detector and im-
+age backbone in POSTER V1. In difference, we remove
+the POSTER V1 pyramid architecture and the image-to-
+landmark branch of the two-stream design. Meanwhile, we
+perform multi-scale feature extraction directly from the fa-
+cial landmark detector and image backbone. And we in-
+troduce a small vision transformer consisting of only two
+layers of vanilla tranformer blocks in POSTER V2 to in-
+tegrate multi-scale features. Moreover, we design the new
+cross-fusion transformer encoder with window-based cross-
+attention mechanism. Next, we discuss the detailed modifi-
+cations to POSTER V2.
+3.3. Two-stream
+Methods
+RAF-DB
+AffectNet
+Baseline
+91
+65.06
+POSTER V1
+92.05
+67.31
+POSTER w/o image to landmark branch
+91.82
+65.96
+POSTER w/o landmark to image branch
+91.62
+65.28
+Table 1. Ablation study of two branches in cross-fusion of
+POSTER V1. The baseline in the table keeps the baseline setting
+in POSTER V1.
+Although two-stream is central to the design of POSTER
+V1, POSTER V1 does not explore which branch of two-
+stream actually plays a major role. Thus, in this section, we
+first perform an ablation study of the two-stream to learn the
+contribution of the two branches to the FER. Table 1 shows
+the ablation results. We see that on the RAF-DB dataset, the
+accuracy of POSTER V1 slips by 0.23 after missing the im-
+age to landmark branch. If the landmark-to-image branch
+is missing, the accuracy of POSTER V1 on RAF-DB is re-
+duced by 0.43. Meanwhile, we observe a similar situation
+on the AffectNet dataset. This indicates that although the
+image-to-landmark branch contributes to the POSTER V1
+FER performance, it is the landmark-to-image branch that
+plays a decisive role in POSTER V1. Next, we analyze the
+above results at the theoretical level.
+Discussion.
+The two-stream design in POSTER V1 is
+mainly used to solve the issues of intra-class discrepancy
+and inter-class similarity in FER. It includes landmark-to-
+
+2nd POSTER-V2 level
+1st POSTER-V2 level
+ 3rd POSTER-V2 level
+Landmark Stage 2
+ Stage
+LMFi
+LMF2
+..
+Landmark
+Input Image
+LMFs
+LMF2
+ViT Model
+LMFi
+head
+IMFi
+IMF2
+IMFs
+Image Stage 2
+Image Stage 3
+IMFi
+IMF2
+Low-Level Feature Extraction (LFE)
+High-Level Feature Extraction (HFE)
+Multi-Level Feature Integration (MFI)Figure 4. Input images (row 1), facial landmark images (row 2),
+landmark-to-image branching attention visualization results (row
+3). We visualize the attention map belonging to the last layer of the
+landmarks to image branching for high-level features in POSTER
+V1. We can observe that with the help of landmark features, the
+attention map focuses more on the outstanding areas of face and
+less on the areas common to face.
+image and image-to-landmark branches.
+We revisit the
+influence of the two branches on POSTER V1.
+In the
+landmark-to-image branch, the landmark features inter-
+act with the image features as queries Qlm in the cross-
+attention mechanism. Image features are guided by land-
+mark features to more easily represent salient regions of fa-
+cial expressions when dealing with intra-class discrepancy
+issue. Also benefiting from the sparsity of landmark fea-
+tures, image features guided by landmark features reduce
+the focus on regions where faces are prevalent. This helps
+to reduce the impact of inter-class similarity in FER. The
+results of the visualization of landmark-to-image branch
+attention in Figure 4 also validate the above statements.
+Therefore, the landmark-to-image branch in the two-stream
+is essential and needs to be retained.
+For the image-to-
+landmark branch, the image features interact with the land-
+mark features as query Qimg to compensate for the lack
+of landmark features. Although this also benefits the FER
+task to some extent, it does not contribute to solving the
+issues of inter-class similarity and intra-class discrepancy
+as well as comes with a huge computational cost. This is
+consistent with the results we observed in the ablation ex-
+periments of Table 1. Thus, by making a trade-off between
+computational cost and accuracy, we eventually remove the
+image-to-landmark branch in the two-stream design.
+3.4. Cross-fusion
+In POSTER V2 we use window-based cross-attention
+mechanism instead of vanilla cross-attention mechanism in
+POSTER V1 for the purpose of linear computation. Fig-
+ure 5 illustrates the detailed differences between the two
+cross-attention mechanisms. For image features Ximg ∈
+RN×D, we first divide them into several non-overlapping
+windows zimg
+∈ RM×D, where zimg contains M to-
+Figure 5. Window-based cross attention mechanism and vanilla
+cross attention mechanism.
+kens. For the landmark feature Xlm ∈ RC×H×W , we first
+down-sample it to the window size zlm ∈ Rc×h×w, where
+c = D, M = h × w. Then we reshape it according to
+the shape of Zimg. At this point, the cross-attention with I
+heads in a local window can be formulated as:
+q = zlmwq, k = zimgwk, v = zimgwv,
+o(i) = θ(q(i)k(i)T/
+√
+d + b)v(i), i = 1,...,I,
+o = [o(1), . . . , o(I)]wo,
+(4)
+where wq, wk, wv, wo are the mapping matrix, respectively.
+θ (·) is the softmax function. [·] denotes the merge operation
+and b ∈ RI×I is the relative position bias.
+We perform the above cross-attention calculation for
+all windows. We refer to this cross-attention mechanism
+as window-based multi-head cross-attention (W-MCSA).
+Thus the cross-fusion transformer encoder in POSTER V2
+can be expressed as follows:
+X’img = W-MCSA(img) + Ximg,
+Ximg o = MLP(Norm(X’img)) + X’img,
+(5)
+Computational Complexity Analysis. Since the query in
+the two types of cross-attention computation keeps the same
+shape as the key, value, we can use the multi-head self-
+attention and the window-based multi-head self-attention
+complexity to represent their computational complexity.
+This can be indicated as follows:
+Ω(MCSA) = 4ND2 + 2N2D,
+Ω(W-MCSA) = 4ND2 + 2M2ND,
+(6)
+
+Attention Query
+Window-based Cross Attention Mechanism
+Vanilla Cross Attention MechanismAccording to Eqn 6, we can find that the window-based
+cross-attention mechanism we use successfully reduces the
+computational complexity of cross-fusion in POSTER V1
+from square level to linear level. This further improves the
+computational efficiency of POSTER V2.
+3.5. Multi-scale feature extraction
+From Figure 3, we can observe that POSTER V2 re-
+moves the pyramid design from POSTER V1. Moreover, in
+POSTER V2, we extract multi-scale features directly from
+facial landmark detector and image backbone. And we also
+add a small vision transformer network to POSTER V2 for
+the integration of multi-scale features.
+For the obtained
+multi-scale features o1, o2, o3, we directly merge in the to-
+ken dimension and using the vanilla transformer blocks for
+processing. This process is specifically described as:
+o = [o1, o2, o3],
+o’ = MSA(o) + o,
+oout = MLP(Norm(o’)) + o’,
+(7)
+where MSA (·) represents multi-head self-attention mech-
+anism. For above design we discuss as follows.
+Discussion. POSTER V1 adopts the pyramid structure to
+solve the scale sensitivity problem in FER. However, we
+consider that the pyramid structure design is only an up-
+sampling and down-sampling operation on the basis of the
+same scale feature map. Although it provides multi-scale
+information to some extent, we believe that it is not as good
+as multi-scale feature extraction directly from the network.
+The method analysis in section 4.3 also proves our point.
+For the integration of multi-scale features, we believe that
+the vanilla transformer block is sufficient for this task. We
+combine the tokens of all scale feature maps together, and
+the attention mechanism can model long-range dependen-
+cies for all scale tokens. Thus, different scales of token in-
+formation are delivered in the transformer block.
+4. Experiments
+We verify the effectiveness of POSTER V2 on several
+standard FER datasets such as RAF-DB [29], AffectNet
+[32] and CAER-S [27]. In the following, we first compare
+POSTER V2 with SOTA methods. We then conduct a se-
+ries of method analysis and ablation studies on POSTER
+V2. More detailed experimental setup, more experimen-
+tal results and visualization results are detailed in the Ap-
+pendix.
+4.1. Experiment Setup
+Datasets. We evaluat the FER performance of POSTER
+V2 on the widely used RAF-DB, AffectNet and CAER-S
+Dataset
+Train size
+Test size
+Classes
+RAF-DB
+12271
+3068
+7
+AffectNet (7 cls)
+280401
+3500
+7
+AffectNet (8 cls)
+283501
+4000
+8
+CAER-S
+44996
+20987
+7
+Table 2. Detailed size of the experimental dataset.
+datasets. The Real-world Affective Faces Database (RAF-
+DB) is a large-scale database of facial expressions, anno-
+tated by 315 staff members (students and faculty members
+of the University). For the selection of expressions, RAF-
+DB selected six basic emotions as well as neutral emotions
+from a range of expressions (e.g., smile, cackle, cry, anger,
+fear, dread, fear, shock, surprise, disgust, and no expres-
+sion), for a total of seven expressions for expression anno-
+tation. It mainly contains 12,271 training images as well
+as 3,068 test images. AffectNet is currently the largest pub-
+licly available dataset in the FER field. It contains about 1M
+images of faces associated with emotional words. It mainly
+contains 8 categories of primary emotions (neutral, happy,
+angry, sad, fear, surprise, disgust,contempt). We mainly use
+AffectNet settings based on class 7 (excluding contempt) as
+well as class 8. AffectNet (7 cls) consists of 280K training
+images and 3.500 validation images (500 images per cat-
+egory). AffectNet (8 cls) consists of 283K training images
+and 4.000 validation images (500 images per category). The
+CAER-S dataset was obtained from the CAER dataset con-
+taining 65,983 images. It is mainly divided into 7 types of
+expressions: neutral, happy, sad, surprised, fear, disgust and
+anger. In the FER task we used 44996 images for training
+and 20987 images for testing. The specific dataset configu-
+ration is shown in Table 2.
+Methods
+Year
+RAF-DB
+AffectNet (7 cls)
+AffectNet (8 cls)
+SCN [46]
+CVPR 2020
+87.03
+-
+60.23
+PSR [45]
+CVPR 2020
+88.98
+63.77
+60.68
+LDL-ALSG [5]
+CVPR 2020
+85.53
+59.35
+-
+RAN [47]
+TIP 2020
+86.9
+-
+-
+DACL [11]
+WACV 2020
+87.78
+65.2
+-
+KTN [28]
+TIP 2021
+88.07
+63.97
+-
+DMUE [39]
+CVPR 2021
+89.42
+63.11
+-
+FDRL [36]
+CVPR 2021
+89.47
+-
+-
+VTFF [31]
+TAC 2021
+88.14
+61.85
+-
+ARM [40]
+2021
+90.42
+65.2
+61.33
+TransFER [51]
+ICCV 2021
+90.91
+66.23
+-
+DAN [49]
+2021
+89.7
+65.69
+62.09
+EfficientFace [57]
+AAAI 2021
+88.36
+63.7
+60.23
+MA-Net [56]
+TIP 2021
+88.42
+64.53
+60.29
+Meta-Face2Exp [53]
+CVPR 2022
+88.54
+64.23
+-
+EAC [54]
+ECCV 2022
+90.35
+65.32
+-
+POSTER V1 [58]
+2022
+92.05
+67.31
+63.34
+POSTER V2
+-
+92.21
+67.49
+63.77
+Table 3. Comparison results with SOTA FER algorithm on RAF-
+DB and AffectNet.
+Settings. Similar to POSTER V1 [58], we also use the ir50
+[7] network pre-trained on the Ms-Celeb-1M [14] dataset as
+the image backbone. And MobileFaceNet [2] with frozen
+weights is used as our facial landmark detector. We employ
+
+Dataset
+Method
+Neutral
+Happy
+Sad
+Surprise
+Fear
+Disgust
+Anger
+Contempt
+mean Acc
+RAF-DB
+POSTER V1
+92.35
+96.96
+91.21
+90.27
+67.57
+75
+88.89
+-
+86.04
+RAF-DB
+POSTER V2
+92.06
+97.22
+92.89
+90.58
+68.92
+71.88
+88.27
+-
+85.97
+AffectNet (7 cls)
+POSTER V1
+67.2
+89
+67
+64
+64.8
+56
+62.6
+-
+67.23
+AffectNet (7 cls)
+POSTER V2
+65.4
+89.4
+68
+66
+64.2
+54.4
+65
+-
+67.45
+AffectNet (8 cls)
+POSTER V1
+59.4
+80.2
+66.6
+63.6
+63.6
+59.8
+58.8
+54.71
+63.34
+AffectNet (8 cls)
+POSTER V2
+60.6
+76.4
+66.8
+65.6
+63
+58
+60.2
+59.52
+63.76
+Table 4. Class-wise accuracy of POSTER V1 and POSTER V2 on RAF-DB, AffectNet (7 cls), and AffectNet (8 cls) datasets. Green, blue
+and red mark the highest value of single category in RAF-DB, AffectNet (7 cls) and AffectNet (8 cls) respectively.
+the Adam [25] optimizer for 200 epochs training. A train-
+ing scheme with a batch size of 144, a learning rate of 3.5e-4
+and a weight decay of 1e-4 was used. We use random hor-
+izontal flipping and random erasing as our data augmenta-
+tion methods. For the loss function, we choose the standard
+cross-entropy loss. We eventually realized POSTER V2 on
+a single NVIDIA RTX 3090 via Pytorch.
+4.2. Comparison with SOTA FER Methods
+Results on RAF-DB. We compare POSTER V2 with the
+SOTA FER algorithms in recent years on the RAF-DB
+datasets in Table 3.
+The experimental results show that
+POSTER V2 exhibits SOTA performance on RAF-DB.
+Compared with POSTER V1 (92.05), POSTER V2 im-
+proved by 0.16. +1.86 for POSTER V2 over EAC (90.35),
+and +1.3 for POSTER V2 over TransFER (90.91). This
+shows the superiority of PSTER V2 on RAF-DB. Table 4
+shows the comparison of POSTER V2 with POSTER V1
+for RAF-DB individual classes and average accuracy. Al-
+though POSTER V2 outperformed POSTER V1 in sev-
+eral categories, the average accuracy was slightly inferior
+to POSTER V1.
+Results on AffectNet. In Table 3, we also conduct FER ex-
+periments on AffectNet (7 cls) as well as AffectNet (8 cls).
+We observe that POSTER V2 exhibits SOTA FER effect
+in both AffectNet (7 cls) and AffectNet (8 cls). Compared
+with POSTER V1 (67.31, 63.34), POSTER V2 increases
+0.18, 0.43 on AffectNet (7 cls) and AffectNet (8 cls), re-
+spectively. On AffectNet (8 cls), POSTER V2 is higher than
+DAN (62.09) by 1.68. On AffectNet (7 cls), POSTER V2
+is greater than TransFER (66.23) with 1.26. This demon-
+strates that POSTER V2 can maintain excellent FER perfor-
+mance even on larger datasets. Table 4 shows that POSTER
+V2 exceeds POSTER V1 for the majority of individual class
+accuracies in both AffectNet (7 cls) and AffectNet (8 cls).
+As a result, POSTER V2 achieves better average accuracy
+than POSTER V1 on AffectNet.
+Results on CAER-S. We compare POSTER V2 with SOTA
+FER methods of recent years on the CAER-S dataset.
+Our POSTER V2 in Table 5 performs extremely well on
+the CAER-S dataset.
+Specifically, POSTER V2 scored
+92.98 on CAER-S. +0.27 for POSTER V2 over POSTER
+Methods
+Year
+CAER-S
+DSN [10]
+ICML 2018
+75.19
+CAER-Net-S [27]
+ICCV 2019
+73.51
+GRERN [12]
+IEEE Access 2020
+81.31
+EfficientFace [57]
+AAAI 2021
+85.87
+MA-Net [56]
+TIP 2021
+88.42
+GLAMOR-Net [26]
+NCA 2021
+89.88
+POSTER V1 [58]
+2022
+92.73
+POSTER V2
+-
+93
+Table 5. Comparison results with SOTA FER algorithm on CAER-
+S.
+V1 (92.73). +3.12 for POSTER V2 over GLAMOR-Net
+(89.88), and +4.58 for POSTER V2 over MA-Net (88.42).
++7.13 for POSTER V2 over EfficientFace (85.87).
+The
+excellent results on CAER-S prove that the success of
+POSTER V2 is no accident. It shows the powerful gen-
+eralization ability of POSTER V2.
+4.3. FLOPs and Param Comparison
+Methods
+#Param
+#FLOPs
+RAF-DB
+AffectNet
+POSTER V1-T
+52.2M
+13.6G
+91.36
+66.87
+POSTER V1-S
+62.0M
+14.7G
+91.54
+67.13
+POSTER V1
+71.8M
+15.7G
+92.05
+67.31
+POSTER V2
+43.7M
+8.4G
+92.21
+67.49
+Table 6. Comparison of Param and FLOPs with POSTER V1.
+From Table 6, we can see that POSTER V2 achieves
+better FER results with smaller Param and FLOPs than
+POSTER V1. Compared to POSTER V1-T, POSTER V2
+reduces 8.5M Param and 5.2G FLOPs, while increasing
+0.85% on RAF-DB and 0.62% on AffectNet. Compared
+to POSTER V1-S, POSTER V2 reduces 18.3M Param and
+6.3G FLOPs, while increasing 0.67% on RAF-DB and
+0.36% on AffectNet. Compared to POSTER V1, POSTER
+V2 reduces 28.1M Param and 7.3G FLOPs, while increas-
+ing 0.16% on RAF-DB and 0.18% on AffectNet. Therefore,
+POSTER V2 would be a better choice for the FER task.
+4.4. Method Analysis
+In this sub-section, we present a method analysis for the
+small ViT model we used in POSTER V2 on RAF-DB.
+
+Figure 6. Influence of different depth ViT models on POSTER V2
+for RAF-DB.
+Vit depth.
+Here, we investigate the impact of different
+depths for ViT on the FER performance of POSTER V2.
+In Figure 6, we show the influence of the ViT model with
+depth {2,4,6,8} on POSTER V2. We observe that for multi-
+scale integration we do not need to increase the depth of the
+ViT model. The ViT model with a depth of 2 is sufficient to
+handle the FER task. A deeper ViT model hurts the perfor-
+mance of POSTER V2 instead.
+ViT w/ pre-trained weights
+RAF-DB
+AffectNet
+
+92.21
+67.49
+
+91.49
+60.2
+Table 7. Impact of pre-trained ViT models for POSTER V2 on
+FER.
+Pre-trained Vit. We study the influence of the pre-trained
+ViT model on POSTER V2. We use the ViT pre-trained
+weights on ImagenNet-21K [35] for POSTER V2. Table 7
+shows that the performance of POSTER V2 on FER drops
+after using the pre-trained ViT model. We argue that this is
+mainly due to the fact that the pre-trained ViT model acts
+mainly on the feature extraction of the image-level inputs.
+However, in POSTER V2, ViT performs the multi-scale fea-
+ture integration task of feature-level inputs. The difference
+in input and task resulted in the pre-trained ViT not working
+on POSTER V2.
+4.5. Ablation Study
+Methods
+RAF-DB
+AffectNet
+POSTER V2
+92.21
+67.49
+w/o multi-scale feature extraction
+91.47
+66.51
+w/o ViT
+91.86
+66.92
+w/o W-MCSA
+91.56
+67.24
+w/o cross-fusion
+91.39
+66.35
+Table 8. Results of ablation experiments of key components of
+POSTER V2.
+We validate the effectiveness of our POSTER V1 im-
+provement component on the RAF-DB as well as on the
+AffectNet dataset.
+Multi-scale feature extraction. We first verify the effec-
+tiveness of extracting multi-scale features directly in the
+network. In this ablation experiment, we only use the im-
+age backbone as well as the last layer of feature maps from
+the facial landmark detector for cross-fusion. From Table 8
+we observe that POSTER V2 degrades significantly on the
+RAF-DB and AffectNet datasets when multi-scale feature
+extraction is not performed. This shows that our method
+of directly extracting multi-scale features can also solve the
+scale sensitivity issue of FER. Also, this indicates the im-
+portance of multi-scale features for FER.
+Vit. For the ViT used for multi-scale feature integration, we
+ablate it. We directly sum several different scale features
+for FER. According to the experimental results in Table 8,
+POSTER V2 decreases by 0.35 on RAF-DB and 0.57 on
+AffectNet when multi-scale feature integration is not per-
+formed by ViT. This suggests that ViT facilitates multi-scale
+feature integration.
+W-MCSA. We validate the effectiveness of W-MCSA for
+cross-fusion by ablation experiments. In this experiment,
+we use the vanilla cross-attention mechanism to replace our
+window-based cross-attention mechanism.
+We observed
+that POSTER V2 degraded on both RAF-DB and Affect-
+Net datasets. This shows that the W-MCSA we use both
+improves the FER accuracy and reduces the computational
+complexity of POSTER V1. Thus, W-MCSA is essential
+for POSTER V2.
+Cross-fusion. This experiment mainly verifies the role of
+landmark-to-image branch for POSTER V2. In the abla-
+tion experiments on cross-fusion, we merge the extracted
+image multi-scale features and landmark multi-scale fea-
+tures directly and integrate them by ViT. Table 8 shows that
+the effectiveness of POSTER V2 on RAF-DB as well as
+AffectNet drops sharply when cross-fusion is not applied.
+This shows that cross-fusion is the key for POSTER V2
+to achieve SOTA FER. Also, this indicates that addressing
+inter-class similarity and intra-class discrepancy are partic-
+ularly important for FER task.
+5. Conclusion
+In this paper, we improve POSTER V1 from three direc-
+tions: two-stream, cross-fusion, and multi-scale feature ex-
+traction to obtain a simpler and stronger vision transformer
+for FER, POSTER V2. Extensive FER experimental results
+show that POSTER V2 achieves the state-of-the-art FER
+performance while greatly reducing the Param and FLOPs
+of POSTER V1. This suggests that POSTER V2 achieves a
+better trade-off between accuracy and computational com-
+plexity. Therefore, POSTER V2 is a better choice for the
+FER task.
+
+92.4
+92.2
+RAF-DB Top-1 Accuracy (%)
+92
+91.8
+91.6
+91.4
+91.2
+2
+4
+6
+8
+ViT DepthAcknowledge
+This work was supported by Public-welfare Technology
+Application Research of Zhejiang Province in China un-
+der Grant LGG22F020032, and Key Research and Devel-
+opment Project of Zhejiang Province in China under Grant
+2021C03137.
+References
+[1] Peter F Brown, Vincent J Della Pietra, Peter V Desouza,
+Jennifer C Lai, and Robert L Mercer. Class-based n-gram
+models of natural language.
+Computational linguistics,
+18(4):467–480, 1992. 4
+[2] Cunjian Chen. PyTorch Face Landmark: A fast and accurate
+facial landmark detector, 2021. 6
+[3] Chun-Fu Chen, Rameswar Panda, and Quanfu Fan.
+Re-
+gionvit: Regional-to-local attention for vision transformers.
+arXiv preprint arXiv:2106.02689, 2021. 3
+[4] Chun-Fu Richard Chen, Quanfu Fan, and Rameswar Panda.
+Crossvit: Cross-attention multi-scale vision transformer for
+image classification. In Proceedings of the IEEE/CVF in-
+ternational conference on computer vision, pages 357–366,
+2021. 3
+[5] Shikai Chen, Jianfeng Wang, Yuedong Chen, Zhongchao
+Shi, Xin Geng, and Yong Rui. Label distribution learning
+on auxiliary label space graphs for facial expression recog-
+nition. In Proceedings of the IEEE/CVF conference on com-
+puter vision and pattern recognition, pages 13984–13993,
+2020. 6
+[6] Navneet Dalal and Bill Triggs. Histograms of oriented gra-
+dients for human detection. In 2005 IEEE computer soci-
+ety conference on computer vision and pattern recognition
+(CVPR’05), volume 1, pages 886–893. Ieee, 2005. 1
+[7] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos
+Zafeiriou. Arcface: Additive angular margin loss for deep
+face recognition.
+In Proceedings of the IEEE/CVF con-
+ference on computer vision and pattern recognition, pages
+4690–4699, 2019. 6
+[8] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov,
+Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner,
+Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl-
+vain Gelly, et al. An image is worth 16x16 words: Trans-
+formers for image recognition at scale.
+arXiv preprint
+arXiv:2010.11929, 2020. 3
+[9] Tongle Fan, Guanglei Wang, Yan Li, and Hongrui Wang.
+Ma-net: A multi-scale attention network for liver and tumor
+segmentation. IEEE Access, 8:179656–179665, 2020. 3
+[10] Yingruo Fan, Jacqueline CK Lam, and Victor OK Li. Video-
+based emotion recognition using deeply-supervised neu-
+ral networks.
+In Proceedings of the 20th ACM Interna-
+tional Conference on Multimodal Interaction, pages 584–
+588, 2018. 7
+[11] Amir Hossein Farzaneh and Xiaojun Qi. Facial expression
+recognition in the wild via deep attentive center loss. In Pro-
+ceedings of the IEEE/CVF winter conference on applications
+of computer vision, pages 2402–2411, 2021. 6
+[12] Qinquan Gao, Hanxin Zeng, Gen Li, and Tong Tong. Graph
+reasoning-based emotion recognition network. IEEE Access,
+9:6488–6497, 2021. 7
+[13] Benjamin Graham, Alaaeldin El-Nouby, Hugo Touvron,
+Pierre Stock, Armand Joulin, Herv´e J´egou, and Matthijs
+Douze. Levit: a vision transformer in convnet’s clothing for
+faster inference. In Proceedings of the IEEE/CVF interna-
+tional conference on computer vision, pages 12259–12269,
+2021. 3
+[14] Yandong Guo, Lei Zhang, Yuxiao Hu, Xiaodong He, and
+Jianfeng Gao. Ms-celeb-1m: A dataset and benchmark for
+large-scale face recognition.
+In European conference on
+computer vision, pages 87–102. Springer, 2016. 6
+[15] Dongyoon Han,
+Sangdoo Yun,
+Byeongho Heo,
+and
+YoungJoon Yoo. Rexnet: Diminishing representational bot-
+tleneck on convolutional neural network.
+arXiv preprint
+arXiv:2007.00992, 6, 2020. 1
+[16] Ali Hassani, Steven Walton, Nikhil Shah, Abulikemu
+Abuduweili, Jiachen Li, and Humphrey Shi. Escaping the
+big data paradigm with compact transformers. arXiv preprint
+arXiv:2104.05704, 2021. 3
+[17] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
+Deep residual learning for image recognition. In Proceed-
+ings of the IEEE conference on computer vision and pattern
+recognition, pages 770–778, 2016. 3
+[18] Byeongho Heo, Sangdoo Yun, Dongyoon Han, Sanghyuk
+Chun, Junsuk Choe, and Seong Joon Oh. Rethinking spa-
+tial dimensions of vision transformers.
+In Proceedings of
+the IEEE/CVF International Conference on Computer Vi-
+sion, pages 11936–11945, 2021. 3
+[19] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry
+Kalenichenko, Weijun Wang, Tobias Weyand, Marco An-
+dreetto, and Hartwig Adam. Mobilenets: Efficient convolu-
+tional neural networks for mobile vision applications. arXiv
+preprint arXiv:1704.04861, 2017. 1
+[20] Yuxiao Hu, Zhihong Zeng, Lijun Yin, Xiaozhou Wei, Xi
+Zhou, and Thomas S Huang. Multi-view facial expression
+recognition. In 2008 8th IEEE International Conference on
+Automatic Face & Gesture Recognition, pages 1–6. IEEE,
+2008. 1
+[21] Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kil-
+ian Q Weinberger.
+Densely connected convolutional net-
+works. In Proceedings of the IEEE conference on computer
+vision and pattern recognition, pages 4700–4708, 2017. 2
+[22] Yin-Fu Huang and Chia-Hsin Tsai. Pidvit: Pose-invariant
+distilled vision transformer for facial expression recognition
+in the wild.
+IEEE Transactions on Affective Computing,
+2022. 2
+[23] Taskeed Jabid, Md Hasanul Kabir, and Oksam Chae. Lo-
+cal directional pattern (ldp) for face recognition. In 2010
+digest of technical papers international conference on con-
+sumer electronics (ICCE), pages 329–330. IEEE, 2010. 1
+[24] Sangwon Kim, Jaeyeal Nam, and Byoung Chul Ko. Facial
+expression recognition based on squeeze vision transformer.
+Sensors, 22(10):3729, 2022. 2
+[25] Diederik P Kingma and Jimmy Ba. Adam: A method for
+stochastic optimization.
+arXiv preprint arXiv:1412.6980,
+2014. 7
+
+[26] Nhat Le, Khanh Nguyen, Anh Nguyen, and Bac Le. Global-
+local attention for emotion recognition. Neural Computing
+and Applications, 34(24):21625–21639, 2022. 7
+[27] Jiyoung Lee, Seungryong Kim, Sunok Kim, Jungin Park, and
+Kwanghoon Sohn. Context-aware emotion recognition net-
+works. In Proceedings of the IEEE/CVF international con-
+ference on computer vision, pages 10143–10152, 2019. 6,
+7
+[28] Hangyu Li, Nannan Wang, Xinpeng Ding, Xi Yang, and
+Xinbo Gao. Adaptively learning facial expression represen-
+tation via cf labels and distillation. IEEE Transactions on
+Image Processing, 30:2016–2028, 2021. 6
+[29] Shan Li, Weihong Deng, and JunPing Du. Reliable crowd-
+sourcing and deep locality-preserving learning for expres-
+sion recognition in the wild. In 2017 IEEE Conference on
+Computer Vision and Pattern Recognition (CVPR), pages
+2584–2593. IEEE, 2017. 2, 6
+[30] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng
+Zhang, Stephen Lin, and Baining Guo. Swin transformer:
+Hierarchical vision transformer using shifted windows. In
+Proceedings of the IEEE/CVF International Conference on
+Computer Vision, pages 10012–10022, 2021. 3
+[31] Fuyan Ma, Bin Sun, and Shutao Li. Facial expression recog-
+nition with visual transformers and attentional selective fu-
+sion. IEEE Transactions on Affective Computing, 2021. 2,
+6
+[32] Ali Mollahosseini, Behzad Hasani, and Mohammad H Ma-
+hoor. Affectnet: A database for facial expression, valence,
+and arousal computing in the wild. IEEE Transactions on
+Affective Computing, 10(1):18–31, 2017. 2, 6
+[33] Stephen Moore and Richard Bowden. Local binary patterns
+for multi-view facial expression recognition. Computer vi-
+sion and image understanding, 115(4):541–558, 2011. 1
+[34] Timo Ojala, Matti Pietikainen, and Topi Maenpaa. Multires-
+olution gray-scale and rotation invariant texture classification
+with local binary patterns.
+IEEE Transactions on pattern
+analysis and machine intelligence, 24(7):971–987, 2002. 1,
+2
+[35] Tal Ridnik, Emanuel Ben-Baruch, Asaf Noy, and Lihi
+Zelnik-Manor.
+Imagenet-21k pretraining for the masses.
+arXiv preprint arXiv:2104.10972, 2021. 8
+[36] Delian Ruan, Yan Yan, Shenqi Lai, Zhenhua Chai, Chunhua
+Shen, and Hanzi Wang. Feature decomposition and recon-
+struction learning for effective facial expression recognition.
+In Proceedings of the IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, pages 7660–7669, 2021. 6
+[37] Dinh Viet Sang, Pham Thai Ha, et al. Discriminative deep
+feature learning for facial emotion recognition. In 2018 1st
+International Conference on Multimedia Analysis and Pat-
+tern Recognition (MAPR), pages 1–6. IEEE, 2018. 2
+[38] Andrey V Savchenko. Facial expression and attributes recog-
+nition based on multi-task learning of lightweight neural net-
+works. In 2021 IEEE 19th International Symposium on Intel-
+ligent Systems and Informatics (SISY), pages 119–124. IEEE,
+2021. 1, 2
+[39] Jiahui She, Yibo Hu, Hailin Shi, Jun Wang, Qiu Shen, and
+Tao Mei.
+Dive into ambiguity: Latent distribution min-
+ing and pairwise uncertainty estimation for facial expression
+recognition. In Proceedings of the IEEE/CVF Conference
+on Computer Vision and Pattern Recognition, pages 6248–
+6257, 2021. 6
+[40] Jiawei Shi, Songhao Zhu, and Zhiwei Liang. Learning to
+amend facial expression representation via de-albino and
+affinity. arXiv preprint arXiv:2103.10189, 2021. 6
+[41] Mingxing Tan and Quoc Le. Efficientnet: Rethinking model
+scaling for convolutional neural networks. In International
+conference on machine learning, pages 6105–6114. PMLR,
+2019. 1
+[42] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco
+Massa, Alexandre Sablayrolles, and Herv´e J´egou. Training
+data-efficient image transformers & distillation through at-
+tention. In International Conference on Machine Learning,
+pages 10347–10357. PMLR, 2021. 3
+[43] Hugo Touvron, Matthieu Cord, Alexandre Sablayrolles,
+Gabriel Synnaeve, and Herv´e J´egou. Going deeper with im-
+age transformers. In Proceedings of the IEEE/CVF Interna-
+tional Conference on Computer Vision, pages 32–42, 2021.
+3
+[44] Laurens Van der Maaten and Geoffrey Hinton.
+Visualiz-
+ing data using t-sne. Journal of machine learning research,
+9(11), 2008. 14
+[45] Thanh-Hung Vo, Guee-Sang Lee, Hyung-Jeong Yang, and
+Soo-Hyung Kim. Pyramid with super resolution for in-the-
+wild facial expression recognition. IEEE Access, 8:131988–
+132001, 2020. 2, 6
+[46] Kai Wang, Xiaojiang Peng, Jianfei Yang, Shijian Lu, and
+Yu Qiao. Suppressing uncertainties for large-scale facial ex-
+pression recognition. In Proceedings of the IEEE/CVF con-
+ference on computer vision and pattern recognition, pages
+6897–6906, 2020. 6
+[47] Kai Wang, Xiaojiang Peng, Jianfei Yang, Debin Meng, and
+Yu Qiao. Region attention networks for pose and occlusion
+robust facial expression recognition. IEEE Transactions on
+Image Processing, 29:4057–4069, 2020. 6
+[48] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao
+Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao.
+Pyramid vision transformer: A versatile backbone for dense
+prediction without convolutions.
+In Proceedings of the
+IEEE/CVF International Conference on Computer Vision,
+pages 568–578, 2021. 3
+[49] Zhengyao Wen, Wenzhong Lin, Tao Wang, and Ge Xu.
+Distract your attention:
+Multi-head cross attention net-
+work for facial expression recognition.
+arXiv preprint
+arXiv:2109.07270, 2021. 6
+[50] Haiping Wu, Bin Xiao, Noel Codella, Mengchen Liu,
+Xiyang Dai, Lu Yuan, and Lei Zhang.
+Cvt: Introducing
+convolutions to vision transformers. In Proceedings of the
+IEEE/CVF International Conference on Computer Vision,
+pages 22–31, 2021. 3
+[51] Fanglei Xue, Qiangchang Wang, and Guodong Guo. Trans-
+fer: Learning relation-aware facial expression representa-
+tions with transformers. In Proceedings of the IEEE/CVF
+International Conference on Computer Vision, pages 3601–
+3610, 2021. 1, 2, 6
+[52] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi,
+Zi-Hang Jiang, Francis EH Tay, Jiashi Feng, and Shuicheng
+
+Yan. Tokens-to-token vit: Training vision transformers from
+scratch on imagenet. In Proceedings of the IEEE/CVF In-
+ternational Conference on Computer Vision, pages 558–567,
+2021. 3
+[53] Dan Zeng, Zhiyuan Lin, Xiao Yan, Yuting Liu, Fei Wang,
+and Bo Tang. Face2exp: Combating data biases for facial ex-
+pression recognition. In Proceedings of the IEEE/CVF Con-
+ference on Computer Vision and Pattern Recognition, pages
+20291–20300, 2022. 6
+[54] Yuhang Zhang, Chengrui Wang, Xu Ling, and Weihong
+Deng.
+Learn from all: Erasing attention consistency for
+noisy label facial expression recognition. In European Con-
+ference on Computer Vision, pages 418–434. Springer, 2022.
+2, 6
+[55] Guoying Zhao and Matti Pietikainen.
+Dynamic texture
+recognition using local binary patterns with an application
+to facial expressions. IEEE transactions on pattern analysis
+and machine intelligence, 29(6):915–928, 2007. 1, 2
+[56] Zengqun Zhao, Qingshan Liu, and Shanmin Wang. Learning
+deep global multi-scale and local attention features for facial
+expression recognition in the wild. IEEE Transactions on
+Image Processing, 30:6544–6556, 2021. 6, 7
+[57] Zengqun Zhao, Qingshan Liu, and Feng Zhou.
+Robust
+lightweight facial expression recognition network with la-
+bel distribution training. In Proceedings of the AAAI confer-
+ence on artificial intelligence, volume 35, pages 3510–3519,
+2021. 1, 6, 7
+[58] Ce Zheng, Matias Mendieta, and Chen Chen. Poster: A pyra-
+mid cross-fusion transformer network for facial expression
+recognition. arXiv preprint arXiv:2204.04083, 2022. 2, 3, 6,
+7
+[59] Lin Zhong, Qingshan Liu, Peng Yang, Bo Liu, Junzhou
+Huang, and Dimitris N Metaxas.
+Learning active facial
+patches for expression analysis. In 2012 IEEE Conference
+on Computer Vision and Pattern Recognition, pages 2562–
+2569. IEEE, 2012. 1, 2
+[60] Daquan Zhou, Bingyi Kang, Xiaojie Jin, Linjie Yang, Xi-
+aochen Lian, Zihang Jiang, Qibin Hou, and Jiashi Feng.
+Deepvit: Towards deeper vision transformer. arXiv preprint
+arXiv:2103.11886, 2021. 3
+
+Appendix
+A. Implementation Details
+For POSTER V2, we conduct FER experiments on
+the RAF-DB, AffectNet, and CAER-S datasets, respec-
+tively. For different datasets, we adopt different detail set-
+tings. Specifically, for different datasets, we exploit differ-
+ent learning rates for training according to the settings of
+POSTER V1. Moreover, for AffectNet (8 cls), POSTER
+V2 uses a classification head with a category number of 8
+for prediction. The rest of the settings are consistent with
+the experimental sections in the main text.
+config
+value
+optimizer
+Adam
+base learning rate
+3.50E-05
+weight decay
+1.00E-04
+batch size
+144
+training epochs
+200
+learning rate schedule
+ExponentialLR (gamma=0.98)
+augmentation
+RandomHorizontalFlip(),
+RandomErasing(scale=(0.02, 0.1)).
+drop path
+linspace(0, 0.5, 5)
+num classes
+7
+Table 9. Supervised training POSTER V2 from scratch on RAF-
+DB.
+RAF-DB Settings.
+We use the Adam optimizer with a
+learning rate of 3.5e-5 for 200 epochs training. The batch
+size is maintained at 144 and the weight decay remains at
+1e-4. The learning rate schedule uses an exponential decay
+with a gamma of 0.98. Data augmentation includes random
+horizontal flipping and random erasure. The specific set-
+tings are shown in Table 9.
+config
+value
+optimizer
+Adam
+base learning rate
+1.00E-06
+weight decay
+1.00E-04
+batch size
+144
+training epochs
+200
+learning rate schedule
+ExponentialLR (gamma=0.98)
+augmentation
+RandomHorizontalFlip(),
+RandomErasing(p=1, scale=(0.05, 0.05)).
+drop path
+linspace(0, 0.5, 5)
+num classes
+7
+Table 10. Supervised training POSTER V2 from scratch on Af-
+fectNet (7 cls).
+AffectNet (7 cls) Settings. On the AffcetNet (7 cls) dataset,
+we adjust the learning rate to 1e-6. The training epochs re-
+mains at 200. The batch size is maintained at 144 and the
+weight decay remains at 1e-4. The learning rate schedule
+uses an exponential decay with a gamma of 0.98. Data aug-
+mentation includes random horizontal flipping and random
+erasure. The detailed settings are shown in Table 10.
+config
+value
+optimizer
+Adam
+base learning rate
+1.00E-06
+weight decay
+1.00E-04
+batch size
+144
+training epochs
+200
+learning rate schedule
+ExponentialLR (gamma=0.98)
+augmentation
+RandomHorizontalFlip(),
+RandomErasing(p=1, scale=(0.05, 0.05)).
+drop path
+linspace(0, 0.5, 5)
+num classes
+8
+Table 11. Supervised training POSTER V2 from scratch on Af-
+fectNet (8 cls).
+AffectNet (8 cls) Settings. We use the Adam optimizer
+with a learning rate of 1e-6 for 200 epochs training. The
+batch size is maintained at 144 and the weight decay re-
+mains at 1e-4. The learning rate schedule uses an expo-
+nential decay with a gamma of 0.98. Data augmentation
+includes random horizontal flipping and random erasure. In
+addition, we set the number of categories to 8. Table 11
+shows the specific experimental settings.
+config
+value
+optimizer
+Adam
+base learning rate
+4.00E-05
+weight decay
+1.00E-04
+batch size
+144
+training epochs
+200
+learning rate schedule
+ExponentialLR (gamma=0.98)
+augmentation
+RandomHorizontalFlip(),
+RandomErasing(p=1, scale=(0.05, 0.05)).
+drop path
+linspace(0, 0.5, 5)
+num classes
+7
+Table 12. Supervised training POSTER V2 from scratch on
+CAER-S.
+CAER-S Settings. On the CAER-S dataset, we employ the
+Adam optimizer with a learning rate of 4e-5 for 200 epochs
+of training. The batch size is maintained at 144 and the
+weight decay remains at 1e-4. The learning rate schedule
+uses an exponential decay with a gamma of 0.98. Data aug-
+mentation includes random horizontal flipping and random
+erasure. The specific settings are shown in Table 12.
+B. Detailed Experimental Results
+In this section, we show more detailed experimental re-
+sults of POSTER V2 on each dataset. And we also show
+the confusion matrix of POSTER V2 in each dataset in Fig-
+ure 7.
+RAF-DB Results. Figure 8 shows the specific training pro-
+cess of POSTER V2 on RAF-DB. We observe that the train-
+ing loss and validation loss of POSTER V2 decrease un-
+til saturation during the training process. Furthermore, the
+training accuracy and validation accuracy of POSTER V2
+
+Figure 7. The confusion matrix of POSTER V2 on each dataset.
+Figure 8. The specific training process of POSTER V2 on RAF-
+DB.
+continue to increase until a small fluctuation.
+Figure 9. The detailed training process of POSTER V2 on Affect-
+Net (7 cls).
+AffectNet (7 cls) Results. We show in Figure 9 the detailed
+training of POSTER V2 on AffectNet (7 cls). POSTER V2
+achieves the best training results on AffectNet (7 cls) at an
+early stage. At this point, POSTER V2 achieves the highest
+accuracy on AffectNet (7 cls) for both the training and test
+sets. Therefore, we stop training in time to save training
+costs.
+AffectNet (8 cls) Results. Figure 10 shows the exact per-
+formance of POSTER V2 on AffectNet (8 cls). We observe
+a similar phenomenon on AffectNet (8 cls) as POSTER V2
+did on AffectNet (7 cls). POSTER V2 also reach saturation
+in the early stages of AffectNet (8 cls). POSTER V2 train-
+ing loss continues to show a decreasing trend, yet there is a
+small increase in validation loss. Nevertheless, the training
+Figure 10. The detailed training process of POSTER V2 on Af-
+fectNet (8 cls).
+accuracy of POSTER V2 on AffectNet (8 cls) continues to
+increase, and the validation accuracy has largely been op-
+timal and remains constant. Therefore, we take the same
+early end operation for POSTER V2 on AffectNet (8 cls) as
+we do for AffectNet (7 cls).
+Figure 11. The detailed training process of POSTER V2 on
+CAER-S.
+CAER-S Results. We show the specific training perfor-
+mance of POSTER V2 on CAER-S in Figure 11. Compared
+with other datasets, POSTER V2 has a relatively long sat-
+uration time on the CAER-S dataset. During the training
+process, the loss on the POSTER V2 training and validation
+sets decreases and saturates at a late stage. Meanwhile, the
+accuracy of POSTER V2 on both the training and validation
+sets has been increasing.
+
+the accuracy/loss curve of train/val
+100
+95
+90
+85 
+80
+75 
+70 
+65
+60
+accuracy
+55
+45
+40
+35
+30 
++..
+ 25 
+20 
+15 
+10 
+train-accuracy
+valid-accuracy
+5 
+valid-loss-x30
+0
+10
+15
+20
+25
+OE
+35
+40
+55
+90
+95
+100
+105
+110
+115
+180
+185
+195
+200
+the training epochthe accuracy/loss curve of train/val
+100
+95
+90 
+85
+80 
+75 
+70 
+65
+60 
+45
+35
+OE
+25
+20 
+15 
+10 
+.++,+++++++++.+
+++++*++*++
+train-accuracy
+valid-accuracy
+5 
+train-loss-x30
+valid-loss-x30
+0
+10
+15
+20
+25
+30 
+35
+40 
+45
+50
+55
+60
+65
+70
+75
+08
+85
+90
+95
+100
+105
+110
+115
+130
+135
+140
+145
+160
+180
+185
+190
+195
+200
+the training epochRAF-DB
+AffectNet (7 cls)
+AffectNet (8 cls)
+CAER-S
+0.0182 0.0122 0.0182 0.000 0.0122 0.0334
+0.0660 0.0940 0.0960 0.0120 0.0140 0.0640
+Neutral 
+0. 6060
+0.0200.0960.0840.0120.0140.000.1080
+Surprise
+0.0020 0.0060 0. 0177 0. 0073 0.0067 0.0210
+0. 8
+0.0020 0.0360 0.0020 0.0140 0.00800.1461
+0.00000.02700.10810.01350.0135
+Happy J 0. 0460
+0.00200.03800.00200.01200.0060
+ 0. 7
+ 0.6
+Fear J0.0000
+0.00030.0010
+0.8
+Sad Jo.1260 0.0120 0.668
+0. 0563 0. 0938 0.0437 0.0688
+0.6
+0380 0.0260 0.0420 0.0660 0.0220
+Disgust J0.0125 0.0030.7188
+Sad /0.1320 0. 0180
+0.03600.03000.03600.0680
+Disgust J0. 0043 0. 0003
+0.984
+0.00300.00300.0013
+0. 6
+0.0680 0.0620 0.0320
+0. 0034 0.0008 0.0042
+0.9722
+0.0034 0.0017 0. 0143
+ Surprise -0.0780 0.0760 0. 0260
+0.12000.02400.0160
+.0050~0.0070
+label
+Happy 
+0.01230.0407
+True
+0.9289
+0.00000.0439
+0. 4
+0.04800.0280
+0.0050 0.0080
+0060 0.0127
+ 0.4
+0.16200.0420
+0. 0185 0.0062
+0. 0309
+.0740 0.0240 0. 05800.5440
+Anger
+0.950
+0. 2
+0. 1
+0.9200
+0.03100.0440
+Conte
+Predicted label
+Predicted label
+Predicted labelthe accuracy/loss curve of train/val
+100
+95
+90
+85 
+80 
+75
+10
+65 
+60 
+55
+45 
+40 
+35 
+30 卡
+25 
+20 
+15 
+.
+10 -
+train-accuracy
+valid-accuracy
+5 
+train-loss-x30
+.
+valid-loss-x30
+0
+10
+15
+20
+25
+OE
+35
+40
+45
+55
+60
+65
+70
+80
+90
+95
+100
+105
+110
+120125
+130
+135140
+145
+150155
+160
+170175
+180
+185
+190
+195
+200
+the training epochthe accuracy/loss curve of train/val
+100
+95
+90
+85 
+80
+75 
+70
+65
+60
+ 55 
+ 50 
+45
+35
+30 -
+ 25 
+20 
+15 
+train-accuracy
+valid-accuracy
+5 
+valid-loss-x30
+0
+15
+20
+25
+30
+35404550
+55
+90
+95
+100
+105
+110
+115
+180
+185
+195
+200
+the training epochFigure 12. Comparison of POSTER V2 and POSTER V1 high-dimensional space t-SNE visualization results. POSTER V1 t-SNE visual-
+ization results (first row), POSTER V2 t-SNE visualization results (second row).
+Figure 13. POSTER V2 cross-fusion stage attention visualization results. For each triplet, we show the input image (left), the landmark
+image (middle), and attention map (right).
+C. Visualization
+T-SNE Visualization. We visualized the high-dimensional
+features of POSTER V1 and POSTER V2 using t-SNE
+[44]. As can be seen in Figure 12, both POSTER V2 and
+POSTER V1 present good t-SNE visualization results on
+RAF-DB and CAER-S datasets. There is almost no signif-
+icant difference between the t-SNE visualization results of
+POSTER V1 and POSTER V2 on CAER-S. POSTER V2
+has a closer intra-class distance than POSTER V1 on RAF-
+DB. Although POSTER V1 and POSTER V2 have poor t-
+SNE visualization results on AffectNet (7 cls) and Affect-
+Net (8 cls). But the inter-class distance between clusters in
+POSTER V2 is further than POSTER V1. Above results
+indicates that POSTER V2 is better than POSTER V1 in al-
+leviating the issues of inter-class similarity and intra-class
+discrepancy in FER.
+Attention Visualization. We visualize the attention map of
+the highest-level features of the POSTER V2 cross-fusion
+stage. From Figure 13, we observe that POSTER V2 suc-
+cessfully captures important facial expression features with
+the help of facial landmark features.
+
+RAF-DB
+AffectNet (7 cls)
+AffectNet (8 cls)
+CAER-SNeutral
+Happy
+Sad
+Surprise
+Fear
+Disgust
+Angry
+Contempt
\ No newline at end of file
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+Impact Invariant Trajectory Optimization of 5-Link Biped Robot 
+Using Hybrid Optimization 
+Aref Amiri, Hasan Salarieh1 
+Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran 
+ 
+Abstract 
+Bipedal robots have received much attention because of the variety of motion maneuvers that they can produce, and the many 
+applications they have in various areas including rehabilitation. One of these motion maneuvers is walking. In this study, we 
+presented a framework for the trajectory optimization of a 5-link (planar) Biped Robot using hybrid optimization. The walking is 
+modeled with two phases of single-stance (support) phase and the collision phase. The dynamic equations of the robot in each 
+phase are extracted by the Lagrange method. It is assumed that the robot heel strike to the ground is full plastic. The gait is optimized 
+with a method called hybrid optimization. The objective function of this problem is considered to be the integral of torque-squared 
+along the trajectory, and also various constraints such as zero dynamics are satisfied without any approximation. Furthermore, in a 
+new framework, there is presented a constraint called impact invariance, which ensures the periodicity of the time-varying 
+trajectories. On the other hand, other constraints provide better and more human-like movement..  
+Keywords: Trajectory optimization, bipedal robots, walking robots, zero dynamics; 
+ 
+ 
+  1. Introduction 
+The mechanism of movement and transfer of objects has always been one of the most important and active areas of 
+human research. Due to the limitations of moving with a wheel, replacing it with feet is an attractive but difficult 
+option, so this field is a hot topic in today's robotic world. With the advancement of robotics science and the usefulness 
+of this issue, a lot of research has been done on the design, optimization, and control of legged robots [1-6]. As the 
+science of bipedal robots has advanced in recent years, there have been significant efforts to improve the performance 
+of these robots in important maneuvers, such as walking and running, but research is still ongoing to find ideal answers 
+[7,8]. Designing reference trajectories for human walking cycles is very important. Several techniques have been 
+adopted to define reference trajectories. So far, many researchers have studied low-energy (or low input torques) paths 
+for bipedal robots [7,9]. We are looking for a periodic path that meets a specific goal in terms of speed and minimizes 
+the torque required to produce the gate. In general, this open and non-trivial problem is solved by finding numerical 
+answers. Various parameters can be considered to optimize the problem, for example, torques, Cartesian coordinate 
+or joint coordinates constraints can be used[10-12]. Many authors have used polynomial functions for Cartesian 
+coordinates of swing leg’s foot, hip, and trunk angle [13,14]. Polynomial functions are used for the coordinates of the 
+joints to limit the number of optimization parameters [15]. The optimal path for each coordinate of joints is usually 
+written in the form of polynomials with unknown coefficients. The coefficients should be obtained through the 
+optimization process [15]. For all bipedal robots, it is important to define optimal periodic motions despite the fact 
+that the number of actuators is less than the degree of freedom of the system, and also zero dynamics problem there 
+exists which should be satisfied during optimization. 
+In this paper, a new method is presented to produce a periodic path for the walking of bipedal robots which satisfies 
+the impact invariance constraint. Also, in order to achieve the feasible trajectory, the zero dynamics constraint is 
+satisfied without any approximation. In addition, by considering some other kinematic and dynamic constraints, and 
+                                                           
+1P.O.B. 11155-9567, Tehran, Iran 
+  salarieh@sharif.edu 
+
+using the hybrid optimization method, an optimal reference trajectory for human-like walking of bipedal robots has 
+been presented.  
+Section 2 presents the dynamics and kinematics of a model of the biped robot. Section 3 is devoted to the formulation 
+of the optimization variables. The constraints are defined in section 4 and the optimization method is also described 
+in section 5. Finally, in sections 5 and 6, the results and conclusion are given. 
+2. Dynamics and kinematics 
+Bipedal robots have different dynamics depending on their movement maneuvers. For example, a running robot with 
+5 links and without an ankle actuator in the flight phase has 7 degrees of freedom and only 4 actuators, so the system 
+is 3 degrees under-actuated. Here a bipedal walking robot will be examined. We assume that the robot is completely 
+on the ground and does not slip while walking. 
+On the other hand, during the single support phase, the other leg rises from the ground when the swing leg hits the 
+ground.  During the single support phase, the model has 5 degrees of freedom and needs at least 5 generalized 
+coordinates to identify the system. On the other hand, the robot has only 4 actuation, so the system has a degree of 
+under-actuation. In under-actuated systems, some parts of the dynamics are not affected by the actuator called the zero 
+dynamics. Here, zero dynamics is affected only by the earth's gravity. The robot's model can be modeled with absolute 
+or relative angles, if relative angles are used, zero dynamics can be easily separated from the main total dynamics. 
+Figure 1 shows the absolute and relative coordinates of a 5-link robot with point feet. 
+ 
+Figure 1 Relative and absolute angles 
+ 
+The general hybrid walking gait model is obtained by combining the single support phase model and the impact model: 
+Σ: {
+𝑥̇ = 𝑓(𝑥) + 𝑔(𝑥)𝑢    𝑥− ∉ Γ
+𝑥+ =  (𝑥−)    
+𝑥− ∈ Γ
+                                                                                                                                   (1) 
+where   is a mapping that transforms the states just before the contact to the states just after the contact. 𝑥: =
+(𝑞𝑇, 𝑞̇ 𝑇)𝑇 is the state vector that contains 𝑞: = (𝑞1, 𝑞2, … , 𝑞𝑛)
+𝑇 which is the vector of joint coordinates and 𝑞̇: =
+(𝑞̇ 1, 𝑞̇ 2, … , 𝑞̇ 𝑛)
+𝑇 is the vector of angular velocities, and 𝑥+ denotes the state vector just after the impact and 𝑥− shows 
+just before this event. 
+The switching set is shown as, 
+  
+  
+  
+  
+  
+𝑞 
+𝑞 
+𝑞 
+𝑞 
+𝑞 
+𝑞 : relative coordinates 
+: absolute coordinates 
+  
+: swing leg's foot
+1
+1
+2 : stance leg's foot
+2
+
+Γ = {(𝑞, 𝑞̇) ∈ 𝑥 ∣ 𝑃 
+𝑣(𝑞) = 0, 𝑃 
+ℎ(𝑞) > 0}                                                                                                                                 (2) 
+ 𝑃 
+𝑣(𝑞) and 𝑃 
+ℎ(𝑞) indicate the vertical and horizontal position of the swing leg, respectively. Now if we model the 
+single support phase alone, we have: 
+𝑀(𝑞)𝑞̈ + 𝑐(𝑞, 𝑞̇)𝑞̇ + 𝐺(𝑞) = (0, 𝑈𝑇)𝑇                                                                                                                          (3) 
+where 𝑀(𝑞) ∈ ℜ𝑛×𝑛 (𝑛 = 5) is the inertia matrix, 𝑐(𝑞, 𝑞̇) ∈ ℜ𝑛×𝑛 is the Coriolis matrix, and 𝐺(𝑞) ∈ ℜ𝑛 is the gravity 
+vector. As shown in Figure 2, the robot does not have any actuators (torques) on the feet, i.e. the robot has not the 
+ankle joint actuator, so the robot is under-actuated which adds a zero dynamic constraint to the problem as mentioned 
+in [16]. The vector 𝑈 ∈ ℜ𝑛−   is as follows: 
+𝑈 = [𝜏 , 𝜏 , 𝜏 , 𝜏 ]𝜏                                                                                                                                                        (4) 
+which represents 4 actuators (torques) on the robot. 2 actuators (torques) on the pelvis (hip) and 2 on the knee of each 
+leg. By separating the equations of (3) the first equation which produces the zero dynamics is written as:  
+∑
+ 
+ 
+𝑗= (𝑀 ,𝑗𝑞̈𝑗 + 𝑐 ,𝑗𝑞̇𝑗) + 𝐺 = 0                                                                                                                                (5) 
+which is called zero-hybrid dynamics and: 
+∑
+ 
+ 
+𝑗= (𝑀 ,𝑗𝑞̈𝑗 + 𝑐 ,𝑗𝑞̇𝑗) + 𝐺 = 𝜏 −                                                                                                                              (6) 
+are other rows of equation (3) (i = 2,…, 5). 
+ 
+Figure 2 Robot configuration and control torques 
+The trunk angle is assumed independent from other links with a separate actuator, In other words, one actuator is 
+responsible for moving the trunk. So if we temporarily separate the trunk from the other components, we are faced 
+with 4 degrees of freedom system. By determining the swing leg's foot (link number 5 in figure 2), the system still has 
+2 degrees of freedom, so the inverse kinematics has infinite answers. Therefore, By determining the position of the 
+hip, 2 more degrees of freedom are determined from the system, in this case, the inverse kinematic robot has 4 answers. 
+Among these 4 answers, the only acceptable answers are the one that satisfies the condition of not breaking the knee. 
+It is important to note that in order to find a suitable periodic answer, we assume that the initial configuration is the 
+same as the final one. 
+3. Optimization variables 
+One convenient way is to select the angles of each link based on a polynomial function of time with a series of 
+unknown coefficients. This choice enables us to have a smooth function with time. Here it is assumed that each angle 
+is a polynomial function of degree 4. It should be noted that the initial and final configuration of the system in each 
+step affects determining two parameters of the polynomial coefficients, the impact invariance constraint is also 
+1
+5
+4
+2
+3
+  =0
+  
+  
+  
+  
+
+effective on another coefficient. Therefore, in order to have at least 2 optimization parameters for each angle, we 
+consider a fourth-order polynomial function with unknown coefficients for the trajectories of each angle. 
+ 
+𝑞𝑘(𝑡) = ∑
+ 
+𝑛= 
+ =0 𝛼𝑘, 𝑡  (𝑘 = 1, … , 5)                                                                                                                                           (7)                       
+4. Definition of constraints 
+These constraints are to find the right trajectory to walk. It makes the shapes of the joint trajectories, the links 
+orientations, and the required torques for walking be within a reasonable range. 
+The constraints are defined as follows: 
+1) Constraints on the initial and final configuration: Initial and final configurations of the robot must be specified. 
+Since the robot moves in a periodic pattern, its initial and final configuration must coincide. 
+𝑞(@𝑡=0)=𝑞𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ,   𝑞(@𝑡=𝑇)=𝑞𝑓𝑖𝑛𝑎𝑙 ,                                                                                                                                       (8) 
+2) Knee movement constraints: In order to have human-like movement, the robot's knees should not be opened and 
+closed excessively ( 𝑚  and  𝑚  are two pre-especified upper bounds in Eq. (9)). 
+   𝑚 ≥ 𝑞 (𝑡) ≥ 0 ,  𝑚 ≥ 𝑞 (𝑡) ≥ 0,                                                                                                                             (9)
+ 
+ 
+3) Swing leg's foot constraint: The swing leg's foot should not collide with the ground except at the beginning and end 
+of the phase. 
+ 𝑝(0)
+𝑣
+=  𝑝(𝑇)
+𝑣
+= 0  𝑝(𝑡)
+𝑣 >0 for 0 < 𝑡 < 𝑇                                                                                                                                   (10)
+ 
+                                                                                                                                   
+ 
+4) Limitation of torques: In order to the physical limitations of the motors, the actuator torques have a certain limit. 
+|𝜏 − (𝑡)| ≤ 𝜏𝑚𝑎𝑥      𝑖 = 2, … ,5                                                                                                                                      (11) 
+5) Limitation of angular velocities: In order to the physical limitations of the motors, the actuator velocities have a 
+certain limit. 
+|𝑞̇ (𝑡)| ≤ 𝑞̇𝑚𝑎𝑥      𝑖 = 1, … ,5                                                                                                                                         (12) 
+6) Limitation of friction coefficient: The reaction of the heels, which is the result of the acceleration of the various 
+members of the robot, must observe a certain ratio. This ratio should be less than the coefficient of friction between 
+the heels and the ground. 
+−𝜇 ≤ |
+𝐹𝑥
+𝐹𝑦| ≤ 𝜇                                                                                                                                                              (13) 
+In the above equation, 𝜇 is the coefficient of friction, and 𝐹𝑥 and 𝐹𝑦 are sequentially the horizontal and vertical ground 
+reactions. 
+7) Zero dynamic constraint: the satisfaction of this constraint is important in two ways. First, if this constraint is not 
+satisfied, the problem of optimizing the input torques is practically ambiguous, because these torques are not really 
+applicable to the problem. Although it may lead to a feasible kinematic equation (kinematically possible), it is not 
+feasible in terms of control, or in other words, it is not dynamically possible.  
+8) Impact invariance constraint: this constraint means that in order to produce a periodic motion, in addition to the 
+configuration, the initial velocities at the beginning point of each cycle should be exactly the same as its previous 
+cycle. Since the velocities after the collision are dependent on the velocities before the collision, by satisfying this 
+constraint, the velocities before the collision are adjusted in such a way as to guarantee the periodicity of the motion. 
+Through the following formulae, this purpose is achieved. At first, the impact mapping formula is written as, 
+
+𝑞̇ + = Δ̃(𝑞−)𝑞̇ −                                                                                                                                                               (14) 
+Δ̃(𝑞−) ∈ ℜ ×  is the impact mapping which maps the angular rates of the leg before contact to the angular rates of 
+that leg after contact. The inverse of Δ̃ is denoted by, 
+𝜂̃(𝑞−) = (Δ̃(𝑞−))
+− 
+                                                                                                                                                   (15) 
+So 𝑞̇ − can be found as :  
+𝑞̇ − = 𝜂̃(𝑞−)𝑞̇ +                                                                                                                                                            (16) 
+The mathematical formulation of this mapping is obtained from the governing differential equations of the system. 
+After the swing leg's foot hits the ground, the positions do not change but the angular velocities change, which can be 
+achieved as following (see [17] for more information), 
+ 
+Δ𝑞̇ = 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− ⋅ Δ𝑣𝑒                                                                                                                       (17) 
+ 
+where 𝑣  is the velocity vector of the end of the swing leg and 𝑀 ∈ ℜ𝑛×𝑛 is the inertia matrix as mentioned in (3), the 
+matrix𝐽 ∈ ℜ𝑚×𝑛  (𝑚 = 2 for planar motions) is also obtained as:  
+𝐽 =
+∂𝑝𝑒
+∂𝑞                                                                                                                                                                             (18) 
+𝑝𝑒 is the position of the end of the swing leg. Assuming that the swing leg sticks to the ground after impact, the velocity 
+of the swing leg's foot after impact is zero, so 
+𝑞̇ + = 𝑞̇ − + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− ⋅ (−𝑣𝑒)                                                                                                                        (19) 
+We know that due to the placement of a leg on the ground, we can write: 
+𝑣𝑒 = 𝛼(𝑞)𝑞̇                                                                                                                                                                  (20) 
+where 𝛼(𝑞) is: 
+𝛼(𝑞) =
+∂𝑣𝑒
+∂𝑞̇                                                                                                                                                                    (21) 
+Finally, by placing )20( into )19( and separating 𝑞̇ −, the pre-impact angular velocity is obtained as follows: 
+𝑞̇ − = (𝐼 + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− − 𝛼(𝑞))
+− 𝑞̇ +                                                                                                  (22) 
+where  𝐼 ∈ ℜ𝑛×𝑛 is the identity matrix. In the above relation, both velocity vectors are written in the same coordinate 
+system, which requires a coordinate conversion, because the coordinate changes after the collision due to the change 
+in the role of the legs. For this purpose, consider the following mapping that converts the relative angles and angular 
+velocities to absolute ones: 
+1𝑟𝑒𝑙κ= 𝐻  𝑎𝑏𝑠𝜿                                                                                                                                                               (23) 
+where 𝜿 ∈ ℜ𝑛 can be the angles vector, the angular velocities vector or the angular accelerations vector. Superscripts  
+1𝑟𝑒𝑙 and 1𝑎𝑏𝑠  represent relative and absolute coordinates in which the vectors are defined, and also 𝐻 ∈ ℜ𝑛×𝑛 is 
+a square matrix. On the other hand, we have a mapping that converts old and new coordinates to each other. This 
+mapping can just be defined for an absolute angular coordinate. If we define the absolute coordinates in this way, we 
+have: 
+1 𝜓 = Γ 𝜓                                                                                                                                                                    (24) 
+
+where indices 1 and 2 indicate the coordinate system before and after the impact, 𝜓 ∈ ℜ𝑛×𝑛 can be velocity vector or 
+angular acceleration vector, and  Γ ∈ ℜ𝑛×𝑛 is the mapping matrix. Finally, with the above transformations, the 
+coordinate systems can be connected suitably as: 
+1 𝑞̇ + = 𝐻Γ𝐻− 1 𝑞̇ +                                                                                                                                                        (25) 
+So the invariancy of the impact during walking is written as it follows, 
+𝑞̇ − = (𝐼 + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− − 𝛼(𝑞))
+− 𝐻Γ𝐻− 𝑞̇ +                                                                                        (26)                                               
+As a result, according to Equation (26), the impact invariance constraint is obtained. In this way, by satisfying this 
+equality constraint, the velocity after impact will be similar to the initial velocity in the previous cycle. 
+5. Optimization 
+According to figure 3, optimization is performed using a hybrid method. This means that first, with the penalty method, 
+the constrained problem becomes unconstrained. Then, using the genetic algorithm, the first level of optimization is 
+applied. Finally, in the second level, the outputs of the first level are used as the input of a gradient-based method and 
+the problem is solved. The objective function is the Euclidean norm of input torques: 
+𝐽(𝛼) = ∫
+ 
+𝑇(𝜁−)
+0
+∥∥𝑈𝛼(𝑡)∥∥ 
+ 𝑑𝑡 = ∫
+ 
+𝑇(𝜁−)
+0
+⟨𝜏, 𝜏⟩𝑑𝑡                                                                                                             (27) 
+where 𝑇(𝜁−) corresponds to the step duration, 𝑈𝛼(𝑡) is the resulting torque obtained from (3) along the periodic 
+solution of the hybrid zero dynamics. To solve the problem more easily and accurately, we tried to satisfy 
+configuration constraints in the problem itself. Therefore, 2 coefficients of each coordinate and a total of 10 parameters 
+of equation (7) are determined by the configuration constraints. 
+ 
+ 
+Figure 3 optimization diagram
+According to equation (7), the number of unknown coefficients for a polynomial of order 4 is equal to 5. On the other 
+hand, due to the existence of 5 independent angles, the number of unknown coefficients in the problem is 25. By 
+Dynamics
+Kinematics
+Setting
+Initializing
+Barrier/Penalty
+Method
+Genetic 
+Algorithm
+Gradient
+Based
+Method
+Physically 
+constraints
+constraints
+kinematically
+constraints
+Cost
+Function
+1
+3
+2
+1: Setting: Type of optimization variables – Desired velocity – Initial and final configuration
+2: Initialization reduces the number of variables and simplifies optimization.
+3: Using penalty/barrier functions, the constrained problem becomes unconstrained.
+F(x, r) = f (x) + P(h(x), g(x), r)
+where f (x) is the cost function h(x) is the vector of equalities constraint, g(x) is the vector of
+inequalities constraint, r is a vector of penalty parameters and P is a real-valued function whose
+action of imposing the penalty on the cost function is controlled by r.
+
+determining the initial and final configuration of the robot, the number of optimization variables for this problem is 
+reduced to 15 (by initializing). 
+6. Results 
+The simulation is based on the specifications of the RABBIT robot (Table 1). As a review, the nonlinear and 
+constrained optimization problem is first converted to a non-constrained problem by the penalty method, then with 
+the values and parameters in Tables 2 and 3, the first layer optimization problem is solved using the genetic algorithm. 
+Next, the outputs of the first layer of optimization are considered as the start point (initial condition) of the second 
+layer of optimization. The maximum violation of the constraints will be equal to .01 and the maximum iteration of the 
+interior-point algorithm is equal to 20. The initial and final configuration of the system as well as other specifications 
+and constraint bounds are given in Tables 3 and 4, respectively. 
+Table 1 RABBIT parameters[18] 
+Symbol 
+Value 
+Name 
+m1, m5 
+3.2 kg 
+mass of lower leg 
+m2, m4 
+6.8 kg 
+mass of upper leg 
+m3 
+20 kg 
+mass of trunk 
+I1, I5 
+0.93 kg-m2 
+rotational inertia of lower leg, about its center of mass 
+I2, I4 
+1.08 kg-m2 
+rotational inertia of upper leg, about its center of mass 
+I3 
+2.22 kg-m2 
+rotational inertia of trunk, about its center of mass 
+l1, l5 
+0.4 m 
+length of lower leg 
+l2, l4 
+0.4 m   
+length of femur 
+l3 
+0.625 m 
+length of trunk 
+d1, d5 
+0.128 m 
+distance from lower leg center of mass to knee 
+d2, d4 
+0.163 m 
+distance from upper leg center of mass to hip 
+d3 
+0.2 m 
+distance from trunk center of mass to hip 
+ 
+Table 2 Quantities and specifications of genetic algorithms 
+Population size 
+300 
+Initial range 
+[-12,12] 
+Elite count 
+15 
+Crossover fraction 
+.8 
+Migration fraction 
+.2 
+Stall generation 
+50 
+Function count 
+10401 
+ 
+Table 3 Problem physical parameters and constraints 
+Maximum angular rate 
+5 rad/s 
+Maximum actuator torque 
+150 N.m 
+Step length 
+0.5 m 
+Velocity 
+1m/s 
+Maximum Friction coefficient                     
+0.7 
+
+ 
+ 
+Table 4 Initial and final configuration 
+Relative angles 
+Initial value@(t=0) 
+Final value@(t=T) 
+q1 
+-0.1681 
+0.4754 
+q2 
+0.3073 
+0.3073 
+q3 
+-0.6499 
+-0.0064 
+q4 
+0.0064 
+0.6499 
+q5 
+0.3073 
+0.3073 
+ 
+  
+Figure 4 The phase plots of joint angles vs. Joint angular rates 
+As can be seen from the results of Figure 4, simulation results show that optimization by considering zero-dynamics 
+constraint can produce an ideal limit cycle in walking of the biped. It is clear that angular velocities, like angles, are 
+quite smooth and without fractures or discontinuities. They are also a long distance from their saturation limit (5 
+radians per second). 
+
+ 
+Figure 5 Force reactions and Friction coefficient 
+It is also clear from Figure 5 that the ground reaction force is also a positive value to ensure that the robot does not 
+rise completely from the ground and the static friction coefficient required between the heels and the ground. As it is 
+known, the coefficient of friction has desirable values that do not reach the upper bound [19]. 
+ 
+Figure 6 Input torques 
+As can be seen from figure 6, the torques are without fractures and are also far from their saturation limits. 
+
+ 
+        Figure 7 Walking motion 
+ 
+ 
+Figure 8  Position of the swing leg's foot 
+As shown in Figures 7 and 8, the swing leg does not collide with the ground except at the beginning and end of the 
+phase.  
+7. Conclusion 
+This paper proposes a two-layer framework for generating optimal time-varying trajectories for bipedal robots. The 
+novelties of the proposed work are presenting and satisfying the impact invariance constraint in a new way to ensure 
+the periodicity of the gait in each phase and satisfying the hybrid zero dynamics simultaneously without any 
+
+approximation. Also to find a better optimal solution, a hybrid optimization is used. On the other hand, various 
+constraints were considered for a better motion of the robot. According to the simulation results, the accuracy of the 
+proposed method and the obtained optimal solution were confirmed. 
+ 
+References 
+[1]Shi, F., Homberger, T., Lee, J., Miki, T., Zhao, M., Farshidian, F., ... & Hutter, M. (2020). Circus ANYmal: A Quadruped Learning Dexterous 
+Manipulation with Its Limbs. arXiv preprint arXiv:2011.08811.Strunk, W., Jr., & White, E. B. (1979).The elements of style. (3rd ed.).New 
+York: Macmillan, (Chapter 4).  
+[2]Grizzle, J. W., Hurst, J., Morris, B., Park, H. W., & Sreenath, K. (2009, June). MABEL, a new robotic bipedal walker and runner. In 2009 
+American Control Conference (pp. 2030-2036). IEEE. 
+[3]Kakaei, M. M., & Salarieh, H. (2020). New Robust Control Method Applied to the Locomotion of a 5-Link Biped Robot. Robotica, 38(11), 
+2023-2038.Van der Geer, J., Hanraads, J. A. J., & Lupton R. A. (2000). The art of writing a scientific article. Journal of Scientific 
+Communications, 163, 51-59.  
+[4]Meghdari, Ali, et al. "A novel method of gait synthesis for bipedal fast locomotion." Journal of Intelligent and Robotic Systems 53.2 (2008): 
+101-118. 
+[5]Wright, Joe, and Ivan Jordanov. "Intelligent approaches in locomotion-a review." Journal of Intelligent & Robotic Systems 80.2 (2015): 255-
+277. 
+[6]Tzafestas, Spyros G., Thanassis E. Krikochoritis, and Costas S. Tzafestas. "Robust sliding-mode control of nine-link biped robot 
+walking." Journal of Intelligent and Robotic Systems 20.2 (1997): 375-402. 
+[7]Khan, Ameer Tamoor, Shuai Li, and Xuefeng Zhou. "Trajectory optimization of 5-link biped robot using beetle antennae search." IEEE 
+Transactions on Circuits and Systems II: Express Briefs 68.10 (2021): 3276-3280. 
+[8]Li, Jingchao, et al. "Online Robust Gait Generator of Biped Robots Inspired by Human Anti-disturbance Strategies." Journal of Intelligent & 
+Robotic Systems 105.1 (2022): 1-16. 
+[9] Beletskii, V. V., Berbyuk, V. E., & Samsonov, V. A. (1982). Parametric optimization of motions of a bipedal walking robot. Mechanics of 
+solids, 17(1), 24-35. 
+[10] Selim, Erman, Musa Alcı, and Mert Altıntas. "Variable-time-interval trajectory optimization-based dynamic walking control of bipedal robot." 
+Robotica (2021): 1-21. 
+[11] Westervelt, Eric R., Jessy W. Grizzle, and Daniel E. Koditschek. "Hybrid zero dynamics of planar biped walkers." IEEE transactions on 
+automatic control 48.1 (2003): 42-56. 
+[12] Wang, Helin, et al. "Finite-time stabilization of periodic orbits for under-actuated biped walking with hybrid zero dynamics." Communications 
+in Nonlinear Science and Numerical Simulation 80 (2020): 104949. 
+[13]Sarkar, Abhishek, and Ashish Dutta. "Optimal trajectory generation and design of an 8-dof compliant biped robot for walk on inclined 
+ground." Journal of Intelligent & Robotic Systems 94.3 (2019): 583-602. 
+[14]Tlalolini, D., Chevallereau, C., & Aoustin, Y. (2009). Comparison of different gaits with rotation of the feet for a planar biped. Robotics and 
+Autonomous Systems, 57(4), 371-383. 
+[15] Chevallereau, C., & Aoustin, Y. (2001). Optimal reference trajectories for walking and running of a biped robot. Robotica, 19(5), 557-569. 
+[16] Kelly, Matthew. "An introduction to trajectory optimization: How to do your own direct collocation." SIAM Review 59.4 (2017): 849-904. 
+[17] Zheng, Yuan‐Fang, and Hooshang Hemami. "Mathematical modeling of a robot collision with its environment." Journal of Robotic Systems 
+2.3 (1985): 289-307. 
+[18] Chevallereau, Christine, et al. "Rabbit: A testbed for advanced control theory." IEEE Control Systems Magazine 23.5 (2003): 57-79. 
+[19] Channon, P. H., S. H. Hopkins, and D. T. Pham. "Derivation of optimal walking motions for a bipedal walking robot." Robotica 10.2 (1992): 
+165-172. 
+ 
+ 
+
diff --git a/C9AyT4oBgHgl3EQfSPck/content/tmp_files/load_file.txt b/C9AyT4oBgHgl3EQfSPck/content/tmp_files/load_file.txt
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@@ -0,0 +1,316 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf,len=315
+page_content='Impact Invariant Trajectory Optimization of 5-Link Biped Robot Using Hybrid Optimization Aref Amiri, Hasan Salarieh1 Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran  Abstract Bipedal robots have received much attention because of the variety of motion maneuvers that they can produce, and the many applications they have in various areas including rehabilitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' One of these motion maneuvers is walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In this study, we presented a framework for the trajectory optimization of a 5-link (planar) Biped Robot using hybrid optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The walking is modeled with two phases of single-stance (support) phase and the collision phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The dynamic equations of the robot in each phase are extracted by the Lagrange method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' It is assumed that the robot heel strike to the ground is full plastic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The gait is optimized with a method called hybrid optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The objective function of this problem is considered to be the integral of torque-squared along the trajectory, and also various constraints such as zero dynamics are satisfied without any approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Furthermore, in a new framework, there is presented a constraint called impact invariance, which ensures the periodicity of the time-varying trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, other constraints provide better and more human-like movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='. Keywords: Trajectory optimization, bipedal robots, walking robots, zero dynamics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Introduction The mechanism of movement and transfer of objects has always been one of the most important and active areas of human research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" Due to the limitations of moving with a wheel, replacing it with feet is an attractive but difficult option, so this field is a hot topic in today's robotic world." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' With the advancement of robotics science and the usefulness of this issue, a lot of research has been done on the design, optimization, and control of legged robots [1-6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' As the science of bipedal robots has advanced in recent years, there have been significant efforts to improve the performance of these robots in important maneuvers, such as walking and running, but research is still ongoing to find ideal answers [7,8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Designing reference trajectories for human walking cycles is very important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Several techniques have been adopted to define reference trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' So far, many researchers have studied low-energy (or low input torques) paths for bipedal robots [7,9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' We are looking for a periodic path that meets a specific goal in terms of speed and minimizes the torque required to produce the gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In general, this open and non-trivial problem is solved by finding numerical answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Various parameters can be considered to optimize the problem, for example, torques, Cartesian coordinate or joint coordinates constraints can be used[10-12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Many authors have used polynomial functions for Cartesian coordinates of swing leg’s foot, hip, and trunk angle [13,14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Polynomial functions are used for the coordinates of the joints to limit the number of optimization parameters [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The optimal path for each coordinate of joints is usually written in the form of polynomials with unknown coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The coefficients should be obtained through the optimization process [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' For all bipedal robots, it is important to define optimal periodic motions despite the fact that the number of actuators is less than the degree of freedom of the system, and also zero dynamics problem there exists which should be satisfied during optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In this paper, a new method is presented to produce a periodic path for the walking of bipedal robots which satisfies the impact invariance constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Also, in order to achieve the feasible trajectory, the zero dynamics constraint is satisfied without any approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In addition, by considering some other kinematic and dynamic constraints, and  1P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 11155 9567, Tehran, Iran  salarieh@sharif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='edu  using the hybrid optimization method, an optimal reference trajectory for human-like walking of bipedal robots has been presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Section 2 presents the dynamics and kinematics of a model of the biped robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Section 3 is devoted to the formulation of the optimization variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The constraints are defined in section 4 and the optimization method is also described in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Finally, in sections 5 and 6, the results and conclusion are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Dynamics and kinematics Bipedal robots have different dynamics depending on their movement maneuvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' For example, a running robot with 5 links and without an ankle actuator in the flight phase has 7 degrees of freedom and only 4 actuators, so the system is 3 degrees under-actuated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Here a bipedal walking robot will be examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' We assume that the robot is completely on the ground and does not slip while walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, during the single support phase, the other leg rises from the ground when the swing leg hits the ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' During the single support phase, the model has 5 degrees of freedom and needs at least 5 generalized coordinates to identify the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, the robot has only 4 actuation, so the system has a degree of under-actuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In under-actuated systems, some parts of the dynamics are not affected by the actuator called the zero dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" Here, zero dynamics is affected only by the earth's gravity." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content="  The robot's model can be modeled with absolute or relative angles, if relative angles are used, zero dynamics can be easily separated from the main total dynamics." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Figure 1 shows the absolute and relative coordinates of a 5-link robot with point feet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Figure 1 Relative and absolute angles  The general hybrid walking gait model is obtained by combining the single support phase model and the impact model: Σ: { 𝑥̇ = 𝑓(𝑥) + 𝑔(𝑥)𝑢    𝑥− ∉ Γ 𝑥+ = \uf044 (𝑥−) 𝑥− ∈ Γ (1) where \uf044  is a mapping that transforms the states just before the contact to the states just after the contact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 𝑥: = (𝑞𝑇, 𝑞̇ 𝑇)𝑇 is the state vector that contains 𝑞: = (𝑞1, 𝑞2, … , 𝑞𝑛) 𝑇 which is the vector of joint coordinates and 𝑞̇: = (𝑞̇ 1, 𝑞̇ 2, … , 𝑞̇ 𝑛) 𝑇 is the vector of angular velocities, and 𝑥+ denotes the state vector just after the impact and 𝑥− shows just before this event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" The switching set is shown as,  𝑞  𝑞  𝑞  𝑞  𝑞  𝑞 : relative coordinates  : absolute coordinates  : swing leg's foot 1 1 2 : stance leg's foot 2  Γ = {(𝑞, 𝑞̇) ∈ 𝑥 ∣ 𝑃 𝑣(𝑞) = 0, 𝑃 ℎ(𝑞) > 0}                                                                                                                                 (2) 𝑃 𝑣(𝑞) and 𝑃 ℎ(𝑞) indicate the vertical and horizontal position of the swing leg, respectively." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Now if we model the single support phase alone, we have: 𝑀(𝑞)𝑞̈ + 𝑐(𝑞, 𝑞̇)𝑞̇ + 𝐺(𝑞) = (0, 𝑈𝑇)𝑇                                                                                                                          (3) where 𝑀(𝑞) ∈ ℜ𝑛×𝑛 (𝑛 = 5) is the inertia matrix, 𝑐(𝑞, 𝑞̇) ∈ ℜ𝑛×𝑛 is the Coriolis matrix, and 𝐺(𝑞) ∈ ℜ𝑛 is the gravity vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' As shown in Figure 2, the robot does not have any actuators (torques) on the feet, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the robot has not the ankle joint actuator, so the robot is under-actuated which adds a zero dynamic constraint to the problem as mentioned in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The vector 𝑈 ∈ ℜ𝑛−   is as follows: 𝑈 = [𝜏 , 𝜏 , 𝜏 , 𝜏 ]𝜏                                                                                                                                                        (4) which represents 4 actuators (torques) on the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 2 actuators (torques) on the pelvis (hip) and 2 on the knee of each leg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' By separating the equations of (3) the first equation which produces the zero dynamics is written as: ∑  𝑗= (𝑀 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='𝑗𝑞̈𝑗 + 𝑐 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='𝑗𝑞̇𝑗) + 𝐺 = 0                                                                                                                                (5) which is called zero-hybrid dynamics and: ∑  𝑗= (𝑀 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='𝑗𝑞̈𝑗 + 𝑐 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='𝑗𝑞̇𝑗) + 𝐺 = 𝜏 −                                                                                                                              (6) are other rows of equation (3) (i = 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='…,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Figure 2 Robot configuration and control torques The trunk angle is assumed independent from other links with a separate actuator, In other words, one actuator is responsible for moving the trunk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' So if we temporarily separate the trunk from the other components, we are faced with 4 degrees of freedom system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" By determining the swing leg's foot (link number 5 in figure 2), the system still has 2 degrees of freedom, so the inverse kinematics has infinite answers." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Therefore, By determining the position of the hip, 2 more degrees of freedom are determined from the system, in this case, the inverse kinematic robot has 4 answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Among these 4 answers, the only acceptable answers are the one that satisfies the condition of not breaking the knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' It is important to note that in order to find a suitable periodic answer, we assume that the initial configuration is the same as the final one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Optimization variables One convenient way is to select the angles of each link based on a polynomial function of time with a series of unknown coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' This choice enables us to have a smooth function with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Here it is assumed that each angle is a polynomial function of degree 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' It should be noted that the initial and final configuration of the system in each step affects determining two parameters of the polynomial coefficients, the impact invariance constraint is also 1 5 4 2 3 =0  effective on another coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Therefore, in order to have at least 2 optimization parameters for each angle, we consider a fourth-order polynomial function with unknown coefficients for the trajectories of each angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  𝑞𝑘(𝑡) = ∑  𝑛= =0 𝛼𝑘, 𝑡  (𝑘 = 1, … , 5)                                                                                                                                           (7) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Definition of constraints These constraints are to find the right trajectory to walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' It makes the shapes of the joint trajectories, the links orientations, and the required torques for walking be within a reasonable range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The constraints are defined as follows: 1) Constraints on the initial and final configuration: Initial and final configurations of the robot must be specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Since the robot moves in a periodic pattern, its initial and final configuration must coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" 𝑞(@𝑡=0)=𝑞𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ,   𝑞(@𝑡=𝑇)=𝑞𝑓𝑖𝑛𝑎𝑙 ,                                                                                                                                       (8) 2) Knee movement constraints: In order to have human-like movement, the robot's knees should not be opened and closed excessively ( 𝑚  and  𝑚  are two pre-especified upper bounds in Eq." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (9)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" 𝑚 ≥ 𝑞 (𝑡) ≥ 0 ,  𝑚 ≥ 𝑞 (𝑡) ≥ 0,                                                                                                                             (9)  3) Swing leg's foot constraint: The swing leg's foot should not collide with the ground except at the beginning and end of the phase." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 𝑝(0) 𝑣 =  𝑝(𝑇) 𝑣 = 0  𝑝(𝑡) 𝑣 >0 for 0 < 𝑡 < 𝑇                                                                                                                                   (10)  4) Limitation of torques: In order to the physical limitations of the motors, the actuator torques have a certain limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' |𝜏 − (𝑡)| ≤ 𝜏𝑚𝑎𝑥      𝑖 = 2, … ,5                                                                                                                                      (11) 5) Limitation of angular velocities: In order to the physical limitations of the motors, the actuator velocities have a certain limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' |𝑞̇ (𝑡)| ≤ 𝑞̇𝑚𝑎𝑥      𝑖 = 1, … ,5                                                                                                                                         (12) 6) Limitation of friction coefficient: The reaction of the heels, which is the result of the acceleration of the various members of the robot, must observe a certain ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' This ratio should be less than the coefficient of friction between the heels and the ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' −𝜇 ≤ | 𝐹𝑥 𝐹𝑦| ≤ 𝜇                                                                                                                                                              (13) In the above equation, 𝜇 is the coefficient of friction, and 𝐹𝑥 and 𝐹𝑦 are sequentially the horizontal and vertical ground reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 7) Zero dynamic constraint: the satisfaction of this constraint is important in two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' First, if this constraint is not satisfied, the problem of optimizing the input torques is practically ambiguous, because these torques are not really applicable to the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Although it may lead to a feasible kinematic equation (kinematically possible), it is not feasible in terms of control, or in other words, it is not dynamically possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 8) Impact invariance constraint: this constraint means that in order to produce a periodic motion, in addition to the configuration, the initial velocities at the beginning point of each cycle should be exactly the same as its previous cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Since the velocities after the collision are dependent on the velocities before the collision, by satisfying this constraint, the velocities before the collision are adjusted in such a way as to guarantee the periodicity of the motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Through the following formulae, this purpose is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' At first, the impact mapping formula is written as,  𝑞̇ + = Δ̃(𝑞−)𝑞̇ −                                                                                                                                                               (14) Δ̃(𝑞−) ∈ ℜ ×  is the impact mapping which maps the angular rates of the leg before contact to the angular rates of that leg after contact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The inverse of Δ̃ is denoted by, 𝜂̃(𝑞−) = (Δ̃(𝑞−)) − (15) So 𝑞̇ − can be found as : 𝑞̇ − = 𝜂̃(𝑞−)𝑞̇ +                                                                                                                                                            (16) The mathematical formulation of this mapping is obtained from the governing differential equations of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" After the swing leg's foot hits the ground," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the positions do not change but the angular velocities change,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' which can be achieved as following (see [17] for more information),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Δ𝑞̇ = 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− ⋅ Δ𝑣𝑒                                                                                                                       (17)  where 𝑣  is the velocity vector of the end of the swing leg and 𝑀 ∈ ℜ𝑛×𝑛 is the inertia matrix as mentioned in (3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the matrix𝐽 ∈ ℜ𝑚×𝑛  (𝑚 = 2 for planar motions) is also obtained as: 𝐽 = ∂𝑝𝑒 ∂𝑞                                                                                                                                                                             (18) 𝑝𝑒 is the position of the end of the swing leg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Assuming that the swing leg sticks to the ground after impact,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=" the velocity of the swing leg's foot after impact is zero," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' so 𝑞̇ + = 𝑞̇ − + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− ⋅ (−𝑣𝑒)                                                                                                                        (19) We know that due to the placement of a leg on the ground,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' we can write: 𝑣𝑒 = 𝛼(𝑞)𝑞̇                                                                                                                                                                  (20) where 𝛼(𝑞) is: 𝛼(𝑞) = ∂𝑣𝑒 ∂𝑞̇                                                                                                                                                                    (21) Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' by placing )20( into )19( and separating 𝑞̇ −,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the pre-impact angular velocity is obtained as follows: 𝑞̇ − = (𝐼 + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− − 𝛼(𝑞)) − 𝑞̇ +                                                                                                  (22) where  𝐼 ∈ ℜ𝑛×𝑛 is the identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  In the above relation, both velocity vectors are written in the same coordinate system, which requires a coordinate conversion, because the coordinate changes after the collision due to the change in the role of the legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' For this purpose, consider the following mapping that converts the relative angles and angular velocities to absolute ones: 1𝑟𝑒𝑙κ= 𝐻  𝑎𝑏𝑠𝜿                                                                                                                                                               (23) where 𝜿 ∈ ℜ𝑛 can be the angles vector, the angular velocities vector or the angular accelerations vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Superscripts 1𝑟𝑒𝑙\uf0a3 and 1𝑎𝑏𝑠\uf0a3  represent relative and absolute coordinates in which the vectors are defined, and also 𝐻 ∈ ℜ𝑛×𝑛 is a square matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, we have a mapping that converts old and new coordinates to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' This mapping can just be defined for an absolute angular coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' If we define the absolute coordinates in this way, we have: 1 𝜓 = Γ 𝜓                                                                                                                                                                    (24)  where indices 1 and 2 indicate the coordinate system before and after the impact, 𝜓 ∈ ℜ𝑛×𝑛 can be velocity vector or angular acceleration vector, and  Γ ∈ ℜ𝑛×𝑛 is the mapping matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' with the above transformations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the coordinate systems can be connected suitably as: 1 𝑞̇ + = 𝐻Γ𝐻− 1 𝑞̇ +                                                                                                                                                        (25) So the invariancy of the impact during walking is written as it follows,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 𝑞̇ − = (𝐼 + 𝑀− ⋅ 𝐽𝑇 ⋅ (𝐽 ⋅ 𝑀− ⋅ 𝐽𝑇)− − 𝛼(𝑞)) − 𝐻Γ𝐻− 𝑞̇ +                                                                                        (26) As a result,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' according to Equation (26),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' the impact invariance constraint is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In this way, by satisfying this equality constraint, the velocity after impact will be similar to the initial velocity in the previous cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Optimization According to figure 3, optimization is performed using a hybrid method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' This means that first, with the penalty method, the constrained problem becomes unconstrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Then, using the genetic algorithm, the first level of optimization is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Finally, in the second level, the outputs of the first level are used as the input of a gradient-based method and the problem is solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The objective function is the Euclidean norm of input torques: 𝐽(𝛼) = ∫  𝑇(𝜁−)  0  ∥∥𝑈𝛼(𝑡)∥∥  𝑑𝑡 = ∫  𝑇(𝜁−) 0 ⟨𝜏, 𝜏⟩𝑑𝑡                                                                                                             (27) where 𝑇(𝜁−) corresponds to the step duration, 𝑈𝛼(𝑡) is the resulting torque obtained from (3) along the periodic solution of the hybrid zero dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' To solve the problem more easily and accurately, we tried to satisfy configuration constraints in the problem itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Therefore, 2 coefficients of each coordinate and a total of 10 parameters of equation (7) are determined by the configuration constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Figure 3 optimization diagram According to equation (7), the number of unknown coefficients for a polynomial of order 4 is equal to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, due to the existence of 5 independent angles, the number of unknown coefficients in the problem is 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' By Dynamics Kinematics Setting Initializing Barrier/Penalty Method Genetic Algorithm Gradient Based Method Physically constraints constraints kinematically constraints Cost Function 1 3 2 1: Setting: Type of optimization variables – Desired velocity – Initial and final configuration 2: Initialization reduces the number of variables and simplifies optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 3: Using penalty/barrier functions, the constrained problem becomes unconstrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' F(x, r) = f (x) + P(h(x), g(x), r) where f (x) is the cost function h(x) is the vector of equalities constraint, g(x) is the vector of inequalities constraint, r is a vector of penalty parameters and P is a real-valued function whose action of imposing the penalty on the cost function is controlled by r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  determining the initial and final configuration of the robot, the number of optimization variables for this problem is reduced to 15 (by initializing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Results The simulation is based on the specifications of the RABBIT robot (Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' As a review, the nonlinear and constrained optimization problem is first converted to a non-constrained problem by the penalty method, then with the values and parameters in Tables 2 and 3, the first layer optimization problem is solved using the genetic algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Next, the outputs of the first layer of optimization are considered as the start point (initial condition) of the second layer of optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The maximum violation of the constraints will be equal to .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='01 and the maximum iteration of the interior-point algorithm is equal to 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The initial and final configuration of the system as well as other specifications and constraint bounds are given in Tables 3 and 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Table 1 RABBIT parameters[18] Symbol Value Name m1, m5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 kg mass of lower leg m2, m4 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='8 kg mass of upper leg m3 20 kg mass of trunk I1, I5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='93 kg-m2 rotational inertia of lower leg, about its center of mass I2, I4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='08 kg-m2 rotational inertia of upper leg, about its center of mass I3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='22 kg-m2 rotational inertia of trunk, about its center of mass l1, l5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='4 m length of lower leg l2, l4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='4 m length of femur l3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='625 m length of trunk d1, d5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='128 m distance from lower leg center of mass to knee d2, d4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='163 m distance from upper leg center of mass to hip d3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 m distance from trunk center of mass to hip  Table 2 Quantities and specifications of genetic algorithms Population size 300 Initial range [-12,12] Elite count 15 Crossover fraction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='8 Migration fraction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 Stall generation 50 Function count 10401  Table 3 Problem physical parameters and constraints Maximum angular rate 5 rad/s Maximum actuator torque 150 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='m Step length 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='5 m Velocity 1m/s Maximum Friction coefficient 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='7  Table 4 Initial and final configuration Relative angles Initial value@(t=0) Final value@(t=T) q1 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='1681 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='4754 q2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3073 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3073 q3 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='6499 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='0064 q4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='0064 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='6499 q5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3073 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3073  Figure 4 The phase plots of joint angles vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Joint angular rates As can be seen from the results of Figure 4, simulation results show that optimization by considering zero-dynamics constraint can produce an ideal limit cycle in walking of the biped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' It is clear that angular velocities, like angles, are quite smooth and without fractures or discontinuities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' They are also a long distance from their saturation limit (5 radians per second).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Figure 5 Force reactions and Friction coefficient It is also clear from Figure 5 that the ground reaction force is also a positive value to ensure that the robot does not rise completely from the ground and the static friction coefficient required between the heels and the ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' As it is known, the coefficient of friction has desirable values that do not reach the upper bound [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Figure 6 Input torques As can be seen from figure 6, the torques are without fractures and are also far from their saturation limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content="  Figure 7 Walking motion  Figure 8  Position of the swing leg's foot As shown in Figures 7 and 8, the swing leg does not collide with the ground except at the beginning and end of the phase." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Conclusion This paper proposes a two-layer framework for generating optimal time-varying trajectories for bipedal robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The novelties of the proposed work are presenting and satisfying the impact invariance constraint in a new way to ensure the periodicity of the gait in each phase and satisfying the hybrid zero dynamics simultaneously without any  approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Also to find a better optimal solution, a hybrid optimization is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' On the other hand, various constraints were considered for a better motion of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' According to the simulation results, the accuracy of the proposed method and the obtained optimal solution were confirmed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  References [1]Shi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Homberger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Miki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Zhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Farshidian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' & Hutter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Circus ANYmal: A Quadruped Learning Dexterous Manipulation with Its Limbs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' arXiv preprint arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='08811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='Strunk, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & White, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='The elements of style.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (3rd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='New York: Macmillan, (Chapter 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [2]Grizzle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Hurst, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Morris, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Park, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Sreenath, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2009, June).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' MABEL, a new robotic bipedal walker and runner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' In 2009 American Control Conference (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' 2030-2036).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [3]Kakaei, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Salarieh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' New Robust Control Method Applied to the Locomotion of a 5-Link Biped Robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Robotica, 38(11), 2023-2038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='Van der Geer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Hanraads, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Lupton R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' The art of writing a scientific article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Journal of Scientific Communications, 163, 51-59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [4]Meghdari, Ali, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "A novel method of gait synthesis for bipedal fast locomotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Intelligent and Robotic Systems 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 (2008): 101-118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [5]Wright, Joe, and Ivan Jordanov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Intelligent approaches in locomotion-a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Intelligent & Robotic Systems 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 (2015): 255- 277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [6]Tzafestas, Spyros G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Thanassis E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Krikochoritis, and Costas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Tzafestas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Robust sliding-mode control of nine-link biped robot walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Intelligent and Robotic Systems 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 (1997): 375-402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [7]Khan, Ameer Tamoor, Shuai Li, and Xuefeng Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Trajectory optimization of 5-link biped robot using beetle antennae search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='"  IEEE Transactions on Circuits and Systems II: Express Briefs 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='10 (2021): 3276-3280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [8]Li, Jingchao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Online Robust Gait Generator of Biped Robots Inspired by Human Anti-disturbance Strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Intelligent & Robotic Systems 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='1 (2022): 1-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [9] Beletskii, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Berbyuk, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Samsonov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Parametric optimization of motions of a bipedal walking robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Mechanics of solids, 17(1), 24-35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [10] Selim, Erman, Musa Alcı, and Mert Altıntas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Variable-time-interval trajectory optimization-based dynamic walking control of bipedal robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Robotica (2021): 1-21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [11] Westervelt, Eric R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Jessy W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Grizzle, and Daniel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Koditschek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Hybrid zero dynamics of planar biped walkers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" IEEE transactions on automatic control 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='1 (2003): 42-56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [12] Wang, Helin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Finite-time stabilization of periodic orbits for under-actuated biped walking with hybrid zero dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Communications in Nonlinear Science and Numerical Simulation 80 (2020): 104949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [13]Sarkar, Abhishek, and Ashish Dutta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Optimal trajectory generation and design of an 8-dof compliant biped robot for walk on inclined ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Intelligent & Robotic Systems 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3 (2019): 583-602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [14]Tlalolini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', Chevallereau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Aoustin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Comparison of different gaits with rotation of the feet for a planar biped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Robotics and Autonomous Systems, 57(4), 371-383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [15] Chevallereau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', & Aoustin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Optimal reference trajectories for walking and running of a biped robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='  Robotica, 19(5), 557-569.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [16] Kelly, Matthew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "An introduction to trajectory optimization: How to do your own direct collocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" SIAM Review 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='4 (2017): 849-904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [17] Zheng, Yuan‐Fang, and Hooshang Hemami.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Mathematical modeling of a robot collision with its environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Journal of Robotic Systems 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='3 (1985): 289-307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [18] Chevallereau, Christine, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Rabbit: A testbed for advanced control theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" IEEE Control Systems Magazine 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='5 (2003): 57-79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' [19] Channon, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Hopkins, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' Pham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content=' "Derivation of optimal walking motions for a bipedal walking robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='" Robotica 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
+page_content='2 (1992): 165-172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9AyT4oBgHgl3EQfSPck/content/2301.00080v1.pdf'}
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+ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training
+for E-Commerce Product Search
+Xuange Cui
+cuixuange@jd.com
+JD.com
+Beijing, China
+Wei Xiong
+xiongwei9@jd.com
+JD.com
+Beijing, China
+Songlin Wang
+wangsonglin3@jd.com
+JD.com
+Beijing, China
+ABSTRACT
+In this paper, we propose a robust multilingual model to improve the
+quality of search results. Our model not only leverage the processed
+class-balanced dataset, but also benefit from multitask pre-training
+that leads to more general representations. In pre-training stage,
+we adopt mlm task, classification task and contrastive learning task
+to achieve considerably performance. In fine-tuning stage, we use
+confident learning, exponential moving average method (EMA), ad-
+versarial training (FGM) and regularized dropout strategy (R-Drop)
+to improve the model’s generalization and robustness. Moreover,
+we use a multi-granular semantic unit to discover the queries and
+products textual metadata for enhancing the representation of the
+model. Our approach obtained competitive results and ranked top-8
+in three tasks. We release the source code and pre-trained models
+associated with this work1.
+CCS CONCEPTS
+• Information systems → Retrieval models and ranking.
+KEYWORDS
+search relevance, e-commerce, semantic matching, multilingual
+1
+INTRODUCTION
+With the rapid growth of e-Commerce, online product search has
+emerged as a popular and effective paradigm for customers to find
+desired products and engage in online shopping [7, 9, 11]. It is very
+challenging to accurately find and display relevant products. This
+is because the customer queries are ambiguous and implicit [12].
+For example, many users search for "iPhone" to find and purchase
+an "iPhone charger". However, the traditional binary classification
+model is difficult to clearly characterize this relationship. The Ama-
+zon KDD Cup 2022 presents a novel multilingual dataset [17] across
+English, Japanese and Spanish, and consists of three different sub-
+tasks to evaluate the model’s abilities of ranking and classifying.
+In this paper, our contributions can be summarized as follows:
+1) Data Augmentation. We use the translation model to convert
+Spanish to English for expanding the dataset. Through splitting
+the complement and irrelevant product text information, we could
+get a bigger dataset with balanced labels. We use confident learn-
+ing [14, 15] to find the potential label errors and remove ∼4% data
+from the training dataset. 2) MultiTask Pre-training. In pre-training
+stage, we use MLM task, classification task and contrastive learn-
+ing task for improving the model’s performance. 3) In fine-tuning
+stage, we use a multi-granular semantic unit to discover the queries
+and products textual metadata for enhancing the representation
+1https://github.com/cuixuage/KDDCup2022-ESCI
+SubTask
+Train Dataset
+Test dataset
+Languages
+Task1
+781K
+48K
+Spanish
+Task2
+1834K
+277K
+& English
+Task3
+1834K
+277K
+& Japanese
+Table 1: The statistics of datasets.
+of the model. And we observe that exponential moving average
+method(EMA) [6], adversarial training(FGM) [5] and regularized
+dropout strategy(R-Drop) [10] could improve the model’s general-
+ization and robustness.
+Our team participated in all tasks, and achieved considerably
+performance gain over the baseline solution. Specifically, our ap-
+proach ranked 5th in task1, ranked 7th in task2 and ranked 8th in
+task3.
+2
+BACKGROUND
+The Amazon KDD Cup 2022 [17] provides three subtasks. The
+task1 consists of a query-product ranking task aimed at ranking the
+results list. The Normalized Discounted Cumulative Gain(nDCG)
+[18] will be used to evaluate the model’s abilities of ranking.
+The task2 and task3 are classification tasks which require the
+model to classify the query/product pairs into correct categories.
+These tasks are designed to test the model’s ability of classifying.
+The micro-F1 [16] will be used as an evaluation metric. Moreover,
+the task2 consists of a multi-class product classification task aimed
+at classifying each product as being an Exact, Substitute, Comple-
+ment, or Irrelevant match for the query. The task3 will measure the
+model’s abilities of identifying the substitute products in the list of
+results for a given query.
+The statistics of the corpus are shown in Table 1. In this challenge,
+the organizers provide two different versions of the data set. One
+for task 1 which is reduced version in terms of number of examples
+and ones for tasks 2 and 3 which is a larger [17]. It is noted that the
+reduced version of the data set has more difficult samples. Our team
+participated in all subtasks, and the next section will introduce an
+overview of our system.
+3
+SYSTEM OVERVIEW
+3.1
+Multi-Task Pre-Training
+We compare several pre-trained multilingual language models from
+the XTREME Leaderboard2, and then we use the "microsoft/infoxlm-
+large3" as text encoder.
+2https://sites.research.google/xtreme
+3https://huggingface.co/microsoft/infoxlm-large
+arXiv:2301.13455v1  [cs.CL]  31 Jan 2023
+
+KDDCup ’22, August 17, 2022, Washington, DC, USA
+Xuange Cui, Wei Xiong, and Songlin Wang
+The InfoXLM𝑙𝑎𝑟𝑔𝑒 model [1] containing 94 languages and pre-
+trained with CCNet dataset, and has the same configurations of
+XLM-R [2] and a shared vocabulary size of 250002. Figure 1 shows
+a high-level overview of our proposed pretext tasks.
+Figure 1: A schematic overview of our novel pre-training
+tasks. These tasks encourage the encoded representations to
+be more general.
+MLM Task, is widely used for learning text representations [3].
+MLM trains a model to predict a random sample of input tokens
+that have been replaced by a [MASK] placeholder in a multi-class
+setting over the entire vocabulary [20]. We adopt MLM-Task on the
+multilingual product-catalogue dataset.
+Classification Task, contains three classification subtasks. One
+of them is Product2Query-Task, this task is a binary classification
+task. Based on the Poisson distribution, a piece of text is intercepted
+from commodity text information as the faked query. The Parame-
+ters passed to the Poisson distribution and more details can be found
+in appendix A.1. Product2Brand-Task and Product2Color-Task are
+multi-class classification that using product text information to
+predict the brand and the color of current item.
+Contrastive Learning Task, is mainly inspired by SimCSE [4]
+and EsimCSE [19]. During training, each data point is trained to
+find out its counterpart among (𝑁 − 1) from in-batch negative
+samples and the queue of data samples. The samples in the queue
+are progressively replaced.
+− log
+𝑒sim(h𝑖,h+
+𝑖 )/𝜏
+�𝑁
+𝑗=1 𝑒sim
+�
+h𝑖,h+
+𝑗
+�
+/𝜏 + �𝑄
+𝑞=1 𝑒sim
+�
+h𝑖,h+𝑞
+�
+/𝜏
+(1)
+The ℎ∗ is the sentence representation, where ℎ𝑖 and ℎ+
+𝑖 are se-
+mantically related. The ℎ+𝑞 denotes a sentence embedding in the
+momentum-updated queue. And the 𝑄 is the size of the queue,
+𝑠𝑖𝑚(ℎ1,ℎ2) is the cosine similarity scores of sentence representa-
+tions, 𝜏 is a temperature hyperparameter. In the end, we average
+the all N Li losses to calculate the contrastive loss Lcon.
+Algorithm 1: Training a MultiTask model.
+Input: DataSet D =
+�
+(𝑥,𝑦,𝑧)𝑖
+� |D |
+𝑖=1
+1 Initialize model parameters Θ randomly ;
+2 Model trainer 𝑇 that takes batches of training data as input
+to optimize the model parameters Θ ;
+3 Set the max number of epoch: 𝑒𝑝𝑜𝑐ℎmax ;
+4 for epoch in 1, 2, ...,𝑒𝑝𝑜𝑐ℎmax do
+5
+Shuffle D by mixing data from different tasks ;
+6
+for B in D do
+7
+// B is a mini-batch of pre-training task ;
+8
+Compute loss : 𝐿(Θ) ;
+9
+1. 𝐿(Θ) = Mask LM Loss ;
+10
+2. 𝐿(Θ) += Classification Loss ;
+11
+3. 𝐿(Θ) += Contrastive Learning Loss ;
+12
+Optimize the model using 𝐿(Θ) ;
+13
+end
+14 end
+Output: Pre-trained Model Θ
+3.2
+Fine-Tuning Methods
+After pre-training, we remove the classifiers for pre-training multi-
+task and concatenate some embeddings with an extra MLP classifier.
+The embeddings consist of three sets of representations. One of
+them is done by concatenating the queries’ 3-gram mean-pooling,
+bullet points’ 3-gram mean-pooling and descriptions’ 3-gram mean-
+pooling embeddings. The others consist of country embedding,
+brand embedding and color embedding, as shown in Figure 2.
+Exponential Moving Average Our model uses EMA [6] to
+smooth the trained parameters. Evaluations that use averaged pa-
+rameters sometimes produce significantly better results than the
+final trained values. Formally, we define the smoothed variables
+and trained variables as 𝜃𝑠 and 𝜃𝑡, EMA decay weight as: 𝜂. After
+each training step, we update 𝜃𝑠 by:
+𝜃𝑠 ← 𝜂𝜃𝑠 + (1 − 𝜂)𝜃𝑡
+(2)
+Adversarial Training Recently, adversarial attack has been
+widely applied in computer vision and natural language processing
+[5, 8, 13, 21]. Many works use it during fine-tuning, we explore the
+influence of adversarial training strategies and compare the FGSM,
+PGD, FREELB and SMART methods. The adversarial attack works
+by augmenting the input with a small perturbation that maximizes
+the adversarial loss:
+min
+𝜃
+E(𝑥,𝑦)∼D
+�
+max
+Δ𝑥 ∈Ω 𝐿(𝑥 + Δ𝑥,𝑦;𝜃)
+�
+(3)
+where the D is dataset, 𝑥 is input, 𝑦 is the gold label, 𝜃 is the model
+parameters, 𝐿(𝑥,𝑦;𝜃) is the loss function and Δ𝑥 is the perturbation.
+In our experiments, we adopt FGSM method in all tasks which based
+on the actual performances.
+R-Drop is proved to be an effective regularization method based
+on dropout, by minimizing the KL-divergence of the output distri-
+butions of every two sub-models generated via dropout in model
+training.
+L𝐾𝐿 = 𝛼 · [D𝐾𝐿 (𝐿𝑜𝑔𝑖𝑡1, 𝐿𝑜𝑔𝑖𝑡2) + D𝐾𝐿 (𝐿𝑜𝑔𝑖𝑡2, 𝐿𝑜𝑔𝑖𝑡1)]
+(4)
+
+ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training for E-Commerce Product Search
+KDDCup ’22, August 17, 2022, Washington, DC, USA
+Figure 2: In fine-tuning stage, we concatenate the multi-granular semantic units, the [CLS] embedding from XLM encoder and
+the IDs’ embeddings.
+We use the origin logits of model’s output as 𝐿𝑜𝑔𝑖𝑡1, and the logits
+after adversarial attack as 𝐿𝑜𝑔𝑖𝑡2.
+Embedding Mixup is widely used data augmentation method
+through linearly interpolating inputs and modeling targets of ran-
+dom samples. We use the contextual embedding vector of [CLS]
+and the corresponding label to generate synthetic examples for
+training. Such training has been shown to act as an effective model
+regularization strategy for text classification task. In conclusion, we
+present the self-supervised multitask pre-training tasks and the sev-
+eral fine-tuning methods for improving the models’ generalization
+and robustness.
+4
+EXPERIMENTS
+4.1
+Settings
+We use InfoXLM𝑙𝑎𝑟𝑔𝑒 as the text encoder, the EMA decay weight is
+set to 0.999. And our learning rate is set to 1e-5 with warm-up ratio
+over 10%, batch size is 32 and gradient clip norm threshold is set to
+1. In pre-training stage, the maximum number of epochs was set to
+10. And in the fine-tuning stage, the maximum number of epochs
+was set to 5. During adversarial training, we set 𝜀 to 1.0 in FGM that
+means calculate only one step in the adversarial attack. We find
+that the dataset has imbalanced label and use some data processing
+steps. Through splitting the complement and irrelevant product text
+information, we could get more pairs which have the same label
+and get a more balanced dataset. We use confident learning to find
+the potential label errors and remove ∼4% data from the training
+dataset. As presented in appendix A.1, the median of Spanish and
+English queries is 14 which satisfies the Poisson distribution of 𝜇 is
+set to 4. And the median of the Japanese query is 31 which satisfies
+the Poisson distribution with 𝜇 is set to 8.
+4.2
+Main Results
+Our approach achieved considerably performance gain over the
+baseline solution, and ranked top-8 in three tasks. The main results
+are shown in Table 2. In task1, we calculated the mean of all model
+outputs as the final ranking results. In task2 and task3, we almost
+used the same network structure except the number of neurons
+in the classifier. Finally, Our approach ranked 5th, 7th and 8th,
+respectively.
+SubTask
+Model
+Metric
+Ranking
+task1
+6 large models
+ndcg=0.9025
+5th
+task2
+only 1 large model
+micro f1=0.8194
+7th
+task3
+only 1 large model
+micro f1=0.8686
+8th
+Table 2: Performance of our approach on the private leader-
+board. In task1, we used six InfoXLM𝑙𝑎𝑟𝑔𝑒 models that fine-
+tuned by different datasets or methods. In task2 and task3,
+we used only one InfoXLM𝑙𝑎𝑟𝑔𝑒 model with the same net-
+work structure, as shown in Figure 2.
+Pre-Training Task
+CV-MLM Loss
+CV-Micro F1
+Mask LM
+1.966
+74.97
++Product2Query
+1.969
+75.05
+++Product2Brand
+1.978
+75.08
++++Contrastive Learning
+2.047
+75.08
+Table 3: The effect of different pre-training tasks and keep
+accumulating from top to bottom. We report the cross vali-
+dation MLM-Loss and Micro-F1 Score × 100 in the task2 set-
+ting.
+4.3
+Ablation Studies
+We investigate the impact of adopting different pre-training task
+in the task2 setting. In Table 3, we show the Mask-LM losses after
+5 epochs of pre-training and Micro-F1 scores after 2 epochs of
+fine-tuning. We find that the Product2Query task achieves an 0.008
+improvement compared to the baseline, and the contrastive learning
+task doesn’t get a significant gain.
+As shown in Table 4, we compare several loss functions, and we
+adopt Poly1 loss function in task2 and task3 which based on the
+actual performances. We observe that the Focal loss function and
+GHM loss function have worse performance than the cross-entropy
+loss function in the task2 setting.
+In this subsection, we explore several methods for further im-
+proving the model’s performance in fine-tuning stage. As presented
+
+KDDCup ’22, August 17, 2022, Washington, DC, USA
+Xuange Cui, Wei Xiong, and Songlin Wang
+Classification Loss
+CV-Micro F1
+CE Loss
+75.08
+Focal Loss
+74.73
+GHM Loss
+74.85
+Poly1 Loss
+75.21
+Table 4: The effect of different losses in the task2 setting. We
+report the cross validation Micro-F1 Score × 100.
+Methods
+CV-Micro F1
++EMA
+75.19
+++FGM
+75.30
++++R-Drop
+75.43
+++++Embedding Mixup
+75.43
+Table 5: The effect of different strategies and keep accumu-
+lating from top to bottom. We report the cross validation
+Micro-F1 Score × 100 in the task2 setting.
+Confident Learning
+CV-Metric
+with-in-task1
+NDCG, +0.005
+with-in-task2
+Micro-F1, -0.003
+with-in-task3
+Micro-F1, -0.002
+Table 6: The effect of removing 4% noisy labels.
+in Table 5, we adopt all of these methods to improve the model’s gen-
+eralization and robustness. We observe that the exponential moving
+average method(EMA), adversarial training(FGM) and regularized
+dropout strategy(R-Drop) could improve the model’s generalization
+and robustness. But the Embedding Mixup strategy doesn’t get a
+significant gain.
+As shown in Table 7, we consider using smaller datasets with
+removing ∼4% noisy labels. We used the smaller dataset to achieve
+an 0.005 improvement in task1, but we get worse results in tash2
+and task3. It could be explained that since task1 contains more
+difficult samples, the manually annotated data contains more label
+errors.
+5
+CONCLUSION AND FUTURE WORK
+In this work, we provide an overview of the combined approach to
+improve the quality of search results. We use data augmentation,
+multitask pretraining strategy and several fine-tuning methods to
+achieve considerably performance. Specifically, we use mlm task,
+classification task and contrastive learning task in pre-training
+stage. And we use exponential moving average method(EMA), ad-
+versarial training(FGM) and regularized dropout strategy(R-Drop)
+to improve the model’s generalization and robustness in fine-tuning
+stage. Moreover, we use a multi-granular semantic unit to discover
+the queries and products textual metadata for enhancing the repre-
+sentation of the model. Future work of our system includes: 1) Com-
+paring with other pre-trained language models, such as deborta𝑙𝑎𝑟𝑔𝑒.
+2) Using other training strategies, such as self-distillation.
+REFERENCES
+[1] Zewen Chi, Li Dong, Furu Wei, Nan Yang, Saksham Singhal, Wenhui Wang,
+Xia Song, Xian-Ling Mao, Heyan Huang, and Ming Zhou. 2020.
+InfoXLM:
+An Information-Theoretic Framework for Cross-Lingual Language Model Pre-
+Training. CoRR abs/2007.07834 (2020). arXiv:2007.07834 https://arxiv.org/abs/
+2007.07834
+[2] Alexis Conneau, Kartikay Khandelwal, Naman Goyal, Vishrav Chaudhary, Guil-
+laume Wenzek, Francisco Guzmán, Edouard Grave, Myle Ott, Luke Zettle-
+moyer, and Veselin Stoyanov. 2019. Unsupervised Cross-lingual Representa-
+tion Learning at Scale. CoRR abs/1911.02116 (2019). arXiv:1911.02116 http:
+//arxiv.org/abs/1911.02116
+[3] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2018. BERT:
+Pre-training of Deep Bidirectional Transformers for Language Understanding.
+CoRR abs/1810.04805 (2018). arXiv:1810.04805 http://arxiv.org/abs/1810.04805
+[4] Tianyu Gao, Xingcheng Yao, and Danqi Chen. 2021. SimCSE: Simple Contrastive
+Learning of Sentence Embeddings. In Empirical Methods in Natural Language
+Processing (EMNLP).
+[5] Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy. 2015. Explaining and
+Harnessing Adversarial Examples. arXiv:1412.6572 [stat.ML]
+[6] Seng Hansun. 2013. A new approach of moving average method in time series
+analysis. In 2013 Conference on New Media Studies (CoNMedia). 1–4.
+https:
+//doi.org/10.1109/CoNMedia.2013.6708545
+[7] Rahul Radhakrishnan Iyer, Rohan Kohli, and Shrimai Prabhumoye. 2020. Mod-
+eling Product Search Relevance in e-Commerce. CoRR abs/2001.04980 (2020).
+arXiv:2001.04980 https://arxiv.org/abs/2001.04980
+[8] Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and
+Tuo Zhao. 2020.
+SMART: Robust and Efficient Fine-Tuning for Pre-trained
+Natural Language Models through Principled Regularized Optimization. In Pro-
+ceedings of the 58th Annual Meeting of the Association for Computational Lin-
+guistics. Association for Computational Linguistics, Online, 2177–2190. https:
+//doi.org/10.18653/v1/2020.acl-main.197
+[9] Sen Li, Fuyu Lv, Taiwei Jin, Guli Lin, Keping Yang, Xiaoyi Zeng, Xiao-Ming Wu,
+and Qianli Ma. 2021. Embedding-based Product Retrieval in Taobao Search. CoRR
+abs/2106.09297 (2021). arXiv:2106.09297 https://arxiv.org/abs/2106.09297
+[10] Xiaobo Liang, Lijun Wu, Juntao Li, Yue Wang, Qi Meng, Tao Qin, Wei Chen, Min
+Zhang, and Tie-Yan Liu. 2021. R-Drop: Regularized Dropout for Neural Networks.
+CoRR abs/2106.14448 (2021). arXiv:2106.14448 https://arxiv.org/abs/2106.14448
+[11] Yiqun Liu, Kaushik Rangadurai, Yunzhong He, Siddarth Malreddy, Xunlong Gui,
+Xiaoyi Liu, and Fedor Borisyuk. 2021. Que2Search: Fast and Accurate Query and
+Document Understanding for Search at Facebook. Proceedings of the 27th ACM
+SIGKDD Conference on Knowledge Discovery & Data Mining (2021).
+[12] Hanqing Lu, Youna Hu, Tong Zhao, Tony Wu, Yiwei Song, and Bing Yin. 2021.
+Graph-based Multilingual Product Retrieval in E-commerce Search.
+CoRR
+abs/2105.02978 (2021). arXiv:2105.02978 https://arxiv.org/abs/2105.02978
+[13] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and
+Adrian Vladu. 2019. Towards Deep Learning Models Resistant to Adversarial
+Attacks. arXiv:1706.06083 [stat.ML]
+[14] Curtis G. Northcutt, Lu Jiang, and Isaac L. Chuang. 2021. Confident Learning:
+Estimating Uncertainty in Dataset Labels. Journal of Artificial Intelligence Research
+(JAIR) 70 (2021), 1373–1411.
+[15] Curtis G. Northcutt, Tailin Wu, and Isaac L. Chuang. 2017.
+Learning with
+Confident Examples: Rank Pruning for Robust Classification with Noisy La-
+bels. In Proceedings of the Thirty-Third Conference on Uncertainty in Artifi-
+cial Intelligence (Sydney, Australia) (UAI’17). AUAI Press, 10 pages.
+http:
+//auai.org/uai2017/proceedings/papers/35.pdf
+[16] Juri Opitz and Sebastian Burst. 2019. Macro F1 and Macro F1. CoRR abs/1911.03347
+(2019). arXiv:1911.03347 http://arxiv.org/abs/1911.03347
+[17] Chandan K. Reddy, Lluís Màrquez, Fran Valero, Nikhil Rao, Hugo Zaragoza,
+Sambaran Bandyopadhyay, Arnab Biswas, Anlu Xing, and Karthik Subbian. 2022.
+Shopping Queries Dataset: A Large-Scale ESCI Benchmark for Improving Product
+Search. arXiv:2206.06588
+[18] Yining Wang, Liwei Wang, Yuanzhi Li, Di He, Tie-Yan Liu, and Wei Chen. 2013.
+A Theoretical Analysis of NDCG Type Ranking Measures. CoRR abs/1304.6480
+(2013). arXiv:1304.6480 http://arxiv.org/abs/1304.6480
+[19] Xing Wu, Chaochen Gao, Liangjun Zang, Jizhong Han, Zhongyuan Wang, and
+Songlin Hu. 2021. ESimCSE: Enhanced Sample Building Method for Contrastive
+Learning of Unsupervised Sentence Embedding. CoRR abs/2109.04380 (2021).
+arXiv:2109.04380 https://arxiv.org/abs/2109.04380
+[20] Atsuki Yamaguchi, George Chrysostomou, Katerina Margatina, and Nikolaos
+Aletras. 2021. Frustratingly Simple Pretraining Alternatives to Masked Language
+
+ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training for E-Commerce Product Search
+KDDCup ’22, August 17, 2022, Washington, DC, USA
+Methods
+CV-Micro F1
+Random♦
+-
+Word2vec♣
+85.33
+Freeze♥
+85.29
+Table 7: The performance of different initialization methods
+of the multi-granular semantic unit. We report the cross val-
+idation Micro-F1 Score × 100 in the task3 setting.
+Modeling. CoRR abs/2109.01819 (2021). arXiv:2109.01819 https://arxiv.org/abs/
+2109.01819
+[21] Chen Zhu, Yu Cheng, Zhe Gan, Siqi Sun, Tom Goldstein, and Jingjing Liu. 2020.
+FreeLB: Enhanced Adversarial Training for Natural Language Understanding. In
+International Conference on Learning Representations. https://openreview.net/
+forum?id=BygzbyHFvB
+A
+APPENDIX
+A.1
+Poisson Distribution
+Figure 3: The length distribution of queries in different lan-
+guages.
+As presented in Figure 3, the median of Spanish and English
+queries is 14 which satisfies the Poisson distribution of 𝜇 is set to
+4. And the median of the Japanese query is 31 which satisfies the
+Poisson distribution with 𝜇 is set to 8.
+A.2
+EmbeddingBag Initialization
+The multi-granular semantic unit implemented by Embedding-
+Bag4. As presented in Table 7, the way of random initialization
+converges slowly, so we don’t record the final result. And when the
+Embedding-Bag is initialized by Word2vec, our approach obtain
+the best performance.
+4https://pytorch.org/docs/stable/generated/torch.nn.EmbeddingBag.html
+
+query_len distribution
+0.35
+geometric_p=0.2
+poisson_miu=4
+0.30
+es
+sn
+0.25
+Jp
+0.20
+Y-axis
+0.15
+0.10
+0.05
+0.00
+0
+5
+10
+15
+20
+25
+30
+X-axis
\ No newline at end of file
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+page_content='ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training  for E-Commerce Product Search  Xuange Cui  cuixuange@jd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  Beijing, China  Wei Xiong  xiongwei9@jd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  Beijing, China  Songlin Wang  wangsonglin3@jd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com  Beijing, China  ABSTRACT  In this paper, we propose a robust multilingual model to improve the  quality of search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Our model not only leverage the processed  class-balanced dataset, but also benefit from multitask pre-training  that leads to more general representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In pre-training stage,  we adopt mlm task, classification task and contrastive learning task  to achieve considerably performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In fine-tuning stage, we use  confident learning, exponential moving average method (EMA), ad-  versarial training (FGM) and regularized dropout strategy (R-Drop)  to improve the model’s generalization and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Moreover,  we use a multi-granular semantic unit to discover the queries and  products textual metadata for enhancing the representation of the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Our approach obtained competitive results and ranked top-8  in three tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We release the source code and pre-trained models  associated with this work1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  CCS CONCEPTS  Information systems → Retrieval models and ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  KEYWORDS  search relevance, e-commerce, semantic matching, multilingual  1  INTRODUCTION  With the rapid growth of e-Commerce, online product search has  emerged as a popular and effective paradigm for customers to find  desired products and engage in online shopping [7, 9, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' It is very  challenging to accurately find and display relevant products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' This  is because the customer queries are ambiguous and implicit [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  For example, many users search for "iPhone" to find and purchase  an "iPhone charger".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' However, the traditional binary classification  model is difficult to clearly characterize this relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The Ama-  zon KDD Cup 2022 presents a novel multilingual dataset [17] across  English, Japanese and Spanish, and consists of three different sub-  tasks to evaluate the model’s abilities of ranking and classifying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  In this paper, our contributions can be summarized as follows:  1) Data Augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We use the translation model to convert  Spanish to English for expanding the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Through splitting  the complement and irrelevant product text information, we could  get a bigger dataset with balanced labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We use confident learn-  ing [14, 15] to find the potential label errors and remove ∼4% data  from the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2) MultiTask Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In pre-training  stage, we use MLM task, classification task and contrastive learn-  ing task for improving the model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 3) In fine-tuning  stage, we use a multi-granular semantic unit to discover the queries  and products textual metadata for enhancing the representation  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='com/cuixuage/KDDCup2022-ESCI  SubTask  Train Dataset  Test dataset  Languages  Task1  781K  48K  Spanish  Task2  1834K  277K  & English  Task3  1834K  277K  & Japanese  Table 1: The statistics of datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And we observe that exponential moving average  method(EMA) [6], adversarial training(FGM) [5] and regularized  dropout strategy(R-Drop) [10] could improve the model’s general-  ization and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Our team participated in all tasks, and achieved considerably  performance gain over the baseline solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Specifically, our ap-  proach ranked 5th in task1, ranked 7th in task2 and ranked 8th in  task3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  2  BACKGROUND  The Amazon KDD Cup 2022 [17] provides three subtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The  task1 consists of a query-product ranking task aimed at ranking the  results list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The Normalized Discounted Cumulative Gain(nDCG)  [18] will be used to evaluate the model’s abilities of ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  The task2 and task3 are classification tasks which require the  model to classify the query/product pairs into correct categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  These tasks are designed to test the model’s ability of classifying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  The micro-F1 [16] will be used as an evaluation metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Moreover,  the task2 consists of a multi-class product classification task aimed  at classifying each product as being an Exact, Substitute, Comple-  ment, or Irrelevant match for the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The task3 will measure the  model’s abilities of identifying the substitute products in the list of  results for a given query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  The statistics of the corpus are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In this challenge,  the organizers provide two different versions of the data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' One  for task 1 which is reduced version in terms of number of examples  and ones for tasks 2 and 3 which is a larger [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' It is noted that the  reduced version of the data set has more difficult samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Our team  participated in all subtasks, and the next section will introduce an  overview of our system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  3  SYSTEM OVERVIEW  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1  Multi-Task Pre-Training  We compare several pre-trained multilingual language models from  the XTREME Leaderboard2, and then we use the "microsoft/infoxlm-  large3" as text encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  2https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='google/xtreme  3https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='co/microsoft/infoxlm-large  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='13455v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='CL]  31 Jan 2023  KDDCup ’22, August 17, 2022, Washington, DC, USA  Xuange Cui, Wei Xiong, and Songlin Wang  The InfoXLM𝑙𝑎𝑟𝑔𝑒 model [1] containing 94 languages and pre-  trained with CCNet dataset, and has the same configurations of  XLM-R [2] and a shared vocabulary size of 250002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Figure 1 shows  a high-level overview of our proposed pretext tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Figure 1: A schematic overview of our novel pre-training  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' These tasks encourage the encoded representations to  be more general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  MLM Task, is widely used for learning text representations [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  MLM trains a model to predict a random sample of input tokens  that have been replaced by a [MASK] placeholder in a multi-class  setting over the entire vocabulary [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We adopt MLM-Task on the  multilingual product-catalogue dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Classification Task, contains three classification subtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' One  of them is Product2Query-Task, this task is a binary classification  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Based on the Poisson distribution, a piece of text is intercepted  from commodity text information as the faked query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The Parame-  ters passed to the Poisson distribution and more details can be found  in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Product2Brand-Task and Product2Color-Task are  multi-class classification that using product text information to  predict the brand and the color of current item.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Contrastive Learning Task, is mainly inspired by SimCSE [4]  and EsimCSE [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' During training, each data point is trained to  find out its counterpart among (𝑁 − 1) from in-batch negative  samples and the queue of data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The samples in the queue  are progressively replaced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  − log  𝑒sim(h𝑖,h+  𝑖 )/𝜏  �𝑁  𝑗=1 𝑒sim  �  h𝑖,h+  𝑗  �  /𝜏 + �𝑄  𝑞=1 𝑒sim  �  h𝑖,h+𝑞  �  /𝜏  (1)  The ℎ∗ is the sentence representation, where ℎ𝑖 and ℎ+  𝑖 are se-  mantically related.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The ℎ+𝑞 denotes a sentence embedding in the  momentum-updated queue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And the 𝑄 is the size of the queue,  𝑠𝑖𝑚(ℎ1,ℎ2) is the cosine similarity scores of sentence representa-  tions, 𝜏 is a temperature hyperparameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In the end, we average  the all N Li losses to calculate the contrastive loss Lcon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Algorithm 1: Training a MultiTask model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Input: DataSet D =  �  (𝑥,𝑦,𝑧)𝑖  � |D |  𝑖=1  1 Initialize model parameters Θ randomly ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  2 Model trainer 𝑇 that takes batches of training data as input  to optimize the model parameters Θ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  3 Set the max number of epoch: 𝑒𝑝𝑜𝑐ℎmax ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  4 for epoch in 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=',𝑒𝑝𝑜𝑐ℎmax do  5  Shuffle D by mixing data from different tasks ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  6  for B in D do  7  // B is a mini-batch of pre-training task ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  8  Compute loss : 𝐿(Θ) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 𝐿(Θ) = Mask LM Loss ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 𝐿(Θ) += Classification Loss ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 𝐿(Θ) += Contrastive Learning Loss ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  12  Optimize the model using 𝐿(Θ) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  13  end  14 end  Output: Pre-trained Model Θ  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='2  Fine-Tuning Methods  After pre-training, we remove the classifiers for pre-training multi-  task and concatenate some embeddings with an extra MLP classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  The embeddings consist of three sets of representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' One of  them is done by concatenating the queries’ 3-gram mean-pooling,  bullet points’ 3-gram mean-pooling and descriptions’ 3-gram mean-  pooling embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The others consist of country embedding,  brand embedding and color embedding, as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Exponential Moving Average Our model uses EMA [6] to  smooth the trained parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Evaluations that use averaged pa-  rameters sometimes produce significantly better results than the  final trained values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Formally, we define the smoothed variables  and trained variables as 𝜃𝑠 and 𝜃𝑡, EMA decay weight as: 𝜂.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' After  each training step, we update 𝜃𝑠 by:  𝜃𝑠 ← 𝜂𝜃𝑠 + (1 − 𝜂)𝜃𝑡  (2)  Adversarial Training Recently, adversarial attack has been  widely applied in computer vision and natural language processing  [5, 8, 13, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Many works use it during fine-tuning, we explore the  influence of adversarial training strategies and compare the FGSM,  PGD, FREELB and SMART methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The adversarial attack works  by augmenting the input with a small perturbation that maximizes  the adversarial loss:  min  𝜃  E(𝑥,𝑦)∼D  �  max  Δ𝑥 ∈Ω 𝐿(𝑥 + Δ𝑥,𝑦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='𝜃)  �  (3)  where the D is dataset, 𝑥 is input, 𝑦 is the gold label, 𝜃 is the model  parameters, 𝐿(𝑥,𝑦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='𝜃) is the loss function and Δ𝑥 is the perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  In our experiments, we adopt FGSM method in all tasks which based  on the actual performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  R-Drop is proved to be an effective regularization method based  on dropout, by minimizing the KL-divergence of the output distri-  butions of every two sub-models generated via dropout in model  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  L𝐾𝐿 = 𝛼 · [D𝐾𝐿 (𝐿𝑜𝑔𝑖𝑡1, 𝐿𝑜𝑔𝑖𝑡2) + D𝐾𝐿 (𝐿𝑜𝑔𝑖𝑡2, 𝐿𝑜𝑔𝑖𝑡1)]  (4)  ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training for E-Commerce Product Search  KDDCup ’22, August 17, 2022, Washington, DC, USA  Figure 2: In fine-tuning stage, we concatenate the multi-granular semantic units, the [CLS] embedding from XLM encoder and  the IDs’ embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  We use the origin logits of model’s output as 𝐿𝑜𝑔𝑖𝑡1, and the logits  after adversarial attack as 𝐿𝑜𝑔𝑖𝑡2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Embedding Mixup is widely used data augmentation method  through linearly interpolating inputs and modeling targets of ran-  dom samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We use the contextual embedding vector of [CLS]  and the corresponding label to generate synthetic examples for  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Such training has been shown to act as an effective model  regularization strategy for text classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In conclusion, we  present the self-supervised multitask pre-training tasks and the sev-  eral fine-tuning methods for improving the models’ generalization  and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  4  EXPERIMENTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1  Settings  We use InfoXLM𝑙𝑎𝑟𝑔𝑒 as the text encoder, the EMA decay weight is  set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And our learning rate is set to 1e-5 with warm-up ratio  over 10%, batch size is 32 and gradient clip norm threshold is set to  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In pre-training stage, the maximum number of epochs was set to  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And in the fine-tuning stage, the maximum number of epochs  was set to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' During adversarial training, we set 𝜀 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='0 in FGM that  means calculate only one step in the adversarial attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We find  that the dataset has imbalanced label and use some data processing  steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Through splitting the complement and irrelevant product text  information, we could get more pairs which have the same label  and get a more balanced dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We use confident learning to find  the potential label errors and remove ∼4% data from the training  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' As presented in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1, the median of Spanish and  English queries is 14 which satisfies the Poisson distribution of 𝜇 is  set to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And the median of the Japanese query is 31 which satisfies  the Poisson distribution with 𝜇 is set to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='2  Main Results  Our approach achieved considerably performance gain over the  baseline solution, and ranked top-8 in three tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' The main results  are shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In task1, we calculated the mean of all model  outputs as the final ranking results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In task2 and task3, we almost  used the same network structure except the number of neurons  in the classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Finally, Our approach ranked 5th, 7th and 8th,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  SubTask  Model  Metric  Ranking  task1  6 large models  ndcg=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='9025  5th  task2  only 1 large model  micro f1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='8194  7th  task3  only 1 large model  micro f1=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='8686  8th  Table 2: Performance of our approach on the private leader-  board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In task1, we used six InfoXLM𝑙𝑎𝑟𝑔𝑒 models that fine-  tuned by different datasets or methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In task2 and task3,  we used only one InfoXLM𝑙𝑎𝑟𝑔𝑒 model with the same net-  work structure, as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Pre-Training Task  CV-MLM Loss  CV-Micro F1  Mask LM  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='966  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='97  +Product2Query  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='969  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='05  ++Product2Brand  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='978  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='08  +++Contrastive Learning  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='047  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='08  Table 3: The effect of different pre-training tasks and keep  accumulating from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We report the cross vali-  dation MLM-Loss and Micro-F1 Score × 100 in the task2 set-  ting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='3  Ablation Studies  We investigate the impact of adopting different pre-training task  in the task2 setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In Table 3, we show the Mask-LM losses after  5 epochs of pre-training and Micro-F1 scores after 2 epochs of  fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We find that the Product2Query task achieves an 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='008  improvement compared to the baseline, and the contrastive learning  task doesn’t get a significant gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  As shown in Table 4, we compare several loss functions, and we  adopt Poly1 loss function in task2 and task3 which based on the  actual performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We observe that the Focal loss function and  GHM loss function have worse performance than the cross-entropy  loss function in the task2 setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  In this subsection, we explore several methods for further im-  proving the model’s performance in fine-tuning stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' As presented  KDDCup ’22, August 17, 2022, Washington, DC, USA  Xuange Cui, Wei Xiong, and Songlin Wang  Classification Loss  CV-Micro F1  CE Loss  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='08  Focal Loss  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='73  GHM Loss  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='85  Poly1 Loss  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='21  Table 4: The effect of different losses in the task2 setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We  report the cross validation Micro-F1 Score × 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Methods  CV-Micro F1  +EMA  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='19  ++FGM  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='30  +++R-Drop  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='43  ++++Embedding Mixup  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='43  Table 5: The effect of different strategies and keep accumu-  lating from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We report the cross validation  Micro-F1 Score × 100 in the task2 setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Confident Learning  CV-Metric  with-in-task1  NDCG, +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='005  with-in-task2  Micro-F1, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='003  with-in-task3  Micro-F1, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='002  Table 6: The effect of removing 4% noisy labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  in Table 5, we adopt all of these methods to improve the model’s gen-  eralization and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We observe that the exponential moving  average method(EMA), adversarial training(FGM) and regularized  dropout strategy(R-Drop) could improve the model’s generalization  and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' But the Embedding Mixup strategy doesn’t get a  significant gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  As shown in Table 7, we consider using smaller datasets with  removing ∼4% noisy labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We used the smaller dataset to achieve  an 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='005 improvement in task1, but we get worse results in tash2  and task3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' It could be explained that since task1 contains more  difficult samples, the manually annotated data contains more label  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  5  CONCLUSION AND FUTURE WORK  In this work, we provide an overview of the combined approach to  improve the quality of search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We use data augmentation,  multitask pretraining strategy and several fine-tuning methods to  achieve considerably performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Specifically, we use mlm task,  classification task and contrastive learning task in pre-training  stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And we use exponential moving average method(EMA), ad-  versarial training(FGM) and regularized dropout strategy(R-Drop)  to improve the model’s generalization and robustness in fine-tuning  stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Moreover, we use a multi-granular semantic unit to discover  the queries and products textual metadata for enhancing the repre-  sentation of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Future work of our system includes: 1) Com-  paring with other pre-trained language models, such as deborta𝑙𝑎𝑟𝑔𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  2) Using other training strategies, such as self-distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  REFERENCES  [1] Zewen Chi, Li Dong, Furu Wei, Nan Yang, Saksham Singhal, Wenhui Wang,  Xia Song, Xian-Ling Mao, Heyan Huang, and Ming Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  InfoXLM:  An Information-Theoretic Framework for Cross-Lingual Language Model Pre-  Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='07834 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='07834 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='07834  [2] Alexis Conneau, Kartikay Khandelwal, Naman Goyal, Vishrav Chaudhary, Guil-  laume Wenzek, Francisco Guzmán, Edouard Grave, Myle Ott, Luke Zettle-  moyer, and Veselin Stoyanov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Unsupervised Cross-lingual Representa-  tion Learning at Scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02116 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02116 http:  //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02116  [3] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' BERT:  Pre-training of Deep Bidirectional Transformers for Language Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  CoRR abs/1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04805 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04805 http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04805  [4] Tianyu Gao, Xingcheng Yao, and Danqi Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' SimCSE: Simple Contrastive  Learning of Sentence Embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In Empirical Methods in Natural Language  Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  [5] Ian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Goodfellow, Jonathon Shlens, and Christian Szegedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Explaining and  Harnessing Adversarial Examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='6572 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='ML]  [6] Seng Hansun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' A new approach of moving average method in time series  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In 2013 Conference on New Media Studies (CoNMedia).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1109/CoNMedia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='6708545  [7] Rahul Radhakrishnan Iyer, Rohan Kohli, and Shrimai Prabhumoye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Mod-  eling Product Search Relevance in e-Commerce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04980 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04980 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
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+page_content='04980  [8] Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and  Tuo Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  SMART: Robust and Efficient Fine-Tuning for Pre-trained  Natural Language Models through Principled Regularized Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In Pro-  ceedings of the 58th Annual Meeting of the Association for Computational Lin-  guistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Association for Computational Linguistics, Online, 2177–2190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
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+page_content='197  [9] Sen Li, Fuyu Lv, Taiwei Jin, Guli Lin, Keping Yang, Xiaoyi Zeng, Xiao-Ming Wu,  and Qianli Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Embedding-based Product Retrieval in Taobao Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR  abs/2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='09297 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='09297 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='09297  [10] Xiaobo Liang, Lijun Wu, Juntao Li, Yue Wang, Qi Meng, Tao Qin, Wei Chen, Min  Zhang, and Tie-Yan Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' R-Drop: Regularized Dropout for Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  CoRR abs/2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='14448 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='14448 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
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+page_content='14448  [11] Yiqun Liu, Kaushik Rangadurai, Yunzhong He, Siddarth Malreddy, Xunlong Gui,  Xiaoyi Liu, and Fedor Borisyuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Que2Search: Fast and Accurate Query and  Document Understanding for Search at Facebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Proceedings of the 27th ACM  SIGKDD Conference on Knowledge Discovery & Data Mining (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  [12] Hanqing Lu, Youna Hu, Tong Zhao, Tony Wu, Yiwei Song, and Bing Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Graph-based Multilingual Product Retrieval in E-commerce Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  CoRR  abs/2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02978 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02978 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='02978  [13] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and  Adrian Vladu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Towards Deep Learning Models Resistant to Adversarial  Attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='06083 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='ML]  [14] Curtis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Northcutt, Lu Jiang, and Isaac L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Chuang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Confident Learning:  Estimating Uncertainty in Dataset Labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Journal of Artificial Intelligence Research  (JAIR) 70 (2021), 1373–1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  [15] Curtis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Northcutt, Tailin Wu, and Isaac L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Chuang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Learning with  Confident Examples: Rank Pruning for Robust Classification with Noisy La-  bels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In Proceedings of the Thirty-Third Conference on Uncertainty in Artifi-  cial Intelligence (Sydney, Australia) (UAI’17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' AUAI Press, 10 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  http:  //auai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/uai2017/proceedings/papers/35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='pdf  [16] Juri Opitz and Sebastian Burst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Macro F1 and Macro F1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='03347  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='03347 http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='03347  [17] Chandan K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Reddy, Lluís Màrquez, Fran Valero, Nikhil Rao, Hugo Zaragoza,  Sambaran Bandyopadhyay, Arnab Biswas, Anlu Xing, and Karthik Subbian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Shopping Queries Dataset: A Large-Scale ESCI Benchmark for Improving Product  Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='06588  [18] Yining Wang, Liwei Wang, Yuanzhi Li, Di He, Tie-Yan Liu, and Wei Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  A Theoretical Analysis of NDCG Type Ranking Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='6480  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='6480 http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='6480  [19] Xing Wu, Chaochen Gao, Liangjun Zang, Jizhong Han, Zhongyuan Wang, and  Songlin Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' ESimCSE: Enhanced Sample Building Method for Contrastive  Learning of Unsupervised Sentence Embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04380 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04380 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='04380  [20] Atsuki Yamaguchi, George Chrysostomou, Katerina Margatina, and Nikolaos  Aletras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' Frustratingly Simple Pretraining Alternatives to Masked Language  ZhichunRoad at Amazon KDD Cup 2022: MultiTask Pre-Training for E-Commerce Product Search  KDDCup ’22, August 17, 2022, Washington, DC, USA  Methods  CV-Micro F1  Random♦ Word2vec♣  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='33  Freeze♥  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='29  Table 7: The performance of different initialization methods  of the multi-granular semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' We report the cross val-  idation Micro-F1 Score × 100 in the task3 setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  Modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' CoRR abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='01819 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='01819 https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/abs/  2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='01819  [21] Chen Zhu, Yu Cheng, Zhe Gan, Siqi Sun, Tom Goldstein, and Jingjing Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  FreeLB: Enhanced Adversarial Training for Natural Language Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' In  International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' https://openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='net/  forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='id=BygzbyHFvB  A  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='1  Poisson Distribution  Figure 3: The length distribution of queries in different lan-  guages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  As presented in Figure 3, the median of Spanish and English  queries is 14 which satisfies the Poisson distribution of 𝜇 is set to  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And the median of the Japanese query is 31 which satisfies the  Poisson distribution with 𝜇 is set to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='2  EmbeddingBag Initialization  The multi-granular semantic unit implemented by Embedding-  Bag4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' As presented in Table 7, the way of random initialization  converges slowly, so we don’t record the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content=' And when the  Embedding-Bag is initialized by Word2vec, our approach obtain  the best performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='  4https://pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='org/docs/stable/generated/torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='EmbeddingBag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='html  query_len distribution  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='35  geometric_p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='2  poisson_miu=4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='30  es  sn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
+page_content='25  Jp  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CNFQT4oBgHgl3EQf-jfx/content/2301.13455v1.pdf'}
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+arXiv:2301.04681v1  [math.DG]  11 Jan 2023
+STABILITY OF STANDARD EINSTEIN METRICS ON
+HOMOGENEOUS SPACES OF NON-SIMPLE LIE GROUPS
+VALERIA GUTI´ERREZ AND JORGE LAURET
+Abstract. The classification of compact homogeneous spaces of the form M = G/K,
+where G is a non-simple Lie group, such that the standard metric is Einstein is still
+open. The only known examples are 4 infinite families and 3 isolated spaces found by
+Nikonorov and Rodionov in the 90s. In this paper, we prove that most of these standard
+Einstein metrics are unstable as critical points of the scalar curvature functional on the
+manifold of all unit volume G-invariant metrics on M, providing a lower bound for the
+coindex in the case of Ledger-Obata spaces. On the other hand, examples of stable (in
+particular, local maxima) invariant Einstein metrics on certain homogeneous spaces of
+non-simple Lie groups are also given.
+Contents
+1.
+Introduction
+1
+2.
+Preliminaries
+3
+3.
+G-instability of standard Einstein metrics
+4
+4.
+Ledger-Obata spaces
+6
+5.
+G-stable Einstein metrics with G non-simple
+8
+References
+9
+1. Introduction
+Any manifold M on which a given compact semisimple Lie group G is acting transitively
+can be endowed with a canonical G-invariant Riemannian metric gB provided by the Killing
+form of the Lie algebra g of G, so called the standard metric. In the case when G is simple,
+the Einstein condition for gB was studied by Wang and Ziller in [WZ], where it is obtained
+a complete classification.
+The list of homogeneous spaces M = G/K with G simple,
+beyond isotropy irreducible spaces, on which gB is Einstein consists of 10 infinite families
+and 2 isolated examples for G classical and 20 isolated examples with G exceptional. The
+stability types of these metrics as critical points of the scalar curvature functional
+Sc : MG
+1 −→ R,
+where MG
+1 is the manifold of all G-invariant metrics of some fixed volume on M, have
+recently been obtained in [LL]. The standard metric is G-unstable on most of the spaces
+with G classical, being even a local minimum on many of them (see [LL, Table 1]), while
+gB is G-stable and therefore a local maximum on 14 of the 20 spaces with exceptional G
+(see [LL, Tables 2,3,4]).
+On the other hand, in the case when G is not simple, the classification of standard
+Einstein metrics is still an open question (see [NRS, Section 4.14] and references therein).
+Under certain conditions, Nikonorov obtained in [N] the following algebraic constraints on
+Date: January 13, 2023.
+This research was partially supported by grants from FONCyT and Univ. Nac. de C´ordoba.
+1
+
+2
+VALERIA GUTI´ERREZ AND JORGE LAURET
+the structure of homogeneous spaces on which the standard metric gB is Einstein. We fix
+a decomposition
+(1)
+g = g1 ⊕ g2 ⊕ · · · ⊕ gm,
+of the semisimple Lie algebra g in simple ideals and consider πj : k → gj, the corresponding
+projections.
+Theorem 1.1. [N, Theorem 6]. Let (G/K, gB) be a connected irreducible standard ho-
+mogeneous Einstein space with semisimple isotropy group K such that either πj(k) = gj
+or πj(k) consists of two simple summands. Then it is defined by the following scheme of
+inclusion:
+K := H × L1 × · · · × Ln ⊂ H × · · · × H
+�
+��
+�
+m
+×L1 × · · · × Ln
+⊂ H × · · · × H
+�
+��
+�
+m−n
+×G1 × · · · × Gn = G,
+where H, Li and Gi are simple Lie groups, the first inclusion has the form diag(H) ×
+Id × · · · × Id, the second has the form Id × · · · × Id ×ι1 × · · · × ιn, where ιi : H × Li → Gi
+are some inclusions.
+This is a strong obstruction to have gB Einstein, in particular, it implies that the simple
+factors of G on which the projection of K is onto are pairwise isomorphic. In [N, Theorem
+7], a complete list of homogeneous spaces of the above form on which gB is Einstein is
+obtained, consisting of 4 infinite families and 3 isolated examples.
+We study in this paper the stability of these Einstein metrics. Our main result is the
+following.
+Theorem 1.2. Let M = G/K be a homogeneous space as in Theorem 1.1 and assume
+that the standard metric gB is Einstein and n + 4 ≤ m.
+(i) gB is G-unstable, i.e., there is a positive direction for the Hessian of Sc at gB (see
+Theorem 3.2).
+(ii) On the Ledger-Obata space M = Hm/∆mH (i.e., when n = 0 and m ≥ 3), gB has
+coindex ≥ m − 3 if 12 ≤ m and coindex ≥ m − 2 if 3 ≤ m ≤ 11 (see Theorem 4.3).
+It is worth noting that we do not use the classification given in [N, Theorem 7] to prove
+part (i), we only use the structure provided by Theorem 1.1 and the general formulas for
+the Hessian of Sc given in [L] and [LW]. Most cases in [N, Theorem 7] are covered by the
+above theorem (see Remark 3.3).
+The only other stability result on G-invariant Einstein metrics with a non-simple G we
+were able to find in the literature is in [L, Section 7], where it is proved that the so called
+Jensen’s metric on a simple Lie group H is always G-unstable viewed as a G-invariant
+metric on M = G/∆K, where G := H × K, for some semisimple subgroup K ⊂ H. The
+following natural question arises: is any G-invariant Einstein metric on a homogeneous
+space G/K with G non-simple G-unstable? The following result answers this question in
+the negative.
+Theorem 1.3. (See Theorem 5.2). For any simple Lie group H and simple subgroup
+K ⊂ H such that the homogeneous space H/K is isotropy irreducible and (H, K) ̸=
+(Sp(n), Sp(n−1)), there exists an (H ×K)-invariant Einstein metric on M = H ×K/∆K
+which is (H × K)-stable.
+Acknowledgements. The authors thank Yuri Nikonorov for very helpful conversations on
+the subject of this paper.
+
+STABILITY OF STANDARD EINSTEIN METRICS
+3
+2. Preliminaries
+We fix an almost-effective transitive action of a compact connected Lie group G on a
+manifold Md, determining a presentation M = G/K of M as a homogeneous space, where
+K ⊂ G is the isotropy subgroup at some point o ∈ M. Let MG denote the manifold of all
+G-invariant metrics on M, which satisfies 1 ≤ dim MG ≤ d(d+1)
+2
+.
+If MG
+1 ⊂ MG is the codimension one submanifold of all unit volume metrics, then
+g ∈ MG
+1 is Einstein if and only if g is a critical point of the scalar curvature functional
+Sc : MG
+1 −→ R and the stability type of g is therefore encoded in the signature of the
+second derivative or Hessian Sc′′
+g. An Einstein metric g ∈ MG
+1 with Rc(g) = ρg is said
+to be G-stable when Sc′′
+g |T T G
+g < 0, where T T G
+g
+is the space of all G-invariant TT-tensors,
+which in particular implies that g is a local maximum of Sc |MG
+1 . On the other hand, it is
+called G-unstable when there exists T ∈ T T G
+g
+such that Sc′′
+g(T, T) > 0, being the coindex
+the dimension of the maximal subspace of T T G
+g
+on which Sc′′
+g is positive (see [L, Section
+3], [LW, Section 2] and [LL, Section 2] for more detailed treatments on G-stability).
+We assume from now on that G is semisimple and consider the standard metric gB, i.e.,
+the G-invariant metric determined by the inner product
+⟨·, ·⟩ := − Bg |p×p,
+where Bg is the Killing form of g and g = k⊕p is the Bg-orthogonal reductive decomposition.
+Here g and k are the Lie algebras of G and K, respectively. Consider the vector space
+sym0(p)K := {A : p → p : At = A, tr A = 0, [Ad(K), A] = 0} ≡ T T G
+gB,
+where At denotes the transpose of A with respect to gB (see [LL, Section 2]).
+We also assume that gB is Einstein, say with Rc(g) = ρg. The second variation of the
+scalar curvature at gB ∈ MG is given by
+(2)
+Sc′′
+gB(T, T) = 1
+2(2ρ⟨A, A⟩ − ⟨Lp A, A⟩),
+∀T = gB(A·, ·) ∈ T T G
+gB,
+A ∈ sym0(p)K,
+where ⟨A, B⟩ := tr AB,
+Lp = Lp(gB) : sym0(p)K −→ sym0(p)K,
+is the self-adjoint operator defined by
+(3)
+Lp A := − 1
+2
+�
+[adp Xi, [adp Xi, A]],
+∀A ∈ sym0(p)K,
+and {Xi} is any gB-orthonormal basis of p (see [L, Section 5]).
+It follows from (2) that the G-stability type of gB is determined by how is the constant
+2ρ suited relative to the spectrum of Lp. Indeed, if λp is the minimum eigenvalue of Lp,
+then
+• gB is G-stable if and only if 2ρ < λp;
+• gB is G-unstable if and only if λp < 2ρ.
+Given any orthogonal decomposition p = p1 ⊕· · ·⊕pr in Ad(K)-invariant (not necessar-
+ily irreducible) subspaces p1, . . . , pr (di := dim pi), consider the corresponding structural
+constants given by,
+(4)
+[ijk] :=
+�
+α,β,γ
+⟨[Xi
+α, Xj
+β], Xk
+γ ⟩2,
+where {Xi
+α} is an orthonormal basis of pi. Note that the number [ijk] is invariant under
+any permutation of ijk. According to [L, Theorem 5.3] (see also [LW, Theorem 3.1]), if
+
+4
+VALERIA GUTI´ERREZ AND JORGE LAURET
+{I1, . . . , Ir} is the orthonormal subset of sym(p)K := RIp ⊕ sym0(p)K defined by Ik|pi :=
+δki
+1
+√dk Ipk (Iv denotes the identity map on the vector space v), then
+(5)
+⟨Lp Ik, Ik⟩ =
+1
+dk
+�
+j̸=k;i
+[ijk],
+∀k,
+⟨Lp Ik, Im⟩ = −
+1
+√dk
+√dm
+�
+i
+[ikm],
+∀k ̸= m.
+In the multiplicity-free case (i.e., the subspaces pk’s are Ad(K)-irreducible and pairwise
+inequivalent), {I1, . . . , Ir} is actually an orthonormal basis of sym(p)K and so the above
+numbers are precisely the entries of the matrix of Lp.
+In any case, the spectrum of
+the symmetric r × r matrix [⟨Lp Ik, Im⟩] defined as in (5) (restricted to the hyperplane
+{(a1, . . . , as) : � diai = 0}) is still contained in [λp, λmax
+p
+], where λmax
+p
+is the maximum
+eigenvalue of Lp, so this always provides a very useful tool to compute or estimate λp.
+3. G-instability of standard Einstein metrics
+Let M = G/K be a homogeneous space as in Theorem 1.1. Thus
+(6)
+g = h ⊕ · · · ⊕ h
+�
+��
+�
+m−n
+⊕g1 ⊕ · · · ⊕ gn,
+k = h ⊕ l1 ⊕ · · · ⊕ ln,
+and πj(k) = ιj(h × lj) ⊂ gj for all j = 1, . . . , n (note that we are using the index j instead
+of m − n + j for simplicity). For each homogeneous space Gj/πj(K), we consider the
+Bgj-orthogonal reductive decomposition
+gj = ιj(h ⊕ lj) ⊕ qj,
+j = 1, . . . , n.
+Since πj(h) is a subalgebra of gj, there exists 0 ≤ cj ≤ 1 such that
+Bπj(h) = cj Bgj |πj(h),
+j = 1, . . . , n.
+Note that cj = 0 if and only if πj(h) is abelian and cj = 1 if and only if πj(h) = gj.
+It is easy to check that the Bg-orthogonal reductive complement for G/K is given by
+p := {(X1, . . . , Xm−n, π1(Xm−n+1) + Y1, . . . , πn(Xm) + Yn)
+: Xi ∈ h, Yj ∈ qj and X1 + . . . + Xm−n + 1
+c1Xm−n+1 + . . . + 1
+cn Xm = 0}.
+(7)
+In particular, dim M = dim p = (m − 1) dim h + dim q1 + · · · + dim qn.
+Given α := (a1, . . . , am−n, . . . , am) ∈ Rm such that � ai = 0, we define an Ad(K)-
+irreducible subspace of p by,
+gα := {(a1X, . . . , am−nX, c1am−n+1π1(X), . . . , cnamπn(X)) : X ∈ h} ,
+and if
+(8)
+αi := (
+i
+� �� �
+1, . . . , 1, −i,
+m−1−i
+� �� �
+0, . . . , 0),
+i = 1, . . . , m − 1,
+then we consider the following gB-orthogonal decomposition of p in Ad(K)-invariant sub-
+spaces:
+p = gα1 ⊕ gα2 ⊕ · · · ⊕ gαm−1 ⊕ q1 ⊕ · · · ⊕ qn,
+where qj also denotes the subspace (0, . . . , 0, qj, 0, . . . , 0) ⊂ g. Note that dim gαi = dim h
+for all i.
+Concerning the corresponding structural constants [ijk] defined in (4) (set pi := gαi,
+i = 1, . . . , m − 1 and pm+j := qj+1, j = 0, . . . , n − 1), we have that:
+• [gαi, gαk] ⊂ gαi for all i < k ≤ m − n − 1, so [iik] > 0 for all i < k ≤ m − n − 1.
+• [iik] is also positive when i < m − n ≤ k ≤ m − 1.
+
+STABILITY OF STANDARD EINSTEIN METRICS
+5
+• There are others positive structural constants involving the spaces qj’s but we do not
+need them for our computations.
+Lemma 3.1. Let M = G/K be a homogeneous space as in Theorem 1.1 such that n < m.
+(i) For any 1 ≤ i ̸= k ≤ m − n − 1 and 0 ≤ j ≤ n − 1,
+[iik] = dim h
+k + k2 ,
+[ii(m − n + j)] = dim h
+∆j
+,
+where ∆j := m − n + c1 + . . . + cj + cj+1(m − n + j)2.
+(ii) If gB is Einstein, say Rc(gB) = ρgB, then
+ρ = 3
+4 − m − n − 1
+2(m − n) − 1
+2
+n−1
+�
+j=0
+1
+∆j
+.
+Proof. Let {X1, . . . , Xdim h} be a Bh-orthonormal basis of h. For each X ∈ h we denote
+α(X) := (a1X, . . . , am−nX, c1am−n+1π1(X), . . . , cnamπn(X)) ∈ gα,
+where α = (a1, . . . , am) and � ai = 0.
+Thus for each i = 1, . . . , m − n − 1, the set
+�
+1
+|αi|αi(Xl)
+�
+is a − Bg-orthonormal basis of pi (see (8)) and we obtain that
+[iik] =
+�
+l,m,r
+��
+αi(Xr)
+|αi| , αi(Xl)
+|αi|
+�
+, αk(Xm)
+|αk|
+�2
+=
+�
+⟨αi·αi,αk⟩
+|αi|2|αk|
+�2 �
+l,m,r
+⟨[Xr, Xl], Xm⟩2 ,
+for all i < k ≤ m − n − 1. where αi · αi := (1, 1, . . . 1, i2, 0, . . . 0). Since ⟨·, ·⟩ is the usual
+inner product in Rm, the formula for these structural constants follows.
+For the cases pm−n+j with j = 0, . . . , n − 1 we have that
+�
+1
+√
+∆j αm−n+j(Xl)
+�
+is a − Bg-
+orthonormal basis of pm−n+j and so a computation similar to the above completes the
+proof of part (i).
+To prove part (ii), we use the well known formula for the Ricci eigenvalues of gB in terms
+of the structural constants (see e.g. [L] or [LW]) assuming that M = G/K is a standard
+homogeneous Einstein space, it is given by
+ρ = ρ1 = 1
+2 −
+1
+4 dim h
+�
+i,j
+[ij1] ,
+concluding the proof.
+□
+Theorem 3.2. If M = G/K is a homogeneous space as in Theorem 1.1 such that n+4 ≤
+m and the standard metric gB is Einstein, then gB is G-unstable.
+Remark 3.3. The spaces in [N, Table 4] covered by the above theorem are items 3 (s ≥ 2)
+and 6, as well as most cases in items 1 and 2 (see [NR, Section 2]). Thus the only missing
+spaces from [N, Theorem 7] are the space in part 3) and items 4 and 5 in the table.
+Proof. Consider, as in §2, the orthonormal subset C = {I1, . . . Im−n−1} of sym(p)K given
+by Ik|pi := δik
+1
+√dim hIpk and Ik|qj = 0 for all j. By the formula given in (5), if r, s =
+
+6
+VALERIA GUTI´ERREZ AND JORGE LAURET
+1, . . . , m − n − 1, then
+⟨Lp Ir, Is⟩ = −
+1
+dim h
+�
+i
+[irs] = −
+1
+dim h([srs] + [rrs]) =
+
+
+
+
+
+−1
+s + s2
+if s > r,
+−1
+r + r2
+if s < r,
+⟨Lp Is, Is⟩ =
+1
+dim h
+�
+k̸=s;i
+[iks] =
+1
+dim h
+s−1
+�
+i=1
+[iis] +
+1
+dim h
+m−1
+�
+k=s+1
+[kss]
+=s − 1 − s2
+s + s2
++ m − n − 1
+m − n
++
+n−1
+�
+j=0
+1
+∆j
+�
+��
+�
+−2(ρ− 3
+4 )
+=s − 1 − s2
+s + s2
+− 2ρ + 3
+2.
+It is therefore easy to check that with respect to the basis C, A :=
+1
+√
+6(1, 1, −2, 0, . . . , 0) is
+a unit direction such that,
+λp ≤ ⟨Lp A, A⟩ = 1 − 2ρ < 2ρ,
+which implies that gB is G-unstable. The inequality 1
+4 < ρ is well known, see e.g. [LL,
+Section 3.1].
+□
+4. Ledger-Obata spaces
+In this section, given a connected compact simple Lie group F, we consider the so-called
+Ledger-Obata spaces
+M = G/K = F m+1/∆m+1F,
+2 ≤ m,
+where F m+1 := F × · · · × F ((m + 1)-times) and ∆m+1F := {(x, . . . , x) : x ∈ F}. The Lie
+group G = F m+1 acts transitively on G := F m by
+(x1, . . . , xm+1) · (y1, . . . , ym) = (x1y1x−1
+m+1, . . . , xmymx−1
+m+1),
+with isotropy group at the identity given by K = ∆m+1F. This is therefore a particular
+case of the family of spaces studied in §3 (i.e., n = 0 and m + 1 instead of m). The
+standard metric gB is always Einstein, say Rc(gB) = ρgB, on any Ledger-Obata space (see
+[CNN]). We aim to obtain a lower bound for the coindex of this G-unstable critical point.
+If f denotes the Lie algebra of F, then the Bg-orthogonal reductive decomposition g =
+k ⊕ p is given by g = fm+1, k = ∆m+1f and
+p :=
+�
+(X1, . . . , Xm+1) : Xi ∈ f and
+�
+Xi = 0
+�
+.
+Thus any Ad(K)- irreducible subspace of p has the form
+gα := {(a1X, . . . , am+1X) : X ∈ f} ,
+for some fixed α := (a1, . . . , am+1) such that � ai = 0.
+Note that Bg(gα, gβ) = 0 if
+and only if α ⊥ β and [gα, gβ] = gα·β, where α · β = (a1b1, . . . , am+1bm+1). As before,
+we consider an orthogonal decomposition p = gα1 ⊕ gα2 ⊕ · · · ⊕ gαm in Ad(K)-invariant
+subspaces, where
+αi = (1, . . . , 1
+� �� �
+i
+, −i, 0, . . . , 0
+� �� �
+m−i
+) ∈ Rm+1.
+Note that dim gαi = dim f for all i = 1, . . . , m.
+
+STABILITY OF STANDARD EINSTEIN METRICS
+7
+Lemma 4.1.
+(i) [CNN] For all 1 ≤ i < k ≤ m,
+[iii] = (1 − i)2 dim f
+i(1 + i)
+,
+[iik] = dim f
+k + k2 .
+(ii) [CNN] ρ =
+m+3
+4(m+1).
+(iii) If C = {I1, . . . Im} ⊂ sym(p)K as in the proof of Theorem 3.2, then the corresponding
+symmetric m × m matrix is given by,
+�
+�
+Lp
+�
+rs =
+
+
+
+
+
+−1
+r + r2
+if r > s,
+−1
+s + s2
+if r < s,
+�
+�
+Lp
+�
+ss = s − 1 − s2
+s + s2
++
+m
+m + 1.
+Proof. Let {X1, . . . , Xdim f} be a − Bg-orthonormal basis of f, as before we can compute
+the structural constants using that the set
+�
+1
+|αi|αi(Xl)
+�
+is a − Bg-orthonormal basis of
+gαi and formula (4):
+[iik] =
+�
+lmr
+��
+αi(Xr)
+|αi| , αi(Xl)
+|αi|
+�
+, αk(Xm)
+|αj|
+�2
+=
+�
+⟨αi·αi,αk⟩
+|αi|2|αk|
+�2 �
+lmr
+⟨[Xr, Xl], Xm⟩2 .
+Since,
+⟨αi · αi, αk⟩ =
+�
+i + i2
+if i < k
+i − i3
+if i = k
+,
+the formulas stated in part (i) follow.
+Parts (ii) and (iii) follow by setting n = 0 in Lemma 3.1, (ii) and the proof of Theorem
+3.2, respectively. Note that in this case we have m irreducible factors of p.
+□
+Lemma 4.2. The spectrum of �
+Lp is given by 0 and
+ai :=
+m
+m + 1 −
+i
+i + 2,
+i = 1, . . . , m − 1.
+Proof. If we set ηs :=
+�
+�
+Lp
+�
+ss, then by Lemma 4.1, (iii), we have that the m × m matrix of
+�
+Lp is given by
+�
+�
+Lp
+�
+C =
+
+
+η1
+− 1
+6
+− 1
+12
+···
+−
+1
+m+m2
+− 1
+6
+η2
+− 1
+12
+···
+−
+1
+m+m2
+− 1
+12
+− 1
+12
+η3
+···
+...
+ηm−1
+−
+1
+m+m2
+−
+1
+m+m2 −
+1
+m+m2 −
+1
+m+m2
+··· −
+1
+m+m2
+ηm
+
+
+.
+It is now easy to check that each vector
+(1, . . . , 1
+� �� �
+i
+, −i, 0, . . . , 0
+� �� �
+m−1−i
+) ∈ Rm,
+i = 1, . . . , m − 1,
+is an eigenvector of �
+Lp with eigenvalue ai and its kernel is generated by (1, . . . , 1), con-
+cluding the proof (we are using here that �i
+j=1
+1
+j+j2 =
+i
+i+1).
+□
+Theorem 4.3. The standard metric gB on the Ledger-Obata space M = F m+1/∆m+1F
+is G-unstable and has coindex ≥ m − 2 if 11 ≤ m and coindex ≥ m − 1 if 2 ≤ m ≤ 10.
+
+8
+VALERIA GUTI´ERREZ AND JORGE LAURET
+Proof. The smallest non-zero eigenvalue of �
+Lp is am−1 =
+1
+m+1. Thus
+λp ≤ am−1 =
+1
+m+1 <
+m+3
+2(m+1) = 2ρ,
+which implies that the standard metric on every Ledger-Obata space is G-unstable. On
+the other hand, since ai < 2ρ if and only if 2m−6
+m+5 < i, we obtain the lower bounds for the
+coindex as stated, concluding the proof.
+□
+5. G-stable Einstein metrics with G non-simple
+In the light of the G-instability results obtained in §3 and §4, it is natural to ask whether
+any G-invariant Einstein metric on a homogeneous space G/K such that G is not simple
+is G-unstable. The aim of this section is to show that this is not true.
+Given a simple Lie group H and a simple proper subgroup K ⊂ H, we consider the
+semisimple Lie group G := H × K, which acts transitively on H by
+(¯h, k) · h = ¯hhk−1,
+with isotropy subgroup at the identity given by ∆K, the diagonal subgroup of K. This
+provides a presentation M = G/∆K of the Lie group M = H as a homogeneous space.
+If h = k ⊕ a is the Bh-orthogonal decomposition, then the Bg-orthogonal reductive
+decomposition of M = G/∆K is given by,
+g = h ⊕ k = ∆k ⊕ p,
+p := a ⊕ �p,
+where �p := {X ∈ g : Xk = − 1
+cXh} (note that dim�p = dim k), Xh and Xk denote the
+projections of X relative to g = h⊕k, respectively, and Bk = c Bh |k×k (note that 0 < c < 1).
+It is easy to see that the differential at the origin of the diffeomorphism ψ : G/∆K → H
+determined by the above action is given by the Ad(K)-invariant map
+dψ|o : p → h,
+dψ|o(Xh + Xk) = Xh − Xk,
+∀X ∈ p,
+and its inverse ϕ := (dψ|o)−1 : h → p by
+ϕ(Z) =
+�
+Z
+if Z ∈ a,
+c
+c+1Z + (− 1
+c)
+c
+c+1Z
+if Z ∈ k.
+Using that ϕ is Ad(K)-equivariant, one obtains the following diffeomorphism:
+�ϕ : MH,K → MG,
+�ϕ(¯g) := ¯g(ϕ−1·, ϕ−1·),
+where MH,K is the manifold of all left-invariant metrics on H which are in addition
+Ad(K)-invariant and MG is the manifold of all G-invariant metrics on G/∆K.
+Note
+that �ϕ is actually an isomorphism between the vectors spaces sym2(h)K and sym2(p)K of
+Ad(K)-invariant symmetric 2-tensors, respectively.
+It is well known that the Killing metric ¯gB := − Bh on the simple Lie group H is
+Einstein with 1
+4 as Einstein constant, thus the above diffeomorphism maps ¯gB to a G-
+invariant metric g0 on G/∆K which is also Einstein with Rc(g0) = 1
+4g0.
+Proposition 5.1. For any simple Lie group H ̸= SU(n), Sp(n) and simple subgroup K ⊂
+H, there exists an (H × K)-invariant Einstein metric g0 on the homogeneous space M =
+H × K/∆K which is (H × K)-stable.
+Proof. Since the corresponding scalar curvature functionals Sc : MH,K → R and Sc :
+MG → R satisfy that Sc = Sc ◦�ϕ, for all T ∈ sym2(h)K,
+Sc
+′′
+g(T, T) = d2
+dt2
+����
+0
+Sc(g + tT) = d2
+dt2
+����
+0
+Sc(�ϕ(g + tT)) = Sc′′
+�ϕ(g)(�ϕ(T), �ϕ(T)).
+
+STABILITY OF STANDARD EINSTEIN METRICS
+9
+In particular, Sc
+′′
+g and Sc′′
+�ϕ(g) have the same signature as bilinear forms, but it is well known
+that ¯gB is H-stable if H ̸= SU(n), Sp(n) (see e.g. [L, Proposition 5.1]), so g0 = �ϕ(¯gB) is
+(H × K)-stable on M = H × K/∆K.
+□
+In what follows, we study the existence of (H × K)-stable Einstein metrics on M =
+H × K/∆K, including the case when H is SU(n) or Sp(n).
+We fix the standard metric gB := − Bg |p ∈ MG as a background metric. Using [L,
+Section 7], we obtain that the structural constants of the decomposition p = p1 ⊕ p2,
+where p1 := a and p2 := ˜p, are given by
+[111] = d1 − 2(1 − c)d2
+[112] = c(1 − c)
+1 + c d2
+[222] = (c − 1)2
+c + 1 d2,
+where d1 := dim a and d2 := dim k. Since Bg = Bh + Bk, it is easy to check that
+g0 = x1gB|p1 + x2gB|p2,
+where
+x1 = 1,
+x2 = c + 1
+c
+.
+One can verify that indeed Rc(g0) = 1
+4g0 by using e.g. [LW, Section 2.5].
+Theorem 5.2. For any simple Lie group H and simple subgroup K ⊂ H such that the
+homogeneous space H/K is isotropy irreducible and (H, K) ̸= (Sp(n), Sp(n − 1)), there
+exists an (H × K)-stable Einstein metric g0 on M = H × K/∆K.
+Proof. We first note that the Ad(K)-representations p1 and p2 are irreducible and inequiv-
+alent (see [DZ]). It follows from [LW, Theorem 3.1] that, for g0 = gB|p1 + c+1
+c gB|p2, the
+matrix of the Lichnerowicz Laplacian with respect to the orthonormal basis {
+1
+√d1 I1,
+1
+√d2 I2}
+of sym(p)K is given by
+[Lp] = (1 − c)
+
+
+d2
+d1
+−
+�
+d2
+d1
+−
+�
+d2
+d1
+1
+
+ .
+Its eigenvalues are 0 and λp = (d1+d2)(1−c)
+d1
+, and by the bounds given in [DZ, Theorem
+11] we can conclude that if (H, K) ̸= (Sp(n), Sp(n − 1)), then λp > 1
+2 = 2ρ and so g0 is
+(H × K)-stable.
+□
+Remark 5.3. For the case (H, K) = (Sp(n), Sp(n − 1)) with n ≥ 2, we can use all the
+previous computations except the last bound of [DZ]. Replacing in the formula, we get
+that
+λp =
+n(2n+1)
+(4n−1)(n+1) < 1
+2 = 2ρ,
+so g0 is (H × K)-unstable in this case.
+References
+[CNN] Z. Chen, Yu.G. Nikonorov, Y. V. Nikonorova, Invariant Einstein metrics on Ledger-Obata
+spaces, Diff. Geom. App. 50 (2017), 7-87.
+[DZ]
+J. D’Atri, W. Ziller, Naturally reductive metrics and Einstein metrics on compact Lie groups,
+Mem. Amer. Math. Soc. 215 (1979).
+[LL]
+E.A. Lauret, J. Lauret, The stability of standard homogeneous Einstein manifolds, Math. Z.,
+303, 16 (2023).
+[L]
+J. Lauret, On the stability of homogeneous Einstein manifolds, Asian J. Math., in press (arXiv).
+[LW]
+J. Lauret, C.E. Will, On the stability of homogeneous Einstein manifolds II, J. London Math.
+Soc. 106 (2022), 3638-3669.
+[N]
+Yu. G. Nikonorov, Algebraic structure of standard homogeneous Einstein manifolds, Siberian
+Adv. Math. 10 (2000), 59-82.
+[NR]
+Yu.G. Nikonorov, E.D. Rodionov, Standard homogeneous Einstein manifolds and Diophantine
+equations, Archivum Math (Brno) 32 (1996) 123–136.
+
+10
+VALERIA GUTI´ERREZ AND JORGE LAURET
+[NRS] Yu.G. Nikonorov, E.D. Rodionov, V.V. Slavskii, Geometry of homogeneous Riemannian man-
+ifolds, J. Math. Sci. (N.Y.) 146 (2007) 6313–6390.
+[WZ] M.Y. Wang, W. Ziller, On normal homogeneous Einstein manifolds, Ann. Sci. ´Ecole Norm. Sup.
+18 (1985), 563–633.
+FaMAF, Universidad Nacional de C´ordoba and CIEM, CONICET (Argentina)
+Email address: valeria.gutierrez@unc.edu.ar, jorgelauret@unc.edu.ar
+
diff --git a/HdE3T4oBgHgl3EQfuAus/content/tmp_files/load_file.txt b/HdE3T4oBgHgl3EQfuAus/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,441 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf,len=440
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='04681v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='DG]  11 Jan 2023  STABILITY OF STANDARD EINSTEIN METRICS ON  HOMOGENEOUS SPACES OF NON-SIMPLE LIE GROUPS  VALERIA GUTI´ERREZ AND JORGE LAURET  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The classification of compact homogeneous spaces of the form M = G/K,  where G is a non-simple Lie group, such that the standard metric is Einstein is still  open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The only known examples are 4 infinite families and 3 isolated spaces found by  Nikonorov and Rodionov in the 90s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' In this paper, we prove that most of these standard  Einstein metrics are unstable as critical points of the scalar curvature functional on the  manifold of all unit volume G-invariant metrics on M, providing a lower bound for the  coindex in the case of Ledger-Obata spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' On the other hand, examples of stable (in  particular, local maxima) invariant Einstein metrics on certain homogeneous spaces of  non-simple Lie groups are also given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Introduction  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Preliminaries  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  G-instability of standard Einstein metrics  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Ledger-Obata spaces  6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  G-stable Einstein metrics with G non-simple  8  References  9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Introduction  Any manifold M on which a given compact semisimple Lie group G is acting transitively  can be endowed with a canonical G-invariant Riemannian metric gB provided by the Killing  form of the Lie algebra g of G, so called the standard metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' In the case when G is simple,  the Einstein condition for gB was studied by Wang and Ziller in [WZ], where it is obtained  a complete classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  The list of homogeneous spaces M = G/K with G simple,  beyond isotropy irreducible spaces, on which gB is Einstein consists of 10 infinite families  and 2 isolated examples for G classical and 20 isolated examples with G exceptional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The  stability types of these metrics as critical points of the scalar curvature functional  Sc : MG  1 −→ R,  where MG  1 is the manifold of all G-invariant metrics of some fixed volume on M, have  recently been obtained in [LL].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The standard metric is G-unstable on most of the spaces  with G classical, being even a local minimum on many of them (see [LL, Table 1]), while  gB is G-stable and therefore a local maximum on 14 of the 20 spaces with exceptional G  (see [LL, Tables 2,3,4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  On the other hand, in the case when G is not simple, the classification of standard  Einstein metrics is still an open question (see [NRS, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='14] and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Under certain conditions, Nikonorov obtained in [N] the following algebraic constraints on  Date: January 13, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  This research was partially supported by grants from FONCyT and Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' de C´ordoba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  1  2  VALERIA GUTI´ERREZ AND JORGE LAURET  the structure of homogeneous spaces on which the standard metric gB is Einstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' We fix  a decomposition  (1)  g = g1 ⊕ g2 ⊕ · · · ⊕ gm,  of the semisimple Lie algebra g in simple ideals and consider πj : k → gj, the corresponding  projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' [N, Theorem 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let (G/K, gB) be a connected irreducible standard ho-  mogeneous Einstein space with semisimple isotropy group K such that either πj(k) = gj  or πj(k) consists of two simple summands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Then it is defined by the following scheme of  inclusion:  K := H × L1 × · · · × Ln ⊂ H × · · · × H  �  ��  �  m  ×L1 × · · · × Ln  ⊂ H × · · · × H  �  ��  �  m−n  ×G1 × · · · × Gn = G,  where H, Li and Gi are simple Lie groups, the first inclusion has the form diag(H) ×  Id × · · · × Id, the second has the form Id × · · · × Id ×ι1 × · · · × ιn, where ιi : H × Li → Gi  are some inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  This is a strong obstruction to have gB Einstein, in particular, it implies that the simple  factors of G on which the projection of K is onto are pairwise isomorphic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' In [N, Theorem  7], a complete list of homogeneous spaces of the above form on which gB is Einstein is  obtained, consisting of 4 infinite families and 3 isolated examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  We study in this paper the stability of these Einstein metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Our main result is the  following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let M = G/K be a homogeneous space as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1 and assume  that the standard metric gB is Einstein and n + 4 ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (i) gB is G-unstable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=', there is a positive direction for the Hessian of Sc at gB (see  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (ii) On the Ledger-Obata space M = Hm/∆mH (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=', when n = 0 and m ≥ 3), gB has  coindex ≥ m − 3 if 12 ≤ m and coindex ≥ m − 2 if 3 ≤ m ≤ 11 (see Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is worth noting that we do not use the classification given in [N, Theorem 7] to prove  part (i), we only use the structure provided by Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1 and the general formulas for  the Hessian of Sc given in [L] and [LW].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Most cases in [N, Theorem 7] are covered by the  above theorem (see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  The only other stability result on G-invariant Einstein metrics with a non-simple G we  were able to find in the literature is in [L, Section 7], where it is proved that the so called  Jensen’s metric on a simple Lie group H is always G-unstable viewed as a G-invariant  metric on M = G/∆K, where G := H × K, for some semisimple subgroup K ⊂ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The  following natural question arises: is any G-invariant Einstein metric on a homogeneous  space G/K with G non-simple G-unstable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The following result answers this question in  the negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' (See Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For any simple Lie group H and simple subgroup  K ⊂ H such that the homogeneous space H/K is isotropy irreducible and (H, K) ̸=  (Sp(n), Sp(n−1)), there exists an (H ×K)-invariant Einstein metric on M = H ×K/∆K  which is (H × K)-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The authors thank Yuri Nikonorov for very helpful conversations on  the subject of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  STABILITY OF STANDARD EINSTEIN METRICS  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Preliminaries  We fix an almost-effective transitive action of a compact connected Lie group G on a  manifold Md, determining a presentation M = G/K of M as a homogeneous space, where  K ⊂ G is the isotropy subgroup at some point o ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let MG denote the manifold of all  G-invariant metrics on M, which satisfies 1 ≤ dim MG ≤ d(d+1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  If MG  1 ⊂ MG is the codimension one submanifold of all unit volume metrics, then  g ∈ MG  1 is Einstein if and only if g is a critical point of the scalar curvature functional  Sc : MG  1 −→ R and the stability type of g is therefore encoded in the signature of the  second derivative or Hessian Sc′′  g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' An Einstein metric g ∈ MG  1 with Rc(g) = ρg is said  to be G-stable when Sc′′  g |T T G  g < 0, where T T G  g  is the space of all G-invariant TT-tensors,  which in particular implies that g is a local maximum of Sc |MG  1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' On the other hand, it is  called G-unstable when there exists T ∈ T T G  g  such that Sc′′  g(T, T) > 0, being the coindex  the dimension of the maximal subspace of T T G  g  on which Sc′′  g is positive (see [L, Section  3], [LW, Section 2] and [LL, Section 2] for more detailed treatments on G-stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  We assume from now on that G is semisimple and consider the standard metric gB, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=',  the G-invariant metric determined by the inner product  ⟨·, ·⟩ := − Bg |p×p,  where Bg is the Killing form of g and g = k⊕p is the Bg-orthogonal reductive decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Here g and k are the Lie algebras of G and K, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Consider the vector space  sym0(p)K := {A : p → p : At = A, tr A = 0, [Ad(K), A] = 0} ≡ T T G  gB,  where At denotes the transpose of A with respect to gB (see [LL, Section 2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  We also assume that gB is Einstein, say with Rc(g) = ρg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The second variation of the  scalar curvature at gB ∈ MG is given by  (2)  Sc′′  gB(T, T) = 1  2(2ρ⟨A, A⟩ − ⟨Lp A, A⟩),  ∀T = gB(A·, ·) ∈ T T G  gB,  A ∈ sym0(p)K,  where ⟨A, B⟩ := tr AB,  Lp = Lp(gB) : sym0(p)K −→ sym0(p)K,  is the self-adjoint operator defined by  (3)  Lp A := − 1  2  �  [adp Xi, [adp Xi, A]],  ∀A ∈ sym0(p)K,  and {Xi} is any gB-orthonormal basis of p (see [L, Section 5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It follows from (2) that the G-stability type of gB is determined by how is the constant  2ρ suited relative to the spectrum of Lp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Indeed, if λp is the minimum eigenvalue of Lp,  then  gB is G-stable if and only if 2ρ < λp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  gB is G-unstable if and only if λp < 2ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Given any orthogonal decomposition p = p1 ⊕· · ·⊕pr in Ad(K)-invariant (not necessar-  ily irreducible) subspaces p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , pr (di := dim pi), consider the corresponding structural  constants given by,  (4)  [ijk] :=  �  α,β,γ  ⟨[Xi  α, Xj  β], Xk  γ ⟩2,  where {Xi  α} is an orthonormal basis of pi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Note that the number [ijk] is invariant under  any permutation of ijk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' According to [L, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3] (see also [LW, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1]), if  4  VALERIA GUTI´ERREZ AND JORGE LAURET  {I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Ir} is the orthonormal subset of sym(p)K := RIp ⊕ sym0(p)K defined by Ik|pi :=  δki  1  √dk Ipk (Iv denotes the identity map on the vector space v), then  (5)  ⟨Lp Ik, Ik⟩ =  1  dk  �  j̸=k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='i  [ijk],  ∀k,  ⟨Lp Ik, Im⟩ = −  1  √dk  √dm  �  i  [ikm],  ∀k ̸= m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  In the multiplicity-free case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=', the subspaces pk’s are Ad(K)-irreducible and pairwise  inequivalent), {I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Ir} is actually an orthonormal basis of sym(p)K and so the above  numbers are precisely the entries of the matrix of Lp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  In any case, the spectrum of  the symmetric r × r matrix [⟨Lp Ik, Im⟩] defined as in (5) (restricted to the hyperplane  {(a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , as) : � diai = 0}) is still contained in [λp, λmax  p  ], where λmax  p  is the maximum  eigenvalue of Lp, so this always provides a very useful tool to compute or estimate λp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' G-instability of standard Einstein metrics  Let M = G/K be a homogeneous space as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Thus  (6)  g = h ⊕ · · · ⊕ h  �  ��  �  m−n  ⊕g1 ⊕ · · · ⊕ gn,  k = h ⊕ l1 ⊕ · · · ⊕ ln,  and πj(k) = ιj(h × lj) ⊂ gj for all j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , n (note that we are using the index j instead  of m − n + j for simplicity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For each homogeneous space Gj/πj(K), we consider the  Bgj-orthogonal reductive decomposition  gj = ιj(h ⊕ lj) ⊕ qj,  j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Since πj(h) is a subalgebra of gj, there exists 0 ≤ cj ≤ 1 such that  Bπj(h) = cj Bgj |πj(h),  j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Note that cj = 0 if and only if πj(h) is abelian and cj = 1 if and only if πj(h) = gj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is easy to check that the Bg-orthogonal reductive complement for G/K is given by  p := {(X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Xm−n, π1(Xm−n+1) + Y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , πn(Xm) + Yn)  : Xi ∈ h, Yj ∈ qj and X1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' + Xm−n + 1  c1Xm−n+1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' + 1  cn Xm = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (7)  In particular, dim M = dim p = (m − 1) dim h + dim q1 + · · · + dim qn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Given α := (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am−n, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am) ∈ Rm such that � ai = 0, we define an Ad(K)-  irreducible subspace of p by,  gα := {(a1X, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am−nX, c1am−n+1π1(X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , cnamπn(X)) : X ∈ h} ,  and if  (8)  αi := (  i  � �� �  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 1, −i,  m−1−i  � �� �  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0),  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − 1,  then we consider the following gB-orthogonal decomposition of p in Ad(K)-invariant sub-  spaces:  p = gα1 ⊕ gα2 ⊕ · · · ⊕ gαm−1 ⊕ q1 ⊕ · · · ⊕ qn,  where qj also denotes the subspace (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0, qj, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0) ⊂ g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Note that dim gαi = dim h  for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Concerning the corresponding structural constants [ijk] defined in (4) (set pi := gαi,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − 1 and pm+j := qj+1, j = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , n − 1), we have that:  [gαi, gαk] ⊂ gαi for all i < k ≤ m − n − 1, so [iik] > 0 for all i < k ≤ m − n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [iik] is also positive when i < m − n ≤ k ≤ m − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  STABILITY OF STANDARD EINSTEIN METRICS  5  There are others positive structural constants involving the spaces qj’s but we do not  need them for our computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let M = G/K be a homogeneous space as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1 such that n < m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (i) For any 1 ≤ i ̸= k ≤ m − n − 1 and 0 ≤ j ≤ n − 1,  [iik] = dim h  k + k2 ,  [ii(m − n + j)] = dim h  ∆j  ,  where ∆j := m − n + c1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' + cj + cj+1(m − n + j)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (ii) If gB is Einstein, say Rc(gB) = ρgB, then  ρ = 3  4 − m − n − 1  2(m − n) − 1  2  n−1  �  j=0  1  ∆j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let {X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Xdim h} be a Bh-orthonormal basis of h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For each X ∈ h we denote  α(X) := (a1X, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am−nX, c1am−n+1π1(X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , cnamπn(X)) ∈ gα,  where α = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am) and � ai = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Thus for each i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − n − 1, the set  �  1  |αi|αi(Xl)  �  is a − Bg-orthonormal basis of pi (see (8)) and we obtain that  [iik] =  �  l,m,r  ��  αi(Xr)  |αi| , αi(Xl)  |αi|  �  , αk(Xm)  |αk|  �2  =  �  ⟨αi·αi,αk⟩  |αi|2|αk|  �2 �  l,m,r  ⟨[Xr, Xl], Xm⟩2 ,  for all i < k ≤ m − n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' where αi · αi := (1, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 1, i2, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Since ⟨·, ·⟩ is the usual  inner product in Rm, the formula for these structural constants follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  For the cases pm−n+j with j = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , n − 1 we have that  �  1  √  ∆j αm−n+j(Xl)  �  is a − Bg-  orthonormal basis of pm−n+j and so a computation similar to the above completes the  proof of part (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  To prove part (ii), we use the well known formula for the Ricci eigenvalues of gB in terms  of the structural constants (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' [L] or [LW]) assuming that M = G/K is a standard  homogeneous Einstein space, it is given by  ρ = ρ1 = 1  2 −  1  4 dim h  �  i,j  [ij1] ,  concluding the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' If M = G/K is a homogeneous space as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1 such that n+4 ≤  m and the standard metric gB is Einstein, then gB is G-unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The spaces in [N, Table 4] covered by the above theorem are items 3 (s ≥ 2)  and 6, as well as most cases in items 1 and 2 (see [NR, Section 2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Thus the only missing  spaces from [N, Theorem 7] are the space in part 3) and items 4 and 5 in the table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Consider, as in §2, the orthonormal subset C = {I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Im−n−1} of sym(p)K given  by Ik|pi := δik  1  √dim hIpk and Ik|qj = 0 for all j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' By the formula given in (5), if r, s =  6  VALERIA GUTI´ERREZ AND JORGE LAURET  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − n − 1, then  ⟨Lp Ir, Is⟩ = −  1  dim h  �  i  [irs] = −  1  dim h([srs] + [rrs]) =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  −1  s + s2  if s > r,  −1  r + r2  if s < r,  ⟨Lp Is, Is⟩ =  1  dim h  �  k̸=s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='i  [iks] =  1  dim h  s−1  �  i=1  [iis] +  1  dim h  m−1  �  k=s+1  [kss]  =s − 1 − s2  s + s2  + m − n − 1  m − n  +  n−1  �  j=0  1  ∆j  �  ��  �  −2(ρ− 3  4 )  =s − 1 − s2  s + s2  − 2ρ + 3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is therefore easy to check that with respect to the basis C, A :=  1  √  6(1, 1, −2, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0) is  a unit direction such that,  λp ≤ ⟨Lp A, A⟩ = 1 − 2ρ < 2ρ,  which implies that gB is G-unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The inequality 1  4 < ρ is well known, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' [LL,  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Ledger-Obata spaces  In this section, given a connected compact simple Lie group F, we consider the so-called  Ledger-Obata spaces  M = G/K = F m+1/∆m+1F,  2 ≤ m,  where F m+1 := F × · · · × F ((m + 1)-times) and ∆m+1F := {(x, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , x) : x ∈ F}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The Lie  group G = F m+1 acts transitively on G := F m by  (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , xm+1) · (y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , ym) = (x1y1x−1  m+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , xmymx−1  m+1),  with isotropy group at the identity given by K = ∆m+1F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' This is therefore a particular  case of the family of spaces studied in §3 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=', n = 0 and m + 1 instead of m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The  standard metric gB is always Einstein, say Rc(gB) = ρgB, on any Ledger-Obata space (see  [CNN]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' We aim to obtain a lower bound for the coindex of this G-unstable critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  If f denotes the Lie algebra of F, then the Bg-orthogonal reductive decomposition g =  k ⊕ p is given by g = fm+1, k = ∆m+1f and  p :=  �  (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Xm+1) : Xi ∈ f and  �  Xi = 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Thus any Ad(K)- irreducible subspace of p has the form  gα := {(a1X, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am+1X) : X ∈ f} ,  for some fixed α := (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am+1) such that � ai = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Note that Bg(gα, gβ) = 0 if  and only if α ⊥ β and [gα, gβ] = gα·β, where α · β = (a1b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , am+1bm+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' As before,  we consider an orthogonal decomposition p = gα1 ⊕ gα2 ⊕ · · · ⊕ gαm in Ad(K)-invariant  subspaces, where  αi = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 1  � �� �  i  , −i, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0  � �� �  m−i  ) ∈ Rm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Note that dim gαi = dim f for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  STABILITY OF STANDARD EINSTEIN METRICS  7  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (i) [CNN] For all 1 ≤ i < k ≤ m,  [iii] = (1 − i)2 dim f  i(1 + i)  ,  [iik] = dim f  k + k2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (ii) [CNN] ρ =  m+3  4(m+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  (iii) If C = {I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Im} ⊂ sym(p)K as in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2, then the corresponding  symmetric m × m matrix is given by,  �  �  Lp  �  rs =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  −1  r + r2  if r > s,  −1  s + s2  if r < s,  �  �  Lp  �  ss = s − 1 − s2  s + s2  +  m  m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Let {X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , Xdim f} be a − Bg-orthonormal basis of f, as before we can compute  the structural constants using that the set  �  1  |αi|αi(Xl)  �  is a − Bg-orthonormal basis of  gαi and formula (4):  [iik] =  �  lmr  ��  αi(Xr)  |αi| , αi(Xl)  |αi|  �  , αk(Xm)  |αj|  �2  =  �  ⟨αi·αi,αk⟩  |αi|2|αk|  �2 �  lmr  ⟨[Xr, Xl], Xm⟩2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Since,  ⟨αi · αi, αk⟩ =  �  i + i2  if i < k  i − i3  if i = k  ,  the formulas stated in part (i) follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Parts (ii) and (iii) follow by setting n = 0 in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1, (ii) and the proof of Theorem  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Note that in this case we have m irreducible factors of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The spectrum of �  Lp is given by 0 and  ai :=  m  m + 1 −  i  i + 2,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' If we set ηs :=  �  �  Lp  �  ss, then by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1, (iii), we have that the m × m matrix of  �  Lp is given by  �  �  Lp  �  C =  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  η1  − 1  6  − 1  12  ···  −  1  m+m2  − 1  6  η2  − 1  12  ···  −  1  m+m2  − 1  12  − 1  12  η3  ···  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  ηm−1  −  1  m+m2  −  1  m+m2 −  1  m+m2 −  1  m+m2  ··· −  1  m+m2  ηm  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is now easy to check that each vector  (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 1  � �� �  i  , −i, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 0  � �� �  m−1−i  ) ∈ Rm,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , m − 1,  is an eigenvector of �  Lp with eigenvalue ai and its kernel is generated by (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' , 1), con-  cluding the proof (we are using here that �i  j=1  1  j+j2 =  i  i+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The standard metric gB on the Ledger-Obata space M = F m+1/∆m+1F  is G-unstable and has coindex ≥ m − 2 if 11 ≤ m and coindex ≥ m − 1 if 2 ≤ m ≤ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  8  VALERIA GUTI´ERREZ AND JORGE LAURET  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The smallest non-zero eigenvalue of �  Lp is am−1 =  1  m+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Thus  λp ≤ am−1 =  1  m+1 <  m+3  2(m+1) = 2ρ,  which implies that the standard metric on every Ledger-Obata space is G-unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' On  the other hand, since ai < 2ρ if and only if 2m−6  m+5 < i, we obtain the lower bounds for the  coindex as stated, concluding the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' G-stable Einstein metrics with G non-simple  In the light of the G-instability results obtained in §3 and §4, it is natural to ask whether  any G-invariant Einstein metric on a homogeneous space G/K such that G is not simple  is G-unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' The aim of this section is to show that this is not true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Given a simple Lie group H and a simple proper subgroup K ⊂ H, we consider the  semisimple Lie group G := H × K, which acts transitively on H by  (¯h, k) · h = ¯hhk−1,  with isotropy subgroup at the identity given by ∆K, the diagonal subgroup of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' This  provides a presentation M = G/∆K of the Lie group M = H as a homogeneous space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  If h = k ⊕ a is the Bh-orthogonal decomposition, then the Bg-orthogonal reductive  decomposition of M = G/∆K is given by,  g = h ⊕ k = ∆k ⊕ p,  p := a ⊕ �p,  where �p := {X ∈ g : Xk = − 1  cXh} (note that dim�p = dim k), Xh and Xk denote the  projections of X relative to g = h⊕k, respectively, and Bk = c Bh |k×k (note that 0 < c < 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is easy to see that the differential at the origin of the diffeomorphism ψ : G/∆K → H  determined by the above action is given by the Ad(K)-invariant map  dψ|o : p → h,  dψ|o(Xh + Xk) = Xh − Xk,  ∀X ∈ p,  and its inverse ϕ := (dψ|o)−1 : h → p by  ϕ(Z) =  �  Z  if Z ∈ a,  c  c+1Z + (− 1  c)  c  c+1Z  if Z ∈ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Using that ϕ is Ad(K)-equivariant, one obtains the following diffeomorphism:  �ϕ : MH,K → MG,  �ϕ(¯g) := ¯g(ϕ−1·, ϕ−1·),  where MH,K is the manifold of all left-invariant metrics on H which are in addition  Ad(K)-invariant and MG is the manifold of all G-invariant metrics on G/∆K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Note  that �ϕ is actually an isomorphism between the vectors spaces sym2(h)K and sym2(p)K of  Ad(K)-invariant symmetric 2-tensors, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  It is well known that the Killing metric ¯gB := − Bh on the simple Lie group H is  Einstein with 1  4 as Einstein constant, thus the above diffeomorphism maps ¯gB to a G-  invariant metric g0 on G/∆K which is also Einstein with Rc(g0) = 1  4g0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For any simple Lie group H ̸= SU(n), Sp(n) and simple subgroup K ⊂  H, there exists an (H × K)-invariant Einstein metric g0 on the homogeneous space M =  H × K/∆K which is (H × K)-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Since the corresponding scalar curvature functionals Sc : MH,K → R and Sc :  MG → R satisfy that Sc = Sc ◦�ϕ, for all T ∈ sym2(h)K,  Sc  ′′  g(T, T) = d2  dt2  ����  0  Sc(g + tT) = d2  dt2  ����  0  Sc(�ϕ(g + tT)) = Sc′′  �ϕ(g)(�ϕ(T), �ϕ(T)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  STABILITY OF STANDARD EINSTEIN METRICS  9  In particular, Sc  ′′  g and Sc′′  �ϕ(g) have the same signature as bilinear forms, but it is well known  that ¯gB is H-stable if H ̸= SU(n), Sp(n) (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' [L, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1]), so g0 = �ϕ(¯gB) is  (H × K)-stable on M = H × K/∆K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  In what follows, we study the existence of (H × K)-stable Einstein metrics on M =  H × K/∆K, including the case when H is SU(n) or Sp(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  We fix the standard metric gB := − Bg |p ∈ MG as a background metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Using [L,  Section 7], we obtain that the structural constants of the decomposition p = p1 ⊕ p2,  where p1 := a and p2 := ˜p, are given by  [111] = d1 − 2(1 − c)d2  [112] = c(1 − c)  1 + c d2  [222] = (c − 1)2  c + 1 d2,  where d1 := dim a and d2 := dim k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Since Bg = Bh + Bk, it is easy to check that  g0 = x1gB|p1 + x2gB|p2,  where  x1 = 1,  x2 = c + 1  c  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  One can verify that indeed Rc(g0) = 1  4g0 by using e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' [LW, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For any simple Lie group H and simple subgroup K ⊂ H such that the  homogeneous space H/K is isotropy irreducible and (H, K) ̸= (Sp(n), Sp(n − 1)), there  exists an (H × K)-stable Einstein metric g0 on M = H × K/∆K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' We first note that the Ad(K)-representations p1 and p2 are irreducible and inequiv-  alent (see [DZ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' It follows from [LW, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='1] that, for g0 = gB|p1 + c+1  c gB|p2, the  matrix of the Lichnerowicz Laplacian with respect to the orthonormal basis {  1  √d1 I1,  1  √d2 I2}  of sym(p)K is given by  [Lp] = (1 − c)  \uf8ee  \uf8f0  d2  d1  −  �  d2  d1  −  �  d2  d1  1  \uf8f9  \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Its eigenvalues are 0 and λp = (d1+d2)(1−c)  d1  , and by the bounds given in [DZ, Theorem  11] we can conclude that if (H, K) ̸= (Sp(n), Sp(n − 1)), then λp > 1  2 = 2ρ and so g0 is  (H × K)-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  □  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' For the case (H, K) = (Sp(n), Sp(n − 1)) with n ≥ 2, we can use all the  previous computations except the last bound of [DZ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Replacing in the formula, we get  that  λp =  n(2n+1)  (4n−1)(n+1) < 1  2 = 2ρ,  so g0 is (H × K)-unstable in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  References  [CNN] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Chen, Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nikonorov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nikonorova, Invariant Einstein metrics on Ledger-Obata  spaces, Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 50 (2017), 7-87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [DZ]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' D’Atri, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Ziller, Naturally reductive metrics and Einstein metrics on compact Lie groups,  Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 215 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [LL]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Lauret, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Lauret, The stability of standard homogeneous Einstein manifolds, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=',  303, 16 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [L]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Lauret, On the stability of homogeneous Einstein manifolds, Asian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=', in press (arXiv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [LW]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Lauret, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Will, On the stability of homogeneous Einstein manifolds II, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 106 (2022), 3638-3669.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [N]  Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nikonorov, Algebraic structure of standard homogeneous Einstein manifolds, Siberian  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' 10 (2000), 59-82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [NR]  Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nikonorov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Rodionov, Standard homogeneous Einstein manifolds and Diophantine  equations, Archivum Math (Brno) 32 (1996) 123–136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  10  VALERIA GUTI´ERREZ AND JORGE LAURET  [NRS] Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Nikonorov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Rodionov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Slavskii, Geometry of homogeneous Riemannian man-  ifolds, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=') 146 (2007) 6313–6390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  [WZ] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Ziller, On normal homogeneous Einstein manifolds, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' ´Ecole Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content=' Sup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  18 (1985), 563–633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='  FaMAF, Universidad Nacional de C´ordoba and CIEM, CONICET (Argentina)  Email address: valeria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='gutierrez@unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='ar, jorgelauret@unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
+page_content='ar' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE3T4oBgHgl3EQfuAus/content/2301.04681v1.pdf'}
diff --git a/I9E3T4oBgHgl3EQfuwtu/content/tmp_files/2301.04687v1.pdf.txt b/I9E3T4oBgHgl3EQfuwtu/content/tmp_files/2301.04687v1.pdf.txt
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+INFERENCE ON QUANTILE PROCESSES
+WITH A FINITE NUMBER OF CLUSTERS
+ANDREAS HAGEMANN
+Abstract. I introduce a generic method for inference on entire quantile and
+regression quantile processes in the presence of a finite number of large and arbitrarily
+heterogeneous clusters. The method asymptotically controls size by generating
+statistics that exhibit enough distributional symmetry such that randomization tests
+can be applied. The randomization test does not require ex-ante matching of clusters,
+is free of user-chosen parameters, and performs well at conventional significance
+levels with as few as five clusters. The method tests standard (non-sharp) hypotheses
+and can even be asymptotically similar in empirically relevant situations. The main
+focus of the paper is inference on quantile treatment effects but the method applies
+more broadly. Numerical and empirical examples are provided.
+Keywords: cluster-robust inference, quantiles, treatment effects, randomization
+inference, difference in differences
+JEL codes: C01, C21, C23
+1. Introduction
+Economic data often contain large clusters such as countries, regions, villages,
+or firms.
+Units within these clusters can be expected to influence one another
+or are influenced by the same political, environmental, sociological, or technical
+shocks. Several analytical and computer-intensive procedures such as the bootstrap
+are available to account for the presence of data clusters. These procedures generally
+achieve consistency by letting the number of clusters go to infinity.
+Numerical
+Date: January 13, 2023. University of Michigan Stephen M. Ross School of Business, 701 Tappan
+Ave, Ann Arbor, MI 48109, USA. Tel.: +1 (734) 764-2355. Fax: +1 (734) 764-2769. E-mail:
+hagem@umich.edu. All errors are my own.
+1
+arXiv:2301.04687v1  [econ.EM]  11 Jan 2023
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+2
+evidence by Bertrand, Duflo, and Mullainathan (2004), MacKinnon and Webb (2017),
+and others in the context of mean regression suggests that this type of asymptotic
+approximation often causes substantial size distortions when the number of clusters is
+small or the clusters are heterogenous. True null hypotheses are rejected far too often
+in both situations. Hagemann (2017) shows that this phenomenon is also present
+in quantile regression. In this paper, I develop a generic method for inference on
+the entire quantile or regression quantile process in the presence of a finite number
+of large and arbitrarily heterogeneous clusters. The method, which I refer to as
+cluster-randomized Kolmogorov-Smirnov (CRK) test, asymptotically controls size by
+generating Kolmogorov-Smirnov statistics that exhibit enough distributional symmetry
+at the cluster level such that randomization tests (Fisher, 1935; Canay, Romano, and
+Shaikh, 2017) can be applied. The CRK test is not limited to the pure quantile
+regression setting and can be used in distributional difference-in-differences estimation
+(Callaway and Li, 2019) and related situations where quantile treatment effects are
+identified by between-cluster comparisons.
+The CRK test is free of user-chosen
+parameters, powerful against fixed and root-n local alternatives, and performs well
+at conventional significance levels with as few as twelve clusters if parameters are
+identified between clusters. If parameters are identified within clusters, then even five
+clusters are sufficient for inference.
+Quantile regression (QR), introduced by Koenker and Bassett (1978), is an important
+empirical tool because it can quantify the effect of a set of covariates on the entire
+conditional outcome distribution. An issue with QR in the presence of clustering is
+that estimates normalized by their asymptotic covariance kernel have standard normal
+marginal limit distributions but are no longer pivotal for any choice of weight matrix
+(Hagemann, 2017). Cluster-robust tests about the QR coefficient function therefore
+have asymptotic distributions that cannot be tabulated for inference about ranges
+of quantiles. Even if only individual quantiles are of interest, consistent covariance
+matrix estimation in large clusters is challenging. It requires knowledge of an explicit
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+3
+ordering of the dependence structure within each cluster combined with a kernel and
+bandwidth choice to give distant observations less weight. Because time has a natural
+order, this weighting is easily done for time-dependent data but ordering data within
+states or villages may be difficult or impossible. The common empirical strategy of
+simply assuming that the clusters are small and numerous enough to satisfy a central
+limit theorem circumvents these issues but can lead to substantial size distortions
+with as few as 20 clusters (Hagemann, 2017). This remains true if a cluster-robust
+version of the bootstrap is used. Distortions can be especially severe if clusters differ
+greatly in their size and dependence structure.
+I show that the CRK test is robust to each of these concerns: It performs well even
+when the number of clusters is small, the dependence varies from cluster to cluster,
+and the cluster sizes are heterogenous. The reason for this robustness is that the CRK
+test does not rely on clustered covariance matrices to rescale the estimates. I instead
+use randomization inference to generate random critical values that automatically
+scale to the data. There are no kernels, bandwidths, or spatio-temporal orderings of
+the data to choose. The test achieves consistency with a finite number of large but
+heterogeneous clusters under interpretable high-level conditions. Despite being based
+on randomization inference, the CRK test can perform standard (non-sharp) inference
+on entire quantile or regression quantile processes. Randomization is performed with
+a fixed set of estimates and does not require repeated estimation to obtain its critical
+values.
+The randomization method underlying the CRK test was first used in the cluster
+context by Canay et al. (2017) as a way to perform inference on a finite-dimensional
+parameter with Student t and Wald statistics in least squares regression. They do not
+consider inference on quantile functions or Kolmogorov-Smirnov statistics. Here, I
+considerably extend the scope of their method under explicit regularity conditions to
+allow for inference on the entire QR process and related objects. The proofs below
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+4
+are fundamentally different from those of Canay et al. to account for the infinite-
+dimensional setting and do not rely on the Skorokhod almost-sure representation
+theorem. A practical issue with their method is that they require treated clusters to
+be matched ex-ante with an equal number of control clusters. Each match corresponds
+to a separate test and two researchers working with the same data can reach different
+conclusions based on which matches they choose. If there is not an equal number of
+treated and control clusters, then some clusters have to be combined or dropped in
+an ad-hoc manner. The CRK test sidesteps these issues completely and explicitly
+merges all potential tests into a single, uniquely determined test decision using results
+of R¨uschendorf (1982).
+Cluster-robust inference in linear regression models has a long history; recent surveys
+include Cameron and Miller (2015) and MacKinnon, Nielsen, and Webb (2022). Chen,
+Wei, and Parzen (2003), Wang and He (2007), Wang (2009), Parente and Santos
+Silva (2013), and Hagemann (2017) provide bootstrap and analytical methods for
+cluster-robust inference in QR models. Yoon and Galvao (2020) discuss the situation
+where clusters arise from correlation of individual units over time. All of these papers
+require the number of clusters to go to infinity for consistency. The CRK test differs
+from these papers because it is based on randomization inference and is consistent
+with a finite number of clusters.
+Several papers show that pointwise inference with a fixed number of clusters is
+possible under a variety of conditions. Ibragimov and M¨uller (2010, 2016) use special
+properties of the Student t statistic to perform inference on scale mixtures of normal
+random variables. Bester, Conley, and Hansen (2011) use standard cluster-robust
+covariance matrix estimators but adjust critical values under homogeneity assumptions
+on the clusters. Canay, Santos, and Shaikh (2020) show that certain cluster-robust
+versions of the wild bootstrap can be valid under strong homogeneity assumptions
+with a fixed number of clusters. Hagemann (2019) adjusts permutation inference
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+5
+for arbitrary heterogeneity at the cluster level but his bounds only apply to finite-
+dimensional objects. All of these methods can be used for inference at a single quantile
+but not for simultaneous inference across ranges of quantiles. In contrast, the CRK
+test provides uniformly valid inference on the entire quantile process even if clusters
+are arbitrarily heterogeneous.
+The remainder of the paper is organized as follows: Section 2 establishes new results
+on randomization inference on Gaussian processes. Section 3 uses these results to
+show consistency of the CRK test and gives specific examples where the test applies,
+including quantile difference-in-differences. Section 4 illustrates the finite sample
+behavior of the test in Monte Carlo experiments and an empirical example using
+Project STAR data. The appendix contains proofs.
+I use the following notation: 1{·} is the indicator function, cardinality of a set A is
+|A|, the smallest integer larger than a is ⌈a⌉, and the largest integer smaller than a is
+⌊a⌋. The minimum of a and b is denoted by a ∧ b. Limits are as n → ∞ unless noted
+otherwise. Convergence in distribution under the parameter δ is denoted by
+δ⇝ .
+2. Randomization inference on Gaussian processes
+In this section I study the size of randomization tests when the data come from
+heterogeneous Gaussian processes. I then analyze asymptotic size when a limiting
+experiment is characterized by such processes. The next section applies these generic
+results to the quantile setting.
+I first introduce some notation for randomization tests and Gaussian processes
+that I will use throughout the paper. Define G = {1, −1}q as the q-dimensional
+product of {1, −1} and, for g = (g1, . . . , gq) ∈ G, define g �→ gx as the direct product
+gx = (g1x1, . . . , gqxq) of g and x ∈ Rq. Let u �→ Xj(u), 1 ⩽ j ⩽ q, be independent
+mean-zero Gaussian processes with u ∈ U, where U is a compact subset of (0, 1). A
+stochastic process is Gaussian if and only (Xj(u1), . . . , Xj(um)) is multivariate normal
+for any finite collection of indices u1, . . . , um ∈ U. Symmetry about zero implies that
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+6
+(Xj(u1), . . . , Xj(um)) and −(Xj(u1), . . . , Xj(um)) are identically distributed. Because
+this is true for every finite collection of indices u1, . . . , um ∈ U, Xj and −Xj have the
+same (finite-dimensional) distributions. Independence and symmetry together imply
+that u �→ X(u) = (X1, . . . , Xq)(u) and u �→ gX(u) have the same distribution for
+every g ∈ G as long as X has mean zero. The quantile and quantile-like processes
+discussed in the next section have this property under the null hypothesis. Deviations
+from the null cause non-zero means and therefore also asymmetry in X. The goal of
+this section is to develop a test of the null hypothesis of symmetry about zero,
+H0 : X(u) ∼ gX(u),
+all g ∈ G, all u ∈ U.
+(2.1)
+To test this hypothesis, I use the Kolmogorov-Smirnov-type statistic
+T(X) = sup
+u∈U
+�
+1
+q
+q
+�
+j=1
+Xj(u)
+�
+.
+(2.2)
+This statistic is large if symmetry is violated because the mean of the Xj is positive.
+I focus on one-sided tests to the right for simplicity but this is not restrictive. To
+test whether the mean is negative, simply use −X instead of X in the definition of T.
+These test statistics can be combined for two-sided tests. I explain this in detail at
+the end of Section 3.
+Randomization inference uses distributional invariance to generate null distribu-
+tions and critical values.
+In the present case, X is distributionally invariant to
+all transformations g contained in G because X is symmetric. Let T (1)(X, G) ⩽
+T (2)(X, G) ⩽ . . . ⩽ T (|G|)(X, G) be the |G| = 2q ordered values of T(gX) across g ∈ G
+and let
+T 1−α(X, G) := T (⌈(1−α)|G|⌉)(X, G)
+(2.3)
+be the 1 − α quantile of these values. The randomization test function is then
+ϕα(X, G) = 1{T(X) > T 1−α(X, G)}.
+(2.4)
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+7
+If U is a finite set, distributional invariance under H0 immediately implies Eϕα(X, G) =
+Eϕα(gX, G). By an argument due to Hoeffding (1952), the test function must satisfy
+|G|α ⩾ �
+g∈G ϕα(gX, G) and, after taking expectations on both sides, equality of the
+distributions yields |G|α ⩾ E �
+g∈G ϕα(gX, G) = �
+g∈G Eϕα(gX, G) = |G|Eϕα(X, G).
+This implies Eϕα(X, G) ⩽ α, which makes T 1−α(X, G) an α-level critical value.
+If U is a not finite, this argument does not immediately go through because (2.2)
+is a statement about possibly uncountably many u ∈ U but I have only established
+equivalence of the finite-dimensional distributions. However, as the following theorem
+shows, the conclusion that the test controls size holds nonetheless. The proof of
+the theorem extends Hoeffding’s proof to stochastic processes with smooth sample
+paths by showing that (2.1) implies equality of the distributions of T(gX)g∈G and
+T(g˜g−1X)g∈G for every ˜g ∈ G. (Here g−1 = −g is the inverse of g.) I prove that this is
+enough for Hoeffding’s argument to go through as long as at least one of the processes
+has positive variance at every u.
+Theorem 2.1. Let X1, . . . , Xq be independent mean-zero Gaussian processes with
+continuous sample paths indexed by the compact set U ⊂ (0, 1) and let u �→ X(u) :=
+(X1, . . . , Xq)(u). If there is a j ∈ {1, . . . , q} such that P(Xj(u) = 0) = 0 for all U,
+then Eϕα(X, G) ⩽ α.
+If X is only an approximation in the sense that Xn ⇝ X as a process in ℓ∞(U)q, the
+space of bounded maps from U to Rq, then the conclusions of the theorem still hold
+as long as the non-degeneracy conditions are strengthened. Here and in the following
+I tacitly assume that a process is indexed by a compact U ⊂ (0, 1).
+Theorem 2.2. If Xn ⇝ X = (X1, . . . , Xq), where the X1, . . . , Xq are independent
+mean-zero Gaussian processes with continuous sample paths that satisfy P(Xj(u) =
+0) = 0 and P(Xj(u) = −Xj(u′)) = 0 for all u, u′ ∈ U and 1 ⩽ j ⩽ q, then
+Eϕα(Xn, G) → Eϕα(X, G).
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+8
+Remarks. (i) For the non-degeneracy assumption P(Xj(u) = −Xj(u′)) = 0 to fail,
+a Gaussian process with uniformly continuous sample paths has to traverse, with
+certainty, from Xj(u) to Xj(u′) = −Xj(u) while maintaining a positive variance along
+the entire path. The process would have to have identical variances at time u and u′
+but be perfectly negatively correlated at those times, which is impossible for Brownian
+bridges and related processes that typically arise in a quantile context. Still, such
+Gaussian processes exist and have to be ruled out.
+(ii) The main difficulty of the proof of Theorem 2.2 is that the critical value
+T 1−α(Xn, G) does not settle down in the limit and is highly dependent on T(X). The
+assumptions of Theorem 2.2 rule out degeneracies in the limit process that could
+lead to ties in the order statistics of {T(gX) : g ∈ G}. This would put probability
+mass on the boundary of the set {T(X) > T 1−α(X, G)} and prevent application of
+the portmanteau lemma. Canay et al. (2017) use a delicate construction based on
+Skorokhod’s representation theorem to account for the randomness in the limit. While
+these results could be extended from vectors to processes, I instead give a direct proof
+that I can also use to analyze the behavior of the test under both local and global
+alternatives when I discuss quantile processes in the next section.
+□
+3. Inference on quantile processes with a finite number of clusters
+This section gives high level conditions under which asymptotically valid inference
+on quantile processes and related objects can be performed even if the underlying
+data come from a fixed number of heterogeneous clusters.
+3.1. Inference when parameters are identified within clusters. Suppose data
+from q large clusters (e.g., counties, regions, schools, firms, or stretches of time) are
+available. Throughout the paper, the number of clusters q remains fixed and does not
+grow with the number of observations n. Observations are independent across clusters
+but dependent within clusters. Data from each cluster 1 ⩽ j ⩽ q separately identify a
+quantile or quantile-like scalar function δ : U → R. The δ can be estimated by ˆδj using
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+9
+data from only cluster j such that a total of q separate estimates (ˆδ1, . . . , ˆδq) =: ˆδ of
+u �→ δ(u) are available. The goal is to use randomization inference on a centered and
+scaled version of ˆδ to develop tests of the null hypothesis
+H0 : δ(u) = δ0(u),
+all u ∈ U,
+(3.1)
+for some known function δ0 : U → R. The following two examples describe simple but
+empirically relevant situations that fit this framework.
+Example 3.1 (Regression quantiles). Suppose an outcome Yi,j of individual i in
+cluster j can be represented as Yi,j = Xi,jδ(Ui,j) + Z′
+i,jβj(Ui,j), where u �→ Xi,jδ(u) +
+Z′
+i,jβj(u) is strictly increasing in u and Ui,j is standard uniform conditional on covariates
+(Xi,j, Zi,j). Here Xi,j is the scalar covariate of interest and the Zi,j are additional
+controls. Monotonicity implies that the u-th conditional quantile of Yi,j is Xi,jδ(u) +
+Z′
+i,jβj(u) and linear QR as in Koenker and Bassett (1978) can provide estimates (ˆδj, ˆβj)
+of (δ, βj) for each cluster. Testing (3.1) with δ0 ≡ 0 tests whether Yi,j and Xi,j are
+associated at any quantile after controlling for Zi,j.
+Several related models fit the framework of this example: (i) The βj can be constant
+across clusters. This does not impact the null hypothesis or the computation of the
+ˆδj. (ii) The δ can vary by cluster in the QR model Yi,j = Xi,jδj(Ui,j) + Z′
+i,jβ(Ui,j)
+under the alternative. This has no impact on the computation of the δj and the null
+hypothesis simply becomes H0 : δ1 = · · · = δq = δ0. Identical δj are required only
+under the null hypothesis. (iii) If βj ≡ 0 and Xi,j ≡ 1, then u �→ ˆδ(u) reduces to the
+u-th unconditional empirical quantile of Yi,j. The null (3.1) can then be used to test
+whether δ has a specific functional form, e.g., a standard normal quantile function.
+□
+Example 3.2 (Quantile treatment effects). Consider predetermined pairs {(j, j +
+q) : 1 ⩽ j ⩽ q} of 2q groups. Suppose the first q groups received treatment, indicated by
+Dj = 1{j ⩽ q}, and the remaining groups did not. Groups here could be manufacturing
+plants or villages. Treatment could be management consulting or introduction of a new
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+10
+technology. Denote treatment and control potential outcomes by Yj(1) ∼ FY (1) and
+Yj(0) ∼ FY (0), respectively. The observed outcome is Yj = DjYj(1) + (1 − Dj)Yj(0).
+For each group j, the experimenter observes identically distributed but potentially
+highly dependent copies Yi,j of Yj representing workers i within group j. View each
+pair (j, j + q) for 1 ⩽ j ⩽ q as a cluster and define the quantile treatment effect (QTE)
+as
+u �→ δ(u) = F −1
+Y (1)(u) − F −1
+Y (0)(u).
+This QTE can be estimated as difference of the empirical quantiles
+u �→ ˆδj(u) = ˆF −1
+Yj (u) − ˆF −1
+Yj+q(u)
+or, alternatively, as the coefficient on Dj in a QR of Yi,j on a constant and Dj using
+data only from cluster j. The situation where δ varies with j is again included in
+the analysis as long as the null hypotheses is δ1 = · · · = δq = δ0. Estimation remains
+unchanged. I discuss the more complex scenario where the counterfactual FY (0) has
+to be identified through difference-in-differences methods in Example 3.6 ahead.
+□
+The ˆδ is neither limited to the estimators discussed in the preceding two examples
+nor does it need to have a special functional form. However, I assume that it can be
+approximated by a Gaussian process as in Theorem 2.2. Let 1q be a q-vector of ones.
+Assumption 3.3. The random function ˆδ: U → Rq satisfies
+Xn := {√n(ˆδ − δ1q)(u) : u ∈ U}
+δ⇝ X = (X1, . . . , Xq),
+(3.2)
+where the X1, . . . , Xq are independent mean-zero Gaussian processes with continuous
+sample paths, P(Xj(u) = 0) = 0 and P(Xj(u) = −Xj(u′)) = 0 for all u, u′ ∈ U and
+1 ⩽ j ⩽ q.
+Examples of Xn that can satisfy this assumption include unconditional quantile
+functions, coefficient functions in quantile regressions, quantile treatment effects, and
+other quantile-like objects. El Machkouri, Voln´y, and Wu (2013) present invariance
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+11
+principles and moment bounds that can be used to establish the convergence condition
+(3.2) under explicit weak dependence conditions.
+I now connect the results from Section 2 about heterogeneous Gaussian processes to
+tests about δ under Assumption 3.3. The key property is that if H0 in (3.1) does not
+hold, then √n(ˆδ−δ01q) = Xn+√n(δ−δ0)1q. The Xn converges to a symmetric process
+but √n(δ − δ0)(u) grows without bound for some u, which makes the distribution of
+√n(ˆδ − δ01q) highly asymmetric. Testing for symmetry using randomization inference
+is therefore informative about the hypothesis that δ = δ0. I refer to a test that uses
+ˆδ − δ01q in place of X in test function (2.4) as the cluster-randomized Kolmorogov
+(CRK) test. From a practical perspective, the function δ0 is almost always δ0 ≡ 0.
+This tests the null of no effect at any quantile but more general hypotheses can be
+considered.
+The test function x �→ ϕα(x, G) is invariant to scaling of x by positive constants. If
+H0 : δ = δ0 is true, then the CRK test satisfies
+T(ˆδ − δ01q) > T 1−α(ˆδ − δ01q, G)
+if and only if T(Xn) > T 1−α(Xn, G). That the CRK test is an asymptotic α-level test
+is then an immediate consequence of Theorems 2.1 and 2.2.
+Theorem 3.4 (Size). Suppose Assumption 3.3 holds. If H0 : δ = δ0 is true, then
+limn→∞ Eϕα(ˆδ − δ01q, G) ⩽ α.
+Remarks. (i) The canonical limit of quantile and regression quantile processes such as
+those in Examples 3.1 and 3.2 is a scaled version of a q-dimensional Brownian bridge.
+That process easily satisfies the non-standard condition P(Xj(u) = −Xj(u′)) = 0
+imposed by Assumption 3.3.
+(ii) The inequality in the theorem becomes an equality if (1 − α)2q is an integer. In
+that case, the test in the limit experiment is “similar,” i.e., it has rejection probability
+exactly equal to α for all Gaussian processes that satisfy Assumption 3.3. The CRK
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+12
+test can therefore be asymptotically similar in some situations. If desired, the test
+decision can be randomized to make the CRK test similar in the limit for all choices
+of α.
+□
+To analyze the power of the CRK test, I consider fixed alternatives δ(u) = δ0(u)+λ(u)
+with a positive function u �→ λ(u), and local alternatives δ(u) = δ0(u) + λ(u)/√n
+converging to the maintained null hypothesis H0 : δ = δ0. In the local case, δ0 is fixed
+but δ now depends on n and the convergence (3.2) is under the sequence of functions
+δ = δ0 + λ/√n. As the following results show, the CRK test has power against both
+types of alternatives.
+Theorem 3.5 (Global and local power). Suppose Assumption 3.3 holds and α ⩾
+1/2q. If H1 : δ = δ0 + λ is true with λ: U → [0, ∞) continuous and supu∈U λ(u) > 0,
+then limn→∞ Eϕα(ˆδ − δ01q, G) = 1. If H1 : δ = δ0 + λ/√n is true with supu∈U λ(u) >
+E supu∈U Xj(u), 1 ⩽ j ⩽ q, then
+lim
+n→∞ Eϕα(ˆδ − δ01q, G) ⩾
+q�
+j=1
+�
+1 − e−[sup λ(u)−E sup Xj(u)]2/2 sup EX2
+j (u)�
+> 0,
+where the suprema in the exponent are over u ∈ U.
+Remarks. (i) The lower bound used for the local power result comes from the Borell-
+Tsirelson-Ibragimov-Sudakov (Borell-TIS) inequality (see, e.g., Adler and Taylor, 2007,
+p. 50). For large q, the bound is relatively crude but for small q, the only crude part
+is the assumption that δ is moderately large when compared to X. This is reflected
+in the condition that supu∈U λ(u) > E supu∈U Xj(u) instead of supu∈U λ(u) > 0. The
+local power bound can be made arbitrarily close to 1 by choosing supu∈U λ(u) large
+enough.
+(ii) If (1 − α)|G| > |G| − 1, the power of the test is identically zero. In that case
+T 1−α(X, G) = maxg∈G T(gX) and T(X) > T 1−α(X, G) becomes impossible because
+T(X) is contained in {T(gX) : g ∈ G}. I therefore I focus on the case (1 − α)|G| ⩽
+|G| − 1, which is equivalent to α ⩾ 1/2q.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+13
+(iii) The test also has power against alternatives where λ varies with the cluster
+index j and at least some of the λj are large. However, a precise statement without
+additional conditions on the relative sizes of the λj is involved. I do not pursue this
+here to prevent notational clutter.
+□
+3.2. Inference when parameters are identified across clusters. In applications,
+the treatment effect is often not identified from within a cluster but by comparisons
+across two clusters. This is the case, for example, if treatment is assigned at random
+at the cluster level or if identification comes from comparing changes in one cluster
+to changes in another cluster in a quasi-experimental context. In this situation, each
+individual pairing of a treated cluster j with a control cluster k is generally informative
+about the treatment effect of interest δ and each (j, k) pair gives rise to an estimate
+ˆδj,k of δ that could be used in a CRK-type test. The following example illustrates this
+for difference-in-differences estimation of quantile treatment effects.
+Example 3.6 (Quantile difference in differences). Let ∆Yt(0) = Yt(0) − Yt−1(0)
+be time differences of untreated outcomes. Periods t ∈ {0, −1} are pre-intervention
+periods and t = 1 is the post-intervention period; Y1(1) is a treated potential outcome
+and Yt are observed outcomes. Denote by FY |D=d the distribution of a variable Y
+conditional on the treatment indicator taking on the value d ∈ {0, 1}. Callaway and
+Li (2019) show that the distribution FY1(0)|D=1(y) of the untreated potential outcome
+of a treated observation at time t = 1 can be identified as
+P
+�
+F −1
+∆Y1|D=0
+�
+F∆Y0|D=1(∆Y0)
+�
++ F −1
+Y0|D=0
+�
+FY−1|D=1(Y−1)
+�
+⩽ y | D = 1
+�
+(3.3)
+as long as a distributional version of the standard parallel trends assumption and
+some additional stability and smoothness conditions hold. This identifies the quantile
+treatment on the treated (QTT) effect
+u �→ δ(u) = F −1
+Y1(1)|D=1(u) − F −1
+Y1(0)|D=1(u),
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+14
+where F −1
+Y1(1)|D=1(u) can be estimated by the sample quantile ˆF −1
+Y1|D=1(u). To estimate
+the counterfactual quantile, Callaway and Li replace P and every F in (3.3) with
+sample equivalents. This yields the estimated QTT
+u �→ ˆF −1
+Y1|D=1(u) − ˆF −1
+Y1(0)|D=1(u).
+(3.4)
+Callaway and Li show that √n( ˆF −1
+Y1|D=1 − ˆF −1
+Y1(0)|D=1 − δ) converges to a well-behaved
+Gaussian process under mild regularity conditions.
+Suppose that data come from q1 states that received treatment and q0 states that
+did not. View a single state over time as a cluster. Then two clusters are enough to
+compute (3.4): ˆF −1
+Y1|D=1 can be computed from a treated cluster j and ˆF −1
+Y1(0)|D=1 can
+be computed from j and an untreated cluster k. Denote by ˆδj,k the QTT estimated in
+this fashion using only data from clusters j and k. Each (j, k) pair provides a valid
+estimate of δ and each ˆδj,k could potentially be used in a CRK-type test of the null
+hypothesis H0 : δ = δ0.
+□
+I again assume that centered and scaled ˆδj,k converge in distribution to non-
+degenerate Gaussian processes with smooth sample paths as in Assumption 3.3.
+I only adjust this condition for the fact that estimates are constructed from pairwise
+combination of clusters. Let q1 be the number of treated clusters and let q0 be the
+number of control clusters.
+Assumption 3.7. The process {√n(ˆδj,k − δ)(u) : u ∈ U} converges, jointly in j and
+k, in distribution to mean-zero Gaussian processes Xj,k with continuous sample paths
+that satisfy P(Xj,k(u) = 0) = 0 and P(Xj,k(u) = −Xj,k(u′)) = 0 for all u, u′ ∈ U,
+1 ⩽ j ⩽ q1, and 1 ⩽ k ⩽ q0. If both j ̸= j′ and k ̸= k′, then Xj,k and Xj′,k′ are
+independent.
+A na¨ıve test of H0 : δ ≡ δ0 would now take Xn,j,k := √n(ˆδj,k − δ0) and generate
+randomization distributions from {Xn,j,k : 1 ⩽ j ⩽ q1, 1 ⩽ k ⩽ q0} via sign changes.
+However, Xn,j,k and Xn,j,k′ are dependent for any choice of j, k, k′ because j is used
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+15
+twice. This remains true even in large samples and if the data from all q1 + q0
+groups are independent. Dependence causes problems because (Xn,j,k, Xn,j,k′) and
+(Xn,j,k, −Xn,j,k′) generally do not have the same joint distribution even when n → ∞.
+Invariance under transformations with g therefore fails. This issue can be avoided if
+one works with a subset of {Xn,j,k : 1 ⩽ j ⩽ q1, 1 ⩽ k ⩽ q0} that uses each j and k
+only once. While this solves the dependence issue, it introduces another problem: each
+of the q1 treatment groups now has to be paired with exactly one of the q0 control
+groups. Two researchers working with the same data and methodology could therefore
+arrive at different conclusions because they chose different pairings. To address this
+problem, I now develop a method that maintains invariance under sign changes but
+avoids any decisions on the part of the researcher.
+I first introduce some notation. If q1 ⩽ q0, there are q0 × (q0 − 1)×· · · × (q0 −q1 + 1)
+ways of choosing q1 ordered elements out of (1, . . . , q0). Identify each such choice with
+an h and denote the collection of all h by H. The ordering within H will not affect
+the test decision. For each h ∈ H, denote by
+ˆδ[h] = (ˆδ1,h(1), ˆδ2,h(2), . . . , ˆδq1,h(q1)),
+q1 ⩽ q0,
+(3.5)
+the vector that matches the subset of control groups associated with the label h =
+(h(1), . . . , h(q1)) to the (unpermuted) treated groups. If there are more treated than
+control groups such that q1 > q0, permute treated groups instead and take h as
+enumerating ways of choosing q0 elements out of (1, . . . , q1) to define
+ˆδ[h] = (ˆδh(1),1, ˆδh(2),2, . . . , ˆδh(q0),q0),
+q1 > q0.
+(3.6)
+By construction, the entries of ˆδ[h] are independent of one another but ˆδ[h] and ˆδ[h′] for
+h, h′ ∈ H are potentially highly dependent.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+16
+To address the issue that there are multiple ways of combining clusters, I use an
+adjustment based on the randomization p-value
+p(X, G) = inf{p ∈ (0, 1) : T(X) > T p(X, G)} = 1
+|G|
+�
+g∈G
+1{T(gX) ⩾ T(X)}.
+(3.7)
+Testing with this p-value is equivalent to a test with a critical value because T(X) >
+T 1−α(X, G) if and only if p(X, G) ⩽ α. The multiple comparisons adjustment is based
+on an inequality of R¨uschendorf (1982). It states that arbitrary, possibly dependent
+variables Uh indexed by h ∈ H with the property that P(Uh ⩽ u) ⩽ u for every
+u ∈ [0, 1] satisfy
+P
+�
+2
+|H|
+�
+h∈H
+Uh ⩽ u
+�
+⩽ u,
+every u ∈ [0, 1].
+(3.8)
+This specific form of the inequality is given in Vovk (2012). Here the indexing set H is
+arbitrary and does not need to be related to permutations. The only condition is that
+H = |H| ⩾ 2. The randomization p-value p(ˆδ[h] − δ01q1∧q0, G) for testing whether the
+treatment effect of interest equals δ0 can be expected to behave like the Uh in (3.8) in
+a large enough sample. Combining p-values of the CRK test to reject the null if
+2
+H
+�
+h∈H
+p(ˆδ[h] − δ01q1∧q0, G)
+(3.9)
+does not exceed α should then asymptotically control size. The following theorem
+confirms that this is indeed true.
+Theorem 3.8 (Size with combined p-values). Suppose Assumption 3.7 holds. If
+H0 : δ = δ0, then
+lim sup
+n→∞ P
+�
+2
+H
+�
+h∈H
+p(ˆδ[h] − δ01q1∧q0, G) ⩽ α
+�
+.
+Remarks. (i) The theorem can be improved slightly if α|G|H/2 is not an inte-
+ger. In that case, the limit superior in the theorem is a proper limit that equals
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+17
+P((2/H) �
+h∈H p(X[h], G) ⩽ α), where X[h] is the weak limit of √n(ˆδ[h] − δ01q1∧q0).
+This is because the sum in the preceding display can vary discontinuously at certain
+values. The limit inferior is P((2/H) �
+h∈H p(X[h], G) < α).
+(ii) Results of DiCiccio, DiCiccio, and Romano (2020) suggest that other ways of
+combining p-values such as the median p-value instead of an average p-value are likely
+to be applicable here as well. However, the proof of the theorem given here relies
+crucially on the properties of the R¨uschendorf inequality.
+□
+The price paid for not matching treated and control clusters before the analysis is
+lower relative power. When p-values are averaged, R¨uschendorf’s inequality essentially
+decreases α to α/2 to control size. Meng (1993) shows that the constant 2 cannot
+be improved. Still, as I establish below, the test has power against global and local
+alternatives if α > 1/2q1∧q0−1, which is slightly stronger than what is needed in
+Theorem 3.5. Compared to Theorem 3.5, I also do not state an explicit bound for the
+local power analysis because applying the Borel-TIS inequality to the averaged p-values
+directly yields only relatively crude results. I instead show that if the alternatives
+λ/√n converging to the null hypothesis are scaled up by a constant c, the test can
+detect these alternatives in the limit experiment with arbitrary accuracy if c is large
+enough, that is, if first n → ∞ and then c → ∞.
+Theorem 3.9 (Global and local power with combined p-values). Suppose
+Assumption 3.7 holds and α > 1/2q1∧q0−1. If H1 : δ = δ0 + λ with λ: U → [0, ∞)
+continuous and supu∈U(u) > 0, then limn→∞ P((2/H) �
+h∈H p(ˆδ[h] − δ01q1∧q0, G) ⩽
+α) = 1. If H1 : δ = δ0 + cλ/√n, then
+lim
+c→∞ lim inf
+n→∞ P
+�
+2
+H
+�
+h∈H
+p(ˆδ[h] − δ01q1∧q0, G) ⩽ α
+�
+= 1.
+3.3. Implementation. I now turn to some practical aspects of the CRK test. I
+discuss (i) what to do if G is large, (ii) what to do if H is large, and (iii) how to
+implement the test with a step-by-step guide. First, G can be prohibitively large if the
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+18
+number of clusters is large. If computing the entire randomization distribution is too
+costly, then G can be approximated by a random sample Gm consisting of m draws
+from G with replacement. This is often referred to as “stochastic approximation.” The
+theorems presented in Sections 3.1 and 3.2 continue to hold if Gm is used in place of G
+as long as a limit superior or inferior as m → ∞ is applied before n → ∞. The order of
+limits is not restrictive because, in a given sample of size n, the number of draws can m
+always be made as large as computationally feasible. Under stochastic approximation,
+the statement in Theorem 3.4 becomes limn→∞ lim supm→∞ Eϕα(ˆδ − δ01q, Gm) ⩽ α,
+whereas statements about power use a limit inferior. Limit superior and inferior are
+needed here because of potential discontinuities but can be replaced by regular limits
+for most values of α. Theorems 3.4, 3.8, and 3.9 hold without additional conditions
+but the conditions of Theorem 3.5 have to be strengthened marginally to avoid a
+discontinuity at α = 1/2q.
+Proposition 3.10. Suppose Gm consists of m iid draws from G. If every instance of
+G is replaced by Gm, then
+(i) Theorem 3.4 holds if limn→∞ is replaced by limn→∞ lim supm→∞,
+(ii) Theorem 3.5 holds if every limn→∞ is replaced by limn→∞ lim infm→∞ and α >
+1/2q,
+(iii) Theorem 3.8 holds if lim supn→∞ is replaced by lim supn→∞ lim supm→∞,
+(iv) Theorem 3.9 holds if limn→∞ is replaced by limn→∞ lim infm→∞ and lim infn→∞
+is replaced by lim infn→∞ lim infm→∞.
+If α ̸∈ {j/|G| : 1 ⩽ j ⩽ |G|}, then lim infm→∞ and lim supm→∞ can be replaced by
+limm→∞ in (i)-(iv).
+Second, the number of elements of H can similarly be large if the number of clusters
+is large or if there is a large discrepancy between the number of treated and the
+number of control clusters. In that case one can again work with a random subset I
+of H. The crucial difference to the preceding result is that both Theorems 3.8 and 3.9
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+19
+continue to hold even if I consists of only a finite number of random draws. In fact,
+the result goes through for any I as long as I is independent of the data.
+Proposition 3.11. Let I with |I| ⩾ 2 be a fixed or random subset of H independent
+of the data. Then Theorems 3.8 and 3.9 continue to hold if H is replaced by I.
+Finally, the following two algorithms outline and summarize how to apply the CRK
+test in practice. By Theorems 3.4 and 3.8, the procedures provide an asymptotically
+α-level test in the presence of a finite number of large clusters that are arbitrarily
+heterogeneous. They are free of nuisance parameters and do not require any decisions
+on the part of the researcher. By Theorems 3.5 and 3.9, the tests are able to detect
+fixed and 1/√n-local alternatives. The first algorithm describes the CRK test when
+the parameters are identified within clusters. The second algorithm describes the
+between-cluster case, which is needed for distributional difference in differences. The
+tests can be two-sided or one-sided in either direction.
+Algorithm 3.12 (CRK test for parameters identified within clusters).
+(1) Compute for each j = 1, . . . , q and using only data from cluster j an estimate ˆδj
+of a parameter of interest δ. (See Examples 3.1 and 3.2.) Define ˆδ = (ˆδ1, . . . , ˆδq).
+(2) Compute G, the set of all vectors of length q with entries 1 or −1, or replace
+G with a large random sample Gm from G in the following.
+(3) Reject the null hypothesis H0 : δ(u) = δ0(u) for all u (e.g., δ0 ≡ 0 tests for no
+effect of treatment) against
+(a) δ(u) > δ0(u) for some u if T(ˆδ − δ01q) > T 1−α(ˆδ − δ01q, G) for a test with
+asymptotic level α,
+(b) δ(u) < δ0(u) for some u if T(ˆδ − δ01q) < T α(ˆδ − δ01q, G) for a test with
+asymptotic level α,
+(c) δ(u) ̸= δ0(u) for some u if (a) or (b) are true for a test with asymptotic
+level 2α,
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+20
+where T is defined in (2.2) and T 1−α(·, G) is the ⌈(1 − α)|G|⌉-th largest value
+of the randomization distribution of T, defined in (2.3).
+Algorithm 3.13 (CRK test for parameters identified between clusters).
+(1) Compute H, as defined above (3.5), or replace H with a large subset I in the
+following.
+(2) Compute G, the set of all vectors of length q with entries 1 or −1, or replace
+G with a large random sample Gm from G in the following.
+(3) For each h, compute ˆδ[h] from (3.5) if q1 ⩽ q0 or from (3.6) if q1 > q0. (See
+Example 3.6.) Use (3.7) and (3.9) to compute
+2
+|H|
+�
+h∈H
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α
+(3.10)
+(4) Reject the null hypothesis H0 : δ(u) = δ0(u) for all u (e.g., δ0 ≡ 0 tests for no
+effect of treatment) against
+(a) δ(u) > δ0(u) for some u if (3.10) is true for a test with asymptotic level α,
+(b) δ(u) < δ0(u) for some u if (3.10) is true when ˆδ[h] −δ01min{q1,q0} is replaced
+by −(ˆδ[h] − δ01min{q1,q0}) for a test with asymptotic level α,
+(c) δ(u) ̸= δ0(u) for some u if (a) or (b) are true for a test with asymptotic
+level 2α.
+In some contexts, Algorithm 3.12 can be used even if the parameter of interest is
+identified by comparisons between treated and untreated clusters. For this to work,
+the researcher has to merge each treated cluster with an untreated cluster into a single
+cluster to recover within-cluster identification. If the number of treated clusters and
+control clusters is equal, then every treated cluster can be matched with a control
+cluster according to some rule. If the number of clusters is not equal, then two or
+more clusters can be merged to force an equal number of treated and control clusters.
+The merged clusters can then be reinterpreted as clusters and Algorithm 3.12 can be
+applied to these new clusters. While this comes with a large number of decisions, it is
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+21
+a valid method for inference if these decisions are made before the data are analyzed.
+For example, when estimating quantile treatment effects, a pre-analysis plan can be
+put in place that prescribes how clusters that received treatment will be merged with
+clusters that did not receive treatment. This reduces the problem to the one described
+in Example 3.2.
+The next section investigates the finite sample performance of Algorithms 3.12 and
+3.13 in several sitations.
+4. Numerical results
+This section presents several Monte Carlo experiments to investigate the small-
+sample properties of the CRK test in comparison to other methods of inference. I
+discuss significance tests on quantile regression coefficient functions (Example 4.1),
+inference in experiments when parameters are identified between clusters (Example 4.2),
+and estimation of QTEs in Project STAR (Example 4.3). I test one-sided hypotheses
+to the right but the results apply more broadly.
+Example 4.1 (Regression quantiles, cont.). In this example, I adapt an experi-
+ment of Hagemann (2017) and use the data generating process (DGP)
+Yi,j,k = Ui,j,k + Ui,j,kZi,j,k,
+where Ui,j,k = √ϱVj,k + √1 − ϱWi,j,k with ϱ ∈ [0, 1); Vj,k and Wi,j,k are standard
+normal, independent of one another, and independent across indices. This ensures
+that the Ui,j,k are standard normal and, for a given j, k, any pair Ui,j,k and Ui′,j,k
+has correlation ϱ. The Zi,j,k satisfy Zi,j,k = X2
+i,j,k/3 with Xi,j,k standard normal
+independent of Ui,j,k to ensure that the Ui,j,kZi,j,k have mean zero and variance one.
+Both Xi,j,k and Ui,j,k are independent across j and k, and Xi,j,k is also independent
+across i. I discard information on k after data generation and drop the k subscripts in
+the following because they are not assumed to be known. This induces a dependence
+structure where each cluster j = 1, . . . , q consists of several (unknown) neighborhoods
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+22
+k = 1, . . . , K where observations are dependent if they come from the same k but are
+independent otherwise. If K → ∞ and the size of the neighborhoods is fixed or grows
+slowly with K, then this dependence structure is compatible with Assumptions 3.3 and
+3.7 because it generates the weak dependence needed for central limit theory. In the
+experiments ahead, I set K to either 10 or 20 and draw the size of each neighborhood
+from the uniform distribution on {5, 6, . . . , 15}. The DGP in the preceding display
+corresponds to the QR model
+Q(u | Xi,j, Zi,j) = β0(u) + β1(u)Xi,j + β2(u)Zi,j
+(4.1)
+with β1(u) ≡ 0 and β0(u) = Φ−1(u) = β2(u), where Φ is the standard normal
+distribution function. For the CRK test, I estimated (4.1) separately for each cluster,
+obtained q estimates of β1 and applied Algorithm 3.12 with 1,000 new draws from G
+for each Monte Carlo replication.
+I compare the CRK test to inference with the wild gradient bootstrap of Hagemann
+(2017), a version of the bootstrap that perturbs the gradient of the QR objective
+function in a computationally efficient way while accounting for cluster dependence. It
+requires the number of clusters q → ∞ for consistency. The wild gradient bootstrap
+is the default option for cluster-robust inference in the quantreg package in R. I use
+the package default settings with Mammen bootstrap weights and 200 bootstrap sim-
+ulations. I do uniform inference with sup-Wald statistics as outlined in Algorithm 3.4
+of Hagemann (2017) with critical values and standard errors computed from the wild
+gradient bootstrap. Hagemann (2017) documents excellent performance of the wild
+gradient bootstrap even with challenging DGPs as long as there are more than 20
+clusters. However, Hagemann (2017) notes that size distortions can occur when fewer
+than 20 clusters are present. I focus on this situation in the following.
+Figure 1 shows the rejection frequencies of a true null hypothesis H0 : β1(u) = 0
+for all u as a function of the number of clusters q ∈ {5, 6, . . . , 20} for the wild
+gradient bootstrap (left) and the CRK test (right) at the 5% level (short-dashed
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+23
+5
+10
+15
+20
+0.00 0.05 0.10 0.15 0.20 0.25
+Bootstrap (size, u �→ β1(u))
+Number of clusters
+Rejection frequency
+5
+10
+15
+20
+0.00 0.05 0.10 0.15 0.20 0.25
+CRK test (size, u �→ β1(u))
+Number of clusters
+K = 10, ϱ =.5
+K = 20, ϱ =.5
+K = 10, ϱ =.1
+5% level
+Figure 1. Rejection frequencies in Example 4.1 of a true null H0 : β1(u) = 0 for all
+u as a function of the number of clusters for the bootstrap (left) and the CRK test
+(right) with (i) K = 10 neighborhoods per cluster with intra-neighborhood correlation
+ϱ = .5 (solid lines), (ii) K = 20 with ϱ = .5 (long-dashed), and (iii) K = 10 with
+ϱ = .1 (dotted). Short-dashed line equals nominal level .05.
+line). The figure shows rejection frequencies in 5,000 Monte Carlo replications for
+each horizontal coordinate with (i) K = 10 neighborhoods per cluster with intra-
+neighborhood correlation ϱ = .5 (solid lines), (ii) K = 20 with ϱ = .5 (long-dashed),
+and (iii) K = 10 with ϱ = .1 (dotted). Both methods were faced with the same data
+and I estimated β1 at u = .1, .2, . . . , .9 for both methods. As can be seen, the wild
+gradient bootstrap over-rejected mildly with 20 clusters but over-rejected substantially
+for smaller numbers of clusters. It exceeded a 10% rejection rate if only 12 clusters
+were available. With 5 clusters, the wild gradient bootstrap falsely discovered an effect
+in up to 20.9% of all cases (K = 10, ϱ = .1). In contrast, the CRK test rejected at or
+slightly below nominal level for all q and all configurations of K and ϱ.
+I also experimented with a large number of alternative DGPs under the null. I
+considered (not shown) larger neighborhoods, different values of ϱ, different spatial
+dependence structures such as (spatial) autoregressive models, and different distribu-
+tions for Xi,j,k. However, I found that these changes had little qualitative impact on
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+24
+the results described in the preceding paragraph or in Hagemann (2017). The wild
+gradient bootstrap generally performed very well but experienced size distortions with
+fewer than 20 clusters. The CRK test rejected at or slightly below nominal level in all
+situations I investigated.
+I now turn to the behavior of the test under the alternative. I repeated the experiment
+but now tested the incorrect null hypothesis H0 : β2(u) = 0 for all u ∈ U. Figure 2
+shows the rejection frequencies of this null against the alternative H1 : β2(u) > 0 for
+some u ∈ U, where U was either (0, 1) (black) or (.5, 1) (grey). The null hypothesis
+is false in both situations but the case where U = (0, 1) is more challenging because
+β2(u) < 0 for all u < .5 so that estimates below the median provide evidence in the
+direction away from the alternative. I again considered (i) K = 10 neighborhoods
+per cluster with intra-neighborhood correlation ϱ = .5 (solid lines), (ii) K = 20 with
+ϱ = .5 (long-dashed), and (iii) K = 10 with ϱ = .1 (dotted). As could be expected, the
+bootstrap rejected a large fraction of null hypotheses mostly because it was unable to
+control the size of the test. However, it had high power when the number of clusters
+was above 20 and the size distortions disappeared (not shown). The CRK test had
+high power while maintaining size control even when the number of clusters was below
+20. For example, at q = 12 it detected a deviation from the null between 22.5%
+(K = 10, ϱ = .5, U = (0, 1)) and 84.26% (K = 20, ϱ = .5, U = (.5, 1)) of all cases.
+More generally, additional clusters, lower intra-cluster dependence, and additional
+neighborhoods per cluster increased the power of the CRK test.
+□
+Example 4.2 (Quantile treatment effects, cont.). For this experiment, I reuse
+the setup of Example 4.1 but replace the variable Xi,j,k with a cluster-level treatment
+indicator Dj that equals one if cluster j received treatment and equals zero otherwise.
+I randomly assign q1 = ⌊q/2⌋ clusters to treatment and q0 = ⌈q/2⌉ to control. The
+coefficient of interest is δ in
+Q(u | Dj) = β0(u) + δ(u)Dj + β2(u)Zi,j.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+25
+5
+10
+15
+20
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Bootstrap (power, u �→ β2(u))
+Number of clusters
+Rejection frequency
+K = 10, ϱ =.5
+K = 20, ϱ =.5
+K = 10, ϱ =.1
+K = 10, ϱ =.5
+K = 20, ϱ =.5
+K = 10, ϱ =.1
+5% level
+5
+10
+15
+20
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+CRK test (power, u �→ β2(u))
+Number of clusters
+Figure 2. Rejection frequencies in Example 4.1 of false nulls H0 : β2(u) = 0 for
+u > .5 (grey) and H0 : β2(u) = 0 for all u (black) as a function of the number
+of clusters for the bootstrap (left) and the CRK test (right) with (i) K = 10
+neighborhoods per cluster with intra-neighborhood correlation ϱ = .5 (solid lines),
+(ii) K = 20 with ϱ = .5 (long-dashed), and (iii) K = 10 with ϱ = .1 (dotted).
+I do not assume that pairings are predetermined and therefore use the adjusted p-values
+of the CRK test from Algorithm 3.13. For each Monte Carlo replication, I drew a
+collection I with |I| = 50 from H without replacement. The CRK test with unknown
+cluster parings requires α = .05 > 1/2q1∧q0−1 to have power, which is satisfied here as
+long as q ⩾ 12. I therefore restrict q to be between 12 and 20. All other parameters
+of the experiment are exactly as in Example 4.1.
+The left panel of Figure 3 shows the rejection frequencies of a true null hypothesis
+H0 : δ(u) = 0 for all u in 5,000 Monte Carlo experiments per horizontal coordinate
+as q increases. I again considered (i) K = 10 neighborhoods per cluster with intra-
+neighborhood correlation ϱ = .5 (solid lines), (ii) K = 20 with ϱ = .5 (long-dashed),
+and (iii) K = 10 with ϱ = .1 (dotted). As can be seen, adjusting the CRK test for
+unknown cluster pairings results in a markedly more conservative test relative to
+an unadjusted test from Figure 1. However, as the right panel of Figure 3 shows,
+this did not translate into poor power under the alternative. When I repeated the
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+26
+12
+14
+16
+18
+20
+0.00 0.05 0.10 0.15 0.20 0.25
+CRK test (size, δ(u) ≡ 0)
+Number of clusters
+Rejection frequency
+K = 10, ϱ =.5
+K = 20, ϱ =.5
+K = 10, ϱ =.1
+K = 10, ϱ =.5
+K = 20, ϱ =.5
+K = 10, ϱ =.1
+5% level
+12
+14
+16
+18
+20
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+CRK test (power, δ(u) ≡ .5)
+Number of clusters
+Figure 3. Rejection frequencies in Example 4.2 of a true null (left) H0 : δ(u) = 0
+for all u and false nulls (right) H0 : δ(u) = 0 for u > 0 (grey) and H0 : δ(u) = 0
+for all u (black) as a function of the number of clusters for the CRK test when
+cluster pairings are not known with (i) K = 10 neighborhoods per cluster with intra-
+neighborhood correlation ϱ = .5 (solid lines), (ii) K = 20 with ϱ = .5 (long-dashed),
+and (iii) K = 10 with ϱ = .1 (dotted).
+experiment with δ(u) ≡ .5, the CRK test with identification across clusters had no
+problem detecting the that neither H0 : δ(u) for all u ∈ (0, 1) (black) nor H0 : δ(u) for
+u > .5 (grey) were true. Compared to Example 4.1, the alternative where U = (0, 1)
+rejects slightly more nulls because now every u provides evidence against the null.
+A noteworthy feature of the right panel of Figure 3 is the “zig-zag” pattern in
+the rejection frequencies. The reason for this pattern is the treatment assignment
+mechanism. If q = 12, then q1 = 6 clusters receive treatment and q0 = 6 do not. If
+q = 13, then again 6 = ⌊13/2⌋ clusters receive treatment but now 7 = ⌈13/2⌉ do
+not. Algorithm 3.13 uses a large number of potential pairings of treatment to control
+for inference but effectively reduces the number of clusters to min{q1, q0}. In this
+experiment, inference with 6 + 7 clusters is therefore effectively the same as inference
+with 6 + 6 clusters, which explains the similar performance of the test at q and q − 1
+when q is odd.
+□
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+27
+Example 4.3 (Placebo interventions in Project STAR). In this example, I
+revisit a challenging placebo exercise of Hagemann (2017, Experiment 5.1) in data
+from the first year of the Tennessee Student/Teacher Achievement Ratio experiment,
+known as Project STAR. Details about the data can be found in Word et al. (1990)
+and Graham (2008). I only provide a brief summary.
+In 1985, incoming kindergarten students in 79 project schools were randomly
+assigned to small classes (13-17 students) or regular-size classes (22-25 students) with
+or without a teacher’s aide. Each of the project schools was required to have at least
+one of each kindergarten class type. The outcome is standardized student performance
+on the Stanford Achievement Test (SAT) in mathematics and reading administered at
+the end of the school year. The raw test scores are standardized as in Krueger (1999).
+He finds across several mean regression models that students in small classes perform
+about five percentage points better on average than students in regular classrooms.
+(Assigning teachers aides had no effect uniformly across specifications and I do not
+consider such classes in the following.) Hagemann (2017) documents similar effects in
+quantile regressions but finds that the effects are smaller for students near the bottom
+and top of the conditional outcome distribution and larger near the center of the
+distribution. For example, in the model
+QYi,j(u | Xi,j) = β0(u) + δ(u)small i,j + β2(u)TZi,j
+(4.2)
+where the treatment dummy small indicates whether the student was assigned to a
+small class and Z contains school dummies, the effect of being in a small class relative
+to a regular class varies between 2.78 percentage points at the 10th percentile to 7.23
+percentage points at the 60th percentile.
+For the placebo experiment, I removed all small classes from the sample and only
+kept the 16 schools that had two regular-size classes without aide. In each of these
+16 schools, I then randomly assigned one of the regular-size classes the treatment
+indicator small = 1. This mimics the random assignment of class sizes within schools
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+28
+Table 1. Rejection frequencies of H0 : δ(u) = 0 for all u in placebo interventions in
+Project STAR for the CRK test and the wild gradient bootstrap at 5% level
+size
+power
+δ = 0
+δ = 2
+δ = 3
+δ = 4
+δ = 5
+δ = 6
+δ = 7
+CRK test
+.043
+.122
+.161
+.212
+.318
+.379
+.478
+Bootstrap
+.091
+.233
+.316
+.428
+.580
+.691
+.814
+in the original sample, even though in this case no student actually attended a small
+class. I applied the CRK test as in Algorithm 3.12 by running 16 separate quantile
+regressions, one for each school, on a constant and small to get 16 separate estimates
+of δ. The fixed effects as in (4.2) are not needed here because the constant can vary
+freely by cluster in these quantile regressions. This also means that I am effectively
+clustering at the school level because I am comparing, within each school, classes
+with small = 1 to classes with small = 0. There is only one such comparison per
+school. (If multiple small classes per school were available, then Algorithm 3.13 could
+be used instead.) For the wild gradient bootstrap, I reran the QR in (4.2) in the
+placebo data but clustered at the classroom level as in Hagemann (2017). For both
+methods, I tested at the 5% level the correct null hypothesis that H0 : δ(u) = 0 jointly
+at u ∈ {.1, .2, . . . , .9} against the alternative that δ is positive.
+The rejection frequencies in ‘size’ column in Table 1 show the outcome of repeating
+the placebo assignment 1,000 times. As can be seen, the CRK test provided a nearly
+exact test but the bootstrap over-rejected somewhat. The over-rejection for the
+bootstrap here was documented by Hagemann (2017) and can be attributed to the
+placebo sample being very small with about 69 students per school and the effect of
+interest being identified off of comparisons within these 16 schools.
+I also investigated power by increasing the percentile scores of all students in
+the randomly drawn small classes of the placebo experiment by δ ∈ {2, 3, 4, 5, 6, 7}
+percentage points. These increases are of the same or smaller magnitude as the
+estimated quantile treatment effects in the actual sample. Then I tested the incorrect
+hypothesis H0 : β1(u) = 0 for all u with the same experimental setup as before. The
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+29
+results are shown in ‘power’ column of Table 1. As can be seen, the CRK test was
+able to reliably detect effects for moderate deviations from the null hypothesis. The
+wild gradient bootstrap rejected more often, but this was likely caused by its tendency
+to over-reject in this data set.
+□
+5. Conclusion
+I introduce a generic method for inference on quantile and regression quantile
+processes in the presence of a finite number of large and arbitrarily heterogeneous
+clusters. The method asymptotically controls size by generating statistics that exhibit
+enough distributional symmetry such that randomization tests can be applied. This
+randomization test can even be asymptotically similar in empirically relevant situations.
+The test does not require ex-ante matching of clusters, is free of user-chosen parameters,
+and performs well at conventional significance levels with as few as five clusters. The
+main focus on the paper is inference on quantile treatment effects and quantile
+difference in differences but the method applies more broadly. Numerical examples
+and an empirical application are provided.
+References
+Adler, R. J. and J. E. Taylor (2007). Random Fields and Geometry. Springer, New
+York.
+Bertrand, M., E. Duflo, and S. Mullainathan (2004). How much should we trust
+differences-in-differences estimates? Quarterly Journal of Economics 119, 249–275.
+Bester, C. A., T. G. Conley, and C. B. Hansen (2011). Inference with dependent data
+using cluster covariance estimators. Journal of Econometrics 165, 137–151.
+Callaway, B. and T. Li (2019). Quantile treatment effects in difference in differences
+models with panel data. Quantitative Economics 10, 1579–1618.
+Cameron, A. C. and D. L. Miller (2015). A practitoner’s guide to cluster robust
+inference. Journal of Human Resources 50, 317–372.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+30
+Canay, I., J. P. Romano, and A. M. Shaikh (2017). Randomization tests under an
+approximate symmetry assumption. Econometrica 85, 1013–1030.
+Canay, I. A., A. Santos, and A. M. Shaikh (2020). The wild bootstrap with a “small”
+number of “large” clusters. Review of Economics and Statistics, forthcoming.
+Chen, L., L.-J. Wei, and M. I. Parzen (2003). Quantile regression for correlated
+observations. In Proceedings of the Second Seattle Symposium in Biostatistics:
+Analysis of Correlated Data. Lecture Notes in Statistics. Springer, New York.
+DiCiccio, C. J., T. J. DiCiccio, and J. P. Romano (2020). Exact tests via multiple
+data splitting. Statistics & Probability Letters 166, 108865.
+El Machkouri, M., D. Voln´y, and W. B. Wu (2013). A central limit theorem for
+stationary random fields. Stochastic Processes and their Applications 123, 1–14.
+Fisher, R. A. (1935). “The coefficient of racial likeness” and the future of craniometry.
+Journal of the Royal Anthropological Institute of Great Britain and Ireland 66,
+57–63.
+Graham, B. S. (2008). Identifying social interactions through conditional variance
+restrictions. Econometrica 76, 643–660.
+Hagemann, A. (2017). Cluster-robust bootstrap inference in quantile regression models.
+Journal of the American Statistical Association 112, 446–456.
+Hagemann, A. (2019). Permutation inference with a finite number of heterogeneous
+clusters. University of Michigan working paper, arXiv:1907.01049.
+Hoeffding, W. (1952). The large-sample power of tests based on permutations of
+observations. Annals of Mathematical Statistics 23, 169–192.
+Ibragimov, R. and U. M¨uller (2010). t-statistic based correlation and heterogeneity
+robust inference. Journal of Business & Economic Statistics 28, 453–468.
+Ibragimov, R. and U. M¨uller (2016). Inference with few heterogenous clusters. Review
+of Economics and Statistics 98, 83–06.
+Koenker, R. and G. Bassett (1978). Regression quantiles. Econometrica 46, 33–50.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+31
+Krueger, A. B. (1999). Experimental estimates of education production functions.
+Quarterly Journal of Economics 114, 497–532.
+MacKinnon, J. G., M. Ø. Nielsen, and M. D. Webb (2022). Cluster-robust inference:
+A guide to empirical practice. Journal of Econometrics, forthcoming.
+MacKinnon, J. G. and M. D. Webb (2017). Wild bootstrap inference for wildly
+different cluster sizes. Journal of Applied Econometrics 32, 233–254.
+Meng, X.-L. (1993). Posterior predictive p-values. Annals of Statistics 22, 1142–1160.
+Parente, P. M. and J. M. Santos Silva (2013). Quantile regression with clustered data.
+University of Essex Department of Economics Discussion Paper No. 728.
+R¨uschendorf, L. (1982). Random variables with maximum sums. Advances in Applied
+Probability 14, 623–632.
+Vovk, V. (2012). Combining p-values via averaging. Technical report, arXiv:1212.4966.
+Wang, H. (2009). Inference on quantile regression for heteroscedastic mixed models.
+Statistica Sinica 19, 1247–1261.
+Wang, H. and X. He (2007). Detecting differential expressions in genechip microarray
+studies: a quantile approach. Journal of American Statistical Association 102,
+104–112.
+Word, E., J. Johnston, H. P. Bain, B. D. Fulton, C. M. Achilles, M. N. Lintz, J. Folger,
+and C. Breda (1990). The state of Tennessee’s student/teacher achievement ratio
+(STAR) project: Technical report 1985-1990. Report, Tennessee State University,
+Center of Excellence for Research in Basic Skills.
+Yoon, J. and A. F. Galvao (2020). Cluster robust covariance matrix estimation in
+panel quantile regression with individual fixed effects. Quantitative Economics 11,
+579–608.
+Appendix A. Proofs
+Proof of Theorem 2.1. Denote the inverse element of g ∈ G by g−1 and the identity
+element by id. Take a finite grid of points Um := {i/m : i = 0, 1, . . . , m} ∩ U. Then
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+32
+every u ∈ U is a limit of a sequence in Um. Let x �→ Tm(x) = supu∈Um
+�q
+j=1 xj(u)/q.
+Uniform continuity implies Tm(x) → T(x) and (Tm(gX))g∈G → (T(gX))g∈G almost
+surely and therefore also (Tm(gX))g∈G ⇝ (T(gX))g∈G. Independence and P(Xj(u) =
+0) = 0 ensure that �q
+j=1 Xj(u)/q has a continuous distribution at every u. Because X
+is separable, T(gX) = supu∈U∩Q
+�q
+j=1 Xj(u)/q, where Q are the rationals. Conclude
+that (T(gX))g∈G has a continuous distribution because for arbitrary tg ∈ R,
+P
+�
+g∈G
+{T(gX) = tg} ⩽ P
+�
+sup
+u∈U∩Q
+1
+q
+q
+�
+j=1
+Xj(u) = tid
+�
+⩽
+�
+u∈U∩Q
+P
+�
+1
+q
+q
+�
+j=1
+Xj(u) = tid
+�
+and the extreme right-hand side equals zero. Finite-dimensional distributional in-
+variance implies that (Tm(gX))g∈G and (Tm(g˜g−1X))g∈G have the same distribution
+for every ˜g ∈ G. Because (Tm(gX))g∈G ⇝ (T(gX))g∈G, it must also be true that
+(Tm(g˜g−1X))g∈G ⇝ (T(gX))g∈G and (Tm(g˜g−1X))g∈G ⇝ (T(g˜g−1X))g∈G. Conclude
+from continuity that (T(gX))g∈G and (T(g˜g−1X))g∈G have the same distribution for
+every ˜g ∈ G. These two random vectors are of the form
+(T(X), . . . , T(gX), . . . , T(˜gX), . . . ) ∼ (T(˜g−1X), . . . , T(g˜g−1X), . . . , T(id X), . . . ).
+Because T 1−α(X, G˜g−1) = T 1−α(X, G) = T 1−α(˜gX, G), this implies ϕα(X, G) ∼
+ϕα(˜gX, G). This is true for every ˜g ∈ G and therefore E �
+g∈G ϕα(gX, G) = Eϕα(X, G)|G|.
+The same argument as the finite-dimensional case now yields Eϕα(X, G) ⩽ α.
+□
+Proof of Theorem 2.2. For x, x′ ∈ ℓ∞(U)q and every g ∈ G, sub-additivity and mono-
+tonicity give
+T(gx) − T(gx′) ⩽ sup
+u∈U
+1
+q
+�
+q
+�
+j=1
+gj
+�
+xj(u) − x′
+j(u)
+�
+�
+⩽ sup
+u∈U
+1
+q
+q
+�
+j=1
+��xj(u) − x′
+j(u)
+��.
+The far right of the display is at most |x − x′|U/√q. Reverse the roles of x and x′ to
+conclude |T(gx) − T(gx′)|2 ⩽ |x − x′|2
+U/q for every g ∈ G and therefore
+���
+T(gx) − T(gx′)
+�
+g∈G
+�� ⩽
+�
+2q/q|x − x′|U.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+33
+Let |x − x′|U → 0 to deduce that x �→ (T(gx))g∈G a continuous map from ℓ∞(U)q
+to R|G| with respect to the sup-norm. Because Xn ⇝ X, the continuous mapping
+theorem implies (T(gXn))g∈G ⇝ (T(gX))g∈G.
+Order G so that the identity action g = (1, . . . , 1) is the first element. Define the set
+Bα =
+�
+(t1, t2, . . . , t|G|) : |{2 ⩽ i ⩽ |G| : ti < t1}| ⩾ ⌈(1 − α)|G|⌉
+�
+(A.1)
+to write P(T(X) > T α(X, G)) = P((T(gX))g∈G ∈ Bα). The boundary ∂Bα of Bα can
+be expressed as
+∂Bα =
+�
+j⩾1
+�
+(t1, t2, . . . , t|G|) : |t1 = ti| = j, |{2 ⩽ i ⩽ |G| : ti < t1}| = ⌈(1 − α)|G|⌉ − j
+�
+and therefore ∂Bα ⊂ �
+j⩾1{(t1, t2, . . . , t|G|) : |t1 = ti| = j}. By the portmanteau lemma,
+P((T(gXn))g∈G ∈ Bα) → P((T(gX))g∈G ∈ Bα) as long ∂Bα satisfies P((T(gX))g∈G ∈
+∂Bα) = 0. The goal is therefore to show that
+P
+�
+(T(gX))g∈G ∈
+�
+j⩾1
+{(t1, t2, . . . , t|G|) : |t1 = ti| = j}
+�
+= 0,
+i.e., (T(gX))g∈G has no ties with probability one.
+The main difficulty here is that each component of (T(gX))g∈G is dependent, so the
+preceding display does not follow from smoothness of the marginals of (T(gX))g∈G.
+Instead, for u, u′ ∈ U and g ̸= g′, write
+q
+�
+j=1
+gjXj(u) −
+q
+�
+j=1
+g′
+jXj(u′) = (g, −g′)T(X(u), X(u′))
+Because X is a Gaussian process, it follows that (X(u), X(u′)) is a jointly Gaussian
+vector and therefore (g, −g′)T(X(u), X(u′)) is a normally distributed random variable.
+If u = u′ or u ̸= u′ but X(u) = X(u′), then g ̸= g′ guarantees that �q
+j=1 gjXj(u) −
+�q
+j=1 g′
+jXj(u) = �q
+j=1(gj − g′
+j)Xj(u) has non-zero variance. Hence, suppose u ̸= u′
+and X(u) ̸= X(u′).
+Let c(u, u′) = EX(u)X(u′) be the covariance function and
+note that (g, −g′)T(X(u), X(u′)) is zero with positive probability if and only if
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+34
+(g, −g′)Tc(u, u′)(g, −g′) = 0. Because the elements of X are independent, the co-
+variance function satisfies
+(g, −g′)Tc(u, u′)(g, −g′) =
+n
+�
+j=1
+cjj(u, u) +
+n
+�
+j=1
+cjj(u′, u′) − 2
+n
+�
+j=1
+gjg′
+jcjj(u, u′).
+Apply the Cauchy-Schwarz inequality to the right-hand side to deduce
+0 = (g, −g′)Tc(u, u′)(g, −g′) ⩾
+n
+�
+j=1
+�
+cjj(u, u) − cjj(u′, u′)
+�2,
+which implies Var Xj(u) = Var Xj(u′) for 1 ⩽ j ⩽ q. It follows that
+0 =
+n
+�
+j=1
+�
+cjj(u, u) − gjg′
+jcjj(u, u′)
+�
+Apply the Cauchy-Schwarz inequality again to see that every covariance must be non-
+zero because cjj(u, u) > 0 and either cjj(u, u′) = cjj(u, u) or cjj(u, u′) = −cjj(u, u).
+This implies that either Xj(u) = Xj(u′) or Xj(u) = −Xj(u′).
+Because g ̸= g′,
+X(u) = X(u′) is impossible and at least one j must satisfy Xj(u) = −Xj(u′), which
+is ruled out by assumption. Conclude
+q
+�
+j=1
+gjXj(u) ̸=
+q
+�
+j=1
+g′
+jXj(u′)
+almost surely for all u, u′ ∈ U and all g ̸= g′. Because U is compact and X has
+continuous sample paths, this ensures
+T(gX) − T(g′X) = max
+u∈U
+q
+�
+j=1
+gjXj(u) − max
+u∈U
+q
+�
+j=1
+g′
+jXj(u) ̸= 0
+for almost every sample path unless g = g′.
+□
+Proof of Theorem 3.4. If H0 is true, then scale invariance implies ϕα(ˆδ − δ01q, G) =
+ϕα(Xn, G). Assumption 3.3 and Theorem 2.2 yield Eϕα(ˆδ − δ01q, G) → Eϕα(X, G).
+Eϕα(X, G) ⩽ α holds because X satisfies the conditions of Theorem 2.1.
+□
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+35
+Proof of Theorem 3.5. Suppose δ = δ0 + λ/√n so that Xn + λ1q
+δ⇝ X + λ1q. As
+in the proof of Theorem 3.4, joint continuity of the map x �→ (T(gx))g∈G implies
+(T(g(Xn+λ1q)))g∈G
+δ⇝ T(g(X +λ1q)))g∈G. With Bα as defined in (A.1), I only have to
+show that P(T(g(X+λ))g∈G ∈ ∂Bα) = 0 to conclude P(T(Xn+λ) > T α(Xn+λ, G)) →
+P(T(X + λ) > T α(X + λ, G)).
+The boundary has probability zero if (T(g(X + λ)))g∈G has no ties. For u, u′ ∈ U
+and g ̸= g′, write
+�
+q
+�
+j=1
+gjXj(u) −
+q
+�
+j=1
+g′
+jXj(u′)
+�
++ λ(u)
+q
+�
+j=1
+gj − λ(u′)
+q
+�
+j=1
+g′
+j,
+to see from the proof of Theorem 3.4 that the term in square brackets is nonzero
+almost surely for all u, u′ ∈ U and all g ̸= g′. Because the expression in square brackets
+is normally distributed with mean zero, it cannot take on any fixed nonzero value with
+positive probability. The remainder of the preceding display is constant. Conclude
+that the preceding display is nonzero almost surely for all u, u′ ∈ U and all g ̸= g′. As
+in the proof of Theorem 3.4, this implies T(g(X + λ)) ̸= T(g′(X + λ)) almost surely
+unless g ̸= g′.
+I will now develop a lower bound on P(T(X + λ1q) > T α(X + λ1q, G)). Because
+the original statistic cannot exceed the largest order statistic, monotonicity implies
+P
+�
+T(X + λ1q) > T 1−α(X + λ1q, G)
+�
+⩾ P
+�
+T(X + λ1q) > T (|G|−1)(X + λ1q, G)
+�
+= P
+�
+T(X + λ1q) = max
+g∈G T
+�
+g(X + λ1q)
+��
+and the right-hand side is at most
+P
+��
+T(X + λ1q) = max
+g∈G T
+�
+g(X + λ1q)
+��
+,
+q�
+j=1
+�
+inf
+u∈U(Xj(u) + λ(u)) ⩾ 0
+��
+.
+If infu∈U(Xj(u) + λ(u)) ⩾ 0 for 1 ⩽ j ⩽ q, then T(X + λ1q) = maxg∈G T(g(X + λ1q))
+because T cannot be increased by making large negative values positive through
+multiplication by −1. By independence and symmetry of the Gaussian processes,
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+36
+conclude that the preceding display equals
+q�
+j=1
+P
+�
+inf
+u∈U
+�
+Xj(u) + λ(u)
+�
+⩾ 0
+�
+=
+q�
+j=1
+P
+�
+sup
+u∈U
+�
+Xj(u) − λ(u)
+�
+⩽ 0
+�
+.
+Because sup(f − f ′) ⩾ sup f − sup f ′ for arbitrary f, f ′, this cannot exceed
+q�
+j=1
+P
+�
+sup
+u∈U
+Xj(u) ⩽ sup
+u∈U
+λ(u)
+�
+⩾
+q�
+j=1
+�
+1 − e−[supu λ(u)−E supu Xj(u)]2/2 supu EX2
+j (u)�
+by the Borell-TIS inequality as long as supu λ(u) > E supu Xj(u). In that case, the
+right-hand side of the preceding display is strictly positive, as required.
+Suppose δ = δ0 + λ1q. We have ˆδ − δ0 = Xn/√n + λ1q with Xn/√n ⇝ 0, and by
+arguments as in the proof of Theorem 3.3, the continuous mapping theorem yields
+(T(g(ˆδ − δ01q)))g∈G ⇝ (T(gλ))g∈G. Monotonicity implies
+Eϕ1−α(ˆδ − δ01q, G) ⩾ P
+�
+T(ˆδ − δ01q) > T (|G|−1)(ˆδ − δ01q, G)
+�
+As before, use a set of the form
+B =
+�
+(t1, t2, . . . , t|G|) : |{2 ⩽ i ⩽ |G| : ti < t1}| ⩾ |G| − 1
+�
+to write P(T(λ) > T (|G|−1)(λ, G)) = P((T(gλ))g∈G ∈ B) = 1{(T(gλ))g∈G ∈ B}. The
+boundary ∂B is contained in the set
+�
+j⩾1
+�
+(t1, t2, . . . , t|G|) : |t1 = ti| = j
+�
+.
+Because T(gλ) = supu∈U λ(u) �q
+j=q gj/q with λ ⩾ 0 and supu∈U λ(u) > 0, we have
+T(λ) > T(gλ) for all g ̸= id := (1, . . . , 1). Hence, there are no ties with the first
+element of (T(gλ))g∈G and 1{(T(gλ))g∈G ∈ ∂B} = 0. Conclude from the portmanteau
+lemma that T(ˆδ − δ01q) − T (|G|−1)(ˆδ − δ01q, G) ⇝ supu∈U λ(u) − supu∈U λ(u) �q
+j=q gj/q
+for some g ̸= id. Because this limit is strictly positive,
+Eϕ1−α(ˆδ − δ0, G) ⩾ P
+�
+T(ˆδ − δ0) > T (|G|−1)(ˆδ − θ0, G)
+�
+→ 1,
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+37
+as required.
+□
+Proof of Theorem 3.8. I can work with Xn,[h] = √n(ˆδ[h] − δ01min{q1,q0}) instead of
+ˆδ[h] − δ01min{q1,q0} because x �→ p(x, G) is scale invariant. In the following I make
+repeated use of the fact that the map x �→ (x[h])h∈H, the map x[h] �→ (T(gx[h]))g∈G,
+and their composition are continuous.
+Suppose q1 ⩽ q0.
+The case q1 > q0 requires only notational changes.
+The
+components of Xn,[h] are of the form √n(ˆδj,h(j) − δ0) = √n(ˆδj,h(j) − δ) under the
+null hypothesis. By Assumption 3.7, these components converge in distribution to
+X[h] := (X1,h(1), . . . , Xq1,h(q1)) jointly in h. The same arguments as in the proof of Theo-
+rem 3.4 imply that T(gXn,[h]) converges in distribution, jointly in h and g, to T(gX[h]).
+For the same reasons as in the proof of Theorem 3.4, for a given h, (T(gX[h]))g∈G\id
+has no ties T(X[h]) with probability 1, provided Assumption 3.7 holds.
+Consider
+|G|
+�
+h∈H
+p(Xn,[h], G) =
+�
+h∈H
+�
+g∈G
+1{T(gXn,[h]) ⩾ T(Xn,[h])}.
+This function jumps discretely if, for some h and g, T(gXn,[h]) = T(Xn,[h]). The
+continuous mapping theorem applies to this function if the probability of hitting
+these jumps is zero, i.e., P(T(gXn,[h]) = T(Xn,[h]) for some g ∈ G, h ∈ H) = 0. The
+union bound implies that this probability cannot exceed �
+h∈H
+�
+g∈G P(T(gXn,[h]) =
+T(Xn,[h])) = 0 because (T(gX[h]))g∈G has no ties almost surely. Conclude that the
+preceding display converges in distribution to �
+h∈H
+�
+g∈G 1{T(gX[h]) ⩾ T(X[h])} and
+therefore
+P
+�
+2
+H
+�
+h∈H
+p(Xn,[h], G) ⩽ α
+�
+→ P
+�
+2
+H
+�
+h∈H
+p(X[h], G) ⩽ α
+�
+if α is a continuity point of the right-hand side.
+Because |G| �
+h∈H p(X[h], G) is
+integer-valued, non-integer values of αH|G|/2 are continuity points.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+38
+For integer αH|G|/2, find an ε > 0 such that (α + ε)H|G|/2 is not an integer but
+α + ε ⩽ 1. Monotonicity and weak convergence imply
+lim sup
+n→∞ P
+�
+2
+H
+�
+h∈H
+p(Xn,[h], G) ⩽ α
+�
+⩽ P
+�
+2
+H
+�
+h∈H
+p(X[h], G) ⩽ α + ε
+�
+.
+By the R¨uschendorf (1982) inequality, the right-hand side cannot exceed α + ε. Now
+let ε ↘ 0 to obtain the desired result.
+□
+Proof of Theorem 3.9. As in the proof of Theorem 3.8, let Xn,[h] = √n(ˆδ[h]−δ01min{q1,q0})
+and q1 ⩽ q0 without loss of generality. Consider fixed alternatives δ = δ0 + λ. The
+components of ˆδ[h] − δ01q1 are of the form
+ˆδj,h(j) − δ0 = √n(ˆδj,k − δ)/√n + λ ⇝ λ
+by uniform continuity. Deduce that for every g and h, T(Xn,[h]/√n) − T(gXn,[h]/√n)
+converges in probability to T(λ[h]) − T(gλ[h]). For g ̸= id, this limit equals
+sup
+u∈U
+λ(u) − sup
+u∈U
+λ(u)
+q
+�
+j=q
+gj/q > 0.
+Zero is therefore a continuity point of the (degenerate) limiting distribution of
+T(Xn,[h]/√n) − T(gXn,[h]/√n), which implies
+P
+�
+T(gXn,[h]/√n) ⩾ T(Xn,[h]/√n)
+�
+→ 0
+and 1{T(gXn,[h]/√n) ⩾ T(Xn,[h]/√n)} → 0 for every g ̸= id and h. Conclude that
+1
+H
+�
+h∈H
+p(Xn,[h], G) =
+1
+|G|H
+�
+h∈H
+�
+g∈G
+1{T(gXn,[h]) ⩾ T(Xn,[h])} ⇝ 1
+|G|
+and therefore
+P
+�
+2
+H
+�
+h∈H
+p(ˆδ[h] − δ01q1, G) ⩽ α
+�
+→ 1{2 ⩽ α|G|}
+as long as α|G| ̸= 2 to guarantee that convergence occurs at a continuity point.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+39
+Now consider local alternatives u �→ δ(u) = δ0(u) + cλ(u)/√n with c constant. As
+in the proof of Theorem 3.4, continuity of the maps x �→ x[h] and x[h] �→ (T(gx[h]))g∈G
+implies (T(g(Xn,[h] + cλ1q1)))g∈G ⇝ (T(g(X[h] + cλ1q1)))g∈G jointly in h ∈ H. For a
+given h, (T(g(X[h] +cλ1q1)))g∈G again has no ties with probability 1. As before, deduce
+P
+�
+2
+H
+�
+h∈H
+p(Xn,[h] + cλ1q1, G) ⩽ α
+�
+→ P
+�
+2
+H
+�
+h∈H
+p(X[h] + cλ1q1, G) ⩽ α
+�
+if α is a continuity point of the right-hand side. Because |G| �
+h∈H p(X[h] + cλ1q1, G)
+is integer-valued, non-integer values of αH|G|/2 are continuity points. For integer
+αH|G|/2, find an ε > 0 such that (α − ε)H|G|/2 is not an integer but α − ε > 0.
+lim inf
+n→∞ P
+�
+2
+H
+�
+h∈H
+p(Xn,[h] + cλ1q1, G) ⩽ α
+�
+⩾ P
+�
+2
+H
+�
+h∈H
+p(X[h] + cλ1q1, G) ⩽ α − ε
+�
+by monotonicity. Let ε ↘ 0 to see that the limit inferior is bounded below by
+P
+�
+2
+H
+�
+h∈H
+p(X[h] + cλ1q1) < α
+�
+.
+The same bound holds trivially for non-integer αH|G|/2.
+For the analysis as c → ∞, consider
+2
+H
+�
+h∈H
+p(X[h] + cλ1q1) =
+2
+|G|H
+�
+h∈H
+�
+g∈G
+1
+�
+T(g(X[h] + cλ1q1))
+T(cλ1q1)
+⩾ T(X[h] + cλ1q1)
+T(cλ1q1)
+�
+.
+For g = id, the indicator function in the preceding display equals q.
+Consider
+g ̸= id.
+Because T(cλ1q1) = cT(λ1q1) > 0 and T(gX[h])/T(cλ1q1) → 0 almost
+surely for every g ∈ G as c → ∞, it follows from the subadditivity of suprema
+that T(g(X[h] + cλ1q1))/T(cλ1q1) → T(gλ1q1)/T(λ1q1) almost surely and therefore
+(T(X[h] + cλ1q1) − T(g(X[h] + cλ1q1)))/T(cλ1q1) → 1 − (T(gλ1q1)/T(λ1q1)) almost
+surely. That last limit is a strictly positive constant for every g ̸= id and there is one
+id for every h. Conclude from the continuous mapping theorem that the preceding
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+40
+display converges almost surely to 2/|G| as c → ∞. If α|G| ̸= 2, it follows that
+lim
+c→∞ P
+�
+2
+H
+�
+h∈H
+p(X[h] + cλ1q) < α
+�
+= 1{2 < α|G|},
+as required.
+□
+Proof of Proposition 3.11. If I is fixed, then the proof of Theorems 3.8 and 3.9 goes
+through without any changes. For random I, work conditional on I to see that
+Theorem 3.8 implies
+lim sup
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I
+�
+⩽ α
+almost surely. Apply expectations to conclude from the (reverse) Fatou lemma that
+lim sup
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α
+�
+⩽ E lim sup
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I
+�
+⩽ α
+as needed. Similarly, Fatou’s lemma implies
+lim inf
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α
+�
+⩾ E lim inf
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I
+�
+.
+Now apply the first part of Theorem 3.9 for a given I to get the result for fixed
+alternatives. For local alternatives, the proof of Theorem 3.9 implies
+lim inf
+n→∞ P
+�
+2
+|I|
+�
+h∈I
+p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I
+�
+⩾ P
+�
+2
+|I|
+�
+h∈I
+p(X[h] + cλ1q1) < α | I
+�
+→ 1
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+41
+almost surely as c → ∞, as required.
+□
+Proof of Proposition 3.10. Limits are as m → ∞ unless noted otherwise. Consider a
+process Xn possibly depending on n and recall that T(Xn) > T 1−α(Xn, Gm) if and only
+if ˆpm := p(Xn, Gm) ⩽ α. Let p := p(Xn, G) and notice that E(ˆp | Xn) = p. For almost
+every realization of Xn, ˆpm is an average of bounded iid random variables that satisfies
+P(|ˆpm − p| > ε | Xn) → 0 almost surely for every ε > 0. Conclude from dominated
+convergence that this convergence also holds unconditionally and therefore ˆpm ⇝ p.
+Because p can only vary at the points j/|G|, 1 ⩽ j ⩽ |G|, P(ˆpm ⩽ α) → P(p ⩽ α) as
+long as α ̸= j/|G|. If α equals j/|G| for some j, use 0 < ε < 1/|G| and monotonicity
+to see that P(ˆpm ⩽ α − ε) ⩽ P(ˆpm ⩽ α) ⩽ P(ˆpm ⩽ α + ε) must satisfy
+P(p ⩽ α − ε) ⩽ lim inf
+m→∞ P(ˆpm ⩽ α) ⩽ lim sup
+m→∞ P(ˆpm ⩽ α) ⩽ P(p ⩽ α + ε).
+Let ε ↘ 0 to see that the extreme right-hand side can be decreased to P(p ⩽ α).
+For Theorem 3.4, apply this result to obtain
+lim sup
+m→∞ P
+�
+T(Xn) > T 1−α(Xn, Gm)
+�
+⩽ P
+�
+p(Xn, G) ⩽ α
+�
+= Eϕα(Xn, G).
+Now apply limits as n → ∞.
+For Theorem 3.8, consider stochastic processes Xn,h indexed by h and n. The contin-
+uous mapping theorem implies 2 �
+h∈H p(Xn,h, Gm)/H
+P→ 2 �
+h∈H p(Xn,h, G)/H and
+therefore 2 �
+h∈H p(Xn,h, Gm)/H ⇝ 2 �
+h∈H p(Xn,h, G)/H. Using the same argument
+as before gives
+lim sup
+m→∞ P
+�
+2
+H
+�
+h∈H
+p(Xn,h, Gm) ⩽ α
+�
+⩽ P
+�
+2
+H
+�
+h∈H
+p(Xn,h, G) ⩽ α
+�
+For Theorem 3.5, if α > 1/2q, there is a ε > 0 such that α − ε > 1/2q. Then
+lim inf
+m→∞ P
+�
+T(Xn) > T 1−α(Xn, Gm)
+�
+⩾ P
+�
+p(Xn, G) ⩽ α − ε
+�
+= Eϕα−ε(Xn, G)
+and Theorem 3.5 applies directly to the extreme right-hand side.
+
+QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS
+42
+For Theorem 3.9, there is a ε > 0 such that α − ε > 1/2q−1. Then
+lim inf
+m→∞ P
+�
+2
+H
+�
+h∈H
+p(Xn,h, Gm) ⩽ α
+�
+⩾ P
+�
+2
+H
+�
+h∈H
+p(Xn,h, G) ⩽ α − ε
+�
+and Theorem 3.9 can be applied to the extreme right-hand side.
+□
+University of Michigan Ross School of Business, 701 Tappan Ave, Ann Arbor, MI
+48109, USA. Tel.: +1 (734) 764-2355. Fax: +1 (734) 764-2769. E-mail: hagem@umich.edu.
+
diff --git a/I9E3T4oBgHgl3EQfuwtu/content/tmp_files/load_file.txt b/I9E3T4oBgHgl3EQfuwtu/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,1195 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf,len=1194
+page_content='INFERENCE ON QUANTILE PROCESSES  WITH A FINITE NUMBER OF CLUSTERS  ANDREAS HAGEMANN  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I introduce a generic method for inference on entire quantile and  regression quantile processes in the presence of a finite number of large and arbitrarily  heterogeneous clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The method asymptotically controls size by generating  statistics that exhibit enough distributional symmetry such that randomization tests  can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The randomization test does not require ex-ante matching of clusters,  is free of user-chosen parameters, and performs well at conventional significance  levels with as few as five clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The method tests standard (non-sharp) hypotheses  and can even be asymptotically similar in empirically relevant situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The main  focus of the paper is inference on quantile treatment effects but the method applies  more broadly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Numerical and empirical examples are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Keywords: cluster-robust inference, quantiles, treatment effects, randomization  inference, difference in differences  JEL codes: C01, C21, C23  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Introduction  Economic data often contain large clusters such as countries, regions, villages,  or firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Units within these clusters can be expected to influence one another  or are influenced by the same political, environmental, sociological, or technical  shocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Several analytical and computer-intensive procedures such as the bootstrap  are available to account for the presence of data clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' These procedures generally  achieve consistency by letting the number of clusters go to infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Numerical  Date: January 13, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' University of Michigan Stephen M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Ross School of Business, 701 Tappan  Ave, Ann Arbor, MI 48109, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Tel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' : +1 (734) 764-2355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Fax: +1 (734) 764-2769.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' E-mail:  hagem@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' All errors are my own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='04687v1  [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='EM]  11 Jan 2023  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  2  evidence by Bertrand, Duflo, and Mullainathan (2004), MacKinnon and Webb (2017),  and others in the context of mean regression suggests that this type of asymptotic  approximation often causes substantial size distortions when the number of clusters is  small or the clusters are heterogenous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' True null hypotheses are rejected far too often  in both situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hagemann (2017) shows that this phenomenon is also present  in quantile regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In this paper, I develop a generic method for inference on  the entire quantile or regression quantile process in the presence of a finite number  of large and arbitrarily heterogeneous clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The method, which I refer to as  cluster-randomized Kolmogorov-Smirnov (CRK) test, asymptotically controls size by  generating Kolmogorov-Smirnov statistics that exhibit enough distributional symmetry  at the cluster level such that randomization tests (Fisher, 1935;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Canay, Romano, and  Shaikh, 2017) can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test is not limited to the pure quantile  regression setting and can be used in distributional difference-in-differences estimation  (Callaway and Li, 2019) and related situations where quantile treatment effects are  identified by between-cluster comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The CRK test is free of user-chosen  parameters, powerful against fixed and root-n local alternatives, and performs well  at conventional significance levels with as few as twelve clusters if parameters are  identified between clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If parameters are identified within clusters, then even five  clusters are sufficient for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Quantile regression (QR), introduced by Koenker and Bassett (1978), is an important  empirical tool because it can quantify the effect of a set of covariates on the entire  conditional outcome distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' An issue with QR in the presence of clustering is  that estimates normalized by their asymptotic covariance kernel have standard normal  marginal limit distributions but are no longer pivotal for any choice of weight matrix  (Hagemann, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Cluster-robust tests about the QR coefficient function therefore  have asymptotic distributions that cannot be tabulated for inference about ranges  of quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Even if only individual quantiles are of interest, consistent covariance  matrix estimation in large clusters is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' It requires knowledge of an explicit  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  3  ordering of the dependence structure within each cluster combined with a kernel and  bandwidth choice to give distant observations less weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because time has a natural  order, this weighting is easily done for time-dependent data but ordering data within  states or villages may be difficult or impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The common empirical strategy of  simply assuming that the clusters are small and numerous enough to satisfy a central  limit theorem circumvents these issues but can lead to substantial size distortions  with as few as 20 clusters (Hagemann, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This remains true if a cluster-robust  version of the bootstrap is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Distortions can be especially severe if clusters differ  greatly in their size and dependence structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I show that the CRK test is robust to each of these concerns: It performs well even  when the number of clusters is small, the dependence varies from cluster to cluster,  and the cluster sizes are heterogenous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The reason for this robustness is that the CRK  test does not rely on clustered covariance matrices to rescale the estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I instead  use randomization inference to generate random critical values that automatically  scale to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' There are no kernels, bandwidths, or spatio-temporal orderings of  the data to choose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The test achieves consistency with a finite number of large but  heterogeneous clusters under interpretable high-level conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Despite being based  on randomization inference, the CRK test can perform standard (non-sharp) inference  on entire quantile or regression quantile processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Randomization is performed with  a fixed set of estimates and does not require repeated estimation to obtain its critical  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The randomization method underlying the CRK test was first used in the cluster  context by Canay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2017) as a way to perform inference on a finite-dimensional  parameter with Student t and Wald statistics in least squares regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' They do not  consider inference on quantile functions or Kolmogorov-Smirnov statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Here, I  considerably extend the scope of their method under explicit regularity conditions to  allow for inference on the entire QR process and related objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The proofs below  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  4  are fundamentally different from those of Canay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' to account for the infinite-  dimensional setting and do not rely on the Skorokhod almost-sure representation  theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A practical issue with their method is that they require treated clusters to  be matched ex-ante with an equal number of control clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Each match corresponds  to a separate test and two researchers working with the same data can reach different  conclusions based on which matches they choose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If there is not an equal number of  treated and control clusters, then some clusters have to be combined or dropped in  an ad-hoc manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test sidesteps these issues completely and explicitly  merges all potential tests into a single, uniquely determined test decision using results  of R¨uschendorf (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Cluster-robust inference in linear regression models has a long history;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' recent surveys  include Cameron and Miller (2015) and MacKinnon, Nielsen, and Webb (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Chen,  Wei, and Parzen (2003), Wang and He (2007), Wang (2009), Parente and Santos  Silva (2013), and Hagemann (2017) provide bootstrap and analytical methods for  cluster-robust inference in QR models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Yoon and Galvao (2020) discuss the situation  where clusters arise from correlation of individual units over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' All of these papers  require the number of clusters to go to infinity for consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test differs  from these papers because it is based on randomization inference and is consistent  with a finite number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Several papers show that pointwise inference with a fixed number of clusters is  possible under a variety of conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Ibragimov and M¨uller (2010, 2016) use special  properties of the Student t statistic to perform inference on scale mixtures of normal  random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Bester, Conley, and Hansen (2011) use standard cluster-robust  covariance matrix estimators but adjust critical values under homogeneity assumptions  on the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Canay, Santos, and Shaikh (2020) show that certain cluster-robust  versions of the wild bootstrap can be valid under strong homogeneity assumptions  with a fixed number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hagemann (2019) adjusts permutation inference  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  5  for arbitrary heterogeneity at the cluster level but his bounds only apply to finite-  dimensional objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' All of these methods can be used for inference at a single quantile  but not for simultaneous inference across ranges of quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In contrast, the CRK  test provides uniformly valid inference on the entire quantile process even if clusters  are arbitrarily heterogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The remainder of the paper is organized as follows: Section 2 establishes new results  on randomization inference on Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Section 3 uses these results to  show consistency of the CRK test and gives specific examples where the test applies,  including quantile difference-in-differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Section 4 illustrates the finite sample  behavior of the test in Monte Carlo experiments and an empirical example using  Project STAR data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The appendix contains proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I use the following notation: 1{·} is the indicator function, cardinality of a set A is  |A|, the smallest integer larger than a is ⌈a⌉, and the largest integer smaller than a is  ⌊a⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The minimum of a and b is denoted by a ∧ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Limits are as n → ∞ unless noted  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Convergence in distribution under the parameter δ is denoted by  δ⇝ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Randomization inference on Gaussian processes  In this section I study the size of randomization tests when the data come from  heterogeneous Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I then analyze asymptotic size when a limiting  experiment is characterized by such processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The next section applies these generic  results to the quantile setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I first introduce some notation for randomization tests and Gaussian processes  that I will use throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Define G = {1, −1}q as the q-dimensional  product of {1, −1} and, for g = (g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , gq) ∈ G, define g �→ gx as the direct product  gx = (g1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , gqxq) of g and x ∈ Rq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let u �→ Xj(u), 1 ⩽ j ⩽ q, be independent  mean-zero Gaussian processes with u ∈ U, where U is a compact subset of (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A  stochastic process is Gaussian if and only (Xj(u1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xj(um)) is multivariate normal  for any finite collection of indices u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , um ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Symmetry about zero implies that  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  6  (Xj(u1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xj(um)) and −(Xj(u1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xj(um)) are identically distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because  this is true for every finite collection of indices u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , um ∈ U, Xj and −Xj have the  same (finite-dimensional) distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Independence and symmetry together imply  that u �→ X(u) = (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq)(u) and u �→ gX(u) have the same distribution for  every g ∈ G as long as X has mean zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The quantile and quantile-like processes  discussed in the next section have this property under the null hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Deviations  from the null cause non-zero means and therefore also asymmetry in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The goal of  this section is to develop a test of the null hypothesis of symmetry about zero,  H0 : X(u) ∼ gX(u),  all g ∈ G, all u ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1)  To test this hypothesis, I use the Kolmogorov-Smirnov-type statistic  T(X) = sup  u∈U  �  1  q  q  �  j=1  Xj(u)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2)  This statistic is large if symmetry is violated because the mean of the Xj is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I focus on one-sided tests to the right for simplicity but this is not restrictive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' To  test whether the mean is negative, simply use −X instead of X in the definition of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  These test statistics can be combined for two-sided tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I explain this in detail at  the end of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Randomization inference uses distributional invariance to generate null distribu-  tions and critical values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  In the present case, X is distributionally invariant to  all transformations g contained in G because X is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let T (1)(X, G) ⩽  T (2)(X, G) ⩽ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' ⩽ T (|G|)(X, G) be the |G| = 2q ordered values of T(gX) across g ∈ G  and let  T 1−α(X, G) := T (⌈(1−α)|G|⌉)(X, G)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3)  be the 1 − α quantile of these values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The randomization test function is then  ϕα(X, G) = 1{T(X) > T 1−α(X, G)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4)  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  7  If U is a finite set, distributional invariance under H0 immediately implies Eϕα(X, G) =  Eϕα(gX, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By an argument due to Hoeffding (1952), the test function must satisfy  |G|α ⩾ �  g∈G ϕα(gX, G) and, after taking expectations on both sides, equality of the  distributions yields |G|α ⩾ E �  g∈G ϕα(gX, G) = �  g∈G Eϕα(gX, G) = |G|Eϕα(X, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This implies Eϕα(X, G) ⩽ α, which makes T 1−α(X, G) an α-level critical value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  If U is a not finite, this argument does not immediately go through because (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2)  is a statement about possibly uncountably many u ∈ U but I have only established  equivalence of the finite-dimensional distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, as the following theorem  shows, the conclusion that the test controls size holds nonetheless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The proof of  the theorem extends Hoeffding’s proof to stochastic processes with smooth sample  paths by showing that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) implies equality of the distributions of T(gX)g∈G and  T(g˜g−1X)g∈G for every ˜g ∈ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (Here g−1 = −g is the inverse of g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=') I prove that this is  enough for Hoeffding’s argument to go through as long as at least one of the processes  has positive variance at every u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq be independent mean-zero Gaussian processes with  continuous sample paths indexed by the compact set U ⊂ (0, 1) and let u �→ X(u) :=  (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq)(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If there is a j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , q} such that P(Xj(u) = 0) = 0 for all U,  then Eϕα(X, G) ⩽ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  If X is only an approximation in the sense that Xn ⇝ X as a process in ℓ∞(U)q, the  space of bounded maps from U to Rq, then the conclusions of the theorem still hold  as long as the non-degeneracy conditions are strengthened.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Here and in the following  I tacitly assume that a process is indexed by a compact U ⊂ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If Xn ⇝ X = (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq), where the X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq are independent  mean-zero Gaussian processes with continuous sample paths that satisfy P(Xj(u) =  0) = 0 and P(Xj(u) = −Xj(u′)) = 0 for all u, u′ ∈ U and 1 ⩽ j ⩽ q, then  Eϕα(Xn, G) → Eϕα(X, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  8  Remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (i) For the non-degeneracy assumption P(Xj(u) = −Xj(u′)) = 0 to fail,  a Gaussian process with uniformly continuous sample paths has to traverse, with  certainty, from Xj(u) to Xj(u′) = −Xj(u) while maintaining a positive variance along  the entire path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The process would have to have identical variances at time u and u′  but be perfectly negatively correlated at those times, which is impossible for Brownian  bridges and related processes that typically arise in a quantile context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Still, such  Gaussian processes exist and have to be ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (ii) The main difficulty of the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 is that the critical value  T 1−α(Xn, G) does not settle down in the limit and is highly dependent on T(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  assumptions of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 rule out degeneracies in the limit process that could  lead to ties in the order statistics of {T(gX) : g ∈ G}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This would put probability  mass on the boundary of the set {T(X) > T 1−α(X, G)} and prevent application of  the portmanteau lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Canay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2017) use a delicate construction based on  Skorokhod’s representation theorem to account for the randomness in the limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' While  these results could be extended from vectors to processes, I instead give a direct proof  that I can also use to analyze the behavior of the test under both local and global  alternatives when I discuss quantile processes in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference on quantile processes with a finite number of clusters  This section gives high level conditions under which asymptotically valid inference  on quantile processes and related objects can be performed even if the underlying  data come from a fixed number of heterogeneous clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference when parameters are identified within clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose data  from q large clusters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', counties, regions, schools, firms, or stretches of time) are  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Throughout the paper, the number of clusters q remains fixed and does not  grow with the number of observations n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Observations are independent across clusters  but dependent within clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Data from each cluster 1 ⩽ j ⩽ q separately identify a  quantile or quantile-like scalar function δ : U → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The δ can be estimated by ˆδj using  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  9  data from only cluster j such that a total of q separate estimates (ˆδ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , ˆδq) =: ˆδ of  u �→ δ(u) are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The goal is to use randomization inference on a centered and  scaled version of ˆδ to develop tests of the null hypothesis  H0 : δ(u) = δ0(u),  all u ∈ U,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1)  for some known function δ0 : U → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The following two examples describe simple but  empirically relevant situations that fit this framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (Regression quantiles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose an outcome Yi,j of individual i in  cluster j can be represented as Yi,j = Xi,jδ(Ui,j) + Z′  i,jβj(Ui,j), where u �→ Xi,jδ(u) +  Z′  i,jβj(u) is strictly increasing in u and Ui,j is standard uniform conditional on covariates  (Xi,j, Zi,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Here Xi,j is the scalar covariate of interest and the Zi,j are additional  controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Monotonicity implies that the u-th conditional quantile of Yi,j is Xi,jδ(u) +  Z′  i,jβj(u) and linear QR as in Koenker and Bassett (1978) can provide estimates (ˆδj, ˆβj)  of (δ, βj) for each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Testing (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) with δ0 ≡ 0 tests whether Yi,j and Xi,j are  associated at any quantile after controlling for Zi,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Several related models fit the framework of this example: (i) The βj can be constant  across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This does not impact the null hypothesis or the computation of the  ˆδj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (ii) The δ can vary by cluster in the QR model Yi,j = Xi,jδj(Ui,j) + Z′  i,jβ(Ui,j)  under the alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This has no impact on the computation of the δj and the null  hypothesis simply becomes H0 : δ1 = · · · = δq = δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Identical δj are required only  under the null hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (iii) If βj ≡ 0 and Xi,j ≡ 1, then u �→ ˆδ(u) reduces to the  u-th unconditional empirical quantile of Yi,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The null (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) can then be used to test  whether δ has a specific functional form, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', a standard normal quantile function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 (Quantile treatment effects).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Consider predetermined pairs {(j, j +  q) : 1 ⩽ j ⩽ q} of 2q groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose the first q groups received treatment, indicated by  Dj = 1{j ⩽ q}, and the remaining groups did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Groups here could be manufacturing  plants or villages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Treatment could be management consulting or introduction of a new  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  10  technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Denote treatment and control potential outcomes by Yj(1) ∼ FY (1) and  Yj(0) ∼ FY (0), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The observed outcome is Yj = DjYj(1) + (1 − Dj)Yj(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For each group j, the experimenter observes identically distributed but potentially  highly dependent copies Yi,j of Yj representing workers i within group j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' View each  pair (j, j + q) for 1 ⩽ j ⩽ q as a cluster and define the quantile treatment effect (QTE)  as  u �→ δ(u) = F −1  Y (1)(u) − F −1  Y (0)(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This QTE can be estimated as difference of the empirical quantiles  u �→ ˆδj(u) = ˆF −1  Yj (u) − ˆF −1  Yj+q(u)  or, alternatively, as the coefficient on Dj in a QR of Yi,j on a constant and Dj using  data only from cluster j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The situation where δ varies with j is again included in  the analysis as long as the null hypotheses is δ1 = · · · = δq = δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Estimation remains  unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I discuss the more complex scenario where the counterfactual FY (0) has  to be identified through difference-in-differences methods in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6 ahead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  The ˆδ is neither limited to the estimators discussed in the preceding two examples  nor does it need to have a special functional form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, I assume that it can be  approximated by a Gaussian process as in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let 1q be a q-vector of ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The random function ˆδ: U → Rq satisfies  Xn := {√n(ˆδ − δ1q)(u) : u ∈ U}  δ⇝ X = (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2)  where the X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq are independent mean-zero Gaussian processes with continuous  sample paths, P(Xj(u) = 0) = 0 and P(Xj(u) = −Xj(u′)) = 0 for all u, u′ ∈ U and  1 ⩽ j ⩽ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Examples of Xn that can satisfy this assumption include unconditional quantile  functions, coefficient functions in quantile regressions, quantile treatment effects, and  other quantile-like objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' El Machkouri, Voln´y, and Wu (2013) present invariance  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  11  principles and moment bounds that can be used to establish the convergence condition  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2) under explicit weak dependence conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I now connect the results from Section 2 about heterogeneous Gaussian processes to  tests about δ under Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The key property is that if H0 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) does not  hold, then √n(ˆδ−δ01q) = Xn+√n(δ−δ0)1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The Xn converges to a symmetric process  but √n(δ − δ0)(u) grows without bound for some u, which makes the distribution of  √n(ˆδ − δ01q) highly asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Testing for symmetry using randomization inference  is therefore informative about the hypothesis that δ = δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I refer to a test that uses  ˆδ − δ01q in place of X in test function (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4) as the cluster-randomized Kolmorogov  (CRK) test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' From a practical perspective, the function δ0 is almost always δ0 ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This tests the null of no effect at any quantile but more general hypotheses can be  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The test function x �→ ϕα(x, G) is invariant to scaling of x by positive constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If  H0 : δ = δ0 is true, then the CRK test satisfies  T(ˆδ − δ01q) > T 1−α(ˆδ − δ01q, G)  if and only if T(Xn) > T 1−α(Xn, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' That the CRK test is an asymptotic α-level test  is then an immediate consequence of Theorems 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 (Size).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H0 : δ = δ0 is true, then  limn→∞ Eϕα(ˆδ − δ01q, G) ⩽ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (i) The canonical limit of quantile and regression quantile processes such as  those in Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 is a scaled version of a q-dimensional Brownian bridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  That process easily satisfies the non-standard condition P(Xj(u) = −Xj(u′)) = 0  imposed by Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (ii) The inequality in the theorem becomes an equality if (1 − α)2q is an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In  that case, the test in the limit experiment is “similar,” i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', it has rejection probability  exactly equal to α for all Gaussian processes that satisfy Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  12  test can therefore be asymptotically similar in some situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If desired, the test  decision can be randomized to make the CRK test similar in the limit for all choices  of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  To analyze the power of the CRK test, I consider fixed alternatives δ(u) = δ0(u)+λ(u)  with a positive function u �→ λ(u), and local alternatives δ(u) = δ0(u) + λ(u)/√n  converging to the maintained null hypothesis H0 : δ = δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In the local case, δ0 is fixed  but δ now depends on n and the convergence (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2) is under the sequence of functions  δ = δ0 + λ/√n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As the following results show, the CRK test has power against both  types of alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (Global and local power).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3 holds and α ⩾  1/2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H1 : δ = δ0 + λ is true with λ: U → [0, ∞) continuous and supu∈U λ(u) > 0,  then limn→∞ Eϕα(ˆδ − δ01q, G) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H1 : δ = δ0 + λ/√n is true with supu∈U λ(u) >  E supu∈U Xj(u), 1 ⩽ j ⩽ q, then  lim  n→∞ Eϕα(ˆδ − δ01q, G) ⩾  q�  j=1  �  1 − e−[sup λ(u)−E sup Xj(u)]2/2 sup EX2  j (u)�  > 0,  where the suprema in the exponent are over u ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (i) The lower bound used for the local power result comes from the Borell-  Tsirelson-Ibragimov-Sudakov (Borell-TIS) inequality (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', Adler and Taylor, 2007,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' 50).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For large q, the bound is relatively crude but for small q, the only crude part  is the assumption that δ is moderately large when compared to X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This is reflected  in the condition that supu∈U λ(u) > E supu∈U Xj(u) instead of supu∈U λ(u) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  local power bound can be made arbitrarily close to 1 by choosing supu∈U λ(u) large  enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (ii) If (1 − α)|G| > |G| − 1, the power of the test is identically zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In that case  T 1−α(X, G) = maxg∈G T(gX) and T(X) > T 1−α(X, G) becomes impossible because  T(X) is contained in {T(gX) : g ∈ G}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I therefore I focus on the case (1 − α)|G| ⩽  |G| − 1, which is equivalent to α ⩾ 1/2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  13  (iii) The test also has power against alternatives where λ varies with the cluster  index j and at least some of the λj are large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, a precise statement without  additional conditions on the relative sizes of the λj is involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I do not pursue this  here to prevent notational clutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference when parameters are identified across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In applications,  the treatment effect is often not identified from within a cluster but by comparisons  across two clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This is the case, for example, if treatment is assigned at random  at the cluster level or if identification comes from comparing changes in one cluster  to changes in another cluster in a quasi-experimental context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In this situation, each  individual pairing of a treated cluster j with a control cluster k is generally informative  about the treatment effect of interest δ and each (j, k) pair gives rise to an estimate  ˆδj,k of δ that could be used in a CRK-type test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The following example illustrates this  for difference-in-differences estimation of quantile treatment effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6 (Quantile difference in differences).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let ∆Yt(0) = Yt(0) − Yt−1(0)  be time differences of untreated outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Periods t ∈ {0, −1} are pre-intervention  periods and t = 1 is the post-intervention period;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Y1(1) is a treated potential outcome  and Yt are observed outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Denote by FY |D=d the distribution of a variable Y  conditional on the treatment indicator taking on the value d ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Callaway and  Li (2019) show that the distribution FY1(0)|D=1(y) of the untreated potential outcome  of a treated observation at time t = 1 can be identified as  P  �  F −1  ∆Y1|D=0  �  F∆Y0|D=1(∆Y0)  �  + F −1  Y0|D=0  �  FY−1|D=1(Y−1)  �  ⩽ y | D = 1  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3)  as long as a distributional version of the standard parallel trends assumption and  some additional stability and smoothness conditions hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This identifies the quantile  treatment on the treated (QTT) effect  u �→ δ(u) = F −1  Y1(1)|D=1(u) − F −1  Y1(0)|D=1(u),  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  14  where F −1  Y1(1)|D=1(u) can be estimated by the sample quantile ˆF −1  Y1|D=1(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' To estimate  the counterfactual quantile, Callaway and Li replace P and every F in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3) with  sample equivalents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This yields the estimated QTT  u �→ ˆF −1  Y1|D=1(u) − ˆF −1  Y1(0)|D=1(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4)  Callaway and Li show that √n( ˆF −1  Y1|D=1 − ˆF −1  Y1(0)|D=1 − δ) converges to a well-behaved  Gaussian process under mild regularity conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Suppose that data come from q1 states that received treatment and q0 states that  did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' View a single state over time as a cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then two clusters are enough to  compute (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4): ˆF −1  Y1|D=1 can be computed from a treated cluster j and ˆF −1  Y1(0)|D=1 can  be computed from j and an untreated cluster k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Denote by ˆδj,k the QTT estimated in  this fashion using only data from clusters j and k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Each (j, k) pair provides a valid  estimate of δ and each ˆδj,k could potentially be used in a CRK-type test of the null  hypothesis H0 : δ = δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  I again assume that centered and scaled ˆδj,k converge in distribution to non-  degenerate Gaussian processes with smooth sample paths as in Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I only adjust this condition for the fact that estimates are constructed from pairwise  combination of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let q1 be the number of treated clusters and let q0 be the  number of control clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The process {√n(ˆδj,k − δ)(u) : u ∈ U} converges, jointly in j and  k, in distribution to mean-zero Gaussian processes Xj,k with continuous sample paths  that satisfy P(Xj,k(u) = 0) = 0 and P(Xj,k(u) = −Xj,k(u′)) = 0 for all u, u′ ∈ U,  1 ⩽ j ⩽ q1, and 1 ⩽ k ⩽ q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If both j ̸= j′ and k ̸= k′, then Xj,k and Xj′,k′ are  independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  A na¨ıve test of H0 : δ ≡ δ0 would now take Xn,j,k := √n(ˆδj,k − δ0) and generate  randomization distributions from {Xn,j,k : 1 ⩽ j ⩽ q1, 1 ⩽ k ⩽ q0} via sign changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  However, Xn,j,k and Xn,j,k′ are dependent for any choice of j, k, k′ because j is used  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  15  twice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This remains true even in large samples and if the data from all q1 + q0  groups are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Dependence causes problems because (Xn,j,k, Xn,j,k′) and  (Xn,j,k, −Xn,j,k′) generally do not have the same joint distribution even when n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Invariance under transformations with g therefore fails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This issue can be avoided if  one works with a subset of {Xn,j,k : 1 ⩽ j ⩽ q1, 1 ⩽ k ⩽ q0} that uses each j and k  only once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' While this solves the dependence issue, it introduces another problem: each  of the q1 treatment groups now has to be paired with exactly one of the q0 control  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Two researchers working with the same data and methodology could therefore  arrive at different conclusions because they chose different pairings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' To address this  problem, I now develop a method that maintains invariance under sign changes but  avoids any decisions on the part of the researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I first introduce some notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If q1 ⩽ q0, there are q0 × (q0 − 1)×· · · × (q0 −q1 + 1)  ways of choosing q1 ordered elements out of (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , q0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Identify each such choice with  an h and denote the collection of all h by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The ordering within H will not affect  the test decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For each h ∈ H, denote by  ˆδ[h] = (ˆδ1,h(1), ˆδ2,h(2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , ˆδq1,h(q1)),  q1 ⩽ q0,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5)  the vector that matches the subset of control groups associated with the label h =  (h(1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , h(q1)) to the (unpermuted) treated groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If there are more treated than  control groups such that q1 > q0, permute treated groups instead and take h as  enumerating ways of choosing q0 elements out of (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , q1) to define  ˆδ[h] = (ˆδh(1),1, ˆδh(2),2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , ˆδh(q0),q0),  q1 > q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6)  By construction, the entries of ˆδ[h] are independent of one another but ˆδ[h] and ˆδ[h′] for  h, h′ ∈ H are potentially highly dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  16  To address the issue that there are multiple ways of combining clusters, I use an  adjustment based on the randomization p-value  p(X, G) = inf{p ∈ (0, 1) : T(X) > T p(X, G)} = 1  |G|  �  g∈G  1{T(gX) ⩾ T(X)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7)  Testing with this p-value is equivalent to a test with a critical value because T(X) >  T 1−α(X, G) if and only if p(X, G) ⩽ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The multiple comparisons adjustment is based  on an inequality of R¨uschendorf (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' It states that arbitrary, possibly dependent  variables Uh indexed by h ∈ H with the property that P(Uh ⩽ u) ⩽ u for every  u ∈ [0, 1] satisfy  P  �  2  |H|  �  h∈H  Uh ⩽ u  �  ⩽ u,  every u ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8)  This specific form of the inequality is given in Vovk (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Here the indexing set H is  arbitrary and does not need to be related to permutations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The only condition is that  H = |H| ⩾ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The randomization p-value p(ˆδ[h] − δ01q1∧q0, G) for testing whether the  treatment effect of interest equals δ0 can be expected to behave like the Uh in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8) in  a large enough sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Combining p-values of the CRK test to reject the null if  2  H  �  h∈H  p(ˆδ[h] − δ01q1∧q0, G)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9)  does not exceed α should then asymptotically control size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The following theorem  confirms that this is indeed true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 (Size with combined p-values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If  H0 : δ = δ0, then  lim sup  n→∞ P  �  2  H  �  h∈H  p(ˆδ[h] − δ01q1∧q0, G) ⩽ α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (i) The theorem can be improved slightly if α|G|H/2 is not an inte-  ger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In that case, the limit superior in the theorem is a proper limit that equals  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  17  P((2/H) �  h∈H p(X[h], G) ⩽ α), where X[h] is the weak limit of √n(ˆδ[h] − δ01q1∧q0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This is because the sum in the preceding display can vary discontinuously at certain  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The limit inferior is P((2/H) �  h∈H p(X[h], G) < α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (ii) Results of DiCiccio, DiCiccio, and Romano (2020) suggest that other ways of  combining p-values such as the median p-value instead of an average p-value are likely  to be applicable here as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, the proof of the theorem given here relies  crucially on the properties of the R¨uschendorf inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  The price paid for not matching treated and control clusters before the analysis is  lower relative power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' When p-values are averaged, R¨uschendorf’s inequality essentially  decreases α to α/2 to control size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Meng (1993) shows that the constant 2 cannot  be improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Still, as I establish below, the test has power against global and local  alternatives if α > 1/2q1∧q0−1, which is slightly stronger than what is needed in  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Compared to Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, I also do not state an explicit bound for the  local power analysis because applying the Borel-TIS inequality to the averaged p-values  directly yields only relatively crude results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I instead show that if the alternatives  λ/√n converging to the null hypothesis are scaled up by a constant c, the test can  detect these alternatives in the limit experiment with arbitrary accuracy if c is large  enough, that is, if first n → ∞ and then c → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 (Global and local power with combined p-values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7 holds and α > 1/2q1∧q0−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H1 : δ = δ0 + λ with λ: U → [0, ∞)  continuous and supu∈U(u) > 0, then limn→∞ P((2/H) �  h∈H p(ˆδ[h] − δ01q1∧q0, G) ⩽  α) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H1 : δ = δ0 + cλ/√n, then  lim  c→∞ lim inf  n→∞ P  �  2  H  �  h∈H  p(ˆδ[h] − δ01q1∧q0, G) ⩽ α  �  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I now turn to some practical aspects of the CRK test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I  discuss (i) what to do if G is large, (ii) what to do if H is large, and (iii) how to  implement the test with a step-by-step guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' First, G can be prohibitively large if the  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  18  number of clusters is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If computing the entire randomization distribution is too  costly, then G can be approximated by a random sample Gm consisting of m draws  from G with replacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This is often referred to as “stochastic approximation.” The  theorems presented in Sections 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 continue to hold if Gm is used in place of G  as long as a limit superior or inferior as m → ∞ is applied before n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The order of  limits is not restrictive because, in a given sample of size n, the number of draws can m  always be made as large as computationally feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Under stochastic approximation,  the statement in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 becomes limn→∞ lim supm→∞ Eϕα(ˆδ − δ01q, Gm) ⩽ α,  whereas statements about power use a limit inferior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Limit superior and inferior are  needed here because of potential discontinuities but can be replaced by regular limits  for most values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8, and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 hold without additional conditions  but the conditions of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 have to be strengthened marginally to avoid a  discontinuity at α = 1/2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose Gm consists of m iid draws from G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If every instance of  G is replaced by Gm, then  (i) Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 holds if limn→∞ is replaced by limn→∞ lim supm→∞,  (ii) Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 holds if every limn→∞ is replaced by limn→∞ lim infm→∞ and α >  1/2q,  (iii) Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 holds if lim supn→∞ is replaced by lim supn→∞ lim supm→∞,  (iv) Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 holds if limn→∞ is replaced by limn→∞ lim infm→∞ and lim infn→∞  is replaced by lim infn→∞ lim infm→∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  If α ̸∈ {j/|G| : 1 ⩽ j ⩽ |G|}, then lim infm→∞ and lim supm→∞ can be replaced by  limm→∞ in (i)-(iv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Second, the number of elements of H can similarly be large if the number of clusters  is large or if there is a large discrepancy between the number of treated and the  number of control clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In that case one can again work with a random subset I  of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The crucial difference to the preceding result is that both Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  19  continue to hold even if I consists of only a finite number of random draws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In fact,  the result goes through for any I as long as I is independent of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let I with |I| ⩾ 2 be a fixed or random subset of H independent  of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 continue to hold if H is replaced by I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Finally, the following two algorithms outline and summarize how to apply the CRK  test in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8, the procedures provide an asymptotically  α-level test in the presence of a finite number of large clusters that are arbitrarily  heterogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' They are free of nuisance parameters and do not require any decisions  on the part of the researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9, the tests are able to detect  fixed and 1/√n-local alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The first algorithm describes the CRK test when  the parameters are identified within clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The second algorithm describes the  between-cluster case, which is needed for distributional difference in differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  tests can be two-sided or one-sided in either direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 (CRK test for parameters identified within clusters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (1) Compute for each j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , q and using only data from cluster j an estimate ˆδj  of a parameter of interest δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (See Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=') Define ˆδ = (ˆδ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , ˆδq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (2) Compute G, the set of all vectors of length q with entries 1 or −1, or replace  G with a large random sample Gm from G in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3) Reject the null hypothesis H0 : δ(u) = δ0(u) for all u (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', δ0 ≡ 0 tests for no  effect of treatment) against  (a) δ(u) > δ0(u) for some u if T(ˆδ − δ01q) > T 1−α(ˆδ − δ01q, G) for a test with  asymptotic level α,  (b) δ(u) < δ0(u) for some u if T(ˆδ − δ01q) < T α(ˆδ − δ01q, G) for a test with  asymptotic level α,  (c) δ(u) ̸= δ0(u) for some u if (a) or (b) are true for a test with asymptotic  level 2α,  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  20  where T is defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2) and T 1−α(·, G) is the ⌈(1 − α)|G|⌉-th largest value  of the randomization distribution of T, defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='13 (CRK test for parameters identified between clusters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (1) Compute H, as defined above (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5), or replace H with a large subset I in the  following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (2) Compute G, the set of all vectors of length q with entries 1 or −1, or replace  G with a large random sample Gm from G in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (3) For each h, compute ˆδ[h] from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5) if q1 ⩽ q0 or from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6) if q1 > q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (See  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=') Use (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9) to compute  2  |H|  �  h∈H  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10)  (4) Reject the null hypothesis H0 : δ(u) = δ0(u) for all u (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', δ0 ≡ 0 tests for no  effect of treatment) against  (a) δ(u) > δ0(u) for some u if (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10) is true for a test with asymptotic level α,  (b) δ(u) < δ0(u) for some u if (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10) is true when ˆδ[h] −δ01min{q1,q0} is replaced  by −(ˆδ[h] − δ01min{q1,q0}) for a test with asymptotic level α,  (c) δ(u) ̸= δ0(u) for some u if (a) or (b) are true for a test with asymptotic  level 2α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  In some contexts, Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 can be used even if the parameter of interest is  identified by comparisons between treated and untreated clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For this to work,  the researcher has to merge each treated cluster with an untreated cluster into a single  cluster to recover within-cluster identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If the number of treated clusters and  control clusters is equal, then every treated cluster can be matched with a control  cluster according to some rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If the number of clusters is not equal, then two or  more clusters can be merged to force an equal number of treated and control clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The merged clusters can then be reinterpreted as clusters and Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 can be  applied to these new clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' While this comes with a large number of decisions, it is  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  21  a valid method for inference if these decisions are made before the data are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For example, when estimating quantile treatment effects, a pre-analysis plan can be  put in place that prescribes how clusters that received treatment will be merged with  clusters that did not receive treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This reduces the problem to the one described  in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The next section investigates the finite sample performance of Algorithms 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 and  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='13 in several sitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Numerical results  This section presents several Monte Carlo experiments to investigate the small-  sample properties of the CRK test in comparison to other methods of inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I  discuss significance tests on quantile regression coefficient functions (Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1),  inference in experiments when parameters are identified between clusters (Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2),  and estimation of QTEs in Project STAR (Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I test one-sided hypotheses  to the right but the results apply more broadly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (Regression quantiles, cont.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In this example, I adapt an experi-  ment of Hagemann (2017) and use the data generating process (DGP)  Yi,j,k = Ui,j,k + Ui,j,kZi,j,k,  where Ui,j,k = √ϱVj,k + √1 − ϱWi,j,k with ϱ ∈ [0, 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Vj,k and Wi,j,k are standard  normal, independent of one another, and independent across indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This ensures  that the Ui,j,k are standard normal and, for a given j, k, any pair Ui,j,k and Ui′,j,k  has correlation ϱ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The Zi,j,k satisfy Zi,j,k = X2  i,j,k/3 with Xi,j,k standard normal  independent of Ui,j,k to ensure that the Ui,j,kZi,j,k have mean zero and variance one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Both Xi,j,k and Ui,j,k are independent across j and k, and Xi,j,k is also independent  across i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I discard information on k after data generation and drop the k subscripts in  the following because they are not assumed to be known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This induces a dependence  structure where each cluster j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , q consists of several (unknown) neighborhoods  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  22  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , K where observations are dependent if they come from the same k but are  independent otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If K → ∞ and the size of the neighborhoods is fixed or grows  slowly with K, then this dependence structure is compatible with Assumptions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3 and  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7 because it generates the weak dependence needed for central limit theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In the  experiments ahead, I set K to either 10 or 20 and draw the size of each neighborhood  from the uniform distribution on {5, 6, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , 15}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The DGP in the preceding display  corresponds to the QR model  Q(u | Xi,j, Zi,j) = β0(u) + β1(u)Xi,j + β2(u)Zi,j  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1)  with β1(u) ≡ 0 and β0(u) = Φ−1(u) = β2(u), where Φ is the standard normal  distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For the CRK test, I estimated (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) separately for each cluster,  obtained q estimates of β1 and applied Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 with 1,000 new draws from G  for each Monte Carlo replication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I compare the CRK test to inference with the wild gradient bootstrap of Hagemann  (2017), a version of the bootstrap that perturbs the gradient of the QR objective  function in a computationally efficient way while accounting for cluster dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' It  requires the number of clusters q → ∞ for consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The wild gradient bootstrap  is the default option for cluster-robust inference in the quantreg package in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I use  the package default settings with Mammen bootstrap weights and 200 bootstrap sim-  ulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I do uniform inference with sup-Wald statistics as outlined in Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4  of Hagemann (2017) with critical values and standard errors computed from the wild  gradient bootstrap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hagemann (2017) documents excellent performance of the wild  gradient bootstrap even with challenging DGPs as long as there are more than 20  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, Hagemann (2017) notes that size distortions can occur when fewer  than 20 clusters are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I focus on this situation in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Figure 1 shows the rejection frequencies of a true null hypothesis H0 : β1(u) = 0  for all u as a function of the number of clusters q ∈ {5, 6, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , 20} for the wild  gradient bootstrap (left) and the CRK test (right) at the 5% level (short-dashed  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  23  5  10  15  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='25  Bootstrap (size, u �→ β1(u))  Number of clusters  Rejection frequency  5  10  15  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='25  CRK test (size, u �→ β1(u))  Number of clusters  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 20, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1  5% level  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Rejection frequencies in Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 of a true null H0 : β1(u) = 0 for all  u as a function of the number of clusters for the bootstrap (left) and the CRK test  (right) with (i) K = 10 neighborhoods per cluster with intra-neighborhood correlation  ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines), (ii) K = 20 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed), and (iii) K = 10 with  ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Short-dashed line equals nominal level .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The figure shows rejection frequencies in 5,000 Monte Carlo replications for  each horizontal coordinate with (i) K = 10 neighborhoods per cluster with intra-  neighborhood correlation ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines), (ii) K = 20 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed),  and (iii) K = 10 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Both methods were faced with the same data  and I estimated β1 at u = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 for both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As can be seen, the wild  gradient bootstrap over-rejected mildly with 20 clusters but over-rejected substantially  for smaller numbers of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' It exceeded a 10% rejection rate if only 12 clusters  were available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' With 5 clusters, the wild gradient bootstrap falsely discovered an effect  in up to 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9% of all cases (K = 10, ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In contrast, the CRK test rejected at or  slightly below nominal level for all q and all configurations of K and ϱ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I also experimented with a large number of alternative DGPs under the null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I  considered (not shown) larger neighborhoods, different values of ϱ, different spatial  dependence structures such as (spatial) autoregressive models, and different distribu-  tions for Xi,j,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, I found that these changes had little qualitative impact on  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  24  the results described in the preceding paragraph or in Hagemann (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The wild  gradient bootstrap generally performed very well but experienced size distortions with  fewer than 20 clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test rejected at or slightly below nominal level in all  situations I investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I now turn to the behavior of the test under the alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I repeated the experiment  but now tested the incorrect null hypothesis H0 : β2(u) = 0 for all u ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Figure 2  shows the rejection frequencies of this null against the alternative H1 : β2(u) > 0 for  some u ∈ U, where U was either (0, 1) (black) or (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, 1) (grey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The null hypothesis  is false in both situations but the case where U = (0, 1) is more challenging because  β2(u) < 0 for all u < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 so that estimates below the median provide evidence in the  direction away from the alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I again considered (i) K = 10 neighborhoods  per cluster with intra-neighborhood correlation ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines), (ii) K = 20 with  ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed), and (iii) K = 10 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As could be expected, the  bootstrap rejected a large fraction of null hypotheses mostly because it was unable to  control the size of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, it had high power when the number of clusters  was above 20 and the size distortions disappeared (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test had  high power while maintaining size control even when the number of clusters was below  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For example, at q = 12 it detected a deviation from the null between 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5%  (K = 10, ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, U = (0, 1)) and 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='26% (K = 20, ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, U = (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, 1)) of all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  More generally, additional clusters, lower intra-cluster dependence, and additional  neighborhoods per cluster increased the power of the CRK test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 (Quantile treatment effects, cont.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For this experiment, I reuse  the setup of Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 but replace the variable Xi,j,k with a cluster-level treatment  indicator Dj that equals one if cluster j received treatment and equals zero otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I randomly assign q1 = ⌊q/2⌋ clusters to treatment and q0 = ⌈q/2⌉ to control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  coefficient of interest is δ in  Q(u | Dj) = β0(u) + δ(u)Dj + β2(u)Zi,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  25  5  10  15  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  Bootstrap (power, u �→ β2(u))  Number of clusters  Rejection frequency  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 20, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 20, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1  5% level  5  10  15  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  CRK test (power, u �→ β2(u))  Number of clusters  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Rejection frequencies in Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 of false nulls H0 : β2(u) = 0 for  u > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (grey) and H0 : β2(u) = 0 for all u (black) as a function of the number  of clusters for the bootstrap (left) and the CRK test (right) with (i) K = 10  neighborhoods per cluster with intra-neighborhood correlation ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines),  (ii) K = 20 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed), and (iii) K = 10 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I do not assume that pairings are predetermined and therefore use the adjusted p-values  of the CRK test from Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For each Monte Carlo replication, I drew a  collection I with |I| = 50 from H without replacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The CRK test with unknown  cluster parings requires α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='05 > 1/2q1∧q0−1 to have power, which is satisfied here as  long as q ⩾ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I therefore restrict q to be between 12 and 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' All other parameters  of the experiment are exactly as in Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The left panel of Figure 3 shows the rejection frequencies of a true null hypothesis  H0 : δ(u) = 0 for all u in 5,000 Monte Carlo experiments per horizontal coordinate  as q increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I again considered (i) K = 10 neighborhoods per cluster with intra-  neighborhood correlation ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines), (ii) K = 20 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed),  and (iii) K = 10 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As can be seen, adjusting the CRK test for  unknown cluster pairings results in a markedly more conservative test relative to  an unadjusted test from Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' However, as the right panel of Figure 3 shows,  this did not translate into poor power under the alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' When I repeated the  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  26  12  14  16  18  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='25  CRK test (size, δ(u) ≡ 0)  Number of clusters  Rejection frequency  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 20, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 20, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5  K = 10, ϱ =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1  5% level  12  14  16  18  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='0  CRK test (power, δ(u) ≡ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5)  Number of clusters  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Rejection frequencies in Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 of a true null (left) H0 : δ(u) = 0  for all u and false nulls (right) H0 : δ(u) = 0 for u > 0 (grey) and H0 : δ(u) = 0  for all u (black) as a function of the number of clusters for the CRK test when  cluster pairings are not known with (i) K = 10 neighborhoods per cluster with intra-  neighborhood correlation ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (solid lines), (ii) K = 20 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (long-dashed),  and (iii) K = 10 with ϱ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1 (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  experiment with δ(u) ≡ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, the CRK test with identification across clusters had no  problem detecting the that neither H0 : δ(u) for all u ∈ (0, 1) (black) nor H0 : δ(u) for  u > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 (grey) were true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Compared to Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1, the alternative where U = (0, 1)  rejects slightly more nulls because now every u provides evidence against the null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  A noteworthy feature of the right panel of Figure 3 is the “zig-zag” pattern in  the rejection frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The reason for this pattern is the treatment assignment  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If q = 12, then q1 = 6 clusters receive treatment and q0 = 6 do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If  q = 13, then again 6 = ⌊13/2⌋ clusters receive treatment but now 7 = ⌈13/2⌉ do  not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='13 uses a large number of potential pairings of treatment to control  for inference but effectively reduces the number of clusters to min{q1, q0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In this  experiment, inference with 6 + 7 clusters is therefore effectively the same as inference  with 6 + 6 clusters, which explains the similar performance of the test at q and q − 1  when q is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  27  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3 (Placebo interventions in Project STAR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In this example, I  revisit a challenging placebo exercise of Hagemann (2017, Experiment 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1) in data  from the first year of the Tennessee Student/Teacher Achievement Ratio experiment,  known as Project STAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Details about the data can be found in Word et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1990)  and Graham (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I only provide a brief summary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  In 1985, incoming kindergarten students in 79 project schools were randomly  assigned to small classes (13-17 students) or regular-size classes (22-25 students) with  or without a teacher’s aide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Each of the project schools was required to have at least  one of each kindergarten class type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The outcome is standardized student performance  on the Stanford Achievement Test (SAT) in mathematics and reading administered at  the end of the school year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The raw test scores are standardized as in Krueger (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  He finds across several mean regression models that students in small classes perform  about five percentage points better on average than students in regular classrooms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  (Assigning teachers aides had no effect uniformly across specifications and I do not  consider such classes in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=') Hagemann (2017) documents similar effects in  quantile regressions but finds that the effects are smaller for students near the bottom  and top of the conditional outcome distribution and larger near the center of the  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For example, in the model  QYi,j(u | Xi,j) = β0(u) + δ(u)small i,j + β2(u)TZi,j  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2)  where the treatment dummy small indicates whether the student was assigned to a  small class and Z contains school dummies, the effect of being in a small class relative  to a regular class varies between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='78 percentage points at the 10th percentile to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='23  percentage points at the 60th percentile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For the placebo experiment, I removed all small classes from the sample and only  kept the 16 schools that had two regular-size classes without aide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In each of these  16 schools, I then randomly assigned one of the regular-size classes the treatment  indicator small = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This mimics the random assignment of class sizes within schools  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  28  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Rejection frequencies of H0 : δ(u) = 0 for all u in placebo interventions in  Project STAR for the CRK test and the wild gradient bootstrap at 5% level  size  power  δ = 0  δ = 2  δ = 3  δ = 4  δ = 5  δ = 6  δ = 7  CRK test  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='043  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='122  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='161  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='212  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='318  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='379  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='478  Bootstrap  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='091  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='233  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='316  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='428  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='580  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='691  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='814  in the original sample, even though in this case no student actually attended a small  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I applied the CRK test as in Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='12 by running 16 separate quantile  regressions, one for each school, on a constant and small to get 16 separate estimates  of δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The fixed effects as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2) are not needed here because the constant can vary  freely by cluster in these quantile regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This also means that I am effectively  clustering at the school level because I am comparing, within each school, classes  with small = 1 to classes with small = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' There is only one such comparison per  school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (If multiple small classes per school were available, then Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='13 could  be used instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=') For the wild gradient bootstrap, I reran the QR in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2) in the  placebo data but clustered at the classroom level as in Hagemann (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For both  methods, I tested at the 5% level the correct null hypothesis that H0 : δ(u) = 0 jointly  at u ∈ {.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9} against the alternative that δ is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The rejection frequencies in ‘size’ column in Table 1 show the outcome of repeating  the placebo assignment 1,000 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As can be seen, the CRK test provided a nearly  exact test but the bootstrap over-rejected somewhat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The over-rejection for the  bootstrap here was documented by Hagemann (2017) and can be attributed to the  placebo sample being very small with about 69 students per school and the effect of  interest being identified off of comparisons within these 16 schools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I also investigated power by increasing the percentile scores of all students in  the randomly drawn small classes of the placebo experiment by δ ∈ {2, 3, 4, 5, 6, 7}  percentage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' These increases are of the same or smaller magnitude as the  estimated quantile treatment effects in the actual sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then I tested the incorrect  hypothesis H0 : β1(u) = 0 for all u with the same experimental setup as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  29  results are shown in ‘power’ column of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As can be seen, the CRK test was  able to reliably detect effects for moderate deviations from the null hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  wild gradient bootstrap rejected more often, but this was likely caused by its tendency  to over-reject in this data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclusion  I introduce a generic method for inference on quantile and regression quantile  processes in the presence of a finite number of large and arbitrarily heterogeneous  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The method asymptotically controls size by generating statistics that exhibit  enough distributional symmetry such that randomization tests can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This  randomization test can even be asymptotically similar in empirically relevant situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The test does not require ex-ante matching of clusters, is free of user-chosen parameters,  and performs well at conventional significance levels with as few as five clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  main focus on the paper is inference on quantile treatment effects and quantile  difference in differences but the method applies more broadly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Numerical examples  and an empirical application are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  References  Adler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Taylor (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Random Fields and Geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Springer, New  York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Bertrand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Duflo, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Mullainathan (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' How much should we trust  differences-in-differences estimates?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quarterly Journal of Economics 119, 249–275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Bester, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conley, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hansen (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference with dependent data  using cluster covariance estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of Econometrics 165, 137–151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Callaway, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Li (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quantile treatment effects in difference in differences  models with panel data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quantitative Economics 10, 1579–1618.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Cameron, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Miller (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A practitoner’s guide to cluster robust  inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of Human Resources 50, 317–372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  30  Canay, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Romano, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Shaikh (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Randomization tests under an  approximate symmetry assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Econometrica 85, 1013–1030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Canay, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Santos, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Shaikh (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The wild bootstrap with a “small”  number of “large” clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Review of Economics and Statistics, forthcoming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Wei, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Parzen (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quantile regression for correlated  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In Proceedings of the Second Seattle Symposium in Biostatistics:  Analysis of Correlated Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Lecture Notes in Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Springer, New York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  DiCiccio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' DiCiccio, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Romano (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Exact tests via multiple  data splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Statistics & Probability Letters 166, 108865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  El Machkouri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Voln´y, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Wu (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A central limit theorem for  stationary random fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Stochastic Processes and their Applications 123, 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Fisher, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1935).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' “The coefficient of racial likeness” and the future of craniometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Journal of the Royal Anthropological Institute of Great Britain and Ireland 66,  57–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Graham, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Identifying social interactions through conditional variance  restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Econometrica 76, 643–660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Hagemann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Cluster-robust bootstrap inference in quantile regression models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Journal of the American Statistical Association 112, 446–456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Hagemann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Permutation inference with a finite number of heterogeneous  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' University of Michigan working paper, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='01049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Hoeffding, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1952).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The large-sample power of tests based on permutations of  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Annals of Mathematical Statistics 23, 169–192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Ibragimov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M¨uller (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' t-statistic based correlation and heterogeneity  robust inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of Business & Economic Statistics 28, 453–468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Ibragimov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M¨uller (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference with few heterogenous clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Review  of Economics and Statistics 98, 83–06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Koenker, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Bassett (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Regression quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Econometrica 46, 33–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  31  Krueger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Experimental estimates of education production functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Quarterly Journal of Economics 114, 497–532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  MacKinnon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Nielsen, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Webb (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Cluster-robust inference:  A guide to empirical practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of Econometrics, forthcoming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  MacKinnon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Webb (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Wild bootstrap inference for wildly  different cluster sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of Applied Econometrics 32, 233–254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Posterior predictive p-values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Annals of Statistics 22, 1142–1160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Parente, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Santos Silva (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quantile regression with clustered data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  University of Essex Department of Economics Discussion Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' 728.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  R¨uschendorf, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Random variables with maximum sums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Advances in Applied  Probability 14, 623–632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Vovk, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Combining p-values via averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Technical report, arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Inference on quantile regression for heteroscedastic mixed models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Statistica Sinica 19, 1247–1261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' He (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Detecting differential expressions in genechip microarray  studies: a quantile approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Journal of American Statistical Association 102,  104–112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Word, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Johnston, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Bain, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Fulton, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Achilles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Lintz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Folger,  and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Breda (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The state of Tennessee’s student/teacher achievement ratio  (STAR) project: Technical report 1985-1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Report, Tennessee State University,  Center of Excellence for Research in Basic Skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Yoon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Galvao (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Cluster robust covariance matrix estimation in  panel quantile regression with individual fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Quantitative Economics 11,  579–608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Proofs  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Denote the inverse element of g ∈ G by g−1 and the identity  element by id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Take a finite grid of points Um := {i/m : i = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , m} ∩ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  32  every u ∈ U is a limit of a sequence in Um.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let x �→ Tm(x) = supu∈Um  �q  j=1 xj(u)/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Uniform continuity implies Tm(x) → T(x) and (Tm(gX))g∈G → (T(gX))g∈G almost  surely and therefore also (Tm(gX))g∈G ⇝ (T(gX))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Independence and P(Xj(u) =  0) = 0 ensure that �q  j=1 Xj(u)/q has a continuous distribution at every u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because X  is separable, T(gX) = supu∈U∩Q  �q  j=1 Xj(u)/q, where Q are the rationals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude  that (T(gX))g∈G has a continuous distribution because for arbitrary tg ∈ R,  P  �  g∈G  {T(gX) = tg} ⩽ P  �  sup  u∈U∩Q  1  q  q  �  j=1  Xj(u) = tid  �  ⩽  �  u∈U∩Q  P  �  1  q  q  �  j=1  Xj(u) = tid  �  and the extreme right-hand side equals zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Finite-dimensional distributional in-  variance implies that (Tm(gX))g∈G and (Tm(g˜g−1X))g∈G have the same distribution  for every ˜g ∈ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because (Tm(gX))g∈G ⇝ (T(gX))g∈G, it must also be true that  (Tm(g˜g−1X))g∈G ⇝ (T(gX))g∈G and (Tm(g˜g−1X))g∈G ⇝ (T(g˜g−1X))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude  from continuity that (T(gX))g∈G and (T(g˜g−1X))g∈G have the same distribution for  every ˜g ∈ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' These two random vectors are of the form  (T(X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , T(gX), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , T(˜gX), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' ) ∼ (T(˜g−1X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , T(g˜g−1X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , T(id X), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because T 1−α(X, G˜g−1) = T 1−α(X, G) = T 1−α(˜gX, G), this implies ϕα(X, G) ∼  ϕα(˜gX, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' This is true for every ˜g ∈ G and therefore E �  g∈G ϕα(gX, G) = Eϕα(X, G)|G|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The same argument as the finite-dimensional case now yields Eϕα(X, G) ⩽ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For x, x′ ∈ ℓ∞(U)q and every g ∈ G, sub-additivity and mono-  tonicity give  T(gx) − T(gx′) ⩽ sup  u∈U  1  q  �  q  �  j=1  gj  �  xj(u) − x′  j(u)  �  �  ⩽ sup  u∈U  1  q  q  �  j=1  ��xj(u) − x′  j(u)  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The far right of the display is at most |x − x′|U/√q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Reverse the roles of x and x′ to  conclude |T(gx) − T(gx′)|2 ⩽ |x − x′|2  U/q for every g ∈ G and therefore  ���  T(gx) − T(gx′)  �  g∈G  �� ⩽  �  2q/q|x − x′|U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  33  Let |x − x′|U → 0 to deduce that x �→ (T(gx))g∈G a continuous map from ℓ∞(U)q  to R|G| with respect to the sup-norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because Xn ⇝ X, the continuous mapping  theorem implies (T(gXn))g∈G ⇝ (T(gX))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Order G so that the identity action g = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , 1) is the first element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Define the set  Bα =  �  (t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |{2 ⩽ i ⩽ |G| : ti < t1}| ⩾ ⌈(1 − α)|G|⌉  �  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1)  to write P(T(X) > T α(X, G)) = P((T(gX))g∈G ∈ Bα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The boundary ∂Bα of Bα can  be expressed as  ∂Bα =  �  j⩾1  �  (t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |t1 = ti| = j, |{2 ⩽ i ⩽ |G| : ti < t1}| = ⌈(1 − α)|G|⌉ − j  �  and therefore ∂Bα ⊂ �  j⩾1{(t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |t1 = ti| = j}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By the portmanteau lemma,  P((T(gXn))g∈G ∈ Bα) → P((T(gX))g∈G ∈ Bα) as long ∂Bα satisfies P((T(gX))g∈G ∈  ∂Bα) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The goal is therefore to show that  P  �  (T(gX))g∈G ∈  �  j⩾1  {(t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |t1 = ti| = j}  �  = 0,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', (T(gX))g∈G has no ties with probability one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The main difficulty here is that each component of (T(gX))g∈G is dependent, so the  preceding display does not follow from smoothness of the marginals of (T(gX))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Instead, for u, u′ ∈ U and g ̸= g′, write  q  �  j=1  gjXj(u) −  q  �  j=1  g′  jXj(u′) = (g, −g′)T(X(u), X(u′))  Because X is a Gaussian process, it follows that (X(u), X(u′)) is a jointly Gaussian  vector and therefore (g, −g′)T(X(u), X(u′)) is a normally distributed random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  If u = u′ or u ̸= u′ but X(u) = X(u′), then g ̸= g′ guarantees that �q  j=1 gjXj(u) −  �q  j=1 g′  jXj(u) = �q  j=1(gj − g′  j)Xj(u) has non-zero variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hence, suppose u ̸= u′  and X(u) ̸= X(u′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Let c(u, u′) = EX(u)X(u′) be the covariance function and  note that (g, −g′)T(X(u), X(u′)) is zero with positive probability if and only if  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  34  (g, −g′)Tc(u, u′)(g, −g′) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because the elements of X are independent, the co-  variance function satisfies  (g, −g′)Tc(u, u′)(g, −g′) =  n  �  j=1  cjj(u, u) +  n  �  j=1  cjj(u′, u′) − 2  n  �  j=1  gjg′  jcjj(u, u′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Apply the Cauchy-Schwarz inequality to the right-hand side to deduce  0 = (g, −g′)Tc(u, u′)(g, −g′) ⩾  n  �  j=1  �  cjj(u, u) − cjj(u′, u′)  �2,  which implies Var Xj(u) = Var Xj(u′) for 1 ⩽ j ⩽ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' It follows that  0 =  n  �  j=1  �  cjj(u, u) − gjg′  jcjj(u, u′)  �  Apply the Cauchy-Schwarz inequality again to see that every covariance must be non-  zero because cjj(u, u) > 0 and either cjj(u, u′) = cjj(u, u) or cjj(u, u′) = −cjj(u, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This implies that either Xj(u) = Xj(u′) or Xj(u) = −Xj(u′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because g ̸= g′,  X(u) = X(u′) is impossible and at least one j must satisfy Xj(u) = −Xj(u′), which  is ruled out by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude  q  �  j=1  gjXj(u) ̸=  q  �  j=1  g′  jXj(u′)  almost surely for all u, u′ ∈ U and all g ̸= g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because U is compact and X has  continuous sample paths, this ensures  T(gX) − T(g′X) = max  u∈U  q  �  j=1  gjXj(u) − max  u∈U  q  �  j=1  g′  jXj(u) ̸= 0  for almost every sample path unless g = g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If H0 is true, then scale invariance implies ϕα(ˆδ − δ01q, G) =  ϕα(Xn, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3 and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='2 yield Eϕα(ˆδ − δ01q, G) → Eϕα(X, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Eϕα(X, G) ⩽ α holds because X satisfies the conditions of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  35  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Suppose δ = δ0 + λ/√n so that Xn + λ1q  δ⇝ X + λ1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As  in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, joint continuity of the map x �→ (T(gx))g∈G implies  (T(g(Xn+λ1q)))g∈G  δ⇝ T(g(X +λ1q)))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' With Bα as defined in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='1), I only have to  show that P(T(g(X+λ))g∈G ∈ ∂Bα) = 0 to conclude P(T(Xn+λ) > T α(Xn+λ, G)) →  P(T(X + λ) > T α(X + λ, G)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The boundary has probability zero if (T(g(X + λ)))g∈G has no ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For u, u′ ∈ U  and g ̸= g′, write  �  q  �  j=1  gjXj(u) −  q  �  j=1  g′  jXj(u′)  �  + λ(u)  q  �  j=1  gj − λ(u′)  q  �  j=1  g′  j,  to see from the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 that the term in square brackets is nonzero  almost surely for all u, u′ ∈ U and all g ̸= g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because the expression in square brackets  is normally distributed with mean zero, it cannot take on any fixed nonzero value with  positive probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The remainder of the preceding display is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude  that the preceding display is nonzero almost surely for all u, u′ ∈ U and all g ̸= g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As  in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, this implies T(g(X + λ)) ̸= T(g′(X + λ)) almost surely  unless g ̸= g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  I will now develop a lower bound on P(T(X + λ1q) > T α(X + λ1q, G)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because  the original statistic cannot exceed the largest order statistic, monotonicity implies  P  �  T(X + λ1q) > T 1−α(X + λ1q, G)  �  ⩾ P  �  T(X + λ1q) > T (|G|−1)(X + λ1q, G)  �  = P  �  T(X + λ1q) = max  g∈G T  �  g(X + λ1q)  ��  and the right-hand side is at most  P  ��  T(X + λ1q) = max  g∈G T  �  g(X + λ1q)  ��  ,  q�  j=1  �  inf  u∈U(Xj(u) + λ(u)) ⩾ 0  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  If infu∈U(Xj(u) + λ(u)) ⩾ 0 for 1 ⩽ j ⩽ q, then T(X + λ1q) = maxg∈G T(g(X + λ1q))  because T cannot be increased by making large negative values positive through  multiplication by −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By independence and symmetry of the Gaussian processes,  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  36  conclude that the preceding display equals  q�  j=1  P  �  inf  u∈U  �  Xj(u) + λ(u)  �  ⩾ 0  �  =  q�  j=1  P  �  sup  u∈U  �  Xj(u) − λ(u)  �  ⩽ 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because sup(f − f ′) ⩾ sup f − sup f ′ for arbitrary f, f ′, this cannot exceed  q�  j=1  P  �  sup  u∈U  Xj(u) ⩽ sup  u∈U  λ(u)  �  ⩾  q�  j=1  �  1 − e−[supu λ(u)−E supu Xj(u)]2/2 supu EX2  j (u)�  by the Borell-TIS inequality as long as supu λ(u) > E supu Xj(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In that case, the  right-hand side of the preceding display is strictly positive, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Suppose δ = δ0 + λ1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' We have ˆδ − δ0 = Xn/√n + λ1q with Xn/√n ⇝ 0, and by  arguments as in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='3, the continuous mapping theorem yields  (T(g(ˆδ − δ01q)))g∈G ⇝ (T(gλ))g∈G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Monotonicity implies  Eϕ1−α(ˆδ − δ01q, G) ⩾ P  �  T(ˆδ − δ01q) > T (|G|−1)(ˆδ − δ01q, G)  �  As before, use a set of the form  B =  �  (t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |{2 ⩽ i ⩽ |G| : ti < t1}| ⩾ |G| − 1  �  to write P(T(λ) > T (|G|−1)(λ, G)) = P((T(gλ))g∈G ∈ B) = 1{(T(gλ))g∈G ∈ B}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  boundary ∂B is contained in the set  �  j⩾1  �  (t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , t|G|) : |t1 = ti| = j  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because T(gλ) = supu∈U λ(u) �q  j=q gj/q with λ ⩾ 0 and supu∈U λ(u) > 0, we have  T(λ) > T(gλ) for all g ̸= id := (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Hence, there are no ties with the first  element of (T(gλ))g∈G and 1{(T(gλ))g∈G ∈ ∂B} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude from the portmanteau  lemma that T(ˆδ − δ01q) − T (|G|−1)(ˆδ − δ01q, G) ⇝ supu∈U λ(u) − supu∈U λ(u) �q  j=q gj/q  for some g ̸= id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because this limit is strictly positive,  Eϕ1−α(ˆδ − δ0, G) ⩾ P  �  T(ˆδ − δ0) > T (|G|−1)(ˆδ − θ0, G)  �  → 1,  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  37  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' I can work with Xn,[h] = √n(ˆδ[h] − δ01min{q1,q0}) instead of  ˆδ[h] − δ01min{q1,q0} because x �→ p(x, G) is scale invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' In the following I make  repeated use of the fact that the map x �→ (x[h])h∈H, the map x[h] �→ (T(gx[h]))g∈G,  and their composition are continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Suppose q1 ⩽ q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The case q1 > q0 requires only notational changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The  components of Xn,[h] are of the form √n(ˆδj,h(j) − δ0) = √n(ˆδj,h(j) − δ) under the  null hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' By Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7, these components converge in distribution to  X[h] := (X1,h(1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' , Xq1,h(q1)) jointly in h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The same arguments as in the proof of Theo-  rem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4 imply that T(gXn,[h]) converges in distribution, jointly in h and g, to T(gX[h]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For the same reasons as in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, for a given h, (T(gX[h]))g∈G\\id  has no ties T(X[h]) with probability 1, provided Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='7 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Consider  |G|  �  h∈H  p(Xn,[h], G) =  �  h∈H  �  g∈G  1{T(gXn,[h]) ⩾ T(Xn,[h])}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  This function jumps discretely if, for some h and g, T(gXn,[h]) = T(Xn,[h]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  continuous mapping theorem applies to this function if the probability of hitting  these jumps is zero, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=', P(T(gXn,[h]) = T(Xn,[h]) for some g ∈ G, h ∈ H) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  union bound implies that this probability cannot exceed �  h∈H  �  g∈G P(T(gXn,[h]) =  T(Xn,[h])) = 0 because (T(gX[h]))g∈G has no ties almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude that the  preceding display converges in distribution to �  h∈H  �  g∈G 1{T(gX[h]) ⩾ T(X[h])} and  therefore  P  �  2  H  �  h∈H  p(Xn,[h], G) ⩽ α  �  → P  �  2  H  �  h∈H  p(X[h], G) ⩽ α  �  if α is a continuity point of the right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because |G| �  h∈H p(X[h], G) is  integer-valued, non-integer values of αH|G|/2 are continuity points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  38  For integer αH|G|/2, find an ε > 0 such that (α + ε)H|G|/2 is not an integer but  α + ε ⩽ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Monotonicity and weak convergence imply  lim sup  n→∞ P  �  2  H  �  h∈H  p(Xn,[h], G) ⩽ α  �  ⩽ P  �  2  H  �  h∈H  p(X[h], G) ⩽ α + ε  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  By the R¨uschendorf (1982) inequality, the right-hand side cannot exceed α + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Now  let ε ↘ 0 to obtain the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8, let Xn,[h] = √n(ˆδ[h]−δ01min{q1,q0})  and q1 ⩽ q0 without loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Consider fixed alternatives δ = δ0 + λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The  components of ˆδ[h] − δ01q1 are of the form  ˆδj,h(j) − δ0 = √n(ˆδj,k − δ)/√n + λ ⇝ λ  by uniform continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Deduce that for every g and h, T(Xn,[h]/√n) − T(gXn,[h]/√n)  converges in probability to T(λ[h]) − T(gλ[h]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For g ̸= id, this limit equals  sup  u∈U  λ(u) − sup  u∈U  λ(u)  q  �  j=q  gj/q > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Zero is therefore a continuity point of the (degenerate) limiting distribution of  T(Xn,[h]/√n) − T(gXn,[h]/√n), which implies  P  �  T(gXn,[h]/√n) ⩾ T(Xn,[h]/√n)  �  → 0  and 1{T(gXn,[h]/√n) ⩾ T(Xn,[h]/√n)} → 0 for every g ̸= id and h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude that  1  H  �  h∈H  p(Xn,[h], G) =  1  |G|H  �  h∈H  �  g∈G  1{T(gXn,[h]) ⩾ T(Xn,[h])} ⇝ 1  |G|  and therefore  P  �  2  H  �  h∈H  p(ˆδ[h] − δ01q1, G) ⩽ α  �  → 1{2 ⩽ α|G|}  as long as α|G| ̸= 2 to guarantee that convergence occurs at a continuity point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  39  Now consider local alternatives u �→ δ(u) = δ0(u) + cλ(u)/√n with c constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As  in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, continuity of the maps x �→ x[h] and x[h] �→ (T(gx[h]))g∈G  implies (T(g(Xn,[h] + cλ1q1)))g∈G ⇝ (T(g(X[h] + cλ1q1)))g∈G jointly in h ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For a  given h, (T(g(X[h] +cλ1q1)))g∈G again has no ties with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' As before, deduce  P  �  2  H  �  h∈H  p(Xn,[h] + cλ1q1, G) ⩽ α  �  → P  �  2  H  �  h∈H  p(X[h] + cλ1q1, G) ⩽ α  �  if α is a continuity point of the right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Because |G| �  h∈H p(X[h] + cλ1q1, G)  is integer-valued, non-integer values of αH|G|/2 are continuity points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For integer  αH|G|/2, find an ε > 0 such that (α − ε)H|G|/2 is not an integer but α − ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  lim inf  n→∞ P  �  2  H  �  h∈H  p(Xn,[h] + cλ1q1, G) ⩽ α  �  ⩾ P  �  2  H  �  h∈H  p(X[h] + cλ1q1, G) ⩽ α − ε  �  by monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let ε ↘ 0 to see that the limit inferior is bounded below by  P  �  2  H  �  h∈H  p(X[h] + cλ1q1) < α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  The same bound holds trivially for non-integer αH|G|/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For the analysis as c → ∞, consider  2  H  �  h∈H  p(X[h] + cλ1q1) =  2  |G|H  �  h∈H  �  g∈G  1  �  T(g(X[h] + cλ1q1))  T(cλ1q1)  ⩾ T(X[h] + cλ1q1)  T(cλ1q1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For g = id, the indicator function in the preceding display equals q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Consider  g ̸= id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because T(cλ1q1) = cT(λ1q1) > 0 and T(gX[h])/T(cλ1q1) → 0 almost  surely for every g ∈ G as c → ∞, it follows from the subadditivity of suprema  that T(g(X[h] + cλ1q1))/T(cλ1q1) → T(gλ1q1)/T(λ1q1) almost surely and therefore  (T(X[h] + cλ1q1) − T(g(X[h] + cλ1q1)))/T(cλ1q1) → 1 − (T(gλ1q1)/T(λ1q1)) almost  surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' That last limit is a strictly positive constant for every g ̸= id and there is one  id for every h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude from the continuous mapping theorem that the preceding  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  40  display converges almost surely to 2/|G| as c → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If α|G| ̸= 2, it follows that  lim  c→∞ P  �  2  H  �  h∈H  p(X[h] + cλ1q) < α  �  = 1{2 < α|G|},  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If I is fixed, then the proof of Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 goes  through without any changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For random I, work conditional on I to see that  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8 implies  lim sup  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I  �  ⩽ α  almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Apply expectations to conclude from the (reverse) Fatou lemma that  lim sup  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α  �  ⩽ E lim sup  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I  �  ⩽ α  as needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Similarly, Fatou’s lemma implies  lim inf  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α  �  ⩾ E lim inf  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Now apply the first part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 for a given I to get the result for fixed  alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For local alternatives, the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 implies  lim inf  n→∞ P  �  2  |I|  �  h∈I  p(ˆδ[h] − δ01min{q1,q0}, G) ⩽ α | I  �  ⩾ P  �  2  |I|  �  h∈I  p(X[h] + cλ1q1) < α | I  �  → 1  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  41  almost surely as c → ∞, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Limits are as m → ∞ unless noted otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Consider a  process Xn possibly depending on n and recall that T(Xn) > T 1−α(Xn, Gm) if and only  if ˆpm := p(Xn, Gm) ⩽ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Let p := p(Xn, G) and notice that E(ˆp | Xn) = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' For almost  every realization of Xn, ˆpm is an average of bounded iid random variables that satisfies  P(|ˆpm − p| > ε | Xn) → 0 almost surely for every ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Conclude from dominated  convergence that this convergence also holds unconditionally and therefore ˆpm ⇝ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Because p can only vary at the points j/|G|, 1 ⩽ j ⩽ |G|, P(ˆpm ⩽ α) → P(p ⩽ α) as  long as α ̸= j/|G|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' If α equals j/|G| for some j, use 0 < ε < 1/|G| and monotonicity  to see that P(ˆpm ⩽ α − ε) ⩽ P(ˆpm ⩽ α) ⩽ P(ˆpm ⩽ α + ε) must satisfy  P(p ⩽ α − ε) ⩽ lim inf  m→∞ P(ˆpm ⩽ α) ⩽ lim sup  m→∞ P(ˆpm ⩽ α) ⩽ P(p ⩽ α + ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Let ε ↘ 0 to see that the extreme right-hand side can be decreased to P(p ⩽ α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='4, apply this result to obtain  lim sup  m→∞ P  �  T(Xn) > T 1−α(Xn, Gm)  �  ⩽ P  �  p(Xn, G) ⩽ α  �  = Eϕα(Xn, G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  Now apply limits as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  For Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='8, consider stochastic processes Xn,h indexed by h and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' The contin-  uous mapping theorem implies 2 �  h∈H p(Xn,h, Gm)/H  P→ 2 �  h∈H p(Xn,h, G)/H and  therefore 2 �  h∈H p(Xn,h, Gm)/H ⇝ 2 �  h∈H p(Xn,h, G)/H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Using the same argument  as before gives  lim sup  m→∞ P  �  2  H  �  h∈H  p(Xn,h, Gm) ⩽ α  �  ⩽ P  �  2  H  �  h∈H  p(Xn,h, G) ⩽ α  �  For Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5, if α > 1/2q, there is a ε > 0 such that α − ε > 1/2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then  lim inf  m→∞ P  �  T(Xn) > T 1−α(Xn, Gm)  �  ⩾ P  �  p(Xn, G) ⩽ α − ε  �  = Eϕα−ε(Xn, G)  and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='5 applies directly to the extreme right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  QUANTILE PROCESSES WITH A FINITE NUMBER OF CLUSTERS  42  For Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9, there is a ε > 0 such that α − ε > 1/2q−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Then  lim inf  m→∞ P  �  2  H  �  h∈H  p(Xn,h, Gm) ⩽ α  �  ⩾ P  �  2  H  �  h∈H  p(Xn,h, G) ⩽ α − ε  �  and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='9 can be applied to the extreme right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='  □  University of Michigan Ross School of Business, 701 Tappan Ave, Ann Arbor, MI  48109, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Tel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' : +1 (734) 764-2355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' Fax: +1 (734) 764-2769.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content=' E-mail: hagem@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E3T4oBgHgl3EQfuwtu/content/2301.04687v1.pdf'}
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+A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water
+Ignacio Sanchez-Burgos1,2, Maria Carolina Muniz2, Jorge R. Espinosa1,3 and Athanassios Z. Panagiotopoulos2,∗
+[1] Maxwell Centre, Cavendish Laboratory, Department of Physics,
+University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
+[2] Department of Chemical and Biological Engineering,
+Princeton University, Princeton, New Jersey 08544, USA.
+[3] Departamento de Qu´ımica F´ısica, Facultad de Ciencias Qu´ımicas,
+Universidad Complutense de Madrid, 28040 Madrid, Spain.
+* = To whom correspondence should be sent. email: azp@princeton.edu
+(Dated: January 31, 2023)
+Computational studies of liquid water and its phase transition into vapor have traditionally been
+performed using classical water models. Here we utilize the Deep Potential methodology —a machine
+learning approach— to study this ubiquitous phase transition, starting from the phase diagram in
+the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and
+forces based on the SCAN density functional which has been previously shown to reproduce solid
+phases and other properties of water. Here, we compute the surface tension, saturation pressure and
+enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K, and evaluate the
+Deep Potential model performance against experimental results and the semi-empirical TIP4P/2005
+classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier
+and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation
+rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005
+water model, due to an underestimation in the surface tension from the Deep Potential model. From
+analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water
+model, which is (0.091 ± 0.008) nm at 296.4 K. Lastly, we identify that water molecules display a
+preferential orientation in the liquid-vapor interface, in which H atoms tend to point towards the
+vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behaviour
+is more pronounced for planar interfaces than for the curved interfaces in bubbles.
+This work
+represents the first application of Deep Potential models to the study of liquid-vapor coexistence
+and water cavitation.
+I.
+INTRODUCTION
+Water is a fundamental substance, crucial for life
+and
+relevant
+in
+many
+environmental,
+engineering,
+and biological processes [1–9].
+Due to this, the past
+decades have seen a significant effort devoted to the
+development of models to reproduce the behaviour of
+water in computer simulations [10–22]. Although some
+of these models account for flexibility and polarizability
+[18–21, 23],
+the most widely employed models for
+water are rigid and non-polarizable. These include the
+TIP4P/2005 [10], TIP4P/ICE [11], SPC/E [15], TIP3P
+[13] and TIP4P-Ew [24] among others [16, 17].
+These
+empirical models have parameters obtained by fitting to
+experimentally measured properties, such as coexistence
+lines between thermodynamic phases or critical points.
+They are frequently used to describe ionic solutions
+[25–30] and for biomolecular simulations [31, 32], as well
+as other applications [33–36].
+In contrast to the classic semi-empirical approach
+to water modelling, ab initio models are determined
+from
+first
+principles
+and
+therefore
+do
+not
+require
+fitting to experimental data [37].
+Traditionally this
+approach has not been applied to large systems due
+to its computational cost [38, 39]. Nonetheless, recent
+advances
+in
+Machine
+Learning
+(ML)
+have
+allowed
+the development of deep potential generators [40, 41]
+capable of constructing MD potentials based on ab initio
+models.
+In this work, we use a ML-based model that
+has successfully recapitulated the different solid phases
+of water [42].
+This model has been constructed based
+on the SCAN quantum mechanical density functional,
+which succesfully reproduces several properties of water
+[43, 44].
+This approach to ab initio based models is
+efficient enough to carry out simulations with tens of
+thousands of water molecules in a computationally
+affordable way [45, 46].
+Making use of the machinery provided by ML ab
+initio based models, here we study the liquid-vapor
+coexistence of water by means of Molecular Dynamics
+(MD) simulations. The liquid-vapor properties of water
+are well known from experiments [47]. From the com-
+putational side, the TIP4P/2005 non-polarizable rigid
+water model [10] has been highly successful at describing
+the liquid-vapor coexistence properties, reproducing the
+experimental phase diagram [48] and surface tension
+[49–51] reasonably well, as well as transport properties
+[10, 48, 52].
+The TIP4P/2005 model has also been
+extensively benchmarked in the study of liquid-to-vapor
+and vapor-to-liquid phase transitions [53–59]. Therefore,
+we compare the Deep Potential Molecular Dynam-
+ics (DPMD) water model performance with that of
+TIP4P/2005 in addition to experimental data, when
+available.
+arXiv:2301.12008v1  [cond-mat.soft]  27 Jan 2023
+
+2
+To test the DPMD model we first evaluate the
+liquid-vapor phase diagram and measure properties at
+equilibrium such as the surface tension or the enthalpy
+of vaporization.
+We also focus on the liquid-to-vapor
+phase transition at negative pressure, a phenomenon
+known as cavitation.
+Under negative pressures, water
+can remain metastable with respect to the vapor (the
+most stable phase under these conditions) for a finite
+amount of time before undergoing the phase transition
+[60]. This results from the fact that the phase transition
+is an activated process, and requires the formation of
+a critical bubble, i.e., one that has surmounted a free
+energy barrier and can continue growing irreversibly
+without a free energy penalty [34, 61].
+This happens
+because the formation of a bubble intrinsically requires
+the formation of a liquid-vapor interface, which comes
+associated with an energetic cost, the surface tension.
+When the phase transition is initiated by the formation
+of water bubbles within the liquid bulk and in absence
+of any surface or external agent, the process is termed
+homogeneous cavitation.
+It has been experimentally determined that, at am-
+bient temperature, water can sustain negative pressures
+of up to −120 MPa before transitioning into the vapor
+phase [62–66].
+While experiments have determined
+the cavitation pressure, which is the pressure at which
+the phase transition is observed, computational studies
+using the TIP4P/2005 model have been able to compute
+the nucleation rate, a crucial quantity to characterize
+the cavitation process. The nucleation rate is defined as
+the number of critical clusters formed per unit of time
+and volume. The nucleation rate obtained in previous
+studies for the TIP4P/2005 model [53–55, 58, 59] will
+be used as a reference for our DPMD calculations since
+there are no reliable experimental data for this quantity.
+Aside from the nucleation rate, we also compare in
+this work the nucleation free energy barrier and the
+Tolman length [67], a parameter employed to describe
+the change in surface tension with curvature.
+Finally,
+we characterize the orientational distribution of water
+molecules at the interface.
+We find that the DPMD
+model can reproduce well the phase diagram of water,
+but displays a lower surface tension than experimental
+results or the TIP4P/2005 model. The nucleation rate
+is consequently greater for the DPMD model compared
+to the TIP4P/2005 model.
+II.
+METHODS
+A.
+DPMD Model
+We use the recently developed DPMD model for water
+[42] to perform simulations in the liquid-vapor coexis-
+tence regime. The model was generated using an itera-
+tive concurrent learning scheme, deep potential generator
+[41], to construct a potential energy landscape based on
+SCAN [43], a non-empirical functional that recapitulates
+several properties of water [44], such as molecular geom-
+etry and solid structures. The final training set used to
+construct this model included ice and liquid phases snap-
+shots. In Ref. [42], the phase diagram for this model was
+calculated for the different ice phases, reaching a reason-
+able agreement with experimental data [68–70]. For com-
+putational purposes we employ the compressed version of
+this potential, making use of the scheme developed in Ref.
+[71]. Thanks to this approach, we are capable of reaching
+a computational performance of 5.2 nanoseconds of simu-
+lation time per wall clock day for a system of about 10000
+water molecules running with a single 2.8 GHz Intel Ice
+Lake node using four NVIDIA A100 80GB GPUs and
+28 CPU-cores. Example files of simulations employing
+this potential are available in the Princeton DataSpace
+repository https://doi.org/10.34770/ms7d-wm45 .
+B.
+Simulation details
+Simulations of the DPMD water model were per-
+formed using the LAMMPS package [72], built with
+the DeePMD-kit [73]. Seeding and Direct Coexistence
+(DC) simulations were performed in the NV T ensemble,
+keeping the number of particles N, system volume V ,
+and temperature T
+constant with the Nose-Hoover
+thermostat [74–76]. Additionally, to compute equations
+of state and to observe crystallization directly at high
+supersaturations we performed simulations in the NPT
+ensemble using the Nose-Hoover barostat [74–76]. The
+equations of motion were integrated using the velocity-
+Verlet integrator.
+The simulation timestep was 0.5 fs,
+and the thermostat relaxation time 0.1 ps.
+In NPT
+simulations, the barostat relaxation time was 1 ps.
+For the DC simulations, a system size of 1024 molecules
+was used and the density profiles were obtained with at
+least 10 ns of sampling. Coexistence densities were ob-
+tained by fitting the density profile to the following ex-
+pression:
+ρ(z) = ρl + ρv
+2
+− ρl − ρv
+2
+tanh
+�z − z0
+d
+�
+(1)
+where ρl and ρv are the coexistence liquid and vapor
+densities, respectively, z0 the position of the interface,
+and d its thickness.
+The surface tension was calculated from DC simula-
+tions at each temperature according to the Kirkwood-
+Buff equation [77]:
+γ = Lz
+2 [⟨Pzz⟩ − 0.5(⟨Pxx⟩ + ⟨Pyy⟩)]
+(2)
+
+3
+where Pii are the diagonal components of the pressure
+tensor and Lz, the box length in the elongated dimen-
+sion, perpendicular to the slab interfaces.
+We also performed simulations with the TIP4P/2005
+water model [10] using the GROMACS 4.6.7 Molecular
+Dynamics package [78] in the NPT and NV T ensem-
+bles, keeping temperature constant with the velocity-
+rescale thermostat [79] and pressure constant (for NPT
+simulations) with the Parrinello-Rahman barostat [80].
+In GROMACS we integrated the equations of motion
+using the Leap-Frog integrator [81].
+The simulation
+timestep was 2 fs, and the thermostat and barostat re-
+laxation times were 0.75 and 2 ps, respectively. We set
+the cut-off of both dispersion interactions and the real
+part of the electrostatic interactions at 12 ˚A. Long-range
+Coulombic interactions were treated with the Particle-
+Mesh Ewald (PME) solver [82, 83]. We kept the O-H
+bond length (0.9572 ˚A) and H-O-H angle (104.52o) val-
+ues constant with the LINCS algorithm [84]. With this
+model we reached a computational performance of 40
+nanoseconds of simulation time per wall clock day for a
+system of about 10000 water molecules running with In-
+tel(R) Xeon(R) Platinum 8368Q CPU @ 2.60GHz, using
+32 CPUs in paralel.
+C.
+Seeding and Classical Nucleation Theory
+Seeding is a method that consists of using Classical
+Nucleation Theory (CNT) in combination with MD
+simulations [34, 35]. More specifically, we use the NVT
+seeding approach [85], in which a cluster (in this case a
+bubble) close in size to the critical one is artificially in-
+serted into the system, then spontaneously equilibrated
+into the critical size and tracked along time. With this
+approach, a critical bubble can be characterized for
+long timescales because the maximum in free energy
+barrier in a nucleation process represents a minimum
+in the Helmholtz free energy landscape in the canonical
+ensemble [54, 86]. Therefore, more precise measurements
+can be made compared to seeding in the NPT ensemble,
+where the bubble will rapidly either shrink or grow [85].
+This method is suitable to measure nucleation rates
+along isotherms, since the pressure at which the cluster
+is critical cannot be known a priori, and is obtained
+from the simulations.
+CNT [87, 88] is a theoretical framework that describes
+nucleation processes under saturation conditions. It can
+be used to obtain the free energy barrier, interfacial free
+energy and nucleation rate. The limitations of quanti-
+tatively characterizing nucleation rates using CNT are
+due to assumptions inherent in the theory [89–94]. De-
+spite these potential limitations, multiple studies position
+CNT as a powerful tool to estimate free energy barriers
+and nucleation rates for phase transitions [34, 35, 95–
+105], including cavitation [53, 85, 106, 107]. According
+to CNT [87, 108], the nucleation rate (J) can be com-
+puted as
+J = ρl
+�
+2γ
+πmexp
+�−∆G∗
+kBT
+�
+(3)
+where ρl represents the density of the liquid phase, γ
+the liquid-vapor surface tension, m the mass of water,
+∆G∗ the free energy barrier for nucleation, kB the Boltz-
+mann’s constant and T the temperature.
+Within the
+CNT framework, the free energy barrier is obtained as
+∆G∗ = 4
+3γπRc
+(4)
+where Rc is the critical bubble radius. Additionally, we
+obtain the interfacial free energy from Laplace’s equation
+as
+γ = Rc∆P
+2
+(5)
+where ∆P is the pressure difference between the vapor
+and liquid phases. This approach provides more reliable
+estimations than assuming the capillarity approximation
+(i.e. inserting the surface tension at planar interface and
+coexistence conditions into the CNT) [85, 107, 109, 110].
+Combining Eqs. 3, 4 and 5, we reach the final equation
+for J:
+J = ρl
+�
+Rc∆P
+πm exp
+�−4πR2
+c∆P
+3kBT
+�
+(6)
+To summarize, in order to compute J we require the
+pressure difference between the liquid and the vapor
+phases, and the critical radius of the bubble at the
+corresponding thermodynamic conditions of P and T.
+Although the difference in pressure can be computed in
+principle [85, 109], in this study the pressure inside the
+bubbles is ∼0 [48], therefore ∆P can be easily estimated
+as −Pliq, which is directly obtained through the virial
+expression.
+We additionally confirmed that the virial
+pressure obtained in the system containing a bubble
+matches that of the bulk liquid (Fig. S1).
+Lastly, the critical radius, Rc was obtained employ-
+ing a local order parameter. Although multiple param-
+eters have been proposed to track the size of a simu-
+lated bubble [53, 55, 58, 59, 111, 112], here we adopted
+the ’equidensity’ criterion [113], which was shown to pro-
+vide the surface of tension radius (i.e. the radius that,
+when inserted into Laplace’s equation provides a consis-
+tent value of γ) for the Lennard-Jones system [85, 107].
+As illustrated in Figure 1(a), the center of the bubble is
+first calculated through the minimum in the density pro-
+file along the 3 cartesian directions. Afterwards, a radial
+density profile from the bubble center is computed, in
+
+4
+(a)
+0
+10
+20
+30
+40
+50
+60
+L / Å
+0.85
+0.9
+0.95
+ρ / (g·cm
+-3)
+X direction
+Y direction
+Z direction
+(b)
+0
+10
+20
+30
+r / Å
+0
+0.2
+0.4
+0.6
+0.8
+1
+ρ(r) / (g·cm
+-3)
+Rc
+Figure 1: (a) Density profiles along the three cartesian
+directions. Vertical dashed lines depict the location of
+the minimum density, which corresponds to the center
+of the bubble in each direction. In these density profiles
+we averaged the density of each point with 2 other
+neighbouring points in order to make the curves
+smoother. (b) Radial density profile calculated from the
+center of the bubble. The blue curve indicates the
+density calculated at each distance while the black
+dashed curve is the fit of the blue curve to Eq. 7, from
+which we obtained the critical radius Rc.
+which the critical radius (Rc) corresponds to the point
+in which the density equals the average of the liquid and
+vapor densities (Fig. 1(b)). This point is found via non-
+linear fitting to the equation
+ρ(r) = ρl + ρv
+2
++ ρl − ρv
+2
+tanh
+�r − Rc
+α
+�
+(7)
+where r is the distance from the bubble center, and α is
+a fitting parameter. We confirmed that, as assumed by
+CNT, the bubbles have a close-to-spherical shape (Figure
+S2).
+III.
+RESULTS AND DISCUSSION
+It is important to note that all DPMD data shown in
+this work are shifted by 40 K, so that the simulations for
+a given temperature have been performed at 40 K higher
+than the reported one in the presented figures. Similar
+shifts in temperature have been performed for AIMD
+simulations using SCAN [114] and in other works using
+SCAN-based ML models [115–117].
+The rationale for
+the shift was originally attributed to nuclear quantum
+effects, but it is likely mainly due to the limitations of the
+density functional itself. SCAN is known to overestimate
+the strength of the hydrogen bond [115]. In this work,
+the shift in temperature was adjusted by calculating
+the mean square error between the coexistence vapor
+densities predicted by the model and the experimental
+ones, considering different values for the shift. The value
+for the shift was iteratively modified until we obtained
+the one that gave the minimum mean square error, which
+was 40 K. In all plots and tables that follow the re-
+sults of the DPMD model have this shift already applied.
+A.
+Vapor-liquid equilibrium in the DPMD model
+To test the DPMD model in the liquid-vapor regime,
+we begin by computing the phase diagram. We do so us-
+ing simulations in the canonical ensemble, in which both
+the liquid and vapor phases coexist. In Figure 2(a) (in-
+set) we show a snapshot of a typical DC simulation box.
+In Figure 2(a) we plot the temperature against density
+phase diagram of the DPMD model (green points), where
+the filled points represent the densities directly obtained
+from DC simulations (2 at each temperature). We in-
+clude results for the TIP4P/2005 model [10, 48] (blue
+circles), as well as experimental data [47] (black line).
+We can observe that for the DPMD model the density of
+the liquid branch is slightly higher than the experimental
+results at low temperatures (<500K), but matches well
+at higher ones. The critical point is estimated through
+the universal scaling law of coexistence densities near a
+critical point [119], and the law of rectilinear diameters
+[120]:
+�
+ρl(T) − ρv(T)
+�3.06 = d
+�
+1 − T
+Tc
+�
+(8)
+and
+(ρl(T) + ρv(T))/2 = ρc + s2(Tc − T)
+(9)
+where ρl and ρv refer to the coexisting densities of the
+liquid and vapor phases respectively, ρc is the critical
+density, Tc is the critical temperature, and d and s2 are
+fitting parameters.
+The critical temperature obtained
+for the DPMD model is of 632.6.6 K, which is lower than
+the experimental one by 14.5 K.
+Moreover, we compute the liquid-vapor surface tension
+for the DPMD model at different temperatures from the
+DC simulations. This quantity can be directly estimated
+according to Eq. 2. As can be seen in Figure 2(b), the
+DPMD model provides lower values of γ than both the
+
+5
+(a)
+(b)
+(c)
+0
+0.2
+0.4
+0.6
+0.8
+1
+ρ / g cm
+-3
+400
+500
+600
+700
+T / K
+Experiment
+DPMD
+TIP4P/2005
+300
+400
+500
+600
+700
+T / K
+0
+20
+40
+60
+80
+γ / mN m
+-1
+Experiment
+DPMD
+TIP4P/2005
+400
+500
+600
+T / K
+20
+30
+40
+∆Hvap / kJ mol
+-1
+Experiment
+DPMD
+TIP4P/2005
+400
+500
+600
+T / K
+0
+50
+100
+150
+200
+Psat / bar
+Figure 2: (a) Phase diagram in the T–ρ plane of the DPMD model (green), TIP4P/2005 model (blue) [48] and
+experimental measurements of water (black) [47]. Filled circles represent the vapor and liquid densities, estimated
+from the averaged bulk densities from DC simulations. Inset: Snapshot of a DC simulation performed at 385 K with
+the DPMD model, rendered making use of Ovito software [3]. (b) Liquid-vapor interfacial free energy (γ) as a
+function of temperature for the DPMD model (green), and comparison with the TIP4P/2005 model (blue) [49] and
+experimental values (black) [47]. (c) Vapor saturation pressure (Psat) as a function of temperature for the DPMD
+model (green), TIP4P/2005 (blue) [48] and comparison with experimental values (black) [47]. Inset: Enthalpy of
+vaporization (∆Hvap) as a function of temperature for DPMD, TIP4P/2005 [48] and experimental values [47] as
+indicated in the legend.
+TIP4P/2005 model [49] and experimental measurements
+[47]. From DC simulations we also calculate the satura-
+tion pressure (Psat) as a function of temperature. Psat is
+obtained as the component of the pressure tensor normal
+to the interface. We plot it in Figure 2(c), compared to
+the values obtained from TIP4P/2005 (blue) [48] and
+experiments (black) [47]. This quantity closely matches
+with experimental measurements, while the TIP4P/2005
+model underestimates it, which is a natural consequence
+of the way the DPMD model was shifted to match the
+vapor densities. We note that the temperature shift was
+applied in order to obtain a better match of the vapor
+phase behaviour, nonetheless this shift affects negatively
+on the surface tension prediction.
+With no temper-
+ature shift, the surface tension of the DPMD model
+matches the experimental one at temperatures above
+450 K, and only underestimates it by ∼ 5% at T < 450 K.
+We estimated the enthalpy of vaporization (∆Hvap)
+from independent bulk simulations of both liquid and
+vapor phases.
+For this, we perform canonical simu-
+lations at the equilibrium density of the given phase,
+which was previously obtained from DC simulations.
+From each simulation the enthalpy is directly obtained
+as H
+= U − PV , where U is the internal energy.
+The enthalpy of vaporization is simply calculated as
+∆Hvap = Hvapor − Hliquid for every temperature. The
+values of ∆Hvap are plotted against temperature in
+Figure 2(c) (inset), along with values from TIP4P/2005
+[48] and experiments [47]. This quantity slightly deviates
+from the experimental values at low temperatures (< 550
+K), but matches at higher temperatures. In contrast, the
+TIP4P/2005 model slightly underestimates the enthalpy
+of vaporization across all temperatures examined.
+In summary, the DPMD model describes the liquid-
+vapor coexistence properties after applying the temper-
+ature shift of 40 K reasonably well. Some discrepancies
+may arise from the fact that this model has been trained
+on solid and liquid data only [42], but the main source of
+differences from experimental data are limitations in ac-
+curacy for the SCAN density functions used to train the
+model. . The biggest difference with experimental values
+is found in the surface tension, which is underestimated
+by ∼20 %. Other than this discrepancy, the phase dia-
+gram, saturation pressure, and enthalpy of vaporization
+are well described using the DPMD model. In addition
+to the plots in Figure 2, we provide the equilibrium data
+of the DPMD model in Table I.
+T (K) ρl (g·cm−3) ρv (g·cm−3) Psat (bar) γ (mN·m−1)
+385
+0.9697(5)
+0.0011(3)
+2.3(3)
+41(3)
+410
+0.9484(8)
+0.0022(4)
+4.9(5)
+31(7)
+435
+0.9242(6)
+0.0037(6)
+8.3(9)
+31(7)
+460
+0.8969(8)
+0.0067(9)
+15(1)
+27(4)
+485
+0.865(3)
+0.012(4)
+25(3)
+24(5)
+510
+0.831(2)
+0.016(2)
+35(4)
+19(5)
+535
+0.791(1)
+0.024(1)
+48(7)
+15(7)
+560
+0.740(6)
+0.039(5)
+71(6)
+14(5)
+585
+0.684(8)
+0.058(4)
+98(15)
+7(8)
+597
+0.62(1)
+0.079(5)
+114(5)
+6(9)
+Table I: Data for the liquid (ρl) and vapor (ρv)
+densities, saturation pressure (Psat) and surface tension
+(γ) as a function of temperature for the DPMD model.
+The numbers in parenthesis depict the uncertainty of
+our measurements, and apply to the numeral left of
+themselves, for instance 41(3) stands for 41±3.
+
+6
+B.
+Bubble nucleation
+After establishing the equilibrium properties of the
+DPMD water model, we proceeded to investigate its
+cavitation.
+Although some experimental studies of
+water cavitation have been conducted [62–66], it is
+difficult to establish a direct comparison due to the lack
+of measurements of the nucleation rate.
+Menzl et al.
+[53] performed a nucleation study utilizing Umbrella
+Sampling (US) calculations [121] for the TIP4P/2005
+model, in which the nucleation free energy barrier and
+the nucleation rate were reported, without comparisons
+to experimental data. Here, we employ the NVT seeding
+technique at the same temperature (296.4 K) as in Ref.
+[53] for both the TIP4P/2005 (to establish the validity
+of our methods) and DPMD models (to provide new
+data for this ab-initio based model).
+We prepared various systems in which we artificially
+generated a cavity of a given size, starting from a bulk
+liquid configuration.
+As detailed in Section II C, the
+system spontaneously evolves and equilibrates into a
+state in which there is a critical bubble that remains
+stable over time, due to the fact that in the canonical
+ensemble, a critical bubble represents a local minimum
+in the Helmholtz free energy landscape [54, 86]. Once
+equilibrated, we measured the system pressure by means
+of the virial expression [122] which corresponds to the
+liquid phase pressure [85]. To track the critical radius,
+we made use of our order parameter (see Section II C).
+We repeated this process for each configuration, and
+then averaged over more than 500 independent radial
+density profiles for the calculation of the radius.
+We used our data for ∆P and Rc along with Eq. 6
+to compute J, which is plotted in Figure 3(a) (blue and
+green squares for TIP4P/2005 and DPMD respectively)
+against P. It can be seen that there is agreement within
+the simulation uncertainties between the US and seeding
+simulations for the TIP4P/2005 model. We also include
+a continuous line for each model, which represents a fit
+to the CNT equation, in which we linearly fit γ against
+P, and insert values from such fit to solve Eq. 6. The
+uncertainty is estimated from the standard deviation of
+the radius between different independent configurations.
+We computed J at higher superstreching conditions
+(green and blue diamonds in Fig.
+3) through ”brute
+force” simulations. In these simulations, we observed the
+metastable bulk liquid under high superstreching con-
+ditions in the NPT ensemble for a sufficient time before
+spontaneous cavitation takes place. Then, J is calculated
+as
+J =
+1
+< t > V
+(10)
+where < t > is the average time required for cavitation
+to occur and V is the volume of the metastable liquid
+phase. The onset of cavitation can easily be identified
+with a sudden and sharp change in properties such as
+the simulation box volume or the potential energy. From
+these simulations we obtain J = 2.52·10−6 ps−1nm−3 at
+P = −150 MPa for the DPMD model, and J = 2.44·10−5
+ps−1nm−3 and P = −200 MPa for the TIP4P/2005
+potential. These results are also shown in Figure 3(a),
+and match with the trend of US and seeding simulations.
+This result, in addition to the agreement with the US
+calculations from Menzl et al., provides confidence in
+the validity of the results obtained using CNT.
+In addition to the nucleation rate, we also obtained
+the free energy barrier (∆G∗) which can be estimated
+from Eq.
+4.
+This quantity is the main output from
+US simulations [53].
+In Figure 3(b) we compare the
+calculated free energy barriers for the DPMD (green)
+and TIP4P/2005 (blue) models, also including data from
+Ref. [53]. As expected, we find good agreement between
+seeding and US calculations as for the nucleation rates.
+It can be seen in Figure 3(a) that the DPMD model re-
+turns nucleation rates many orders of magnitude greater
+than the TIP4P/2005 potential, outside the uncertainty
+bounds, despite the close resemblance of the phase dia-
+grams from the two models (Fig. 2(a)). This difference is
+also present for the free energy barrier (Fig. 3(b)), with
+the TIP4P/2005 model possessing a higher free energy
+barrier. This is likely the crucial factor behind its lower
+nucleation rate. In order to understand the differences
+between the two models we also compared the change of
+the surface tension with curvature for both models: In
+Figure 4 we plot γ as a function of P, where filled points
+correspond to the value obtained at the coexistence pres-
+sure from DC simulations, while the empty points depict
+the value of γ obtained through Laplace’s equation (Eq.
+5) from our seeding simulations. From this analysis we
+observe that the surface tension is significantly lower for
+the DPMD model, not only under coexistence conditions,
+but also in the cavitation regime. This directly points to-
+wards the surface tension being the decisive factor behind
+the quantitative difference in J and ∆G∗ between the
+DPMD and TIP4P/2005 models. In Table II we detail
+the different quantities playing a role in Eqs. 2-4. Since
+the kinetic prefactor in the calculation of J is of the same
+order of magnitude in all cases, we can conclude that the
+different nucleation rates between the TIP4P/2005 and
+DPMD models arises from a quantitative difference in
+the surface tension, which is lower for the DPMD.
+C.
+Determination of the Tolman length
+Another quantity we can extract from our simulations
+is the Tolman length, which describes the deviation of
+the surface tension with respect to its value at the planar
+interface and, therefore, the coexistence conditions. The
+
+7
+(a)
+(b)
+-200
+-150
+-100
+-50
+P / MPa
+10
+-160
+10
+-120
+10
+-80
+10
+-40
+10
+0
+J / (ps
+-1nm
+-3)
+TIP4P/2005 Menzl at al. US, PNAS (2016)
+TIP4P/2005 Seeding
+TIP4P/2005 Brute Force
+DPMD Seeding
+DPMD Brute Force
+-200
+-175
+-150
+-125
+-100
+-75
+-50
+P / MPa
+0
+50
+100
+150
+200
+∆G* / kBT
+TIP4P/2005 Menzl et al. US, PNAS (2016)
+TIP4P/2005 Seeding
+DPMD Seeding
+Figure 3: (a) Nucleation rate (J) as a function of pressure (P) for TIP4P/2005 (blue) and DPMD (green) cavitation
+at 296.4 K, including data from Ref. [53]. Continuous lines are obtained by linearly fitting the surface tension (γ) as
+a function of pressure, and then inserting such γ into Eqs. 5 and 6. The shaded region is obtained in the same way
+but making use of the upper and lower bounds of the surface tension error and, therefore, represent the error limits
+in J (b) Free energy barrier for bubble nucleation as a function of pressure at 296.4 K for TIP4P/2005 (blue) and
+DPMD (green) models, estimated from CNT (Eq. 4).
+P (MPa) Rc (nm) ρl (g·cm−3)
+NT
+γ (N·m−1) ∆G∗/kBT log10(J / (ps−1·nm−3))
+DPMD
+-81.9
+1.25
+0.965
+7527
+51.0
+71.5
+-29.5
+-69.1
+1.50
+0.972
+7386
+51.9
+105.7
+-44.4
+-60.3
+1.74
+0.977
+7161
+52.6
+144.4
+-61.2
+-54.4
+1.96
+0.980
+6888
+53.2
+183.5
+-78.2
+-47.1
+2.29
+0.984
+10324
+53.8
+253.7
+-108.6
+-43.7
+2.50
+0.986
+9825
+54.7
+309.2
+-132.7
+TIP4P/2005
+-96.9
+1.24
+0.953
+6855
+59.9
+93.6
+-39.1
+-87.6
+1.38
+0.956
+6796
+60.3
+116.8
+-49.2
+-77.0
+1.59
+0.960
+23814
+61.2
+158.5
+-67.3
+-73.0
+1.68
+0.961
+11385
+61.5
+178.2
+-75.8
+-61.9
+2.01
+0.965
+11006
+62.0
+255.3
+-109.3
+-54.9
+2.29
+0.968
+10570
+62.8
+337.3
+-144.9
+Table II: NVT seeding data for the DPMD and TIP4P/2005 models, including the nucleation pressure (P), the
+critical radius (Rc), the liquid density (ρl), the total number of water molecules in the system (NT ), the surface
+tension (γ), the free energy barrier (∆G∗), and the logarithm of the nucleation rate (log10J).
+Tolman length can also be defined as the deviation of the
+surface of tension from the equimolar dividing surface. In
+1949, Tolman showed that the change in surface tension
+with curvature follows the equation [67]
+γ =
+γ0
+1 + 2δ
+Rc
+(11)
+where γ0 is the value of the surface tension under
+coexistence conditions and δ is the Tolman length. This
+quantity has been extensively studied for Lennard-Jones
+particles [61, 123–126], Hard Spheres [86] and other
+systems [123, 124, 127, 128].
+Here we make use of
+Tolman’s expression and compute δ for both the DPMD
+and TIP4P/2005 models at 296.4 K. We fit our surface
+tension and critical radius data (obtained from the
+NVT seeding simulations) to Eq.
+11, performing a
+non-linear regression.
+We choose to have γ0 and δ as
+fitting parameters, despite having estimated the former
+from the DC simulations.
+We took this approach in
+order to corroborate the value of γ obtained from both
+approaches.
+In Figure 5 we plot the surface tension against the
+inverse of the critical radius for the DPMD (green filled
+points) and TIP4P/2005 (blue filled points) models.
+
+8
+-100
+-80
+-60
+-40
+-20
+0
+P / MPa
+40
+45
+50
+55
+60
+65
+70
+γ / N m
+-1
+TIP4P/2005
+DPMD
+Figure 4: Liquid-vapor surface tension (γ) as a function
+of pressure at 296.4 K for TIP4P/2005 (blue) and
+DPMD (green). Empty circles are obtained from
+cavitation simulations (and therefore with a curved
+interface) by means of Laplace’s equation (see Section
+II C), while filled points were estimated from DC
+simulations as in Fig.2.
+From non-linear regression we obtain δ = (0.091±0.008)
+nm for the DPMD model and δ = (0.070 ± 0.004) nm
+for the TIP4P/2005 model. Both values are positive as
+expected, since the surface tension decreases for smaller
+bubbles.
+In Figure 5 we also show with dashed lines
+how the surface tension changes against the inverse of
+the critical radius according to Eq.
+11.
+From the fit
+we also obtain values for the surface tension at planar
+interface of 58 ± 2 and 67 ± 3 mN·m−1 for the DPMD
+and TIP4P/2005 models respectively.
+These values
+are in agreement, within statistical uncertainties, with
+those obtained from DC simulations (54 and 70 [49]
+mN·m−1 for DPMD and TIP4P/2005 respectively). The
+uncertainty of δ is simply determined by the error in
+the non-linear fit, while the uncertainty in γ0 is the
+sum of the errors coming from NVT seeding simula-
+tions (see Section III B) and the error in the fit to Eq. 11.
+Our results are also in good agreement with previ-
+ous simulation results [54, 129] (at different tempera-
+tures: 0.199 nm at 300 K [54], 0.09 nm at 250 K [129]
+and 0.18 nm at 350 K) which indicate that the Tol-
+man length is positive for water bubbles, in contrast to
+the negative sign in water droplets (i.e. condensation)
+[56, 57], where the surface tension increases with curva-
+ture. We can establish direct comparison with the calcu-
+lations from Menzl et al. [53], which were performed with
+TIP4P/2005 at the same temperature (296.4 K). They
+obtained values of δ = 0.195nm and γ0=82.79 mN·m−1,
+which while having the same order of magnitude, mod-
+erately disagree with our calculations of γ0 and δ. In the
+case of Ref. [53] the employed local order parameter does
+not necessarily identify an accurate value of the radius,
+0
+0.2
+0.4
+0.6
+0.8
+Rc
+-1 / nm
+-1
+45
+50
+55
+60
+65
+70
+γ / mN m
+-1
+DPMD
+TIP4P/2005
+Figure 5: Surface tension γ against the inverse of the
+critical radius (R−1
+c ). Filled points represent the surface
+tension obtained from Laplace’s equation (Eq. 5). The
+dashed lines indicate the change in surface tension
+according to Tolman’s equation (Eq. 11), where the
+parameters δ and γ0 were obtained through non-linear
+regression. We plot the values of surface tension at
+planar interface (R−1
+c =0) obtained from the fit with
+empty points. The surface tension values obtained from
+DC are also represented here with filled diamonds, also
+at P = 0.
+but is instead used to bias the sampling of the configu-
+rational space for US simulations, and may therefore not
+represent accurate values of δ and γ0. As mentioned be-
+fore, the good agreement in the nucleation free energy
+barrier between US and seeding calculations is a good
+sign. In our case, a good indicator for the calculation
+of the Tolman length, although not definitive, is the fact
+that the surface tension obtained from the non-linear re-
+gression to Eq. 11 provides a value of γ0 that matches
+within the uncertainty the surface tension obtained from
+DC simulations, as aforementioned.
+D.
+Liquid-vapor interfacial characterization
+Finally, we examined the organization of the liquid-
+vapor interface in our simulations for both planar and
+curved interfaces.
+The water-air planar interface has
+been widely studied in the past [130] with IR vibrational
+spectra experiments [131–134], ab initio [135–138] and
+MD simulations [139–141], all of which generally agree
+regarding the orientation of water molecules near the
+interface. Interfacial molecules closer to the vapor phase
+tend to orient the O-H bond parallel to the surface
+normal vector and expose the H atom, resembling the
+(1000) crystal face of ice Ih (only in the dimension per-
+pendicular to the surface) [141]. The (1000) ice Ih-liquid
+is the direction with lower interfacial free energy of the
+
+9
+different solid-liquid interfaces [142], therefore in the
+liquid-vapor interface a similar arrangement may also
+reduce the surface tension, apart from maximizing the
+enthalpic gain of the more exposed interfacial molecules
+to the vapor phase. To perform this analysis, we follow
+the same approach as in Refs. [138, 141] where, once the
+interfacial region has been identified, the angle formed
+by the O-H bonds and the vector normal to the interface
+(θH) is computed.
+Fan et al.
+[141] and Vassilev et
+al.
+[138] identified two distinct layers in non-curved
+interfaces:
+an external layer, which comprehends the
+region in which the density is between 5-50% of the
+bulk liquid, and an internal layer, where the density
+ranges between 50-95% of the bulk liquid density. Fan et
+al. [141] measured the orientation distributions for the
+TIP3P, TIP4P-EW, TIP5P and SPC/E water models
+at 300K, and for comparison purposes, we perform the
+same analysis with the DPMD and TIP4P/2005 models,
+and obtain results also for curved interfaces.
+In Figure 6(a) we depict how the different interfacial
+regions and θH angle are identified for both planar (top)
+and curved (bottom) interfaces. There, the dashed black
+line indicates the liquid-vapor interface as defined by our
+order parameter (see section II C and Supplementary
+Material (SM)). In the zoomed image, the internal
+and external layers of the interface are labelled and
+highlighted in black and red, as well as the bulk liquid
+and vapor phases in green and white respectively. The
+two arrows indicate the normal vector to the interface
+and the O-H bond vector, and the angle between these
+two vectors defines θH.
+In Figure 6(b-c) We plot the
+θH distributions normalized by the random distribu-
+tion sin(θH).
+Consistent with previous calculations
+[137, 138, 140, 141], the molecules expose one hydrogen
+atom to the vapor phase in the external layer, as can
+be seen in Figure 6(b)(top) for the TIP4P/2005 model,
+where we show the probability distribution of the angle
+θH for the different interfacial regions.
+Smaller angles
+are more probable in the external layer than in the bulk,
+where all directions are equally probable (flat green
+line). As discussed in Ref. [141], the internal layer of the
+interface also displays preferential orientations, in order
+to maximise the interactions with the structure created
+in the external layer, in an arrangement that leads to
+a maximum near θH ∼80º. It must be noted that the
+preferential molecular orientations are not fixed, but
+rather transient. The distributions presented in Figure
+6(b)(top) are also consistent with the results by Fan et
+al. [141] for other rigid semi-empirical models.
+We extended this analysis to curved interfaces, using
+our NVT seeding simulations.
+In curved interfaces,
+the vector normal to the interface points at the bubble
+center. In Figure 6(b)(bottom) we show the probability
+distribution of θH for the three interfacial regions, and
+observe how these resemble those of planar interface.
+A significant loss of ordering is observed for the curved
+interface since the peaks at ∼ 15º and ∼ 115º in the
+external layer, and at ∼ 80º in the internal layer are
+less prominent compared to the the corresponding peaks
+for the flat interface.
+This could result of the curved
+geometry of the interface sterically impeding a better
+rearrangement of the interfacial molecules.
+We also evaluated the θH distribution for the DPMD
+model. In Figure 6(c)(top) we present the distribution
+of the three interfacial regions for the planar interface
+at 296.4 K. There is an obvious preferential orientation
+towards small angles in the external layer, once again
+indicating the preference of molecules to expose one
+hydrogen atom to the vapor phase.
+The distribution
+is remarkably more prominent for the DPMD model
+relative to TIP4P/2005, although both models result
+in similar molecular arrangements. In Ref. [138], this
+same structure was found in ab initio calculations using
+PW91 functional, confirming that the DPMD model
+based on the SCAN functional yields similar results to
+those obtained from ab initio MD simulations using
+different density functionals.
+Looking at the DPMD model distributions for curved
+interfaces (Figure 6(c)(bottom)), we still find a preferen-
+tial ordering towards small angles, although it is much
+less pronounced than in the case of planar interfaces, in
+agreement with TIP4P/2005 simulations. The bubbles
+generated by both models shown here (TIP4P/2005 and
+DPMD) have comparable sizes, however the effect of cur-
+vature is more dramatic in the case of the DPMD model.
+Other bubble size distributions are reported in the SM,
+where we observe that there is a slight change in the
+distributions, with bigger bubbles resulting curves more
+similar to those found at coexistence (Figure S3).
+IV.
+CONCLUSIONS
+In this work, we explored the liquid-vapor phase behav-
+ior of a Deep Potential model based on ab initio energies
+and forces. This model was derived from the SCAN ap-
+proximation of density functional theory [42]. The model
+has been shown to reproduce the phase diagram for the
+different ice phases [42] and to have a liquid-liquid phase
+transition in the supercooled regime [116]. We computed
+the phase diagram via DC simulations, and adjusted
+our vapor equilibrium densities to the experimental val-
+ues, resulting in a shift of 40 K in the DPMD model.
+Once the model was tested and shifted, we compare its
+equilibrium properties with experimental data and the
+TIP4P/2005 model [10], one of the most benchmarked
+classical models for water [48, 49, 53, 139]. The surface
+tension of the DPMD model is lower than the one ob-
+tained from TIP4P/2005 and experiments. Nonetheless,
+by construction the DPMD model provides accurate re-
+sults for other properties such as the vapor saturation
+pressure for a wide range of temperatures, between 300
+
+10
+(a)
+(b)
+(c)
+TIP4P/2005
+DPMD
+Planar interface
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+2.5
+3
+P(θH)
+External layer
+Internal layer
+Bulk water
+Curved interface
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+Rc=2.01nm
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+Rc=1.96nm
+Figure 6: (a) Top: Slab snapshot (including only a reduced amount of molecules for better visualization) of a planar
+interface. Bottom: Snapshot for a curved interface. (b) Normalized histograms of θH at the external region of the
+interface, the internal one, and bulk water for the TIP4P/2005 model for planar (top) and curved (bottom)
+interfaces. (c) Same as in (b) but for the DPMD model.
+and 600 K (Figure 2). Overall, once the temperature is
+shifted, the model reproduces most of the properties of
+liquid-vapor equilibrium, despite not having this regime
+included in its training. This result is especially remark-
+able since this is the first Deep Potential-based model
+to provide liquid-vapor properties in a computationally
+affordable time, with the primary drawback being the
+∼20% deviation in the surface tension.
+Moreover, we study bubble nucleation in the cavita-
+tion regime. We make use of the NVT seeding method,
+a rare event technique already shown to be successful
+in determining the nucleation free energy barrier and
+the nucleation rate for simpler systems [85, 107] in
+cavitation events.
+We first performed NVT seeding
+calculations at 296.4 K, a temperature at which previous
+data from Umbrella Sampling are available for the
+TIP4P/2005 model and we confirm that the seeding
+technique provides consistent results with those from
+Menzl et al.
+[53].
+The DPMD water model provides
+higher nucleation rates than the TIP4P/2005 model
+under the same stretching conditions. We show that this
+quantitative difference can be explained by the difference
+in surface tension between models, which persists for
+curved interfaces (Figure 4). Our results highlight once
+more the relevance of the surface tension and its change
+with curvature to critically control nucleation events
+[53, 129]. We could have obtained closer agreement be-
+tween the TIP4P/2005 nucleation rates with those from
+the DPMD model if we did not apply the temperature
+shift, nonetheless we prioritised adjusting the model to
+obtain better equilibrium densities, in line with prior
+studies of water properties using the SCAN-derived
+DPMD model [115–117].
+Furthermore, we provide an estimate of the Tolman
+length by performing a non-linear regression to the
+relevant expression [67], which describes how the surface
+tension changes with curvature (Eq.
+11).
+Using data
+from our NVT seeding simulations we obtain estimates
+of δ = (0.091 ± 0.008) nm for the DPMD model and
+δ = (0.070 ± 0.004) nm for the TIP4P/2005 model, both
+at 296.4 K. This confirms that a Deep Potential-based
+model also predicts a positive sign of the Tolman length,
+confirming previous results showing a decrease of the
+surface tension with curvature for the case of water
+bubbles [53, 54, 129].
+Finally,
+we studied the orientation of the water
+molecules
+in
+the
+interface,
+corroborating
+previous
+studies that have indicated that the molecules closer to
+the vapor phase have a preference so as to expose an
+hydrogen atom facing the vapor [130–136, 139–141]. We
+quantify this behavior by measuring the angle formed
+between the normal vector to the interface and the O-H
+bond. We find that a preferential molecular orientation
+appears for both the TIP4P/2005 and DPMD models.
+We also confirm that this phenomenon also takes place
+in the curved interface of water bubbles, although the
+
+Vaporphase
+External layer
+Internal layel
+Bulk water11
+possibility to orient more O-H bonds towards the vapor
+is diminished for curved interfaces due to the increasing
+curvature of the bubbles.
+Overall, this study confirms that machine-learning ab
+initio based models that capture more molecular details
+than semi-empirical models are viable for prediction
+of equilibrium as well as dynamic properties that
+require large system sizes and long sampling times. The
+computational cost of ab initio based models in long
+scale Molecular Dynamics is now affordable being only
+an order of magnitude greater than that for empirical
+potentials,
+thanks to recent improvements such as
+the compressed Deep Potential modelling scheme [71].
+Further work and models trained with more liquid
+and vapor data will only improve the already existing
+models, which will gradually be better in describing the
+real behaviour of water.
+ACKNOWLEDGMENTS
+I. S.-B. acknowledges funding from Derek Brewer
+scholarship of Emmanuel College and EPSRC Doc-
+toral
+Training
+Programme
+studentship,
+number
+EP/T517847/1.
+J.
+R.
+E.
+acknowledges
+funding
+from the Roger Ekins Research Fellowship of Emmanuel
+College, Oppenheimer Research Fellowship of the Uni-
+versity of Cambridge and the Ramon y Cajal fellowship
+(RYC2021-030937-I). M. C. M and A. Z. P acknowledge
+the “Chemistry in Solution and at Interfaces” (CSI)
+Center funded by the U.S. Department of Energy
+Award DE-SC001934 and Award DE-SC0002128. Com-
+putational resources were provided by the Princeton
+Research Computing at Princeton University which is
+a consortium of groups led by the Princeton Institute
+for Computational Science and Engineering (PICSciE)
+and the Office of Information Technology’s Research
+Computing.
+[1] A. Chanda and V. V. Fokin, “Organic synthesis “on wa-
+ter”,” Chemical reviews, vol. 109, no. 2, pp. 725–748, 2009.
+[2] M. Chaplin, “Do we underestimate the importance of wa-
+ter in cell biology?,” Nature Reviews Molecular Cell Biol-
+ogy, vol. 7, no. 11, pp. 861–866, 2006.
+[3] E. Lester, P. Blood, J. Denyer, D. Giddings, B. Azzopardi,
+and M. Poliakoff, “Reaction engineering: The supercriti-
+cal water hydrothermal synthesis of nano-particles,” The
+Journal of Supercritical Fluids, vol. 37, no. 2, pp. 209–214,
+2006.
+[4] A. Ponomarenko, O. Vincent, A. Pietriga, H. Cochard,
+´E. Badel, and P. Marmottant, “Ultrasonic emissions reveal
+individual cavitation bubbles in water-stressed wood,”
+Journal of the Royal Society Interface, vol. 11, no. 99,
+p. 20140480, 2014.
+[5] T. D. Wheeler and A. D. Stroock, “The transpiration of
+water at negative pressures in a synthetic tree,” Nature,
+vol. 455, no. 7210, pp. 208–212, 2008.
+[6] U. Adhikari, A. Goliaei, and M. L. Berkowitz, “Mechanism
+of membrane poration by shock wave induced nanobubble
+collapse: A molecular dynamics study,” The Journal of
+Physical Chemistry B, vol. 119, no. 20, pp. 6225–6234,
+2015.
+[7] D. Yu, B. Liu, and B. Wang, “The effect of ultrasonic
+waves on the nucleation of pure water and degassed wa-
+ter,” Ultrasonics sonochemistry, vol. 19, no. 3, pp. 459–
+463, 2012.
+[8] P. Kumar and R. Saini, “Study of cavitation in hydro tur-
+bines—a review,” Renewable and Sustainable Energy Re-
+views, vol. 14, no. 1, pp. 374–383, 2010.
+[9] J. Ma, A. Michaelides, D. Alfe, L. Schimka, G. Kresse, and
+E. Wang, “Adsorption and diffusion of water on graphene
+from first principles,” Physical Review B, vol. 84, no. 3,
+p. 033402, 2011.
+[10] J. L. Abascal and C. Vega, “A general purpose model for
+the condensed phases of water: Tip4p/2005,” The Journal
+of chemical physics, vol. 123, no. 23, p. 234505, 2005.
+[11] J. Abascal, E. Sanz, R. Garc´ıa Fern´andez, and C. Vega,
+“A potential model for the study of ices and amor-
+phous water: Tip4p/ice,” The Journal of chemical physics,
+vol. 122, no. 23, p. 234511, 2005.
+[12] M. W. Mahoney and W. L. Jorgensen, “Quantum, in-
+tramolecular flexibility, and polarizability effects on the re-
+production of the density anomaly of liquid water by sim-
+ple potential functions,” The Journal of Chemical Physics,
+vol. 115, no. 23, pp. 10758–10768, 2001.
+[13] W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W.
+Impey, and M. L. Klein, “Comparison of simple poten-
+tial functions for simulating liquid water,” The Journal of
+chemical physics, vol. 79, no. 2, pp. 926–935, 1983.
+[14] H. W. Horn, W. C. Swope, and J. W. Pitera, “Character-
+ization of the tip4p-ew water model: Vapor pressure and
+boiling point,” The Journal of chemical physics, vol. 123,
+no. 19, p. 194504, 2005.
+[15] H. Berendsen, J. Grigera, and T. Straatsma, “The miss-
+ing term in effective pair potentials,” Journal of Physical
+Chemistry, vol. 91, no. 24, pp. 6269–6271, 1987.
+[16] M. W. Mahoney and W. L. Jorgensen, “A five-site
+model for liquid water and the reproduction of the density
+anomaly by rigid, nonpolarizable potential functions,” The
+Journal of chemical physics, vol. 112, no. 20, pp. 8910–
+8922, 2000.
+[17] V. Molinero and E. B. Moore, “Water modeled as
+an intermediate element between carbon and silicon,”
+The Journal of Physical Chemistry B, vol. 113, no. 13,
+pp. 4008–4016, 2009.
+[18] T. Hasegawa and Y. Tanimura, “A polarizable water
+model for intramolecular and intermolecular vibrational
+spectroscopies,” The Journal of Physical Chemistry B,
+vol. 115, no. 18, pp. 5545–5553, 2011.
+[19] P. Ahlstr¨om, A. Wallqvist, S. Engstr¨om, and B. J¨ons-
+son, “A molecular dynamics study of polarizable water,”
+Molecular Physics, vol. 68, no. 3, pp. 563–581, 1989.
+[20] L.-P. Wang, T. Head-Gordon, J. W. Ponder, P. Ren, J. D.
+Chodera, P. K. Eastman, T. J. Martinez, and V. S. Pande,
+
+12
+“Systematic improvement of a classical molecular model
+of water,” The Journal of Physical Chemistry B, vol. 117,
+no. 34, pp. 9956–9972, 2013.
+[21] V. Babin, C. Leforestier, and F. Paesani, “Develop-
+ment of a “first principles” water potential with flexible
+monomers: Dimer potential energy surface, vrt spectrum,
+and second virial coefficient,” Journal of chemical theory
+and computation, vol. 9, no. 12, pp. 5395–5403, 2013.
+[22] B. Santra, A. Michaelides, and M. Scheffler, “On the ac-
+curacy of density-functional theory exchange-correlation
+functionals for h bonds in small water clusters: Bench-
+marks approaching the complete basis set limit,” The
+Journal of chemical physics, vol. 127, no. 18, p. 184104,
+2007.
+[23] E. Lambros and F. Paesani, “How good are polarizable
+and flexible models for water: Insights from a many-body
+perspective,” The Journal of Chemical Physics, vol. 153,
+no. 6, p. 060901, 2020.
+[24] H. W. Horn, W. C. Swope, J. W. Pitera, J. D. Madura,
+T. J. Dick, G. L. Hura, and T. Head-Gordon, “Develop-
+ment of an improved four-site water model for biomolec-
+ular simulations:
+Tip4p-ew,” The Journal of chemical
+physics, vol. 120, no. 20, pp. 9665–9678, 2004.
+[25] A. Benavides, J. Aragones, and C. Vega, “Consensus on
+the solubility of nacl in water from computer simulations
+using the chemical potential route,” The Journal of Chem-
+ical Physics, vol. 144, no. 12, p. 124504, 2016.
+[26] J. Espinosa, J. Young, H. Jiang, D. Gupta, C. Vega,
+E. Sanz, P. G. Debenedetti, and A. Z. Panagiotopoulos,
+“On the calculation of solubilities via direct coexistence
+simulations: Investigation of nacl aqueous solutions and
+lennard-jones binary mixtures,” The Journal of chemical
+physics, vol. 145, no. 15, p. 154111, 2016.
+[27] H. Jiang, A. Haji-Akbari, P. G. Debenedetti, and A. Z.
+Panagiotopoulos, “Forward flux sampling calculation of
+homogeneous nucleation rates from aqueous nacl solu-
+tions,” The Journal of chemical physics, vol. 148, no. 4,
+p. 044505, 2018.
+[28] I. Sanchez-Burgos and J. R. Espinosa, “Direct calculation
+of the planar nacl-aqueous solution interfacial free energy
+at the solubility limit,” arXiv preprint arXiv:2208.08322,
+2022.
+[29] C. P. Lamas, C. Vega, and E. G. Noya, “Freezing point
+depression of salt aqueous solutions using the madrid-2019
+model,” The Journal of chemical physics, vol. 156, no. 13,
+p. 134503, 2022.
+[30] S. Blazquez, M. Conde, J. Abascal, and C. Vega, “The
+madrid-2019 force field for electrolytes in water using
+tip4p/2005 and scaled charges: Extension to the ions f-
+, br-, i-, rb+, and cs+,” The Journal of Chemical Physics,
+vol. 156, no. 4, p. 044505, 2022.
+[31] C. Bergonzo and T. E. Cheatham III, “Improved force
+field parameters lead to a better description of rna struc-
+ture,” Journal of chemical theory and computation, vol. 11,
+no. 9, pp. 3969–3972, 2015.
+[32] M. D. Smith, J. S. Rao, E. Segelken, and L. Cruz, “Force-
+field induced bias in the structure of aβ21–30: A compar-
+ison of opls, amber, charmm, and gromos force fields,”
+Journal of Chemical Information and Modeling, vol. 55,
+no. 12, pp. 2587–2595, 2015.
+[33] P. M. Piaggi and R. Car, “Phase equilibrium of liquid wa-
+ter and hexagonal ice from enhanced sampling molecular
+dynamics simulations,” The Journal of chemical physics,
+vol. 152, no. 20, p. 204116, 2020.
+[34] E. Sanz, C. Vega, J. Espinosa, R. Caballero-Bernal,
+J. Abascal, and C. Valeriani, “Homogeneous ice nucle-
+ation at moderate supercooling from molecular simula-
+tion,” Journal of the American Chemical Society, vol. 135,
+no. 40, pp. 15008–15017, 2013.
+[35] J. R. Espinosa, C. Vega, C. Valeriani, and E. Sanz, “Seed-
+ing approach to crystal nucleation,” The Journal of chem-
+ical physics, vol. 144, no. 3, p. 034501, 2016.
+[36] H. Niu, Y. I. Yang, and M. Parrinello, “Temperature
+dependence of homogeneous nucleation in ice,” Physical
+review letters, vol. 122, no. 24, p. 245501, 2019.
+[37] R. A. Friesner, “Ab initio quantum chemistry: Method-
+ology and applications,”
+Proceedings of the National
+Academy of Sciences, vol. 102, no. 19, pp. 6648–6653,
+2005.
+[38] V. Mlynsky, P. Banas, J. Sponer, M. W. van der Kamp,
+A. J. Mulholland, and M. Otyepka, “Comparison of ab ini-
+tio, dft, and semiempirical qm/mm approaches for descrip-
+tion of catalytic mechanism of hairpin ribozyme,” Jour-
+nal of Chemical Theory and Computation, vol. 10, no. 4,
+pp. 1608–1622, 2014.
+[39] R. Gerber, D. Shemesh, M. Varner, J. Kalinowski, and
+B. Hirshberg, “Ab initio and semi-empirical molecular
+dynamics simulations of chemical reactions in isolated
+molecules and in clusters,” Physical Chemistry Chemical
+Physics, vol. 16, no. 21, pp. 9760–9775, 2014.
+[40] L. Zhang, J. Han, H. Wang, R. Car, and E. Weinan,
+“Deep potential molecular dynamics:
+a scalable model
+with the accuracy of quantum mechanics,” Physical re-
+view letters, vol. 120, no. 14, p. 143001, 2018.
+[41] Y. Zhang, H. Wang, W. Chen, J. Zeng, L. Zhang,
+H. Wang, and E. Weinan, “Dp-gen: A concurrent learning
+platform for the generation of reliable deep learning based
+potential energy models,” Computer Physics Communica-
+tions, vol. 253, p. 107206, 2020.
+[42] L. Zhang, H. Wang, R. Car, and E. Weinan, “Phase di-
+agram of a deep potential water model,” Physical review
+letters, vol. 126, no. 23, p. 236001, 2021.
+[43] J. Sun, A. Ruzsinszky, and J. P. Perdew, “Strongly con-
+strained and appropriately normed semilocal density func-
+tional,” Physical review letters, vol. 115, no. 3, p. 036402,
+2015.
+[44] J. Sun, R. C. Remsing, Y. Zhang, Z. Sun, A. Ruzsin-
+szky, H. Peng, Z. Yang, A. Paul, U. Waghmare, X. Wu,
+et al., “Accurate first-principles structures and energies of
+diversely bonded systems from an efficient density func-
+tional,” Nature chemistry, vol. 8, no. 9, pp. 831–836, 2016.
+[45] P. M. Piaggi, J. Weis, A. Z. Panagiotopoulos, P. G.
+Debenedetti, and R. Car, “Homogeneous ice nucleation in
+an ab initio machine-learning model of water,” Proceed-
+ings of the National Academy of Sciences, vol. 119, no. 33,
+p. e2207294119, 2022.
+[46] J. Han, L. Zhang, R. Car, et al., “Deep potential: A
+general representation of a many-body potential energy
+surface,” arXiv preprint arXiv:1707.01478, 2017.
+[47] P. Linstrom and W. Mallard, NIST Chemistry WebBook,
+NIST Standard Reference Database Number 69. Gaithers-
+burg MD: National Institute of Standards and Technology.
+[48] C. Vega, J. Abascal, and I. Nezbeda, “Vapor-liquid
+equilibria from the triple point up to the critical point
+for the new generation of tip4p-like models: Tip4p/ew,
+tip4p/2005, and tip4p/ice,” The Journal of chemical
+physics, vol. 125, no. 3, p. 034503, 2006.
+
+13
+[49] C. Vega and E. de Miguel, “Surface tension of the most
+popular models of water by using the test-area simula-
+tion method,” The Journal of chemical physics, vol. 126,
+no. 15, p. 154707, 2007.
+[50] R. D. Mountain, “An internally consistent method for the
+molecular dynamics simulation of the surface tension: ap-
+plication to some tip4p-type models of water,” The Jour-
+nal of Physical Chemistry B, vol. 113, no. 2, pp. 482–486,
+2009.
+[51] J. Alejandre and G. A. Chapela, “The surface tension
+of tip4p/2005 water model using the ewald sums for the
+dispersion interactions,” The Journal of chemical physics,
+vol. 132, no. 1, p. 014701, 2010.
+[52] H. L. Pi, J. L. Aragones, C. Vega, E. G. Noya, J. L.
+Abascal, M. A. Gonzalez, and C. McBride, “Anomalies
+in water as obtained from computer simulations of the
+tip4p/2005 model: density maxima, and density, isother-
+mal compressibility and heat capacity minima,” Molecular
+Physics, vol. 107, no. 4-6, pp. 365–374, 2009.
+[53] G. Menzl, M. A. Gonzalez, P. Geiger, F. Caupin, J. L.
+Abascal, C. Valeriani, and C. Dellago, “Molecular mech-
+anism for cavitation in water under tension,” Proceedings
+of the National Academy of Sciences, vol. 113, no. 48,
+pp. 13582–13587, 2016.
+[54] S. H. Min and M. L. Berkowitz, “Bubbles in water un-
+der stretch-induced cavitation,” The Journal of Chemical
+Physics, vol. 150, no. 5, p. 054501, 2019.
+[55] J. L. Abascal, M. A. Gonzalez, J. L. Aragones, and C. Va-
+leriani, “Homogeneous bubble nucleation in water at nega-
+tive pressure: A voronoi polyhedra analysis,” The Journal
+of chemical physics, vol. 138, no. 8, p. 084508, 2013.
+[56] M. N. Joswiak, N. Duff, M. F. Doherty, and B. Peters,
+“Size-dependent surface free energy and tolman-corrected
+droplet nucleation of tip4p/2005 water,” The Journal of
+Physical Chemistry Letters, vol. 4, no. 24, pp. 4267–4272,
+2013.
+[57] M. N. Joswiak, R. Do, M. F. Doherty, and B. Peters,
+“Energetic and entropic components of the tolman length
+for mw and tip4p/2005 water nanodroplets,” The Journal
+of chemical physics, vol. 145, no. 20, p. 204703, 2016.
+[58] M. A. Gonzalez,
+J. L. Abascal,
+C. Valeriani,
+and
+F. Bresme, “Bubble nucleation in simple and molecular
+liquids via the largest spherical cavity method,” The Jour-
+nal of Chemical Physics, vol. 142, no. 15, p. 154903, 2015.
+[59] M. A. Gonz´alez, G. Menzl, J. L. Aragones, P. Geiger,
+F. Caupin, J. L. Abascal, C. Dellago, and C. Valeriani,
+“Detecting vapour bubbles in simulations of metastable
+water,” The Journal of chemical physics, vol. 141, no. 18,
+p. 18C511, 2014.
+[60] P. G. Debenedetti, Metastable liquids. Princeton univer-
+sity press, 2021.
+[61] D. Kashchiev, Nucleation. Elsevier, 2000.
+[62] J. Green, D. Durben, G. Wolf, and C. Angell, “Water and
+solutions at negative pressure: Raman spectroscopic study
+to-80 megapascals,” Science, vol. 249, no. 4969, pp. 649–
+652, 1990.
+[63] Q. Zheng, D. Durben, G. Wolf, and C. Angell, “Liquids
+at large negative pressures: water at the homogeneous
+nucleation limit,” Science, vol. 254, no. 5033, pp. 829–832,
+1991.
+[64] A. Alvarenga, M. Grimsditch, and R. Bodnar, “Elastic
+properties of water under negative pressures,” The Journal
+of chemical physics, vol. 98, no. 11, pp. 8392–8396, 1993.
+[65] M. E. M. Azouzi,
+C. Ramboz,
+J.-F. Lenain,
+and
+F. Caupin, “A coherent picture of water at extreme neg-
+ative pressure,” Nature Physics, vol. 9, no. 1, pp. 38–41,
+2013.
+[66] G. Pallares, M. El Mekki Azouzi, M. A. Gonz´alez, J. L.
+Aragones, J. L. Abascal, C. Valeriani, and F. Caupin,
+“Anomalies in bulk supercooled water at negative pres-
+sure,” Proceedings of the National Academy of Sciences,
+vol. 111, no. 22, pp. 7936–7941, 2014.
+[67] R. C. Tolman, “The effect of droplet size on surface ten-
+sion,” The journal of chemical physics, vol. 17, no. 3,
+pp. 333–337, 1949.
+[68] C. G. Salzmann, P. G. Radaelli, B. Slater, and J. L.
+Finney, “The polymorphism of ice: five unresolved ques-
+tions,” Physical Chemistry Chemical Physics, vol. 13,
+no. 41, pp. 18468–18480, 2011.
+[69] W. Wagner, T. Riethmann, R. Feistel, and A. H. Harvey,
+“New equations for the sublimation pressure and melting
+pressure of h2o ice ih,” Journal of Physical and Chemical
+Reference Data, vol. 40, no. 4, p. 043103, 2011.
+[70] A. Brown and E. Whalley, “Preliminary investigation of
+the phase boundaries between ice vi and vii and ice vi and
+viii,” The Journal of Chemical Physics, vol. 45, no. 11,
+pp. 4360–4361, 1966.
+[71] D. Lu, W. Jiang, Y. Chen, L. Zhang, W. Jia, H. Wang,
+and M. Chen, “Dp compress:
+A model compression
+scheme for generating efficient deep potential models,”
+Journal of Chemical Theory and Computation, vol. 18,
+no. 9, pp. 5559–5567, 2022.
+[72] S. Plimpton, “Fast parallel algorithms for short-range
+molecular dynamics,” Journal of Computational Physics,
+vol. 117, pp. 1–19, 3 1995.
+[73] H. Wang, L. Zhang, J. Han, and E. Weinan, “Deepmd-
+kit: A deep learning package for many-body potential en-
+ergy representation and molecular dynamics,” Computer
+Physics Communications, vol. 228, pp. 178–184, 2018.
+[74] S. Nos´e, “A unified formulation of the constant tempera-
+ture molecular dynamics methods,” The Journal of Chem-
+ical Physics, vol. 81, no. 1, pp. 511–519, 1984.
+[75] W. G. Hoover, “Canonical dynamics: Equilibrium phase-
+space distributions,” Phys. Rev. A, vol. 31, pp. 1695–1697,
+Mar 1985.
+[76] W. G. Hoover, “Constant-pressure equations of motion,”
+Physical Review A, vol. 34, no. 3, p. 2499, 1986.
+[77] J. G. Kirkwood and F. P. Buff, “The statistical mechan-
+ical theory of surface tension,” The Journal of Chemical
+Physics, vol. 17, no. 3, pp. 338–343, 1949.
+[78] H. Bekker, H. Berendsen, E. Dijkstra, S. Achterop,
+R.
+Vondrumen,
+D.
+VANDERSPOEL,
+A.
+Sijbers,
+H. Keegstra,
+and M. Renardus,
+“Gromacs-a parallel
+computer for molecular-dynamics simulations,” in 4th
+International Conference on Computational Physics (PC
+92), pp. 252–256, World Scientific Publishing, 1993.
+[79] G. Bussi, D. Donadio, and M. Parrinello, “Canoni-
+cal sampling through velocity rescaling,” The Journal of
+chemical physics, vol. 126, no. 1, p. 014101, 2007.
+[80] M. Parrinello and A. Rahman, “Polymorphic transitions
+in single crystals: A new molecular dynamics method,”
+Journal of Applied physics, vol. 52, no. 12, pp. 7182–7190,
+1981.
+[81] R. W. Hockney, S. Goel, and J. Eastwood, “Quiet high-
+resolution computer models of a plasma,” Journal of Com-
+putational Physics, vol. 14, no. 2, pp. 148–158, 1974.
+
+14
+[82] T. Darden, D. York, and L. Pedersen, “Particle mesh
+ewald: An n log (n) method for ewald sums in large sys-
+tems,” The Journal of chemical physics, vol. 98, no. 12,
+pp. 10089–10092, 1993.
+[83] U. Essmann, L. Perera, M. L. Berkowitz, T. Darden,
+H. Lee, and L. G. Pedersen, “A smooth particle mesh
+ewald method,” The Journal of chemical physics, vol. 103,
+no. 19, pp. 8577–8593, 1995.
+[84] B. Hess, H. Bekker, H. J. Berendsen, and J. G. Fraaije,
+“Lincs: a linear constraint solver for molecular simula-
+tions,” Journal of computational chemistry, vol. 18, no. 12,
+pp. 1463–1472, 1997.
+[85] P.
+Rosales-Pelaez,
+I.
+Sanchez-Burgos,
+C.
+Valeriani,
+C. Vega, and E. Sanz, “Seeding approach to nucleation
+in the n v t ensemble: The case of bubble cavitation in
+overstretched lennard jones fluids,” Physical Review E,
+vol. 101, no. 2, p. 022611, 2020.
+[86] P. Montero de Hijes, J. R. Espinosa, V. Bianco, E. Sanz,
+and C. Vega, “Interfacial free energy and tolman length of
+curved liquid–solid interfaces from equilibrium studies,”
+The Journal of Physical Chemistry C, vol. 124, no. 16,
+pp. 8795–8805, 2020.
+[87] M. Volmer and A. Weber, “Keimbildung in ¨ubers¨attigten
+gebilden,” Zeitschrift f¨ur physikalische Chemie, vol. 119,
+no. 1, pp. 277–301, 1926.
+[88] R. Becker and W. D¨oring, “Kinetische behandlung der
+keimbildung in ¨ubers¨attigten d¨ampfen,”
+Annalen der
+physik, vol. 416, no. 8, pp. 719–752, 1935.
+[89] R. P. Sear, “The non-classical nucleation of crystals: mi-
+croscopic mechanisms and applications to molecular crys-
+tals, ice and calcium carbonate,” International Materials
+Reviews, vol. 57, no. 6, pp. 328–356, 2012.
+[90] J.
+Merikanto,
+E.
+Zapadinsky,
+A.
+Lauri,
+and
+H. Vehkam¨aki, “Origin of the failure of classical nu-
+cleation theory:
+Incorrect description of the smallest
+clusters,”
+Physical
+review
+letters,
+vol.
+98,
+no.
+14,
+p. 145702, 2007.
+[91] A. Cacciuto, S. Auer, and D. Frenkel, “Breakdown of
+classical nucleation theory near isostructural phase tran-
+sitions,” Physical review letters, vol. 93, no. 16, p. 166105,
+2004.
+[92] M. Horsch, J. Vrabec, and H. Hasse, “Modification of the
+classical nucleation theory based on molecular simulation
+data for surface tension, critical nucleus size, and nucle-
+ation rate,” Physical Review E, vol. 78, no. 1, p. 011603,
+2008.
+[93] D. Moroni, P. R. Ten Wolde, and P. G. Bolhuis, “Inter-
+play between structure and size in a critical crystal nu-
+cleus,” Physical review letters, vol. 94, no. 23, p. 235703,
+2005.
+[94] F. Leoni and J. Russo, “Nonclassical nucleation path-
+ways in stacking-disordered crystals,” Physical Review X,
+vol. 11, no. 3, p. 031006, 2021.
+[95] J. R. Espinosa, C. Vega, and E. Sanz, “Homogeneous ice
+nucleation rate in water droplets,” The Journal of Physical
+Chemistry C, vol. 122, no. 40, pp. 22892–22896, 2018.
+[96] B. C. Knott, V. Molinero, M. F. Doherty, and B. Peters,
+“Homogeneous nucleation of methane hydrates: Unreal-
+istic under realistic conditions,” Journal of the American
+Chemical Society, vol. 134, no. 48, pp. 19544–19547, 2012.
+[97] C. Lamas, J. Espinosa, M. Conde, J. Ram´ırez, P. M.
+de Hijes, E. G. Noya, C. Vega, and E. Sanz, “Homogeneous
+nucleation of nacl in supersaturated solutions,” Physical
+Chemistry Chemical Physics, vol. 23, no. 47, pp. 26843–
+26852, 2021.
+[98] I. Saika-Voivod, F. Romano, and F. Sciortino, “Nucle-
+ation barriers in tetrahedral liquids spanning glassy and
+crystallizing regimes,” The Journal of chemical physics,
+vol. 135, no. 12, p. 124506, 2011.
+[99] D. Richard and T. Speck, “Crystallization of hard spheres
+revisited. ii. thermodynamic modeling, nucleation work,
+and the surface of tension,” The Journal of chemical
+physics, vol. 148, no. 22, p. 224102, 2018.
+[100] L. Separdar, J. P. Rino, and E. D. Zanotto, “Molecular
+dynamics simulations of spontaneous and seeded nucle-
+ation and theoretical calculations for zinc selenide,” Com-
+putational Materials Science, vol. 187, p. 110124, 2021.
+[101] I. Sanchez-Burgos, A. Garaizar, C. Vega, E. Sanz, and
+J. R. Espinosa, “Parasitic crystallization of colloidal elec-
+trolytes: growing a metastable crystal from the nucleus of
+a stable phase,” Soft Matter, vol. 17, no. 3, pp. 489–505,
+2021.
+[102] I. Sanchez-Burgos, E. Sanz, C. Vega, and J. R. Es-
+pinosa, “Fcc vs. hcp competition in colloidal hard-sphere
+nucleation: on their relative stability, interfacial free en-
+ergy and nucleation rate,” Physical Chemistry Chemical
+Physics, vol. 23, no. 35, pp. 19611–19626, 2021.
+[103] L. Filion, M. Hermes, R. Ni, and M. Dijkstra, “Crys-
+tal nucleation of hard spheres using molecular dynamics,
+umbrella sampling, and forward flux sampling: A compar-
+ison of simulation techniques,” The Journal of chemical
+physics, vol. 133, no. 24, p. 244115, 2010.
+[104] G. Fiorucci, G. M. Coli, J. T. Padding, and M. Dijkstra,
+“The effect of hydrodynamics on the crystal nucleation of
+nearly hard spheres,” The Journal of Chemical Physics,
+vol. 152, no. 6, p. 064903, 2020.
+[105] P. M. Piaggi, J. Weis, A. Z. Panagiotopoulos, P. G.
+Debenedetti, and R. Car, “Homogeneous ice nucleation in
+an ab initio machine-learning model of water,” Proceed-
+ings of the National Academy of Sciences, vol. 119, no. 33,
+p. e2207294119, 2022.
+[106] V. Baidakov, “Stability of metastable phases and ki-
+netics of nucleation in a simple single-component sys-
+tem (molecular dynamics simulation)(a review),” Russian
+Journal of General Chemistry, vol. 92, no. 4, pp. 611–628,
+2022.
+[107] I. Sanchez-Burgos, P. M. de Hijes, P. Rosales-Pelaez,
+C. Vega, and E. Sanz, “Equivalence between condensation
+and boiling in a lennard-jones fluid,” Physical Review E,
+vol. 102, no. 6, p. 062609, 2020.
+[108] M. Blander and J. L. Katz, “Bubble nucleation in liq-
+uids,” AIChE Journal, vol. 21, no. 5, pp. 833–848, 1975.
+[109] K. M. Bal and E. C. Neyts, “Extending and validating
+bubble nucleation rate predictions in a lennard-jones fluid
+with enhanced sampling methods and transition state the-
+ory,” The Journal of Chemical Physics, vol. 157, no. 18,
+p. 184113, 2022.
+[110] J. Diemand, R. Ang´elil, K. K. Tanaka, and H. Tanaka,
+“Direct simulations of homogeneous bubble nucleation:
+Agreement with classical nucleation theory and no local
+hot spots,” Physical review E, vol. 90, no. 5, p. 052407,
+2014.
+[111] S. L. Meadley and F. A. Escobedo, “Thermodynamics
+and kinetics of bubble nucleation: Simulation methodol-
+ogy,” The Journal of chemical physics, vol. 137, no. 7,
+p. 074109, 2012.
+[112] I. Kusaka and D. W. Oxtoby, “Identifying physical
+clusters in bubble nucleation,” The Journal of chemical
+
+15
+physics, vol. 111, no. 3, pp. 1104–1108, 1999.
+[113] R. Ang´elil, J. Diemand, K. K. Tanaka, and H. Tanaka,
+“Bubble evolution and properties in homogeneous nu-
+cleation simulations,” Physical review E, vol. 90, no. 6,
+p. 063301, 2014.
+[114] M. Chen, H.-Y. Ko, R. C. Remsing, M. F. C. Andrade,
+B. Santra, Z. Sun, A. Selloni, R. Car, M. L. Klein, J. P.
+Perdew, and X. Wu, “Ab initio theory and modeling of
+water,” Proceedings of the National Academy of Sciences,
+vol. 114, no. 41, pp. 10846–10851, 2017.
+[115] Y. Yao and Y. Kanai, “Temperature dependence of nu-
+clear quantum effects on liquid water via artificial neural
+network model based on scan meta-gga functional,” The
+Journal of Chemical Physics, vol. 153, no. 4, p. 044114,
+2020.
+[116] T. E. Gartner, L. Zhang, P. M. Piaggi, R. Car, A. Z.
+Panagiotopoulos, and P. G. Debenedetti, “Signatures of a
+liquid–liquid transition in an ab initio deep neural network
+model for water,” Proceedings of the National Academy of
+Sciences, vol. 117, no. 42, pp. 26040–26046, 2020.
+[117] P. M. Piaggi, A. Z. Panagiotopoulos, P. G. Debenedetti,
+and R. Car, “Phase equilibrium of water with hexagonal
+and cubic ice using the scan functional,” Journal of Chem-
+ical Theory and Computation, vol. 17, no. 5, pp. 3065–
+3077, 2021. PMID: 33835819.
+[118] A. Stukowski, “Visualization and analysis of atomistic
+simulation data with ovito–the open visualization tool,”
+Modelling and simulation in materials science and engi-
+neering, vol. 18, no. 1, p. 015012, 2009.
+[119] J. S. Rowlinson and B. Widom, Molecular theory of cap-
+illarity. Courier Corporation, USA, 2013.
+[120] J. A. Zollweg and G. W. Mulholland, “On the law of the
+rectilinear diameter,” The Journal of Chemical Physics,
+vol. 57, no. 3, pp. 1021–1025, 1972.
+[121] G. M. Torrie and J. P. Valleau, “Monte carlo free
+energy estimates using non-boltzmann sampling: Appli-
+cation to the sub-critical lennard-jones fluid,” Chemical
+Physics Letters, vol. 28, no. 4, pp. 578–581, 1974.
+[122] A. P. Thompson, S. J. Plimpton, and W. Mattson,
+“General formulation of pressure and stress tensor for ar-
+bitrary many-body interaction potentials under periodic
+boundary conditions,” The Journal of chemical physics,
+vol. 131, no. 15, p. 154107, 2009.
+[123] A. E. van Giessen and E. M. Blokhuis, “Direct deter-
+mination of the tolman length from the bulk pressures
+of liquid drops via molecular dynamics simulations,” The
+Journal of chemical physics, vol. 131, no. 16, p. 164705,
+2009.
+[124] T. Bykov and X. C. Zeng, “A patching model for surface
+tension and the tolman length,” The Journal of chemical
+physics, vol. 111, no. 8, pp. 3705–3713, 1999.
+[125] Y. A. Lei, T. Bykov, S. Yoo, and X. C. Zeng, “The
+tolman length: Is it positive or negative?,” Journal of the
+American Chemical Society, vol. 127, no. 44, pp. 15346–
+15347, 2005.
+[126] J. Julin, I. Napari, J. Merikanto, and H. Vehkam¨aki,
+“A thermodynamically consistent determination of surface
+tension of small lennard-jones clusters from simulation and
+theory,” The Journal of chemical physics, vol. 133, no. 4,
+p. 044704, 2010.
+[127] A. Tr¨oster and K. Binder, “Positive tolman length in a
+lattice gas with three-body interactions,” Physical Review
+Letters, vol. 107, no. 26, p. 265701, 2011.
+[128] M. Iwamatsu and K. Horii, “Temperature dependence of
+liquid-vapor nucleation rate for the yukawa model fluid,”
+Aerosol science and technology, vol. 27, no. 5, pp. 563–574,
+1997.
+[129] F. Magaletti, M. Gallo, and C. M. Casciola, “Water
+cavitation from ambient to high temperatures,” Scientific
+reports, vol. 11, no. 1, pp. 1–10, 2021.
+[130] F. Tang, T. Ohto, S. Sun, J. R. Rouxel, S. Imoto, E. H.
+Backus, S. Mukamel, M. Bonn, and Y. Nagata, “Molecu-
+lar structure and modeling of water–air and ice–air inter-
+faces monitored by sum-frequency generation,” Chemical
+reviews, vol. 120, no. 8, pp. 3633–3667, 2020.
+[131] Y. Nagata, T. Hasegawa, E. H. Backus, K. Usui,
+S. Yoshimune, T. Ohto, and M. Bonn, “The surface rough-
+ness, but not the water molecular orientation varies with
+temperature at the water–air interface,” Physical Chem-
+istry Chemical Physics, vol. 17, no. 36, pp. 23559–23564,
+2015.
+[132] M. Bonn, Y. Nagata, and E. H. Backus, “Molecular
+structure and dynamics of water at the water–air interface
+studied with surface-specific vibrational spectroscopy,”
+Angewandte Chemie International Edition, vol. 54, no. 19,
+pp. 5560–5576, 2015.
+[133] S. Nihonyanagi, J. A. Mondal, S. Yamaguchi, and
+T. Tahara, “Structure and dynamics of interfacial water
+studied by heterodyne-detected vibrational sum-frequency
+generation,” Annual review of physical chemistry, vol. 64,
+pp. 579–603, 2013.
+[134] S. Nihonyanagi, T. Ishiyama, T.-k. Lee, S. Yamaguchi,
+M. Bonn, A. Morita, and T. Tahara, “Unified molecu-
+lar view of the air/water interface based on experimental
+and theoretical χ (2) spectra of an isotopically diluted wa-
+ter surface,” Journal of the American Chemical Society,
+vol. 133, no. 42, pp. 16875–16880, 2011.
+[135] C. Liang, J. Jeon, and M. Cho, “Ab initio modeling
+of the vibrational sum-frequency generation spectrum of
+interfacial water,” The Journal of Physical Chemistry Let-
+ters, vol. 10, no. 5, pp. 1153–1158, 2019.
+[136] T. Ohto, K. Usui, T. Hasegawa, M. Bonn, and Y. Na-
+gata, “Toward ab initio molecular dynamics modeling for
+sum-frequency generation spectra; an efficient algorithm
+based on surface-specific velocity-velocity correlation func-
+tion,” The Journal of Chemical Physics, vol. 143, no. 12,
+p. 124702, 2015.
+[137] J.
+Kessler,
+H.
+Elgabarty,
+T.
+Spura,
+K.
+Karhan,
+P. Partovi-Azar, A. A. Hassanali, and T. D. Kuhne,
+“Structure
+and
+dynamics
+of
+the
+instantaneous
+wa-
+ter/vapor interface revisited by path-integral and ab initio
+molecular dynamics simulations,” The Journal of Physical
+Chemistry B, vol. 119, no. 31, pp. 10079–10086, 2015.
+[138] P. Vassilev, C. Hartnig, M. T. Koper, F. Frechard, and
+R. A. van Santen, “Ab initio molecular dynamics simula-
+tion of liquid water and water–vapor interface,” The Jour-
+nal of Chemical Physics, vol. 115, no. 21, pp. 9815–9820,
+2001.
+[139] R. Khatib, T. Hasegawa, M. Sulpizi, E. H. Backus,
+M. Bonn, and Y. Nagata, “Molecular dynamics simu-
+lations of sfg librational modes spectra of water at the
+water–air interface,” The Journal of Physical Chemistry
+C, vol. 120, no. 33, pp. 18665–18673, 2016.
+[140] C.-Y. Lee, J. A. McCammon, and P. Rossky, “The
+structure of liquid water at an extended hydrophobic sur-
+face,” The Journal of chemical physics, vol. 80, no. 9,
+pp. 4448–4455, 1984.
+
+16
+[141] Y. Fan, X. Chen, L. Yang, P. S. Cremer, and Y. Q. Gao,
+“On the structure of water at the aqueous/air interface,”
+The Journal of Physical Chemistry B, vol. 113, no. 34,
+pp. 11672–11679, 2009.
+[142] J. R. Espinosa, C. Vega, and E. Sanz, “Ice–water inter-
+facial free energy for the tip4p, tip4p/2005, tip4p/ice, and
+mw models as obtained from the mold integration tech-
+nique,” The Journal of Physical Chemistry C, vol. 120,
+no. 15, pp. 8068–8075, 2016.
+
+Supplementary Material: A Deep Potential model for liquid-vapor equilibrium and
+cavitation rates of water
+Ignacio Sanchez-Burgos1,2, Maria Carolina Muniz2, Jorge R. Espinosa1,3 and Athanassios Z. Panagiotopoulos2,∗
+[1] Maxwell Centre, Cavendish Laboratory, Department of Physics,
+University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
+[2] Department of Chemical and Biological Engineering,
+Princeton University, Princeton, New Jersey 08544, USA.
+[3] Departamento de Qu´ımica F´ısica, Facultad de Ciencias Qu´ımicas,
+Universidad Complutense de Madrid, 28040 Madrid, Spain.
+* = To whom correspondence should be sent. email: azp@princeton.edu
+SI.
+EQUATION OF STATE
+As mentioned in the main text, we corroborate that we can obtain the density of the liquid phase surrounding the
+critical bubbles. Then, with such density, by means of the ρl against P equation of state we obtain the pressure of the
+liquid phase, which matches the pressure obtained through the virial expression. In Figure S1 we show the equation
+of state at 296.4 K for the DPMD and TIP4P/2005 models.
+-150
+-100
+-50
+0
+P / MPa
+0.9
+0.92
+0.94
+0.96
+0.98
+1
+1.02
+Density / (g cm
+-3)
+EOS Liq 296.4K DPMD
+EOS Liq 296.4K TIP4P/2005
+Figure S1: Density against pressure equation of state at 296.4 K for the DPMD and TIP4P/2005 models.
+SII.
+BUBBLE SPHERICITY
+In order to quantify how spherical the simulated bubbles are, we take the following approach: We divide the
+simulation box into smaller cells of ∼ 200˚A3 each. We classify the cells as liquid or vapor based on their local density,
+taking 0.3 g cm−3 as threshold density. We then identify the surface available to the vapor cluster by means of a
+Surface mesh algorithm [1, 2] available with the OVITO software package [3]. From this, we obtain the surface and
+volume that corresponds to the vapor cluster. Using his information we compute the cluster sphericity (Ψ) as [4]:
+Ψ = π1/3(6V )2/3
+S
+(S1)
+where V is the cluster volume and S the surface. Ψ is equal to 1 for a perfect sphere and decays for less spherical
+geometric bodies. In Figure S2 we show a rendered image of the surface created for a vapor cluster (depicted in
+orange), as well as Ψ against time for our Seeding simulations with the DPMD model.
+The values of Ψ exceed
+0.85 in all cases which means a high sphericity of the simulated bubbles. We show with a blue line Ψ for the initial
+configuration in which a perfect sphere has been generated, and represents the maximum sphericity that our parameter
+is able to account for.
+
+2
+(a)
+(b)
+0
+5
+10
+15
+20
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=1.25 nm
+0
+5
+10
+15
+20
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=1.50 nm
+0
+5
+10
+15
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=1.74 nm
+0
+5
+10
+15
+20
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=1.96 nm
+0
+5
+10
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=2.29 nm
+0
+2.5
+5
+7.5
+10
+t / ns
+0
+0.2
+0.4
+0.6
+0.8
+1
+Ψ
+Rc=2.50 nm
+Figure S2: (a) Snapshot of a vapor cluster (Rc=2.29 nm) identified as detailed in section SII. The identified surface
+is colored in orange. (b) Ψ against time for the 6 simulated bubbles in Seeding simulations with the DPMD model.
+SIII.
+ORIENTATIONAL ANALYSIS
+In the main text we show the orientational analysis of interfacial molecules for one bubble size. In Figure S3,
+we show the same analysis for different bubble size using the DPMD model. We observe how the dependency of
+orientation preference with curvature is moderate but noticeable for the range of bubble sizes studied, being the
+biggest bubble the one resembling more to the coexistence conditions.
+[1] H. Edelsbrunner and E. P. M¨ucke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics (TOG), vol. 13,
+no. 1, pp. 43–72, 1994.
+[2] A. Stukowski, “Computational analysis methods in atomistic modeling of crystals,” Jom, vol. 66, no. 3, pp. 399–407, 2014.
+[3] A. Stukowski, “Visualization and analysis of atomistic simulation data with ovito–the open visualization tool,” Modelling
+and Simulation in Materials Science and Engineering, vol. 18, no. 1, p. 015012, 2009.
+[4] H. Wadell, “Volume, shape, and roundness of quartz particles,” The Journal of Geology, vol. 43, no. 3, pp. 250–280, 1935.
+
+3
+(a)
+(b)
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+2.5
+3
+P(θH)
+External layer
+Internal layer
+Bulk water
+Planar
+interface
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+Rc=2.50 nm
+(c)
+(d)
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+Rc=1.96nm
+0
+30
+60
+90
+120
+150
+180
+θH
+0
+0.5
+1
+1.5
+2
+P(θH)
+External layer
+Internal layer
+Bulk water
+Rc=1.25 nm
+Figure S3: Distribution probability of the O-H bond with respect to the direction normal to the interface,
+renormalized by the random distribution sin(θH). The shown distributions are for (a) planar interface; (b-d) critical
+bubbles. The bubble radius is indicated in the leyend.
+
diff --git a/J9FLT4oBgHgl3EQfKi8f/content/tmp_files/load_file.txt b/J9FLT4oBgHgl3EQfKi8f/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26ac7a6f83eeed496d7ccd420f0f5966896702a6
--- /dev/null
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@@ -0,0 +1,1872 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf,len=1871
+page_content='A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water  Ignacio Sanchez-Burgos1,2, Maria Carolina Muniz2, Jorge R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa1,3 and Athanassios Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos2,∗  [1] Maxwell Centre, Cavendish Laboratory, Department of Physics,  University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [2] Department of Chemical and Biological Engineering,  Princeton University, Princeton, New Jersey 08544, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [3] Departamento de Qu´ımica F´ısica, Facultad de Ciencias Qu´ımicas,  Universidad Complutense de Madrid, 28040 Madrid, Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  = To whom correspondence should be sent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' email: azp@princeton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='edu  (Dated: January 31, 2023)  Computational studies of liquid water and its phase transition into vapor have traditionally been  performed using classical water models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Here we utilize the Deep Potential methodology —a machine  learning approach— to study this ubiquitous phase transition, starting from the phase diagram in  the liquid-vapor coexistence regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The machine learning model is trained on ab initio energies and  forces based on the SCAN density functional which has been previously shown to reproduce solid  phases and other properties of water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Here, we compute the surface tension, saturation pressure and  enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K, and evaluate the  Deep Potential model performance against experimental results and the semi-empirical TIP4P/2005  classical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Moreover, by employing the seeding technique, we evaluate the free energy barrier  and nucleation rate at negative pressures for the isotherm of 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We find that the nucleation  rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005  water model, due to an underestimation in the surface tension from the Deep Potential model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From  analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water  model, which is (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='091 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='008) nm at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lastly, we identify that water molecules display a  preferential orientation in the liquid-vapor interface, in which H atoms tend to point towards the  vapor phase to maximize the enthalpic gain of interfacial molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We find that this behaviour  is more pronounced for planar interfaces than for the curved interfaces in bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This work  represents the first application of Deep Potential models to the study of liquid-vapor coexistence  and water cavitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  INTRODUCTION  Water is a fundamental substance, crucial for life  and  relevant  in  many  environmental,  engineering,  and biological processes [1–9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Due to this, the past  decades have seen a significant effort devoted to the  development of models to reproduce the behaviour of  water in computer simulations [10–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Although some  of these models account for flexibility and polarizability  [18–21, 23],  the most widely employed models for  water are rigid and non-polarizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' These include the  TIP4P/2005 [10], TIP4P/ICE [11], SPC/E [15], TIP3P  [13] and TIP4P-Ew [24] among others [16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  These  empirical models have parameters obtained by fitting to  experimentally measured properties, such as coexistence  lines between thermodynamic phases or critical points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  They are frequently used to describe ionic solutions  [25–30] and for biomolecular simulations [31, 32], as well  as other applications [33–36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In contrast to the classic semi-empirical approach  to water modelling, ab initio models are determined  from  first  principles  and  therefore  do  not  require  fitting to experimental data [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Traditionally this  approach has not been applied to large systems due  to its computational cost [38, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nonetheless, recent  advances  in  Machine  Learning  (ML)  have  allowed  the development of deep potential generators [40, 41]  capable of constructing MD potentials based on ab initio  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In this work, we use a ML-based model that  has successfully recapitulated the different solid phases  of water [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This model has been constructed based  on the SCAN quantum mechanical density functional,  which succesfully reproduces several properties of water  [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This approach to ab initio based models is  efficient enough to carry out simulations with tens of  thousands of water molecules in a computationally  affordable way [45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Making use of the machinery provided by ML ab  initio based models, here we study the liquid-vapor  coexistence of water by means of Molecular Dynamics  (MD) simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The liquid-vapor properties of water  are well known from experiments [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From the com-  putational side, the TIP4P/2005 non-polarizable rigid  water model [10] has been highly successful at describing  the liquid-vapor coexistence properties, reproducing the  experimental phase diagram [48] and surface tension  [49–51] reasonably well, as well as transport properties  [10, 48, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The TIP4P/2005 model has also been  extensively benchmarked in the study of liquid-to-vapor  and vapor-to-liquid phase transitions [53–59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Therefore,  we compare the Deep Potential Molecular Dynam-  ics (DPMD) water model performance with that of  TIP4P/2005 in addition to experimental data, when  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='12008v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='soft]  27 Jan 2023  2  To test the DPMD model we first evaluate the  liquid-vapor phase diagram and measure properties at  equilibrium such as the surface tension or the enthalpy  of vaporization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We also focus on the liquid-to-vapor  phase transition at negative pressure, a phenomenon  known as cavitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Under negative pressures, water  can remain metastable with respect to the vapor (the  most stable phase under these conditions) for a finite  amount of time before undergoing the phase transition  [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This results from the fact that the phase transition  is an activated process, and requires the formation of  a critical bubble, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=', one that has surmounted a free  energy barrier and can continue growing irreversibly  without a free energy penalty [34, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This happens  because the formation of a bubble intrinsically requires  the formation of a liquid-vapor interface, which comes  associated with an energetic cost, the surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  When the phase transition is initiated by the formation  of water bubbles within the liquid bulk and in absence  of any surface or external agent, the process is termed  homogeneous cavitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  It has been experimentally determined that, at am-  bient temperature, water can sustain negative pressures  of up to −120 MPa before transitioning into the vapor  phase [62–66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  While experiments have determined  the cavitation pressure, which is the pressure at which  the phase transition is observed, computational studies  using the TIP4P/2005 model have been able to compute  the nucleation rate, a crucial quantity to characterize  the cavitation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The nucleation rate is defined as  the number of critical clusters formed per unit of time  and volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The nucleation rate obtained in previous  studies for the TIP4P/2005 model [53–55, 58, 59] will  be used as a reference for our DPMD calculations since  there are no reliable experimental data for this quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Aside from the nucleation rate, we also compare in  this work the nucleation free energy barrier and the  Tolman length [67], a parameter employed to describe  the change in surface tension with curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Finally,  we characterize the orientational distribution of water  molecules at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We find that the DPMD  model can reproduce well the phase diagram of water,  but displays a lower surface tension than experimental  results or the TIP4P/2005 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The nucleation rate  is consequently greater for the DPMD model compared  to the TIP4P/2005 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  METHODS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  DPMD Model  We use the recently developed DPMD model for water  [42] to perform simulations in the liquid-vapor coexis-  tence regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The model was generated using an itera-  tive concurrent learning scheme, deep potential generator  [41], to construct a potential energy landscape based on  SCAN [43], a non-empirical functional that recapitulates  several properties of water [44], such as molecular geom-  etry and solid structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The final training set used to  construct this model included ice and liquid phases snap-  shots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [42], the phase diagram for this model was  calculated for the different ice phases, reaching a reason-  able agreement with experimental data [68–70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' For com-  putational purposes we employ the compressed version of  this potential, making use of the scheme developed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Thanks to this approach, we are capable of reaching  a computational performance of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2 nanoseconds of simu-  lation time per wall clock day for a system of about 10000  water molecules running with a single 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8 GHz Intel Ice  Lake node using four NVIDIA A100 80GB GPUs and  28 CPU-cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Example files of simulations employing  this potential are available in the Princeton DataSpace  repository https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='34770/ms7d-wm45 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Simulation details  Simulations of the DPMD water model were per-  formed using the LAMMPS package [72], built with  the DeePMD-kit [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Seeding and Direct Coexistence  (DC) simulations were performed in the NV T ensemble,  keeping the number of particles N, system volume V ,  and temperature T  constant with the Nose-Hoover  thermostat [74–76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Additionally, to compute equations  of state and to observe crystallization directly at high  supersaturations we performed simulations in the NPT  ensemble using the Nose-Hoover barostat [74–76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  equations of motion were integrated using the velocity-  Verlet integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The simulation timestep was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5 fs,  and the thermostat relaxation time 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='1 ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In NPT  simulations, the barostat relaxation time was 1 ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  For the DC simulations, a system size of 1024 molecules  was used and the density profiles were obtained with at  least 10 ns of sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Coexistence densities were ob-  tained by fitting the density profile to the following ex-  pression:  ρ(z) = ρl + ρv  2  − ρl − ρv  2  tanh  �z − z0  d  �  (1)  where ρl and ρv are the coexistence liquid and vapor  densities, respectively, z0 the position of the interface,  and d its thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The surface tension was calculated from DC simula-  tions at each temperature according to the Kirkwood-  Buff equation [77]:  γ = Lz  2 [⟨Pzz⟩ − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5(⟨Pxx⟩ + ⟨Pyy⟩)]  (2)  3  where Pii are the diagonal components of the pressure  tensor and Lz, the box length in the elongated dimen-  sion, perpendicular to the slab interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We also performed simulations with the TIP4P/2005  water model [10] using the GROMACS 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='7 Molecular  Dynamics package [78] in the NPT and NV T ensem-  bles, keeping temperature constant with the velocity-  rescale thermostat [79] and pressure constant (for NPT  simulations) with the Parrinello-Rahman barostat [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In GROMACS we integrated the equations of motion  using the Leap-Frog integrator [81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The simulation  timestep was 2 fs, and the thermostat and barostat re-  laxation times were 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='75 and 2 ps, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We set  the cut-off of both dispersion interactions and the real  part of the electrostatic interactions at 12 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Long-range  Coulombic interactions were treated with the Particle-  Mesh Ewald (PME) solver [82, 83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We kept the O-H  bond length (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9572 ˚A) and H-O-H angle (104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='52o) val-  ues constant with the LINCS algorithm [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' With this  model we reached a computational performance of 40  nanoseconds of simulation time per wall clock day for a  system of about 10000 water molecules running with In-  tel(R) Xeon(R) Platinum 8368Q CPU @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='60GHz, using  32 CPUs in paralel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Seeding and Classical Nucleation Theory  Seeding is a method that consists of using Classical  Nucleation Theory (CNT) in combination with MD  simulations [34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' More specifically, we use the NVT  seeding approach [85], in which a cluster (in this case a  bubble) close in size to the critical one is artificially in-  serted into the system, then spontaneously equilibrated  into the critical size and tracked along time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' With this  approach, a critical bubble can be characterized for  long timescales because the maximum in free energy  barrier in a nucleation process represents a minimum  in the Helmholtz free energy landscape in the canonical  ensemble [54, 86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Therefore, more precise measurements  can be made compared to seeding in the NPT ensemble,  where the bubble will rapidly either shrink or grow [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This method is suitable to measure nucleation rates  along isotherms, since the pressure at which the cluster  is critical cannot be known a priori, and is obtained  from the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  CNT [87, 88] is a theoretical framework that describes  nucleation processes under saturation conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' It can  be used to obtain the free energy barrier, interfacial free  energy and nucleation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The limitations of quanti-  tatively characterizing nucleation rates using CNT are  due to assumptions inherent in the theory [89–94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' De-  spite these potential limitations, multiple studies position  CNT as a powerful tool to estimate free energy barriers  and nucleation rates for phase transitions [34, 35, 95–  105], including cavitation [53, 85, 106, 107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' According  to CNT [87, 108], the nucleation rate (J) can be com-  puted as  J = ρl  �  2γ  πmexp  �−∆G∗  kBT  �  (3)  where ρl represents the density of the liquid phase, γ  the liquid-vapor surface tension, m the mass of water,  ∆G∗ the free energy barrier for nucleation, kB the Boltz-  mann’s constant and T the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Within the  CNT framework, the free energy barrier is obtained as  ∆G∗ = 4  3γπRc  (4)  where Rc is the critical bubble radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Additionally, we  obtain the interfacial free energy from Laplace’s equation  as  γ = Rc∆P  2  (5)  where ∆P is the pressure difference between the vapor  and liquid phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This approach provides more reliable  estimations than assuming the capillarity approximation  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' inserting the surface tension at planar interface and  coexistence conditions into the CNT) [85, 107, 109, 110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Combining Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, 4 and 5, we reach the final equation  for J:  J = ρl  �  Rc∆P  πm exp  �−4πR2  c∆P  3kBT  �  (6)  To summarize, in order to compute J we require the  pressure difference between the liquid and the vapor  phases, and the critical radius of the bubble at the  corresponding thermodynamic conditions of P and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Although the difference in pressure can be computed in  principle [85, 109], in this study the pressure inside the  bubbles is ∼0 [48], therefore ∆P can be easily estimated  as −Pliq, which is directly obtained through the virial  expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We additionally confirmed that the virial  pressure obtained in the system containing a bubble  matches that of the bulk liquid (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Lastly, the critical radius, Rc was obtained employ-  ing a local order parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Although multiple param-  eters have been proposed to track the size of a simu-  lated bubble [53, 55, 58, 59, 111, 112], here we adopted  the ’equidensity’ criterion [113], which was shown to pro-  vide the surface of tension radius (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' the radius that,  when inserted into Laplace’s equation provides a consis-  tent value of γ) for the Lennard-Jones system [85, 107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  As illustrated in Figure 1(a), the center of the bubble is  first calculated through the minimum in the density pro-  file along the 3 cartesian directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Afterwards, a radial  density profile from the bubble center is computed, in  4  (a)  0  10  20  30  40  50  60  L / Å  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='95  ρ / (g·cm  3)  X direction  Y direction  Z direction  (b)  0  10  20  30  r / Å  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8  1  ρ(r) / (g·cm  3)  Rc  Figure 1: (a) Density profiles along the three cartesian  directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vertical dashed lines depict the location of  the minimum density, which corresponds to the center  of the bubble in each direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In these density profiles  we averaged the density of each point with 2 other  neighbouring points in order to make the curves  smoother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (b) Radial density profile calculated from the  center of the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The blue curve indicates the  density calculated at each distance while the black  dashed curve is the fit of the blue curve to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7, from  which we obtained the critical radius Rc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  which the critical radius (Rc) corresponds to the point  in which the density equals the average of the liquid and  vapor densities (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This point is found via non-  linear fitting to the equation  ρ(r) = ρl + ρv  2  + ρl − ρv  2  tanh  �r − Rc  α  �  (7)  where r is the distance from the bubble center, and α is  a fitting parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We confirmed that, as assumed by  CNT, the bubbles have a close-to-spherical shape (Figure  S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  It is important to note that all DPMD data shown in  this work are shifted by 40 K, so that the simulations for  a given temperature have been performed at 40 K higher  than the reported one in the presented figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Similar  shifts in temperature have been performed for AIMD  simulations using SCAN [114] and in other works using  SCAN-based ML models [115–117].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The rationale for  the shift was originally attributed to nuclear quantum  effects, but it is likely mainly due to the limitations of the  density functional itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' SCAN is known to overestimate  the strength of the hydrogen bond [115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In this work,  the shift in temperature was adjusted by calculating  the mean square error between the coexistence vapor  densities predicted by the model and the experimental  ones, considering different values for the shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The value  for the shift was iteratively modified until we obtained  the one that gave the minimum mean square error, which  was 40 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In all plots and tables that follow the re-  sults of the DPMD model have this shift already applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Vapor-liquid equilibrium in the DPMD model  To test the DPMD model in the liquid-vapor regime,  we begin by computing the phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We do so us-  ing simulations in the canonical ensemble, in which both  the liquid and vapor phases coexist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure 2(a) (in-  set) we show a snapshot of a typical DC simulation box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 2(a) we plot the temperature against density  phase diagram of the DPMD model (green points), where  the filled points represent the densities directly obtained  from DC simulations (2 at each temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We in-  clude results for the TIP4P/2005 model [10, 48] (blue  circles), as well as experimental data [47] (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We can observe that for the DPMD model the density of  the liquid branch is slightly higher than the experimental  results at low temperatures (<500K), but matches well  at higher ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The critical point is estimated through  the universal scaling law of coexistence densities near a  critical point [119], and the law of rectilinear diameters  [120]:  �  ρl(T) − ρv(T)  �3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='06 = d  �  1 − T  Tc  �  (8)  and  (ρl(T) + ρv(T))/2 = ρc + s2(Tc − T)  (9)  where ρl and ρv refer to the coexisting densities of the  liquid and vapor phases respectively, ρc is the critical  density, Tc is the critical temperature, and d and s2 are  fitting parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The critical temperature obtained  for the DPMD model is of 632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6 K, which is lower than  the experimental one by 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Moreover, we compute the liquid-vapor surface tension  for the DPMD model at different temperatures from the  DC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This quantity can be directly estimated  according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' As can be seen in Figure 2(b), the  DPMD model provides lower values of γ than both the  5  (a)  (b)  (c)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8  1  ρ / g cm  3  400  500  600  700  T / K  Experiment  DPMD  TIP4P/2005  300  400  500  600  700  T / K  0  20  40  60  80  γ / mN m  1  Experiment  DPMD  TIP4P/2005  400  500  600  T / K  20  30  40  ∆Hvap / kJ mol  1  Experiment  DPMD  TIP4P/2005  400  500  600  T / K  0  50  100  150  200  Psat / bar  Figure 2: (a) Phase diagram in the T–ρ plane of the DPMD model (green), TIP4P/2005 model (blue) [48] and  experimental measurements of water (black) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Filled circles represent the vapor and liquid densities, estimated  from the averaged bulk densities from DC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Inset: Snapshot of a DC simulation performed at 385 K with  the DPMD model, rendered making use of Ovito software [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (b) Liquid-vapor interfacial free energy (γ) as a  function of temperature for the DPMD model (green), and comparison with the TIP4P/2005 model (blue) [49] and  experimental values (black) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (c) Vapor saturation pressure (Psat) as a function of temperature for the DPMD  model (green), TIP4P/2005 (blue) [48] and comparison with experimental values (black) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Inset: Enthalpy of  vaporization (∆Hvap) as a function of temperature for DPMD, TIP4P/2005 [48] and experimental values [47] as  indicated in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  TIP4P/2005 model [49] and experimental measurements  [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From DC simulations we also calculate the satura-  tion pressure (Psat) as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Psat is  obtained as the component of the pressure tensor normal  to the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We plot it in Figure 2(c), compared to  the values obtained from TIP4P/2005 (blue) [48] and  experiments (black) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This quantity closely matches  with experimental measurements, while the TIP4P/2005  model underestimates it, which is a natural consequence  of the way the DPMD model was shifted to match the  vapor densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We note that the temperature shift was  applied in order to obtain a better match of the vapor  phase behaviour, nonetheless this shift affects negatively  on the surface tension prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  With no temper-  ature shift, the surface tension of the DPMD model  matches the experimental one at temperatures above  450 K, and only underestimates it by ∼ 5% at T < 450 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We estimated the enthalpy of vaporization (∆Hvap)  from independent bulk simulations of both liquid and  vapor phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  For this, we perform canonical simu-  lations at the equilibrium density of the given phase,  which was previously obtained from DC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  From each simulation the enthalpy is directly obtained  as H  = U − PV , where U is the internal energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The enthalpy of vaporization is simply calculated as  ∆Hvap = Hvapor − Hliquid for every temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  values of ∆Hvap are plotted against temperature in  Figure 2(c) (inset), along with values from TIP4P/2005  [48] and experiments [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This quantity slightly deviates  from the experimental values at low temperatures (< 550  K), but matches at higher temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In contrast, the  TIP4P/2005 model slightly underestimates the enthalpy  of vaporization across all temperatures examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In summary, the DPMD model describes the liquid-  vapor coexistence properties after applying the temper-  ature shift of 40 K reasonably well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Some discrepancies  may arise from the fact that this model has been trained  on solid and liquid data only [42], but the main source of  differences from experimental data are limitations in ac-  curacy for the SCAN density functions used to train the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The biggest difference with experimental values  is found in the surface tension, which is underestimated  by ∼20 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Other than this discrepancy, the phase dia-  gram, saturation pressure, and enthalpy of vaporization  are well described using the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In addition  to the plots in Figure 2, we provide the equilibrium data  of the DPMD model in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  T (K) ρl (g·cm−3) ρv (g·cm−3) Psat (bar) γ (mN·m−1)  385  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9697(5)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='0011(3)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='3(3)  41(3)  410  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9484(8)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='0022(4)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9(5)  31(7)  435  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9242(6)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='0037(6)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='3(9)  31(7)  460  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8969(8)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='0067(9)  15(1)  27(4)  485  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='865(3)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='012(4)  25(3)  24(5)  510  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='831(2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='016(2)  35(4)  19(5)  535  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='791(1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='024(1)  48(7)  15(7)  560  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='740(6)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='039(5)  71(6)  14(5)  585  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='684(8)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='058(4)  98(15)  7(8)  597  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='62(1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='079(5)  114(5)  6(9)  Table I: Data for the liquid (ρl) and vapor (ρv)  densities, saturation pressure (Psat) and surface tension  (γ) as a function of temperature for the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The numbers in parenthesis depict the uncertainty of  our measurements, and apply to the numeral left of  themselves, for instance 41(3) stands for 41±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  6  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Bubble nucleation  After establishing the equilibrium properties of the  DPMD water model, we proceeded to investigate its  cavitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Although some experimental studies of  water cavitation have been conducted [62–66], it is  difficult to establish a direct comparison due to the lack  of measurements of the nucleation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Menzl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [53] performed a nucleation study utilizing Umbrella  Sampling (US) calculations [121] for the TIP4P/2005  model, in which the nucleation free energy barrier and  the nucleation rate were reported, without comparisons  to experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Here, we employ the NVT seeding  technique at the same temperature (296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K) as in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [53] for both the TIP4P/2005 (to establish the validity  of our methods) and DPMD models (to provide new  data for this ab-initio based model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We prepared various systems in which we artificially  generated a cavity of a given size, starting from a bulk  liquid configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  As detailed in Section II C, the  system spontaneously evolves and equilibrates into a  state in which there is a critical bubble that remains  stable over time, due to the fact that in the canonical  ensemble, a critical bubble represents a local minimum  in the Helmholtz free energy landscape [54, 86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Once  equilibrated, we measured the system pressure by means  of the virial expression [122] which corresponds to the  liquid phase pressure [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' To track the critical radius,  we made use of our order parameter (see Section II C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We repeated this process for each configuration, and  then averaged over more than 500 independent radial  density profiles for the calculation of the radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We used our data for ∆P and Rc along with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6  to compute J, which is plotted in Figure 3(a) (blue and  green squares for TIP4P/2005 and DPMD respectively)  against P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' It can be seen that there is agreement within  the simulation uncertainties between the US and seeding  simulations for the TIP4P/2005 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We also include  a continuous line for each model, which represents a fit  to the CNT equation, in which we linearly fit γ against  P, and insert values from such fit to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  uncertainty is estimated from the standard deviation of  the radius between different independent configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We computed J at higher superstreching conditions  (green and blue diamonds in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  3) through ”brute  force” simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In these simulations, we observed the  metastable bulk liquid under high superstreching con-  ditions in the NPT ensemble for a sufficient time before  spontaneous cavitation takes place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Then, J is calculated  as  J =  1  < t > V  (10)  where < t > is the average time required for cavitation  to occur and V is the volume of the metastable liquid  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The onset of cavitation can easily be identified  with a sudden and sharp change in properties such as  the simulation box volume or the potential energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From  these simulations we obtain J = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='52·10−6 ps−1nm−3 at  P = −150 MPa for the DPMD model, and J = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='44·10−5  ps−1nm−3 and P = −200 MPa for the TIP4P/2005  potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' These results are also shown in Figure 3(a),  and match with the trend of US and seeding simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This result, in addition to the agreement with the US  calculations from Menzl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=', provides confidence in  the validity of the results obtained using CNT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In addition to the nucleation rate, we also obtained  the free energy barrier (∆G∗) which can be estimated  from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This quantity is the main output from  US simulations [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 3(b) we compare the  calculated free energy barriers for the DPMD (green)  and TIP4P/2005 (blue) models, also including data from  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' As expected, we find good agreement between  seeding and US calculations as for the nucleation rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  It can be seen in Figure 3(a) that the DPMD model re-  turns nucleation rates many orders of magnitude greater  than the TIP4P/2005 potential, outside the uncertainty  bounds, despite the close resemblance of the phase dia-  grams from the two models (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This difference is  also present for the free energy barrier (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3(b)), with  the TIP4P/2005 model possessing a higher free energy  barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This is likely the crucial factor behind its lower  nucleation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In order to understand the differences  between the two models we also compared the change of  the surface tension with curvature for both models: In  Figure 4 we plot γ as a function of P, where filled points  correspond to the value obtained at the coexistence pres-  sure from DC simulations, while the empty points depict  the value of γ obtained through Laplace’s equation (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  5) from our seeding simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From this analysis we  observe that the surface tension is significantly lower for  the DPMD model, not only under coexistence conditions,  but also in the cavitation regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This directly points to-  wards the surface tension being the decisive factor behind  the quantitative difference in J and ∆G∗ between the  DPMD and TIP4P/2005 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Table II we detail  the different quantities playing a role in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Since  the kinetic prefactor in the calculation of J is of the same  order of magnitude in all cases, we can conclude that the  different nucleation rates between the TIP4P/2005 and  DPMD models arises from a quantitative difference in  the surface tension, which is lower for the DPMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Determination of the Tolman length  Another quantity we can extract from our simulations  is the Tolman length, which describes the deviation of  the surface tension with respect to its value at the planar  interface and, therefore, the coexistence conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  7  (a)  (b)  200  150  100  50  P / MPa  10  160  10  120  10  80  10  40  10  0  J / (ps  1nm  3)  TIP4P/2005 Menzl at al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' US, PNAS (2016)  TIP4P/2005 Seeding  TIP4P/2005 Brute Force  DPMD Seeding  DPMD Brute Force  200  175  150  125  100  75  50  P / MPa  0  50  100  150  200  ∆G* / kBT  TIP4P/2005 Menzl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' US, PNAS (2016)  TIP4P/2005 Seeding  DPMD Seeding  Figure 3: (a) Nucleation rate (J) as a function of pressure (P) for TIP4P/2005 (blue) and DPMD (green) cavitation  at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K, including data from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Continuous lines are obtained by linearly fitting the surface tension (γ) as  a function of pressure, and then inserting such γ into Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The shaded region is obtained in the same way  but making use of the upper and lower bounds of the surface tension error and, therefore, represent the error limits  in J (b) Free energy barrier for bubble nucleation as a function of pressure at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K for TIP4P/2005 (blue) and  DPMD (green) models, estimated from CNT (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  P (MPa) Rc (nm) ρl (g·cm−3)  NT  γ (N·m−1) ∆G∗/kBT log10(J / (ps−1·nm−3))  DPMD  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='3  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='3  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='968  10570  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8  337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='3  144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9  Table II: NVT seeding data for the DPMD and TIP4P/2005 models, including the nucleation pressure (P), the  critical radius (Rc), the liquid density (ρl), the total number of water molecules in the system (NT ), the surface  tension (γ), the free energy barrier (∆G∗), and the logarithm of the nucleation rate (log10J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Tolman length can also be defined as the deviation of the  surface of tension from the equimolar dividing surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In  1949, Tolman showed that the change in surface tension  with curvature follows the equation [67]  γ =  γ0  1 + 2δ  Rc  (11)  where γ0 is the value of the surface tension under  coexistence conditions and δ is the Tolman length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This  quantity has been extensively studied for Lennard-Jones  particles [61, 123–126], Hard Spheres [86] and other  systems [123, 124, 127, 128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Here we make use of  Tolman’s expression and compute δ for both the DPMD  and TIP4P/2005 models at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We fit our surface  tension and critical radius data (obtained from the  NVT seeding simulations) to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  11, performing a  non-linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We choose to have γ0 and δ as  fitting parameters, despite having estimated the former  from the DC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We took this approach in  order to corroborate the value of γ obtained from both  approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 5 we plot the surface tension against the  inverse of the critical radius for the DPMD (green filled  points) and TIP4P/2005 (blue filled points) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  8  100  80  60  40  20  0  P / MPa  40  45  50  55  60  65  70  γ / N m  1  TIP4P/2005  DPMD  Figure 4: Liquid-vapor surface tension (γ) as a function  of pressure at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K for TIP4P/2005 (blue) and  DPMD (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Empty circles are obtained from  cavitation simulations (and therefore with a curved  interface) by means of Laplace’s equation (see Section  II C), while filled points were estimated from DC  simulations as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  From non-linear regression we obtain δ = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='091±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='008)  nm for the DPMD model and δ = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='070 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='004) nm  for the TIP4P/2005 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Both values are positive as  expected, since the surface tension decreases for smaller  bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 5 we also show with dashed lines  how the surface tension changes against the inverse of  the critical radius according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  From the fit  we also obtain values for the surface tension at planar  interface of 58 ± 2 and 67 ± 3 mN·m−1 for the DPMD  and TIP4P/2005 models respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  These values  are in agreement, within statistical uncertainties, with  those obtained from DC simulations (54 and 70 [49]  mN·m−1 for DPMD and TIP4P/2005 respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  uncertainty of δ is simply determined by the error in  the non-linear fit, while the uncertainty in γ0 is the  sum of the errors coming from NVT seeding simula-  tions (see Section III B) and the error in the fit to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Our results are also in good agreement with previ-  ous simulation results [54, 129] (at different tempera-  tures: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='199 nm at 300 K [54], 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='09 nm at 250 K [129]  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='18 nm at 350 K) which indicate that the Tol-  man length is positive for water bubbles, in contrast to  the negative sign in water droplets (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' condensation)  [56, 57], where the surface tension increases with curva-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We can establish direct comparison with the calcu-  lations from Menzl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [53], which were performed with  TIP4P/2005 at the same temperature (296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' They  obtained values of δ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='195nm and γ0=82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='79 mN·m−1,  which while having the same order of magnitude, mod-  erately disagree with our calculations of γ0 and δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In the  case of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [53] the employed local order parameter does  not necessarily identify an accurate value of the radius,  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8  Rc  1 / nm  1  45  50  55  60  65  70  γ / mN m  1  DPMD  TIP4P/2005  Figure 5: Surface tension γ against the inverse of the  critical radius (R−1  c ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Filled points represent the surface  tension obtained from Laplace’s equation (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  dashed lines indicate the change in surface tension  according to Tolman’s equation (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11), where the  parameters δ and γ0 were obtained through non-linear  regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We plot the values of surface tension at  planar interface (R−1  c =0) obtained from the fit with  empty points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The surface tension values obtained from  DC are also represented here with filled diamonds, also  at P = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  but is instead used to bias the sampling of the configu-  rational space for US simulations, and may therefore not  represent accurate values of δ and γ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' As mentioned be-  fore, the good agreement in the nucleation free energy  barrier between US and seeding calculations is a good  sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In our case, a good indicator for the calculation  of the Tolman length, although not definitive, is the fact  that the surface tension obtained from the non-linear re-  gression to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11 provides a value of γ0 that matches  within the uncertainty the surface tension obtained from  DC simulations, as aforementioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Liquid-vapor interfacial characterization  Finally, we examined the organization of the liquid-  vapor interface in our simulations for both planar and  curved interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The water-air planar interface has  been widely studied in the past [130] with IR vibrational  spectra experiments [131–134], ab initio [135–138] and  MD simulations [139–141], all of which generally agree  regarding the orientation of water molecules near the  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Interfacial molecules closer to the vapor phase  tend to orient the O-H bond parallel to the surface  normal vector and expose the H atom, resembling the  (1000) crystal face of ice Ih (only in the dimension per-  pendicular to the surface) [141].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The (1000) ice Ih-liquid  is the direction with lower interfacial free energy of the  9  different solid-liquid interfaces [142], therefore in the  liquid-vapor interface a similar arrangement may also  reduce the surface tension, apart from maximizing the  enthalpic gain of the more exposed interfacial molecules  to the vapor phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' To perform this analysis, we follow  the same approach as in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [138, 141] where, once the  interfacial region has been identified, the angle formed  by the O-H bonds and the vector normal to the interface  (θH) is computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [141] and Vassilev et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [138] identified two distinct layers in non-curved  interfaces:  an external layer, which comprehends the  region in which the density is between 5-50% of the  bulk liquid, and an internal layer, where the density  ranges between 50-95% of the bulk liquid density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Fan et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [141] measured the orientation distributions for the  TIP3P, TIP4P-EW, TIP5P and SPC/E water models  at 300K, and for comparison purposes, we perform the  same analysis with the DPMD and TIP4P/2005 models,  and obtain results also for curved interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 6(a) we depict how the different interfacial  regions and θH angle are identified for both planar (top)  and curved (bottom) interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' There, the dashed black  line indicates the liquid-vapor interface as defined by our  order parameter (see section II C and Supplementary  Material (SM)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In the zoomed image, the internal  and external layers of the interface are labelled and  highlighted in black and red, as well as the bulk liquid  and vapor phases in green and white respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  two arrows indicate the normal vector to the interface  and the O-H bond vector, and the angle between these  two vectors defines θH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In Figure 6(b-c) We plot the  θH distributions normalized by the random distribu-  tion sin(θH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Consistent with previous calculations  [137, 138, 140, 141], the molecules expose one hydrogen  atom to the vapor phase in the external layer, as can  be seen in Figure 6(b)(top) for the TIP4P/2005 model,  where we show the probability distribution of the angle  θH for the different interfacial regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Smaller angles  are more probable in the external layer than in the bulk,  where all directions are equally probable (flat green  line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' As discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [141], the internal layer of the  interface also displays preferential orientations, in order  to maximise the interactions with the structure created  in the external layer, in an arrangement that leads to  a maximum near θH ∼80º.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' It must be noted that the  preferential molecular orientations are not fixed, but  rather transient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The distributions presented in Figure  6(b)(top) are also consistent with the results by Fan et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [141] for other rigid semi-empirical models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We extended this analysis to curved interfaces, using  our NVT seeding simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  In curved interfaces,  the vector normal to the interface points at the bubble  center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure 6(b)(bottom) we show the probability  distribution of θH for the three interfacial regions, and  observe how these resemble those of planar interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  A significant loss of ordering is observed for the curved  interface since the peaks at ∼ 15º and ∼ 115º in the  external layer, and at ∼ 80º in the internal layer are  less prominent compared to the the corresponding peaks  for the flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  This could result of the curved  geometry of the interface sterically impeding a better  rearrangement of the interfacial molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We also evaluated the θH distribution for the DPMD  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure 6(c)(top) we present the distribution  of the three interfacial regions for the planar interface  at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' There is an obvious preferential orientation  towards small angles in the external layer, once again  indicating the preference of molecules to expose one  hydrogen atom to the vapor phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The distribution  is remarkably more prominent for the DPMD model  relative to TIP4P/2005, although both models result  in similar molecular arrangements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' [138], this  same structure was found in ab initio calculations using  PW91 functional, confirming that the DPMD model  based on the SCAN functional yields similar results to  those obtained from ab initio MD simulations using  different density functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Looking at the DPMD model distributions for curved  interfaces (Figure 6(c)(bottom)), we still find a preferen-  tial ordering towards small angles, although it is much  less pronounced than in the case of planar interfaces, in  agreement with TIP4P/2005 simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The bubbles  generated by both models shown here (TIP4P/2005 and  DPMD) have comparable sizes, however the effect of cur-  vature is more dramatic in the case of the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Other bubble size distributions are reported in the SM,  where we observe that there is a slight change in the  distributions, with bigger bubbles resulting curves more  similar to those found at coexistence (Figure S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  CONCLUSIONS  In this work, we explored the liquid-vapor phase behav-  ior of a Deep Potential model based on ab initio energies  and forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This model was derived from the SCAN ap-  proximation of density functional theory [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The model  has been shown to reproduce the phase diagram for the  different ice phases [42] and to have a liquid-liquid phase  transition in the supercooled regime [116].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We computed  the phase diagram via DC simulations, and adjusted  our vapor equilibrium densities to the experimental val-  ues, resulting in a shift of 40 K in the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Once the model was tested and shifted, we compare its  equilibrium properties with experimental data and the  TIP4P/2005 model [10], one of the most benchmarked  classical models for water [48, 49, 53, 139].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The surface  tension of the DPMD model is lower than the one ob-  tained from TIP4P/2005 and experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nonetheless,  by construction the DPMD model provides accurate re-  sults for other properties such as the vapor saturation  pressure for a wide range of temperatures, between 300  10  (a)  (b)  (c)  TIP4P/2005  DPMD  Planar interface  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  3  P(θH)  External layer  Internal layer  Bulk water  Curved interface  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  Rc=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='01nm  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='96nm  Figure 6: (a) Top: Slab snapshot (including only a reduced amount of molecules for better visualization) of a planar  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bottom: Snapshot for a curved interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (b) Normalized histograms of θH at the external region of the  interface, the internal one, and bulk water for the TIP4P/2005 model for planar (top) and curved (bottom)  interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (c) Same as in (b) but for the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  and 600 K (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Overall, once the temperature is  shifted, the model reproduces most of the properties of  liquid-vapor equilibrium, despite not having this regime  included in its training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This result is especially remark-  able since this is the first Deep Potential-based model  to provide liquid-vapor properties in a computationally  affordable time, with the primary drawback being the  ∼20% deviation in the surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Moreover, we study bubble nucleation in the cavita-  tion regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We make use of the NVT seeding method,  a rare event technique already shown to be successful  in determining the nucleation free energy barrier and  the nucleation rate for simpler systems [85, 107] in  cavitation events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We first performed NVT seeding  calculations at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K, a temperature at which previous  data from Umbrella Sampling are available for the  TIP4P/2005 model and we confirm that the seeding  technique provides consistent results with those from  Menzl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The DPMD water model provides  higher nucleation rates than the TIP4P/2005 model  under the same stretching conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We show that this  quantitative difference can be explained by the difference  in surface tension between models, which persists for  curved interfaces (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Our results highlight once  more the relevance of the surface tension and its change  with curvature to critically control nucleation events  [53, 129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We could have obtained closer agreement be-  tween the TIP4P/2005 nucleation rates with those from  the DPMD model if we did not apply the temperature  shift, nonetheless we prioritised adjusting the model to  obtain better equilibrium densities, in line with prior  studies of water properties using the SCAN-derived  DPMD model [115–117].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Furthermore, we provide an estimate of the Tolman  length by performing a non-linear regression to the  relevant expression [67], which describes how the surface  tension changes with curvature (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Using data  from our NVT seeding simulations we obtain estimates  of δ = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='091 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='008) nm for the DPMD model and  δ = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='070 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='004) nm for the TIP4P/2005 model, both  at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' This confirms that a Deep Potential-based  model also predicts a positive sign of the Tolman length,  confirming previous results showing a decrease of the  surface tension with curvature for the case of water  bubbles [53, 54, 129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Finally,  we studied the orientation of the water  molecules  in  the  interface,  corroborating  previous  studies that have indicated that the molecules closer to  the vapor phase have a preference so as to expose an  hydrogen atom facing the vapor [130–136, 139–141].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We  quantify this behavior by measuring the angle formed  between the normal vector to the interface and the O-H  bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We find that a preferential molecular orientation  appears for both the TIP4P/2005 and DPMD models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  We also confirm that this phenomenon also takes place  in the curved interface of water bubbles, although the  Vaporphase  External layer  Internal layel  Bulk water11  possibility to orient more O-H bonds towards the vapor  is diminished for curved interfaces due to the increasing  curvature of the bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Overall, this study confirms that machine-learning ab  initio based models that capture more molecular details  than semi-empirical models are viable for prediction  of equilibrium as well as dynamic properties that  require large system sizes and long sampling times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The  computational cost of ab initio based models in long  scale Molecular Dynamics is now affordable being only  an order of magnitude greater than that for empirical  potentials,  thanks to recent improvements such as  the compressed Deep Potential modelling scheme [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Further work and models trained with more liquid  and vapor data will only improve the already existing  models, which will gradually be better in describing the  real behaviour of water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' acknowledges funding from Derek Brewer  scholarship of Emmanuel College and EPSRC Doc-  toral  Training  Programme  studentship,  number  EP/T517847/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  acknowledges  funding  from the Roger Ekins Research Fellowship of Emmanuel  College, Oppenheimer Research Fellowship of the Uni-  versity of Cambridge and the Ramon y Cajal fellowship  (RYC2021-030937-I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P acknowledge  the “Chemistry in Solution and at Interfaces” (CSI)  Center funded by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Department of Energy  Award DE-SC001934 and Award DE-SC0002128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Com-  putational resources were provided by the Princeton  Research Computing at Princeton University which is  a consortium of groups led by the Princeton Institute  for Computational Science and Engineering (PICSciE)  and the Office of Information Technology’s Research  Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chanda and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Fokin, “Organic synthesis “on wa-  ter”,” Chemical reviews, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 109, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 725–748, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chaplin, “Do we underestimate the importance of wa-  ter in cell biology?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=',” Nature Reviews Molecular Cell Biol-  ogy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 861–866, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [3] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lester, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Blood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Denyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Giddings, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Azzopardi,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Poliakoff, “Reaction engineering: The supercriti-  cal water hydrothermal synthesis of nano-particles,” The  Journal of Supercritical Fluids, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 209–214,  2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ponomarenko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vincent, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pietriga, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cochard,  ´E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Badel, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Marmottant, “Ultrasonic emissions reveal  individual cavitation bubbles in water-stressed wood,”  Journal of the Royal Society Interface, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 99,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20140480, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wheeler and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Stroock, “The transpiration of  water at negative pressures in a synthetic tree,” Nature,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 455, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7210, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 208–212, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [6] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Adhikari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Goliaei, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berkowitz, “Mechanism  of membrane poration by shock wave induced nanobubble  collapse: A molecular dynamics study,” The Journal of  Physical Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 119, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6225–6234,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Liu, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, “The effect of ultrasonic  waves on the nucleation of pure water and degassed wa-  ter,” Ultrasonics sonochemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 459–  463, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kumar and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Saini, “Study of cavitation in hydro tur-  bines—a review,” Renewable and Sustainable Energy Re-  views, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 374–383, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Michaelides, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Alfe, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Schimka, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kresse, and  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, “Adsorption and diffusion of water on graphene  from first principles,” Physical Review B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 84, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 033402, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, “A general purpose model for  the condensed phases of water: Tip4p/2005,” The Journal  of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 123, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 234505, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Garc´ıa Fern´andez, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega,  “A potential model for the study of ices and amor-  phous water: Tip4p/ice,” The Journal of chemical physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 122, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 234511, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mahoney and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jorgensen, “Quantum, in-  tramolecular flexibility, and polarizability effects on the re-  production of the density anomaly of liquid water by sim-  ple potential functions,” The Journal of Chemical Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10758–10768, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [13] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jorgensen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chandrasekhar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Madura, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Impey, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Klein, “Comparison of simple poten-  tial functions for simulating liquid water,” The Journal of  chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 79, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 926–935, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Horn, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Swope, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pitera, “Character-  ization of the tip4p-ew water model: Vapor pressure and  boiling point,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 123,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 194504, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berendsen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Grigera, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Straatsma, “The miss-  ing term in effective pair potentials,” Journal of Physical  Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 91, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6269–6271, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mahoney and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jorgensen, “A five-site  model for liquid water and the reproduction of the density  anomaly by rigid, nonpolarizable potential functions,” The  Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 112, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8910–  8922, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [17] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Molinero and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Moore, “Water modeled as  an intermediate element between carbon and silicon,”  The Journal of Physical Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 113, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 13,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4008–4016, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hasegawa and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tanimura, “A polarizable water  model for intramolecular and intermolecular vibrational  spectroscopies,” The Journal of Physical Chemistry B,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5545–5553, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ahlstr¨om, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wallqvist, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Engstr¨om, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J¨ons-  son, “A molecular dynamics study of polarizable water,”  Molecular Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 563–581, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Head-Gordon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ponder, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Chodera, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Eastman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Martinez, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pande,  12  “Systematic improvement of a classical molecular model  of water,” The Journal of Physical Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 117,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9956–9972, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [21] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Babin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Leforestier, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Paesani, “Develop-  ment of a “first principles” water potential with flexible  monomers: Dimer potential energy surface, vrt spectrum,  and second virial coefficient,” Journal of chemical theory  and computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5395–5403, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [22] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Santra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Michaelides, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Scheffler, “On the ac-  curacy of density-functional theory exchange-correlation  functionals for h bonds in small water clusters: Bench-  marks approaching the complete basis set limit,” The  Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 127, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 184104,  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lambros and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Paesani, “How good are polarizable  and flexible models for water: Insights from a many-body  perspective,” The Journal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 153,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 060901, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Horn, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Swope, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pitera, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Madura,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dick, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hura, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Head-Gordon, “Develop-  ment of an improved four-site water model for biomolec-  ular simulations:  Tip4p-ew,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 120, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9665–9678, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Benavides, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Aragones, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, “Consensus on  the solubility of nacl in water from computer simulations  using the chemical potential route,” The Journal of Chem-  ical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 144, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 124504, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Young, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jiang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gupta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Debenedetti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos,  “On the calculation of solubilities via direct coexistence  simulations: Investigation of nacl aqueous solutions and  lennard-jones binary mixtures,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 145, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 154111, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Haji-Akbari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Debenedetti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Panagiotopoulos, “Forward flux sampling calculation of  homogeneous nucleation rates from aqueous nacl solu-  tions,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 148, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 044505, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [28] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanchez-Burgos and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, “Direct calculation  of the planar nacl-aqueous solution interfacial free energy  at the solubility limit,” arXiv preprint arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='08322,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [29] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lamas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Noya, “Freezing point  depression of salt aqueous solutions using the madrid-2019  model,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 156, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 13,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 134503, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [30] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Blazquez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Conde, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, “The  madrid-2019 force field for electrolytes in water using  tip4p/2005 and scaled charges: Extension to the ions f-  , br-, i-, rb+, and cs+,” The Journal of Chemical Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 156, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 044505, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bergonzo and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cheatham III, “Improved force  field parameters lead to a better description of rna struc-  ture,” Journal of chemical theory and computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3969–3972, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [32] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Smith, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Segelken, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cruz, “Force-  field induced bias in the structure of aβ21–30: A compar-  ison of opls, amber, charmm, and gromos force fields,”  Journal of Chemical Information and Modeling, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 55,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2587–2595, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Piaggi and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, “Phase equilibrium of liquid wa-  ter and hexagonal ice from enhanced sampling molecular  dynamics simulations,” The Journal of chemical physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 152, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 204116, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [34] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Caballero-Bernal,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani, “Homogeneous ice nucle-  ation at moderate supercooling from molecular simula-  tion,” Journal of the American Chemical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 135,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 40, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15008–15017, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Seed-  ing approach to crystal nucleation,” The Journal of chem-  ical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 144, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 034501, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [36] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Niu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Parrinello, “Temperature  dependence of homogeneous nucleation in ice,” Physical  review letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 122, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 24, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 245501, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [37] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Friesner, “Ab initio quantum chemistry: Method-  ology and applications,”  Proceedings of the National  Academy of Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 102, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6648–6653,  2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [38] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mlynsky, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Banas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sponer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' van der Kamp,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mulholland, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Otyepka, “Comparison of ab ini-  tio, dft, and semiempirical qm/mm approaches for descrip-  tion of catalytic mechanism of hairpin ribozyme,” Jour-  nal of Chemical Theory and Computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1608–1622, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [39] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gerber, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Shemesh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Varner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kalinowski, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hirshberg, “Ab initio and semi-empirical molecular  dynamics simulations of chemical reactions in isolated  molecules and in clusters,” Physical Chemistry Chemical  Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 21, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9760–9775, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [40] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weinan,  “Deep potential molecular dynamics:  a scalable model  with the accuracy of quantum mechanics,” Physical re-  view letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 120, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 14, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 143001, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [41] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zeng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weinan, “Dp-gen: A concurrent learning  platform for the generation of reliable deep learning based  potential energy models,” Computer Physics Communica-  tions, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 253, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 107206, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [42] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weinan, “Phase di-  agram of a deep potential water model,” Physical review  letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 126, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 236001, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ruzsinszky, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Perdew, “Strongly con-  strained and appropriately normed semilocal density func-  tional,” Physical review letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 036402,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [44] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Remsing, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ruzsin-  szky, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Peng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Paul, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Waghmare, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wu,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=', “Accurate first-principles structures and energies of  diversely bonded systems from an efficient density func-  tional,” Nature chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 831–836, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [45] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Piaggi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Debenedetti, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, “Homogeneous ice nucleation in  an ab initio machine-learning model of water,” Proceed-  ings of the National Academy of Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 119, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 33,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' e2207294119, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Han, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=', “Deep potential: A  general representation of a many-body potential energy  surface,” arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='01478, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [47] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Linstrom and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mallard, NIST Chemistry WebBook,  NIST Standard Reference Database Number 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gaithers-  burg MD: National Institute of Standards and Technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [48] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nezbeda, “Vapor-liquid  equilibria from the triple point up to the critical point  for the new generation of tip4p-like models: Tip4p/ew,  tip4p/2005, and tip4p/ice,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 125, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 034503, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  13  [49] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' de Miguel, “Surface tension of the most  popular models of water by using the test-area simula-  tion method,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 126,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 154707, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [50] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mountain, “An internally consistent method for the  molecular dynamics simulation of the surface tension: ap-  plication to some tip4p-type models of water,” The Jour-  nal of Physical Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 113, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 482–486,  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [51] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Alejandre and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chapela, “The surface tension  of tip4p/2005 water model using the ewald sums for the  dispersion interactions,” The Journal of chemical physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 132, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 014701, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [52] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Aragones, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Noya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Abascal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonzalez, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' McBride, “Anomalies  in water as obtained from computer simulations of the  tip4p/2005 model: density maxima, and density, isother-  mal compressibility and heat capacity minima,” Molecular  Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4-6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 365–374, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Menzl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonzalez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Geiger, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Caupin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Abascal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dellago, “Molecular mech-  anism for cavitation in water under tension,” Proceedings  of the National Academy of Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 113, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 48,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 13582–13587, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [54] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Min and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berkowitz, “Bubbles in water un-  der stretch-induced cavitation,” The Journal of Chemical  Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 150, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 054501, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [55] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonzalez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Aragones, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Va-  leriani, “Homogeneous bubble nucleation in water at nega-  tive pressure: A voronoi polyhedra analysis,” The Journal  of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 138, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 084508, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Joswiak, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Duff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Doherty, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Peters,  “Size-dependent surface free energy and tolman-corrected  droplet nucleation of tip4p/2005 water,” The Journal of  Physical Chemistry Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4267–4272,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Joswiak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Do, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Doherty, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Peters,  “Energetic and entropic components of the tolman length  for mw and tip4p/2005 water nanodroplets,” The Journal  of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 145, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 20, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 204703, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonzalez,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani,  and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bresme, “Bubble nucleation in simple and molecular  liquids via the largest spherical cavity method,” The Jour-  nal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 142, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 154903, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonz´alez, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Menzl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Aragones, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Geiger,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Caupin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dellago, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani,  “Detecting vapour bubbles in simulations of metastable  water,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 141, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18C511, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [60] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Debenedetti, Metastable liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Princeton univer-  sity press, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [61] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kashchiev, Nucleation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Elsevier, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [62] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Green, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Durben, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wolf, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Angell, “Water and  solutions at negative pressure: Raman spectroscopic study  to-80 megapascals,” Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 249, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4969, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 649–  652, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [63] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zheng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Durben, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wolf, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Angell, “Liquids  at large negative pressures: water at the homogeneous  nucleation limit,” Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 254, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5033, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 829–832,  1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [64] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Alvarenga, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Grimsditch, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bodnar, “Elastic  properties of water under negative pressures,” The Journal  of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 98, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8392–8396, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [65] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Azouzi,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ramboz,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lenain,  and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Caupin, “A coherent picture of water at extreme neg-  ative pressure,” Nature Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 38–41,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [66] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pallares, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' El Mekki Azouzi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gonz´alez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Aragones, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Abascal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valeriani, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Caupin,  “Anomalies in bulk supercooled water at negative pres-  sure,” Proceedings of the National Academy of Sciences,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 111, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 22, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7936–7941, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [67] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tolman, “The effect of droplet size on surface ten-  sion,” The journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 333–337, 1949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [68] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Salzmann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Radaelli, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Slater, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Finney, “The polymorphism of ice: five unresolved ques-  tions,” Physical Chemistry Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 13,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 41, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18468–18480, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [69] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wagner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Riethmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Feistel, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Harvey,  “New equations for the sublimation pressure and melting  pressure of h2o ice ih,” Journal of Physical and Chemical  Reference Data, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 043103, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [70] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Brown and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Whalley, “Preliminary investigation of  the phase boundaries between ice vi and vii and ice vi and  viii,” The Journal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 45, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4360–4361, 1966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [71] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chen, “Dp compress:  A model compression  scheme for generating efficient deep potential models,”  Journal of Chemical Theory and Computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5559–5567, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [72] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Plimpton, “Fast parallel algorithms for short-range  molecular dynamics,” Journal of Computational Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 117, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1–19, 3 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [73] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Han, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weinan, “Deepmd-  kit: A deep learning package for many-body potential en-  ergy representation and molecular dynamics,” Computer  Physics Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 228, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 178–184, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [74] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nos´e, “A unified formulation of the constant tempera-  ture molecular dynamics methods,” The Journal of Chem-  ical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 81, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 511–519, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [75] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hoover, “Canonical dynamics: Equilibrium phase-  space distributions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 31, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1695–1697,  Mar 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [76] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hoover, “Constant-pressure equations of motion,”  Physical Review A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2499, 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [77] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kirkwood and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Buff, “The statistical mechan-  ical theory of surface tension,” The Journal of Chemical  Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 338–343, 1949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [78] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bekker, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berendsen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dijkstra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Achterop,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Vondrumen,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  VANDERSPOEL,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Sijbers,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Keegstra,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Renardus,  “Gromacs-a parallel  computer for molecular-dynamics simulations,” in 4th  International Conference on Computational Physics (PC  92), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 252–256, World Scientific Publishing, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [79] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bussi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Donadio, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Parrinello, “Canoni-  cal sampling through velocity rescaling,” The Journal of  chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 126, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 014101, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [80] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Parrinello and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rahman, “Polymorphic transitions  in single crystals: A new molecular dynamics method,”  Journal of Applied physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7182–7190,  1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [81] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hockney, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Goel, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Eastwood, “Quiet high-  resolution computer models of a plasma,” Journal of Com-  putational Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 148–158, 1974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  14  [82] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Darden, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' York, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pedersen, “Particle mesh  ewald: An n log (n) method for ewald sums in large sys-  tems,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 98, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10089–10092, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [83] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Essmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Perera, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berkowitz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Darden,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lee, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Pedersen, “A smooth particle mesh  ewald method,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 103,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8577–8593, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [84] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hess, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bekker, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Berendsen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Fraaije,  “Lincs: a linear constraint solver for molecular simula-  tions,” Journal of computational chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1463–1472, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [85] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Rosales-Pelaez,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Sanchez-Burgos,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Valeriani,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Seeding approach to nucleation  in the n v t ensemble: The case of bubble cavitation in  overstretched lennard jones fluids,” Physical Review E,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 101, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 022611, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [86] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Montero de Hijes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bianco, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz,  and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, “Interfacial free energy and tolman length of  curved liquid–solid interfaces from equilibrium studies,”  The Journal of Physical Chemistry C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 124, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 16,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8795–8805, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [87] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Volmer and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weber, “Keimbildung in ¨ubers¨attigten  gebilden,” Zeitschrift f¨ur physikalische Chemie, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 119,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 277–301, 1926.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [88] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Becker and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D¨oring, “Kinetische behandlung der  keimbildung in ¨ubers¨attigten d¨ampfen,”  Annalen der  physik, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 416, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 719–752, 1935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [89] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sear, “The non-classical nucleation of crystals: mi-  croscopic mechanisms and applications to molecular crys-  tals, ice and calcium carbonate,” International Materials  Reviews, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 57, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 328–356, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [90] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Merikanto,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Zapadinsky,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Lauri,  and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vehkam¨aki, “Origin of the failure of classical nu-  cleation theory:  Incorrect description of the smallest  clusters,”  Physical  review  letters,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  98,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  14,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 145702, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [91] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cacciuto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Auer, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Frenkel, “Breakdown of  classical nucleation theory near isostructural phase tran-  sitions,” Physical review letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 93, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 16, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 166105,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [92] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Horsch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vrabec, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hasse, “Modification of the  classical nucleation theory based on molecular simulation  data for surface tension, critical nucleus size, and nucle-  ation rate,” Physical Review E, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 78, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 011603,  2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [93] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Moroni, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ten Wolde, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bolhuis, “Inter-  play between structure and size in a critical crystal nu-  cleus,” Physical review letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 94, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 235703,  2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [94] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Leoni and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Russo, “Nonclassical nucleation path-  ways in stacking-disordered crystals,” Physical Review X,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 031006, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [95] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Homogeneous ice  nucleation rate in water droplets,” The Journal of Physical  Chemistry C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 122, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 40, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 22892–22896, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [96] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Knott, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Molinero, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Doherty, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Peters,  “Homogeneous nucleation of methane hydrates: Unreal-  istic under realistic conditions,” Journal of the American  Chemical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 134, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 48, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19544–19547, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [97] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lamas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Conde, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ram´ırez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  de Hijes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Noya, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Homogeneous  nucleation of nacl in supersaturated solutions,” Physical  Chemistry Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 47, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 26843–  26852, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [98] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Saika-Voivod, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Romano, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sciortino, “Nucle-  ation barriers in tetrahedral liquids spanning glassy and  crystallizing regimes,” The Journal of chemical physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 135, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 124506, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [99] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Richard and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Speck, “Crystallization of hard spheres  revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' thermodynamic modeling, nucleation work,  and the surface of tension,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 148, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 22, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 224102, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [100] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Separdar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rino, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zanotto, “Molecular  dynamics simulations of spontaneous and seeded nucle-  ation and theoretical calculations for zinc selenide,” Com-  putational Materials Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 187, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 110124, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [101] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanchez-Burgos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Garaizar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, “Parasitic crystallization of colloidal elec-  trolytes: growing a metastable crystal from the nucleus of  a stable phase,” Soft Matter, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 489–505,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [102] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanchez-Burgos, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Es-  pinosa, “Fcc vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' hcp competition in colloidal hard-sphere  nucleation: on their relative stability, interfacial free en-  ergy and nucleation rate,” Physical Chemistry Chemical  Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 35, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19611–19626, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [103] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Filion, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hermes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ni, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dijkstra, “Crys-  tal nucleation of hard spheres using molecular dynamics,  umbrella sampling, and forward flux sampling: A compar-  ison of simulation techniques,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 133, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 24, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 244115, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [104] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Fiorucci, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Coli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Padding, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Dijkstra,  “The effect of hydrodynamics on the crystal nucleation of  nearly hard spheres,” The Journal of Chemical Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 152, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 064903, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [105] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Piaggi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Weis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Debenedetti, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, “Homogeneous ice nucleation in  an ab initio machine-learning model of water,” Proceed-  ings of the National Academy of Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 119, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 33,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' e2207294119, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [106] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Baidakov, “Stability of metastable phases and ki-  netics of nucleation in a simple single-component sys-  tem (molecular dynamics simulation)(a review),” Russian  Journal of General Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 92, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 611–628,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [107] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanchez-Burgos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' de Hijes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rosales-Pelaez,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Equivalence between condensation  and boiling in a lennard-jones fluid,” Physical Review E,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 102, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 062609, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [108] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Blander and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Katz, “Bubble nucleation in liq-  uids,” AIChE Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 833–848, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [109] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bal and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Neyts, “Extending and validating  bubble nucleation rate predictions in a lennard-jones fluid  with enhanced sampling methods and transition state the-  ory,” The Journal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 157, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 184113, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [110] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Diemand, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ang´elil, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tanaka, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tanaka,  “Direct simulations of homogeneous bubble nucleation:  Agreement with classical nucleation theory and no local  hot spots,” Physical review E, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 90, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 052407,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [111] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Meadley and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Escobedo, “Thermodynamics  and kinetics of bubble nucleation: Simulation methodol-  ogy,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 137, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 7,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 074109, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [112] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kusaka and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Oxtoby, “Identifying physical  clusters in bubble nucleation,” The Journal of chemical  15  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 111, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1104–1108, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [113] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ang´elil, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Diemand, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tanaka, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tanaka,  “Bubble evolution and properties in homogeneous nu-  cleation simulations,” Physical review E, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 90, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 6,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 063301, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [114] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Remsing, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Andrade,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Santra, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Selloni, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Klein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Perdew, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wu, “Ab initio theory and modeling of  water,” Proceedings of the National Academy of Sciences,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 114, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 41, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10846–10851, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [115] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yao and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kanai, “Temperature dependence of nu-  clear quantum effects on liquid water via artificial neural  network model based on scan meta-gga functional,” The  Journal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 153, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 044114,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [116] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gartner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Piaggi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Panagiotopoulos, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Debenedetti, “Signatures of a  liquid–liquid transition in an ab initio deep neural network  model for water,” Proceedings of the National Academy of  Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 117, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 42, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 26040–26046, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [117] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Piaggi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Debenedetti,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Car, “Phase equilibrium of water with hexagonal  and cubic ice using the scan functional,” Journal of Chem-  ical Theory and Computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3065–  3077, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' PMID: 33835819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [118] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Stukowski, “Visualization and analysis of atomistic  simulation data with ovito–the open visualization tool,”  Modelling and simulation in materials science and engi-  neering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 015012, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [119] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rowlinson and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Widom, Molecular theory of cap-  illarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Courier Corporation, USA, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [120] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zollweg and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mulholland, “On the law of the  rectilinear diameter,” The Journal of Chemical Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 57, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1021–1025, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [121] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Torrie and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Valleau, “Monte carlo free  energy estimates using non-boltzmann sampling: Appli-  cation to the sub-critical lennard-jones fluid,” Chemical  Physics Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 578–581, 1974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [122] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Thompson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Plimpton, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mattson,  “General formulation of pressure and stress tensor for ar-  bitrary many-body interaction potentials under periodic  boundary conditions,” The Journal of chemical physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 131, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 154107, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [123] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' van Giessen and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Blokhuis, “Direct deter-  mination of the tolman length from the bulk pressures  of liquid drops via molecular dynamics simulations,” The  Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 131, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 16, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 164705,  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [124] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bykov and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zeng, “A patching model for surface  tension and the tolman length,” The Journal of chemical  physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 111, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3705–3713, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [125] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lei, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bykov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yoo, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Zeng, “The  tolman length: Is it positive or negative?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=',” Journal of the  American Chemical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 127, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 44, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15346–  15347, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [126] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Julin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Napari, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Merikanto, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vehkam¨aki,  “A thermodynamically consistent determination of surface  tension of small lennard-jones clusters from simulation and  theory,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 133, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 044704, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [127] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tr¨oster and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Binder, “Positive tolman length in a  lattice gas with three-body interactions,” Physical Review  Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 26, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 265701, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [128] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Iwamatsu and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Horii, “Temperature dependence of  liquid-vapor nucleation rate for the yukawa model fluid,”  Aerosol science and technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 563–574,  1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [129] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Magaletti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gallo, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Casciola, “Water  cavitation from ambient to high temperatures,” Scientific  reports, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1–10, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [130] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ohto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rouxel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Imoto, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Backus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mukamel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nagata, “Molecu-  lar structure and modeling of water–air and ice–air inter-  faces monitored by sum-frequency generation,” Chemical  reviews, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 120, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3633–3667, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [131] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nagata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hasegawa, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Backus, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Usui,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yoshimune, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ohto, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, “The surface rough-  ness, but not the water molecular orientation varies with  temperature at the water–air interface,” Physical Chem-  istry Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 36, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 23559–23564,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [132] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nagata, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Backus, “Molecular  structure and dynamics of water at the water–air interface  studied with surface-specific vibrational spectroscopy,”  Angewandte Chemie International Edition, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 19,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5560–5576, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [133] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nihonyanagi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Mondal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yamaguchi, and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tahara, “Structure and dynamics of interfacial water  studied by heterodyne-detected vibrational sum-frequency  generation,” Annual review of physical chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 64,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 579–603, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [134] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nihonyanagi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ishiyama, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yamaguchi,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Morita, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Tahara, “Unified molecu-  lar view of the air/water interface based on experimental  and theoretical χ (2) spectra of an isotopically diluted wa-  ter surface,” Journal of the American Chemical Society,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 133, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 42, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 16875–16880, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [135] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Liang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Jeon, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cho, “Ab initio modeling  of the vibrational sum-frequency generation spectrum of  interfacial water,” The Journal of Physical Chemistry Let-  ters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1153–1158, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [136] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ohto, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Usui, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hasegawa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Na-  gata, “Toward ab initio molecular dynamics modeling for  sum-frequency generation spectra;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' an efficient algorithm  based on surface-specific velocity-velocity correlation func-  tion,” The Journal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 143, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 12,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 124702, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [137] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Kessler,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Elgabarty,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Spura,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Karhan,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Partovi-Azar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hassanali, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Kuhne,  “Structure  and  dynamics  of  the  instantaneous  wa-  ter/vapor interface revisited by path-integral and ab initio  molecular dynamics simulations,” The Journal of Physical  Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 119, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 31, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 10079–10086, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [138] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vassilev, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hartnig, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Koper, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Frechard, and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' van Santen, “Ab initio molecular dynamics simula-  tion of liquid water and water–vapor interface,” The Jour-  nal of Chemical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 21, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9815–9820,  2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [139] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Khatib, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Hasegawa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sulpizi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Backus,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Bonn, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Nagata, “Molecular dynamics simu-  lations of sfg librational modes spectra of water at the  water–air interface,” The Journal of Physical Chemistry  C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 120, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18665–18673, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [140] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' McCammon, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Rossky, “The  structure of liquid water at an extended hydrophobic sur-  face,” The Journal of chemical physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 80, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 9,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 4448–4455, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  16  [141] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Fan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Cremer, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Gao,  “On the structure of water at the aqueous/air interface,”  The Journal of Physical Chemistry B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 113, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 34,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 11672–11679, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [142] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Vega, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Sanz, “Ice–water inter-  facial free energy for the tip4p, tip4p/2005, tip4p/ice, and  mw models as obtained from the mold integration tech-  nique,” The Journal of Physical Chemistry C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 120,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 15, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 8068–8075, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  Supplementary Material: A Deep Potential model for liquid-vapor equilibrium and  cavitation rates of water  Ignacio Sanchez-Burgos1,2, Maria Carolina Muniz2, Jorge R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Espinosa1,3 and Athanassios Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Panagiotopoulos2,∗  [1] Maxwell Centre, Cavendish Laboratory, Department of Physics,  University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [2] Department of Chemical and Biological Engineering,  Princeton University, Princeton, New Jersey 08544, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [3] Departamento de Qu´ımica F´ısica, Facultad de Ciencias Qu´ımicas,  Universidad Complutense de Madrid, 28040 Madrid, Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  = To whom correspondence should be sent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' email: azp@princeton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='edu  SI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  EQUATION OF STATE  As mentioned in the main text, we corroborate that we can obtain the density of the liquid phase surrounding the  critical bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Then, with such density, by means of the ρl against P equation of state we obtain the pressure of the  liquid phase, which matches the pressure obtained through the virial expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure S1 we show the equation  of state at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K for the DPMD and TIP4P/2005 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  150  100  50  0  P / MPa  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='98  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='02  Density / (g cm  3)  EOS Liq 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4K DPMD  EOS Liq 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4K TIP4P/2005  Figure S1: Density against pressure equation of state at 296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4 K for the DPMD and TIP4P/2005 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  SII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  BUBBLE SPHERICITY  In order to quantify how spherical the simulated bubbles are, we take the following approach: We divide the  simulation box into smaller cells of ∼ 200˚A3 each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We classify the cells as liquid or vapor based on their local density,  taking 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='3 g cm−3 as threshold density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We then identify the surface available to the vapor cluster by means of a  Surface mesh algorithm [1, 2] available with the OVITO software package [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' From this, we obtain the surface and  volume that corresponds to the vapor cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Using his information we compute the cluster sphericity (Ψ) as [4]:  Ψ = π1/3(6V )2/3  S  (S1)  where V is the cluster volume and S the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Ψ is equal to 1 for a perfect sphere and decays for less spherical  geometric bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure S2 we show a rendered image of the surface created for a vapor cluster (depicted in  orange), as well as Ψ against time for our Seeding simulations with the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  The values of Ψ exceed  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='85 in all cases which means a high sphericity of the simulated bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We show with a blue line Ψ for the initial  configuration in which a perfect sphere has been generated, and represents the maximum sphericity that our parameter  is able to account for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  2  (a)  (b)  0  5  10  15  20  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='8  1  Ψ  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='25 nm  0  5  10  15  20  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='50 nm  0  5  10  15  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='8  1  Ψ  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='74 nm  0  5  10  15  20  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='8  1  Ψ  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='96 nm  0  5  10  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
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+page_content='8  1  Ψ  Rc=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='29 nm  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  10  t / ns  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='8  1  Ψ  Rc=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='50 nm  Figure S2: (a) Snapshot of a vapor cluster (Rc=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='29 nm) identified as detailed in section SII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The identified surface  is colored in orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (b) Ψ against time for the 6 simulated bubbles in Seeding simulations with the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  SIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  ORIENTATIONAL ANALYSIS  In the main text we show the orientational analysis of interfacial molecules for one bubble size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' In Figure S3,  we show the same analysis for different bubble size using the DPMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' We observe how the dependency of  orientation preference with curvature is moderate but noticeable for the range of bubble sizes studied, being the  biggest bubble the one resembling more to the coexistence conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [1] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Edelsbrunner and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' M¨ucke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 13,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 43–72, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Stukowski, “Computational analysis methods in atomistic modeling of crystals,” Jom, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 66, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 399–407, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Stukowski, “Visualization and analysis of atomistic simulation data with ovito–the open visualization tool,” Modelling  and Simulation in Materials Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 015012, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' Wadell, “Volume, shape, and roundness of quartz particles,” The Journal of Geology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' 250–280, 1935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='  3  (a)  (b)  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  3  P(θH)  External layer  Internal layer  Bulk water  Planar  interface  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  Rc=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='50 nm  (c)  (d)  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='96nm  0  30  60  90  120  150  180  θH  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='5  2  P(θH)  External layer  Internal layer  Bulk water  Rc=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content='25 nm  Figure S3: Distribution probability of the O-H bond with respect to the direction normal to the interface,  renormalized by the random distribution sin(θH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The shown distributions are for (a) planar interface;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' (b-d) critical  bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
+page_content=' The bubble radius is indicated in the leyend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FLT4oBgHgl3EQfKi8f/content/2301.12008v1.pdf'}
diff --git a/JNAzT4oBgHgl3EQfVPyV/content/tmp_files/2301.01281v1.pdf.txt b/JNAzT4oBgHgl3EQfVPyV/content/tmp_files/2301.01281v1.pdf.txt
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+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in
+Magnetohydrodynamic Turbulence and
+Dynamo from Energy Flux Perspectives
+Mahendra K. Verma1*, Manohar K. Sharma2
+and Soumyadeep Chatterjee1
+1*Department of physics, Indian institute of Technology Kanpur,
+Kalyanpur, Kanpur, 208016, Uttar Pradesh, India.
+2Department of Mathematics, University of Grenoble Aples ,
+Gires, Grenoble, 38000, Grenoble, France.
+*Corresponding author(s). E-mail(s): mkv.iitk.ac.in;
+Contributing authors:
+manohar-kumar.sharma@univ-grenoble-aples.fr;
+soumyade@iitk.ac.in;
+Abstract
+In this review, we describe turbulent drag reduction in a variety of
+flows using a universal framework of energy flux. In a turbulent flow
+with dilute polymers and magnetic field, the kinetic energy injected
+at large scales cascades to the velocity field at intermediate scales,
+as well as to the polymers and magnetic field at all scales. Conse-
+quently, the kinetic energy flux, Πu(k), is suppressed in comparison
+to the pure hydrodynamic turbulence. We argue that the suppression
+of Πu(k) is an important factor in the reduction of the inertial force
+⟨u · ∇u⟩ and turbulent drag. This feature of turbulent drag reduction
+is observed in polymeric, magnetohydrodynamic, quasi-static magne-
+tohydrodynamic, and stably-stratified turbulence, and in dynamos. In
+addition, it is shown that turbulent drag reduction in thermal con-
+vection is due to the smooth thermal plates, similar to the turbulent
+drag reduction over bluff bodies. In all these flows, turbulent drag
+reduction often leads to a strong large-scale velocity in the flow.
+Keywords: Turbulent drag reduction, Magnetohydrodynamic turbulence,
+Energy flux, Dynamo, Quasi-static magnetohydrodynamics, Turbulent thernal
+convection
+1
+arXiv:2301.01281v1  [physics.plasm-ph]  29 Dec 2022
+
+Springer Nature 2021 LATEX template
+2
+Turbulent Drag Reduction in MHD Turbulence
+1 Introduction
+It has been observed that an introduction of polymers and magnetic field
+to a turbulent flow reduces turbulent drag [1–11]. Turbulence drag is also
+suppressed over bluff bodies with particular shapes, e.g., aerofoils. This phe-
+nomena, known as turbulent drag reduction, or TDR in short, depends on
+many factors—properties of the boundaries and fluids, bulk turbulence, nature
+of polymers, etc. In this review, using energy flux, we describe a univer-
+sal framework to explain TDR in polymeric, magnetohydrodynamic (MHD),
+quasi-static MHD, and stably-stratified turbulence, and in dynamo.
+A pipe flow exhibits viscous drag at small Reynolds numbers, but it experi-
+ences turbulent drag at large Reynolds numbers [12, 13]. It has been observed
+that an introduction of small amount of polymers in the flow suppresses the
+turbulent drag up to 80% [1–11]. In Fig. 1, we illustrate the mean normal-
+ized velocity profiles (V +) as a function of normalized distance from the wall
+(y+) in a hydrodynamic (HD) flow with and without polymers. The bottom
+curve with green dots represents V + for pure HD turbulence and it exhibits
+K´arman’s log layer, whereas the chained curve with red squares is for polymeric
+turbulence and it shows TDR. L’vov et al. [6] constructed a phenomenological
+model for the maximum drag reduction asymptote (represented by the chained
+curve in the figure) that matches with numerical and experimental data quite
+well. Study of TDR is particularly important due to its wide-ranging practical
+applications. For example, firefighters mix polymers in water to increase the
+range of fire-hoses. Also, polymers are used to increase the flow rates in oil
+pipe, etc.
+Fig. 1 For a wall-bound flow, mean normalized velocity profiles (V +) as a function of
+the normalized distance from the wall (y+). The bottom curve with green dots is for pure
+HD turbulence, whereas the chained-curve with red squares is for the polymeric turbulence.
+From L’vov et al. [6]. Reproduced with permission from APS.
+
+50.
+Newtonian, Warholic, 1999
+MDR, Rollin, 1972
+Rudd, 1969
+40.
+Rollin, 1972
+DNS, De Angelis, 2003
+- MDR, our theory
+. Newtonian, our theory
+30-
+. Newtonian plugs
+X+
+20
+10.
+0
+10
+100
++
+ySpringer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+3
+Bluff bodies too experience viscous and turbulent drag at small and large
+Reynolds numbers respectively. Turbulent drag over bluff bodies depend on
+the surface properties, e.g., smoothness and curvature [14, 15]. Keeping these
+factors in mind, airplanes, automobiles, missiles, and ships are designed to
+minimize turbulent drag.
+In a recent paper, Verma et al. [11] argued that TDR occurs in MHD
+turbulence analogous to TDR in turbulent flows with dilute polymers. They
+showed that the kinetic energy (KE) flux (Πu(k)) is suppressed in polymeric
+and MHD turbulence due to the transfer of energy from the velocity field
+to polymers and magnetic field respectively. The energy fluxes in polymeric
+and MHD turbulence have been studied in a number of earlier works [1, 11,
+16–19]. It was argued that the turbulent drag and the nonlinearity ⟨u · ∇u⟩
+are proportional to Πu(k)/U, where u is the velocity field, U is the large-
+scale velocity, and ⟨.⟩ represents averaging. Thus, Verma et al.’s [11] formalism
+provides a general framework for TDR in variety of flows, including polymeric
+and MHD turbulence.
+An introduction of polymers or magnetic field in a turbulent flow enhances
+the mean flow, but suppresses ⟨u · ∇u⟩ [1–11]. Verma et al. [11] observed the
+above phenomena in a shell model of MHD turbulence. Note that ⟨u · ∇u⟩
+and Πu(k) depend critically on the phase relations between the Fourier modes.
+Verma et al. [11] argued that the velocity correlations in polymeric and MHD
+turbulence are enhanced compared to pure HD turbulence. These correlations
+lead to suppressed ⟨u · ∇u⟩ and Πu(k) in spite of amplification of U. Thus,
+TDR, energy flux, and enhancement of U are related to each other.
+Based on past results, Verma et al. [11] argued for TDR in quasi-static
+MHD (QSMHD) turbulence [20, 21]. The Joule dissipation suppresses Πu(k) at
+all wavenumbers [20–23], and hence Πu(k) for QSMHD turbulence is lower than
+the corresponding flux for HD turbulence. In addition, large-scale U increases
+with the increase of interaction parameter, thus indicating TDR in QSMHD
+turbulence.
+Generation of magnetic field in astrophysical objects, such as planets, stars,
+and galaxies, are explained using dynamo mechanism [24–27]. Here, magnetic
+field grows and saturates at some level due to the self-induced currents. In the
+present review, we discuss TDR in dynamo using the energy flux. Based on
+earlier dynamo simulations (e,g., [27, 28]), we show that the fluctuations in the
+velocity and magnetic fields are suppressed when a large-scale magnetic field
+emerges in the system. This feature signals TDR in dynamo.
+Planetary and stellar atmospheres often exhibit stably stratified turbu-
+lence. In such flows, lighter fluid is above the heavier fluid with gravity acting
+downwards [29, 30]. The KE flux in stably stratified turbulence is suppressed,
+as in polymeric and MHD turbulence. Based on these observations, we argue
+for TDR in stably stratified turbulence.
+Researchers have reported that compared to HD turbulence, viscous dissi-
+pation rate (ϵu) and thermal dissipation rate (ϵT ) are suppressed in turbulent
+thermal convection. For example, Pandey et al. [31] and Bhattacharya et al.
+
+Springer Nature 2021 LATEX template
+4
+Turbulent Drag Reduction in MHD Turbulence
+[32] showed that ϵu ∼ (U 3/d)Ra−0.2 and ϵT ∼ (U(∆T)2/d)Ra−0.2, where ∆T
+is the temperature difference between the top and bottom thermal plates sep-
+arated by distance d, and Ra is the Rayleigh number, which is the ratio of
+buoyancy and diffusion in thermal convection. In addition, Pandey et al. [31]
+observed that ⟨u · ∇u⟩ /(Ud/ν) ≈ ReRa−0.14, where Re is the Reynolds num-
+ber. Thus, nonlinearity is suppressed in turbulent thermal convection. In this
+review, we relate the above suppression of nonlinearity and dissipation rates
+to TDR over bluff bodies. It has been argued that TDR in turbulent convec-
+tion arises due to large-scale circulation (LSC) over thermal plates, and that
+the smooth thermal plates affect bulk turbulence.
+Thus, KE flux and ⟨u · ∇u⟩ provide valuable insights into the physics of
+TDR. TDR is also related to the enhanced correlations in the velocity field.
+The present review focusses on these aspects for a variety of flows—polymeric,
+MHD, QSMHD, and stably-stratified turbulence; dynamo; and turbulent ther-
+mal convection. Here, we focus on bulk turbulence, and avoid discussion on
+boundary layers and smooth surfaces. The latter aspects are covered in many
+books and reviews, e.g., [3–5, 10, 14, 15]. We remark that the energy flux is a
+well known quantity in turbulence literature [33–37]. However, the connection
+between the energy flux and TDR has been brought out only recently [11], and
+the number of papers highlighting the above connection is relatively limited.
+The increase in the mean velocity field during TDR is related to relami-
+narization. Narasimha and Sreenivasan [38] studied relaminarization in stably
+stratified turbulence, rotating turbulence, and thermal convection, and related
+it to the reduction in ⟨u · ∇u⟩. Thus, the mechanism of relaminarization is
+intimately related to the TDR.
+An outline of this review is as follows. In Section 2 we briefly review viscous
+and turbulent drag in a pipe flow and over a bluff body. In Section 3 we describe
+a general framework for TDR using energy fluxes. In Section 4 we review the
+energy fluxes in a turbulent flow with dilute polymers and relate it to TDR
+in the bulk. Section 5 contains a framework of TDR in MHD turbulence via
+energy fluxes. In Section 6 we describe signatures of TDR in direct numerical
+simulations (DNS) and shell models of MHD turbulence. Sections 7 and 8
+deal with TDR in dynamos and in QSMHD turbulence respectively. In Section
+9 we describe TDR in stably stratified turbulence and in turbulent thermal
+convection. We conclude in Section 10.
+2 Viscous and turbulent drag in hydrodynamic
+turbulence
+The equations for incompressible hydrodynamics are
+∂u
+∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fext,
+(1)
+∇ · u = 0,
+(2)
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+5
+(a)
+(b)
+(c)
+d
+Fig. 2 Schematic illustrations of (a) pipe flow and (b) its viscous flow profile. (c) The profile
+of the mean velocity in a turbulent pipe flow.
+where u, p are respectively the velocity and pressure fields; ρ is the density
+which is assumed to be unity; ν is the kinematic viscosity; and Fext is the
+external force employed at large scales that helps maintain a steady state. An
+important parameter for the fluid flows is Reynolds number, which is
+Re = UL
+ν ,
+(3)
+where L and U are the large-scale length and velocity respectively. For homo-
+geneous and isotropic turbulence, Re is the ratio of the nonlinear term and
+the viscous term. However, in more complex flows like polymeric turbulence,
+MHD turbulence, and turbulent convection,
+Nonlinear term
+Viscous term
+= fRe,
+(4)
+where the prefactor f may differ from unity and may provide a signature
+for TDR. For example, f ≈ Ra−0.2 for turbulent convection, where Ra is
+the Rayleigh number [31]. We expect complex f for MHD and polymeric
+turbulence.
+A fluid moving in a pipe of radius d experiences drag (see Fig. 2). At low
+Reynolds numbers, this drag is called viscous drag. In this case, under steady
+state, the pressure gradient, −∇(p/ρ), which can be treated as Fext, matches
+with the viscous term, ν∇2u. Hence, we estimate the viscous drag as [13, 39]
+Fdrag ≈ νU
+d2 .
+(5)
+The proportionality constant is of the order of unity. At large Reynolds
+number, the nonlinear term becomes significant, and hence [12–15],
+Fdrag ≈ U 2
+d + νU
+d2 ,
+(6)
+
+r=a
+ZSpringer Nature 2021 LATEX template
+6
+Turbulent Drag Reduction in MHD Turbulence
+apart from the proportionality constants. In the above formula, U 2/d is the
+turbulent drag that is larger than the viscous drag by a factor of Re. Clearly,
+the turbulent drag dominates the viscous drag at large Re. Note that the above
+drag force is in the units of force per unit mass; we will follow this convention
+throughout the paper.
+A related problem is the frictional force experienced by a bluff body in a
+flow. Analogous to a pipe flow, a bluff body experiences viscous drag at small
+Re, but turbulent drag at large Re. In literature, the drag coefficient is defined
+as [13, 14]
+Cd = Fdrag
+ρU 2A,
+(7)
+where A is the area of the bluff body.
+It is customary to describe fluid flows in Fourier space, where Eqs. (1, 2)
+get transformed to [35–37]
+d
+dtu(k) = −i
+�
+p
+{k · u(q)}u(p) − ikp(k) − νk2u(k) + Fext(k),
+(8)
+where k, p, q are the wavenumbers with k = p + q; and u(k), u(p), u(q) are
+the corresponding velocity Fourier modes. An equation for the modal energy
+Eu(k) = |u(k)|2/2 is [35–37, 40]
+d
+dtEu(k) = Tu(k) + Fext(k) − Du(k),
+(9)
+where
+Tu(k) =
+�
+p
+ℑ [{k · u(q)}{u(p) · u∗(k)}] ,
+(10)
+Fext(k) = ℜ[Fext(k) · u∗(k)],
+(11)
+Du(k) = 2νk2Eu(k).
+(12)
+Here, ℜ, ℑ stand respectively for the real and imaginary parts of the argument;
+Tu(k) is the nonlinear energy transfer to the mode u(k); Du(k) is the energy
+dissipation rate at wavenumber k; and Fext(k) is the KE injection rate to u(k)
+by the external force Fext(k).
+We assume that the external force injects KE at large scales, e.g., in a
+wavenumber band (0, kf) with small kf. Therefore, the total KE injection rate,
+ϵinj, is
+� kf
+0
+dkFext(k) ≈ ϵinj.
+(13)
+This injected KE cascades to intermediate and small scales as KE flux, Πu(K),
+which is defined as the cumulative KE transfer rate from the velocity modes
+inside the sphere of radius K to velocity modes outside the sphere. In Fig. 3,
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+7
+ky
+Force
+Inertial
+Dissip-
+ative
+Πu(K)
+u<
+u>
+Πu(K)
+u>
+K F
+Du
+Du
+kx
+Fig. 3 An illustration of KE flux Πu(K). KE is injected into the small red sphere. Πu(K)
+is constant in the inertial range, and it is dissipated at small scales with a dissipation rate
+of Du. From Verma et al. [11]. Reprinted with permission from AIP.
+we illustrate the inner and outer modes as u< and u> respectively. In terms
+of Fourier modes, the above flux is [16, 37, 41, 42]
+Πu(K) = −
+�
+k≤K
+Tu(k) =
+�
+p≤K
+�
+k>K
+ℑ [{k · u(q)}{u(p) · u∗(k)}] ,
+(14)
+where q = k − p.
+The above energy flux is dissipated in the dissipative range, with the total
+viscous dissipation rate as
+ϵu =
+�
+dkDu(k) =
+�
+dk2νk2Eu(k).
+(15)
+At large Reynolds numbers, it has been shown that in the inertial range [33,
+35, 36, 43, 44],
+Πu(k) ≈ ϵinj ≈ ϵu ≈ U 3
+d .
+(16)
+That is, the inertial-range energy flux, the viscous dissipation rate, and the
+energy injection rate are all equal. Note that in the inertial range, Πu(k) = ϵinj
+due to absence of external force and negligible viscous dissipation [33, 37, 40].
+We show later that the magnetic field and polymers, as well as smooth walls,
+suppress the energy flux relative to ϵinj. We argue that this feature leads to
+TDR.
+
+Springer Nature 2021 LATEX template
+8
+Turbulent Drag Reduction in MHD Turbulence
+For a steady state, an integration of Eq. (1) over a bluff body yields the
+following formula for the drag force:
+Fdrag =
+�
+dr
+�
+(u · ∇)u + ∇(p/ρ) − ν∇2u
+�
+.
+(17)
+The viscous force dominates the inertial term near the surface of a bluff body.
+Hence, for bluff bodies, the inertial term of the above equation is ignored.
+Prandtl [15, 45] was first to compute Fdrag for a bluff body as a sum of viscous
+drag and adverse pressure gradient. The drag forces for a cylinder and aerofoil
+are computed in this manner [13–15].
+Computation of Fdrag for a pipe flow is also quite complex involving many
+factors—walls, fluid properties, bulk turbulence, Reynolds number, etc. In the
+present review, we focus on the turbulent drag in bulk where we can ignore
+the effects of walls. The above simplification enables us to compute turbulent
+drag in many diverse flows—polymeric turbulence, MHD turbulence, dynamo,
+liquid metals—using a common framework.
+We focus on a turbulent flow within a periodic box for which
+�
+dr∇(p/ρ) =
+0. By ignoring the viscous drag, we deduce the turbulent drag as (see Eqs. (1,
+17))
+Fdrag = Fext =
+�
+dr [(u · ∇)u] .
+(18)
+Since the external force is active at large scales, under steady state,
+⟨Fdrag⟩LS ≈ ⟨|(u · ∇)u|⟩LS ≈ ⟨Fext⟩ ,
+(19)
+where ⟨.⟩LS represents ensemble averaging over large scales. To estimate
+⟨Fdrag⟩LS, we perform a dot product of Eq. (1) with u and integrate it over a
+wavenumber sphere of radius kf (forcing wavenumber band) that leads to
+�
+LS
+dr[Fext · u] =
+�
+LS
+dr[Fdrag · u] = f1UFdrag,
+(20)
+with f1 ≈ 1. Under steady state, using Eqs. (9,14) we deduce that
+�
+LS
+dr[Fext · u] = ⟨|[(u · ∇)u] · u|⟩LS = −
+� kf
+0
+Tu(k′)dk′ = Πu(k).
+(21)
+Therefore,
+UFdrag ≈ Πu ≈ U 3
+d ≈ ϵinj,
+(22)
+or
+Fdrag ≈ Πu
+U ≈ U 2
+d .
+(23)
+Note that the viscous dissipation can be ignored at large scales.
+It has been observed that polymers and magnetic field suppress turbulent
+drag. We detail these phenomena in the subsequent sections.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+9
+3 General framework for TDR using energy flux
+In this section, we describe a general framework for TDR in a turbulent flow
+with a secondary field B. At present, for convenience, we assume B to be a
+vector, however, it could also be a scalar or a tensor. The present formalism is
+taken from Verma et al. [11].
+The equations for the velocity and secondary fields are [11, 29, 37, 46]:
+∂u
+∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fu(u, B) + Fext,
+(24)
+∂B
+∂t + (u · ∇)B = η∇2B + FB(u, B),
+(25)
+∇ · u = 0,
+(26)
+where u, p are the velocity and pressure fields respectively; ρ is the density
+which is assumed to be unity; ν is the kinematic viscosity; η is the diffusion
+coefficient for B; and Fu and FB are the force fields acting on u and B respec-
+tively. Note that Fu and FB typically represent interactions between u and
+B. The external field Fext is employed at large scales of the velocity field to
+maintain a steady state.
+Using Eq. (24) we derive the following equation for the KE density u2/2
+(with ρ = 1):
+∂
+∂t
+u2
+2 + ∇ ·
+�u2
+2 u
+�
+= −∇ · (pu) + [Fu + Fext] · u − νu · ∇2u.
+(27)
+In Fourier space, the equation for the modal KE, Eu(k) = |u(k)|2/2, is
+d
+dtEu(k) = Tu(k) + Fu(k) + Fext(k) − Du(k),
+(28)
+where
+Tu(k) =
+�
+p
+ℑ [{k · u(q)}{u(p) · u∗(k)}] ,
+(29)
+Fu(k) = ℜ[Fu(k) · u∗(k)],
+(30)
+Fext(k) = ℜ[Fext(k) · u∗(k)],
+(31)
+Du(k) = −2νk2Eu(k),
+(32)
+with q = k − p. We sum Eq. (28) over the u modes of the wavenumber sphere
+of radius K that yields [37, 40]:
+d
+dt
+�
+k≤K
+Eu(k) =
+�
+k≤K
+Tu(k) +
+�
+k≤K
+Fu(k) +
+�
+k≤K
+Fext(k) −
+�
+k≤K
+Du(k).(33)
+
+Springer Nature 2021 LATEX template
+10
+Turbulent Drag Reduction in MHD Turbulence
+A physical interpretation of the terms in the right-hand side of Eq. (33) are
+as follows:
+1. �
+k≤K Tu(k) is the net KE transfer from the u modes outside the sphere to
+the u modes inside the sphere due to the nonlinearity (u·∇)u. Equivalently,
+�
+k≤K Tu(k) = −Πu(K) of Eq. (14).
+2. �
+k≤K Fu(k) is the total energy transfer rate by the interaction force Fu(k)
+to u(k) modes inside the sphere.
+3. �
+k≤K Fext(k) is the net KE injected by the external force Fext (red sphere
+of Fig. 4). For K > kf, �
+k≤K Fext(k) = ϵinj because Fext = 0 beyond
+k = kf.
+The u< modes lose energy to u> and B modes via nonlinear interactions.
+The term − �
+k≤K Fu(k) of Eq. (33) represents the net energy transfer from
+the u< modes (those inside the sphere) to all the B modes (B< and B>) via
+the interaction force Fu(k). We define the corresponding flux ΠB(K) as
+ΠB(K) = −
+�
+k≤K
+Fu(k).
+(34)
+Thus, u< modes lose energy to u> modes, as well as to B modes, via nonlinear
+interactions. In addition, u< modes lose energy via viscous dissipation, which
+is the last term of Eq. (33). Therefore, under steady state, the kinetic energy
+injected by Fext must match (statistically) with the sum of Πu(K), ΠB(K),
+and the viscous dissipation rate [37, 40]1. That is,
+Πu(K) + ΠB(K) +
+�
+k≤K
+Du(k) = ϵinj.
+(35)
+In the inertial range where Du(k) ≈ 0, we obtain
+Πu(K) + ΠB(K) ≈ ϵinj.
+(36)
+In later sections, we show that ΠB(k) > 0 in MHD, QSMHD, polymeric,
+and stably-stratified turbulence. Therefore, using Eq. (36) we deduce that for
+the same injection rate ϵinj, Πu(k) in the mixture (with field B) is lower than
+that in HD turbulence, that is,
+Πu,mix < Πu,HD.
+(37)
+Now we estimate the drag force in the presence of B. As discussed below,
+there are several ways to estimate this drag force.
+1In this paper we do not discuss the energetics of B field because TDR is related to the energy
+fluxes associated with the velocity field.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+11
+Πu(K) + ΠB(K) = ϵinj
+Πu(K)
+ΠB(K)
+ΠB(K)
+B<
+u<
+u>
+B>
+u>
+B>
+Πu(K)
+ΠB(K)
+K F
+K
+Du
+Du
+DB
+DB
+kx
+kx
+ky
+ky
+Fig. 4 The external force injects KE into the small red sphere with the rate of ϵint. Πu(K)
+is the KE flux for the velocity wavenumber sphere of radius K (yellow sphere), and ΠB(K) is
+the net energy transfer from u modes inside the sphere to all the B modes. The energy flux
+Πu(K) is dissipated with dissipation rates Du. For small wavenumbers and inertial range,
+Πu(K) + ΠB(K) ≈ ϵint. From Verma et al. [11]. Reprinted with permission from AIP.
+1. As discussed in Section 2, we average Eq. (24) over small wavenumbers.
+Using
+�
+LS
+dr[Fext · u] =
+�
+LS
+dr[Fdrag · u] = f2UFdrag,mix.
+(38)
+Under steady state, using Eqs. (9,14) we deduce that
+�
+LS
+dr[Fext · u] = −
+� kf
+0
+[Tu(k′) + Fu(k′)]dk′ = Πu(k) + ΠB(k).
+(39)
+Hence,
+Fdrag,mix ≈ Πu + ΠB
+f2U
+≈ ϵinj
+f2U .
+(40)
+It is observed that in a mixture, U is typically larger than that in HD
+turbulence [5, 11]. Computation of f2 may be quite complex, and it is
+difficult to compare f1 and f2. Still, considering Umix > UHD, we expect
+Fdrag,mix to be weaker than the corresponding drag in HD turbulence. This
+is the origin of TDR in the bulk when B field (polymers or magnetic field)
+is present.
+2. Considering the uncertainties in f2, it is proposed that turbulent drag is
+proportional to (u · ∇)u [11]. For MHD turbulence, the force Fu, which is
+the Lorentz force, may be treated separately, and (u·∇)u may be considered
+
+Springer Nature 2021 LATEX template
+12
+Turbulent Drag Reduction in MHD Turbulence
+as the drag force. This assumption simplifies the calculation with
+Fdrag,mix ≈ Πu
+U .
+(41)
+In a typical scenario, Πu,mix < Πu,HD, and Umix > UHD [5, 11]. Therefore,
+we expect that
+Fdrag,mix < Fdrag,HD.
+(42)
+Thus, turbulent drag is reduced in the presence of a secondary fields, such
+as magnetic field and polymers. Verma et al. [11] adopted this scheme for
+the computation of turbulent drag. We will use this scheme throughout the
+paper.
+In Fig. 5, we present a schematic diagram illustrating TDR in a pipe flow
+and in bulk turbulence. An introduction of polymers in a pipe flow weakens the
+fluctuations and enhances the mean flow (see Fig. 5(a,b)). Similarly, in bulk
+turbulence, polymers and magnetic field can induce strong large-scale U and
+weaken the fluctuations in comparison to HD turbulence (see Fig. 5(c,d)).
+(a)
+(b)
+(c)
+(d)
+Fig. 5 (a) Mean velocity profile (D profile) and fluctuations (green arrows) in a pipe flow
+without polymers. (b) With dilute polymers, the mean flow is enhanced, but the fluctuations
+are suppressed. (c) Velocity fluctuations in HD turbulence. (d) With polymers and magnetic
+field, the fluctuations (green arrows) are suppressed, but the large-scale U (black arrows) is
+enhanced.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+13
+We propose the following drag coefficients to quantify TDR in the bulk:
+¯Cd1 = ⟨Πu⟩
+U 3/L,
+(43)
+¯Cd2 = ⟨|(u · ∇)u|⟩
+U 2/L
+,
+(44)
+where L is the integral length scale, and U is the large-scale velocity. We
+obtain ¯Cd1 ≈ 1 and ¯Cd2 ≈ 1 for HD turbulence. However, ¯Cd1 and ¯Cd2 for
+a mixture are smaller than those for HD turbulence. In subsequent sections,
+we will compute the above drag coefficients for a variety of flows, but with an
+emphasis on MHD and QSMHD turbulence, and dynamo.
+In the next section, we provide a brief introduction to TDR in a turbulent
+flow with dilute polymers.
+4 TDR in flows with dilute polymers via
+energy flux
+An introduction of small amount of polymers in a turbulent flow suppresses
+turbulent drag [1–11]. As discussed in Section 1, TDR in polymeric turbulence
+depends on the boundaries, bulk turbulence, properties of fluids and polymers,
+anisotropy, etc. However, in this paper we focus on the TDR due to suppression
+of KE flux in the presence of polymers. For detailed discussions on TDR due
+to polymers, refer to the references [1–11].
+One of the popular models for polymers is finitely extensible nonlin-
+ear elastic-Peterlin model (FENE-P) [9, 47]. In this model, the governing
+equations for the velocity field u and configuration tensor C are [9, 46, 48]
+∂ui
+∂t + uj∂jui = −∂ip/ρ + ν∂jjui + µ
+τp
+∂j(fCij) + Fext,i,
+(45)
+∂Cij
+∂t + ul∂lCij = Cil∂luj + Cjl∂lui + 1
+τp
+[fCij − δij],
+(46)
+∂iui = 0,
+(47)
+where ρ is the mean density of the solvent, ν is the kinematic viscosity, µ is an
+additional viscosity parameter, τp is the polymer relaxation time, and f is the
+renormalized Peterlin’s function. In the above equations, the following forces
+are associated with u and C (apart from constants) [3, 10, 37, 40, 47]:
+Fu,i = ∂j(fCij),
+(48)
+Fu,i(k) =
+�
+p
+[ikjf(q)Cij(p)] ,
+(49)
+Fu(k) = ℜ[Fu,i(k)u∗
+i (k)] = −c1
+�
+p
+ℑ [kjf(q)Cij(p)u∗
+i (k)] ,
+(50)
+
+Springer Nature 2021 LATEX template
+14
+Turbulent Drag Reduction in MHD Turbulence
+∫
+k
+0
+d k′ 
+u
+∫
+k
+0
+d k′ 
+u<
+ζ
+′ 
+′ 
+Fig. 6 For a polymeric flow with De = 16.2, the energy fluxes Πu(k) and ΠC(k) normalized
+with the KE injection rate P, and dissipation rate Du(k) [19]. The injected KE, P, is
+transferred to u> and C as Πu(k) and ΠC(k) respectively. The rest of the injected energy is
+dissipated. Adapted from a figure from Valente et al. [19]. Reprinted with the permission of
+AIP.
+where q = k − p, and c1 is a constant. Note that the field C replaces B of Eqs.
+(24-26). Using the above equations, we derive the energy flux ΠC(K), which is
+the net energy transfer rate from u< to C, as [37, 40]
+ΠC(K) =
+�
+k≤K
+�
+p
+−c1ℑ [kjf(q)Cij(p)u∗
+i (k)]
+(51)
+with q = k − p.
+Valente et al. [18, 19] analysed the energy fluxes Πu(k) and ΠC(k) in a
+turbulent flow with dilute polymers and observed that ΠC(k) > 0. One of
+their figures illustrating Πu(k) and ΠC(k) is reproduced in Fig. 6 [19]. As
+shown in the figure, for De = 16.2, ΠC(k)/P (P = total injected power) peaks
+at approximately 0.9 when kη ≈ 0.1, where η is Kolmogorov’s wavenumber.
+However, Πu(k)/P remains less than 0.1 for all kη. Valente et al. [18, 19] also
+reported that Πu(k) and ΠC(k) depend on the Deborah number, De, which
+is the ratio of the relaxation time scale of the polymer and the characteristic
+time scale for the energy cascade. Notably, ΠC(k) is maximum when De ∼ 1.
+Thus, Valente et al. [18, 19] showed that Πu(k) is reduced significantly from
+ϵinj due to the energy transfer from the velocity field to polymers. That is,
+Πu(k) < ϵinj.
+
+a
+0.9
+F(k)/P
+I[pl(k)/P
+A
+0.8
+0.7
+D(k)/P
+/ I
+0.6
+/ /
+0.5
+0.4
+0.3
+0.2
+0.1
+H(k)/P
+0
+-0.05
+.
+0.05
+0.1
+kn
+0.5
+1
+2Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+15
+Fig. 7 KE spectra for pure HD turbulence (dashed line with circle) and polymeric turbu-
+lence (solid line with squares). At small wavenumbers, Eu(k) with polymers is larger than
+that without polymers. From Benzi et al. [7]. Reprinted with permission from APS.
+Benzi et al. [7] and Ray and Vincenzi [49] showed that during TDR, the
+large-scale KE is enhanced compared to HD turbulence. Figure 7 illustrates
+the energy spectra of Benzi et al. for pure HD and polymeric turbulence. In
+the figure we observe that at small wavenumbers, Eu(k) is larger for polymeric
+turbulence than that for HD turbulence. Hence, we deduce that large-scale U
+is enhanced in the presence of polymers. Thais et al. [50] and Nguyen et al. [51]
+arrived at similar conclusions using direct numerical simulation of polymeric
+turbulence. Based on these observations, we deduce that
+Πu,Polymeric < Πu,HD
+and
+UPolymeric > UHD.
+(52)
+Therefore, using Fdrag = Πu/U, we deduce that
+Fdrag,Polymeric < Fdrag,HD.
+(53)
+Thus, reduction in KE flux leads to a decrease in nonlinearity, and hence, TDR
+in polymeric turbulence.
+L’vov et al. [52] and others have observed TDR in flows with bubbles.
+In a bubbly flow, the KE is transferred to the elastic energy of the bubbles
+that leads to TDR. We also remark that in the laminar regime, the polymers
+induce additional drag via the term µ∂j(fCij)/τp of Eq. (45). Hence, polymers
+enhance the drag in the viscous limit [5]. Also note that in the present review,
+we focus on TDR in bulk turbulence and have avoided discussions on boundary
+layers, anisotropy, effects of polymer concentration, etc.
+Earlier, Fouxon and Lebedev [46] had related the equations of a turbulent
+flow with dilute polymers to those of MHD turbulence. In the next section, we
+
+-6
+-8
+L
+-10
+2
+-12
+Q
+-14
+-16
+-18
+0
+2
+4
+6
+8
+10
+nSpringer Nature 2021 LATEX template
+16
+Turbulent Drag Reduction in MHD Turbulence
+will show that the energy transfers in MHD turbulence are similar to those in
+polymeric turbulence.
+5 TDR in MHD turbulence via energy flux
+Magnetofluid is quasi-neutral and highly conducting charged fluid, and its
+dynamics is described by magnetohydrodynamics (MHD). Our universe is filled
+with magnetofluids, with prime examples being solar wind, solar corona, stellar
+convection zone, interstellar medium, and intergalactic medium [53–55] .
+The equations for incompressible MHD are [53, 54]
+∂u
+∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fu(B, B) + Fext,
+(54)
+∂B
+∂t + (u · ∇)B = η∇2B + FB(B, u),
+(55)
+∇ · u = 0,
+(56)
+∇ · B = 0,
+(57)
+where u, B are the velocity and magnetic fields respectively; p is the total
+(thermal + magnetic) pressure; ρ is the density which is assumed to be unity;
+ν is the kinematic viscosity; η is the magnetic diffusivity; Fext is the external
+force employed at large scales; and
+Fu = (B · ∇)B,
+(58)
+FB = (B · ∇)u
+(59)
+represent respectively the Lorentz force and the stretching of the magnetic
+field by the velocity field. Note that Fu and FB induce energy exchange among
+u and B modes. In the above equations, the magnetic field B is in velocity
+units, which is achieved by Bcgs → Bcgs/√4πρ.
+The evolution equation for the modal kinetic energy Eu(k) = |u(k)|2/2
+is [16, 36, 37, 40–42, 56]
+d
+dtEu(k) = Tu(k) + Fu(k) + Fext(k) − Du(k),
+(60)
+where
+Tu(k) =
+�
+p
+ℑ [{k · u(q)}{u(p) · u∗(k)}] ,
+(61)
+Fu(k) = ℜ[Fu(k) · u∗(k)] =
+�
+p
+−ℑ [{k · B(q)}{B(p) · u∗(k)}] ,
+(62)
+Fext(k) = ℜ[Fext(k) · u∗(k)],
+(63)
+Du(k) = 2νk2Eu(k),
+(64)
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+17
+with q = k − p. Summing Eq. (60) over the modes of the wavenumber sphere
+of radius K yields [30, 48, 56]:
+− d
+dt
+�
+k≤K
+Eu(k) = −
+�
+k≤K
+Tu(k) −
+�
+k≤K
+Fu(k) −
+�
+k≤K
+Fext(k) +
+�
+k≤K
+Du(k)
+= Πu(K) + ΠB(K) − ϵinj + total viscous dissipation.
+(65)
+Note that
+ΠB(K) = −
+�
+k≤K
+Fu(k) =
+�
+k≤K
+�
+p
+ℑ [{k · B(q)}{B(p) · u∗(k)}] .
+(66)
+In Fig. 4, we illustrate ΠB(K) using the red arrows.
+Under a steady state (dEu(k)/dt = 0),
+Πu(K) + ΠB(K) +
+�
+k≤K
+Du(k) = ϵinj.
+(67)
+In the inertial range where Du(k) ≈ 0, we obtain
+Πu(K) + ΠB(K) ≈ ϵinj.
+(68)
+Following similar lines of arguments as in Section 3, we estimate the turbulent
+drag in MHD turbulence as
+⟨Fdrag,MHD⟩ ≈ ⟨|(u · ∇)u|⟩LS ≈ Πu
+U ≈ ϵinj − ΠB
+U
+.
+(69)
+Researchers have studied the energy fluxes Πu and ΠB in detail for various
+combinations of parameters—forcing functions, boundary condition, ν and η
+(or their ratio Pm = ν/η, which is called the magnetic Prandtl number). For
+example, Dar et al. [16], Debliquy et al. [57], Mininni et al. [17], and Kumar
+et al. [58, 59] computed the fluxes Πu and ΠB using numerical simulations
+and observed that ΠB > 0 on most occasions. Using numerical simulations,
+Mininni et al. [17] showed that Fu(k) < 0, and hence ΠB(k) > 0 (see Fig. 8).
+Hence, using Eq. (69) we deduce that
+Πu,MHD < Πu,HD.
+(70)
+That is, the KE flux in MHD turbulence is lower than the corresponding flux
+in HD turbulence (without magnetic field). In addition, the speed U may
+increase under the inclusion of magnetic field. Therefore, using Fdrag = Πu/U,
+we deduce that
+Fdrag,MHD < Fdrag,HD.
+(71)
+In this next section, we will explore whether the above inequality holds in
+numerical simulations of MHD turbulence.
+
+Springer Nature 2021 LATEX template
+18
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 8
+Numerically computed Fu(k) = ℜ[[J × B](k)·u∗(k)] by Mininni et al. [17]. Clearly,
+Fu(k) > 0, and hence ΠB(K) > 0. From Mininni et al. [17]. Reproduced with permission
+from ApJ.
+6 Numerical verification of TDR in MHD
+turbulence
+Many researchers have simulated MHD turbulence, but TDR in MHD turbu-
+lence has not been explored in detail. In this section, we will present numerical
+results on TDR from direct numerical simulations (DNS) and shell models.
+MHD turbulence exhibits six energy fluxes that are shown in Fig. 9. These
+fluxes represent energy transfers from u< and u> to b< and b> [16, 37, 42].
+However, as we discussed in Section 3, the relevant fluxes for TDR are Πu and
+ΠB. Also, TDR takes place at large scales, hence, we consider energy fluxes
+from small wavenumber spheres. In terms of the fluxes of Fig. 9,
+Πu(K) = Πu<
+u>(K),
+(72)
+ΠB(K) = Πu<
+b< (K) + Πu<
+b> (K).
+(73)
+As discussed in Section 5, ΠB > 0 [16, 17, 57–60]. Hence, Πu < ϵinj that leads
+to TDR in MHD turbulence. In this section, we will report the energy fluxes
+and ⟨|(u · ∇)u|⟩ for HD and MHD turbulence from DNS and shell models, and
+compare them to quantify TDR in MHD turbulence.
+It is important to note that the velocity field receives parts of ΠB via the
+energy fluxes Πb<
+u> and Πb>
+u>. However, these transfers are effective at interme-
+diate and large wavenumbers. In this review we focus on small wavenumbers,
+hence we can ignore these energy transfers. In the following subsection, we
+discuss TDR in DNS of MHD turbulence.
+
+0.30
+0.25
+t=344
+t=352
+0.20
+-(jxB)k.Vk
+t=360
+0.15
+t=368
+0.10
+0.05
+0.00
+-0.05
+2
+4
+6
+8
+10
+12
+14Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+19
+Fig. 9 Six energy fluxes of MHD turbulence: Πu<
+u>, Πu<
+b< , Πu<
+b> , Πb<
+b>, Πb<
+u>, Πu>
+b> . From
+Verma [37]. Reproduced with permission from Verma.
+6.1 TDR in direct numerical simulation of MHD
+turbulence
+We solve the nondimensional MHD equations (54-57) using pseudo-spectral
+code TARANG [61–63] in a cubic periodic box of size (2π)3. We nondimension-
+alize velocity, length, and time using the initial rms speed (U0), box size (2π),
+and the initial eddy turnover time (2π/U0) respectively. We employ the fourth-
+order Runge-Kutta (RK4) scheme for time marching; Courant-Friedrich-Lewis
+(CFL) condition for computing the time step ∆t; and 2/3 rule for dealising.
+We perform our simulations on a 2563 grid for Pm = 1/3, 1, 10/3 (the details
+in the following discussion). The mean magnetic field B0 = 0. Note that the
+2563 grid resolution is sufficient for computing the large-scale Πu, ΠB, and
+⟨u · ∇u⟩. In addition, the low grid resolution helps us carry out simulations
+for many eddy turnover times.
+For the initial condition, we employ random velocity and magnetic fields
+at all wavenumbers. For creating such fields, it is convenient to employ Craya-
+Herring basis [64, 65], whose basis vectors for wavenumber k are
+ˆe3(k) = ˆk;
+ˆe1(k) = (ˆk × ˆn)/|ˆk × ˆn|;
+ˆe2(k) = ˆk × ˆe1(k)
+(74)
+with ˆn along any arbitrary direction, and ˆk as the unit vector along k. We
+choose 3D incompressible flow, hence,
+u(k) = u1(k)ˆe1(k) + u2(k)ˆe2(k).
+(75)
+
++y
+Fext(k)
+<n
+Eu
+(0x)≤nII
+ur
+II(k 0)
+II(ko)
+b<
+Ib%(ko)
+x
+b>
+EbSpringer Nature 2021 LATEX template
+20
+Turbulent Drag Reduction in MHD Turbulence
+For random initial velocity with the total kinetic energy as Eu, we employ
+u1(k) =
+�
+(Eu/2N 3) i (exp(iφ1(k)) − exp(iφ2(k))) ,
+(76)
+u2(k) =
+�
+(Eu/2N 3) (exp(iφ1(k)) + exp(iφ2(k))) ,
+(77)
+where N 3 is the total number of modes, and the phases φ1(k) and φ2(k) are
+chosen randomly from uniform distribution in the band [0, 2π]. The above
+formulas ensure that the kinetic helicity remains zero. We employ Eu = 0.5
+for our simulation. A similar scheme is adopted for the random magnetic field
+with the initial magnetic energy as 0.25. We carry out the above run for ν =
+η = 0.01, or Pm = 1.
+We employ random force to the velocity modes in a wavenumber shell (2, 3),
+denoted by kf = 2, so as to achieve a steady state [66]. The kinetic-energy
+injection rate ϵinj = 0.4. We carry out the simulation till 29 eddy turnover
+times. Note, however, that the flow reaches a steady state in approximately 15
+eddy turnover times.
+At the end of the above simulation, we perform four independent simula-
+tions given below. We take the final state of the above run as the initial state
+(t = 0) for the following simulations.
+1. MHD1: ν = 0.01, η = 0.03, and hence Pm = 1/3.
+2. MHD2: ν = 0.01, η = 0.01, and hence Pm = 1. This is continuation of the
+run described above.
+3. MHD3: ν = 0.01, η = 0.003, and hence Pm = 10/3.
+4. HD: ν = 0.01 with magnetic field turned off.
+We carry out the HD and MHD2 simulations till 40 eddy turnover times,
+whereas MHD1 and MHD3 runs till 5 eddy turnover times. Subsequently, we
+compare the energy fluxes and ⟨|(u · ∇)u|⟩ of the four runs after they have
+reached their respective steady states that occur in several eddy turnover times.
+The Reynolds number (Re = UL/ν) for the steady state of the HD run is 457.
+For the steady state of the MHD runs with Pm = 1/3, 1, and 10/3, Re = 413,
+347, and 338 respectively, while Rm = 137, 347 and 1127 respectively.
+In Fig. 10 (left column), we exhibit the time series of KE of the HD run,
+and as well as KE, magnetic energies (ME), and the total energies of the
+three MHD runs. The corresponding dissipation rates are exhibited in the
+right column of Fig. 10. As shown in the figures, all the runs reach steady
+states after several eddy turnover times. The KE dissipation rate for the
+HD run increases rapidly to 0.4, which is the KE injection rate (ϵinj). The
+KE for the MHD runs with Pm = 1/3, 1, and 10/3 saturate respectively to
+approximate values of 0.65, 0.47 and 0.41, but the respective magnetic energies
+saturate at approximately 0.07, 0.2 and 0.26. Note that energies for the MHD
+runs exhibit significant fluctuations, however, the dissipation rates of the total
+energy remain at 0.4.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+21
+0
+1
+2
+3
+4
+5
+0.0
+0.3
+0.6
+0.9
+E
+(a): Pm = 1/3
+Eu,HD
+Eu,MHD
+Eb,MHD
+Eu,MHD + Eb,MHD
+0
+1
+2
+3
+4
+5
+0.0
+0.3
+0.6
+0.9
+ϵ
+(b): Pm = 1/3
+ϵu,HD
+ϵu,MHD
+ϵb,MHD
+ϵu,MHD + ϵb,MHD
+0
+10
+20
+30
+40
+0.0
+0.3
+0.6
+0.9
+E
+(c): Pm = 1
+0
+10
+20
+30
+40
+0.0
+0.3
+0.6
+0.9
+ϵ
+(d): Pm = 1
+0
+1
+2
+3
+4
+5
+t
+0.0
+0.3
+0.6
+0.9
+E
+(e): Pm = 10/3
+0
+1
+2
+3
+4
+5
+t
+0.0
+0.3
+0.6
+0.9
+ϵ
+(f): Pm = 10/3
+Fig. 10 Left column: (a,c,e) Time series of KE of the HD run (dashed red curve); and
+KE (solid red curve), magnetic energies (solid green curve), and total energies (solid blue
+curve) of the MHD runs for Pm = 1/3, 1, 10/3. Right column: (b,d,f) Corresponding energy
+dissipation rates with the same notation.
+Now, we report the energy spectra for the velocity and magnetic fields for
+a wavenumber k. Numerically, we compute them using
+Eu(k) = 1
+2
+�
+k−1<|k′|≤k
+|u(k′)|2,
+(78)
+Eb(k) = 1
+2
+�
+k−1<|k′|≤k
+|b(k′)|2.
+(79)
+In Fig. 11, we exhibit Eu(k) and Eb(k) for the MHD runs, along with Eu(k)
+for the HD run. These quantities are averaged over several time frames in the
+steady state. We observe that Eu(k) for the HD run is larger than those for
+the MHD runs, except at several small wavenumbers for Pm = 1/3 where
+Eb(k) > Eu(k).
+
+Springer Nature 2021 LATEX template
+22
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 11 (a,b,c) For MHD runs with Pm = 1/3, 1, 10/3, the KE spectra (solid red curve)
+and the magnetic energy spectra (solid green curve). We also exhibit the plots of the KE
+spectra of the HD run (dashed red curve).
+Further, for the HD and MHD runs, we report the large-scale velocity U,
+integral length scales L, and Reynolds numbers based on Taylor microscale,
+Reλ = Uλ/ν, where Taylor microscale λ = (15νU 2/ϵ)1/2 [35, 37]. Following
+Sreenivasan [43], we compute U as the rms value for each component of the
+velocity field, or
+U =
+�2
+3
+�
+dkE(k)
+�1/2
+,
+(80)
+whereas the integral length L is computed using
+L =
+�
+dkk−1E(k)
+�
+dkE(k)
+.
+(81)
+We quantify U in three ways: Urms; and U(K = 1) and U(K = 2), which are
+computed using the KE in the wavenumber spheres of radii 1 and 2 respectively.
+We list Urms in Table 1. In Fig. 12, we exhibit the time series of Urms, U(K = 1),
+U(K = 2), L, and Reλ for the four runs. We observe that Urms, U(K = 1), and
+U(K = 2) for the MHD runs are smaller than the corresponding quantities
+for the HD run, except for MHD1 (Pm = 1/3) where U(K = 1) is comparable
+to that for the HD run. Consequently, Reλ for MHD1 is close to that for the
+HD run, but Reλ for the other two MHD runs are smaller than those for the
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+23
+t
+0.5
+0.6
+0.7
+0.8
+Urms
+(a)
+Pm = 1/3
+HD
+MHD
+(b)
+Pm = 1
+(c)
+Pm = 10/3
+0.04
+0.08
+0.12
+0.16
+U(K = 1)
+(d)
+(e)
+(f)
+0.08
+0.12
+0.16
+0.20
+0.24
+U(K = 2)
+(g)
+(h)
+(i)
+0.61
+0.64
+0.67
+0.70
+L
+(j)
+(k)
+(l)
+0
+1
+2
+3
+4
+t
+20
+25
+30
+35
+Re∏
+(m)
+10
+20
+30
+t
+(n)
+1
+2
+3
+4
+5
+t
+(o)
+Fig. 12 Time evolution of rms velocity (Urms), U(K = 1), U(K = 2), integral length scale
+(L), and Reλ for the HD run (dashed red curve) and the MHD runs (solid red curve) for
+Pm = 1/3, 1, 10/3. U(K = 1) and U(K = 2) are computed using the KE contained in the
+waveumber spheres of radii 1 and 2 respectively.
+HD run. The integral lengths L for the three MHD runs are larger than the
+corresponding L for the HD run. Hence, the velocity fields are more ordered
+in the MHD runs compared to the HD run.
+Next, we compute Πu(K) for the HD and MHD runs, as well as ΠB(K) for
+the MHD runs. These fluxes exhibit significant fluctuations, hence we average
+over several time frames in the steady state. The fluxes, shown in Fig 13,
+clearly show that ΠB > 0, indicating energy transfers from the velocity field
+
+Springer Nature 2021 LATEX template
+24
+Turbulent Drag Reduction in MHD Turbulence
+Table 1 For MHD runs with Pm = 1/3, 1, 10/3, numerical values of average KE flux
+(⟨Πu⟩) in the inertial range, rms velocity (Urms), and
+� ¯Cd1
+�
+. We also list ⟨|(u · ∇)u|⟩ and
+� ¯Cd2
+�
+for the wavenumber spheres of radii K = 1 and K = 2. The table contains the
+corresponding quantities for the HD run. For all the runs, ϵinj = 0.4
+K = 1
+K = 2
+Pm
+⟨Πu⟩
+Urms
+� ¯Cd1
+�
+⟨|(u · ∇)u|⟩
+� ¯Cd2
+�
+⟨|(u · ∇)u|⟩
+� ¯Cd2
+�
+HD
+-
+0.35
+0.72
+0.58
+0.1
+0.13
+0.3
+0.37
+MHD1
+1/3
+0.28
+0.66
+0.65
+0.07
+0.11
+0.3
+0.46
+MHD2
+1
+0.25
+0.55
+0.98
+0.06
+0.13
+0.22
+0.49
+MHD3
+10/3
+0.17
+0.53
+0.8
+0.04
+0.09
+0.17
+0.41
+to magnetic field at all scales, and that
+Πu,MHD < Πu,HD.
+(82)
+Fig. 13 (a,b,c) Plots Πu(K) (solid red curve) and ΠB(K) (solid green curve) for the MHD
+runs with Pm = 1/3, 1, 10/3. Plots also illustrate Πu(K) (dashed red curve) for the HD run.
+We compute the drag coefficient ¯Cd1, which is defined in Eq. (43) as
+⟨Πu⟩ /(U 3
+rms/L), and exhibit its time series in Fig. 14. In Table 1, we list the
+average values of ¯Cd1 for the steady state. We observe that ¯Cd1 for the steady
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+25
+Fig. 14 (a,b,c) Time evolution of the drag reduction coefficient ¯Cd1 for the HD run (dashed
+red curve) and the MHD runs (solid red curve) with Pm = 1/3, 1, 10/3.
+state of the HD run is consistent with the results of Sreenivasan [43], thus val-
+idating our code and diagnostics. However, ¯Cd1 for the steady states of the
+three MHD runs are larger than that for the HD run. This is because the
+decrease in U 3
+rms for the MHD runs overcompensates the decrease in Πu(K).
+Now, we examine the nonlinear term Nu for the HD and MHD runs. Since
+the drag force is effective at large scales, we estimate Nu by its rms value for
+a small wavenumber sphere of radius K, that is,
+⟨|(u · ∇) u|⟩LS = Nu(K) =
+� �
+k≤K
+|Nu(k)|2.
+(83)
+In particular, we choose K = 1 and K = 2. In Fig. 15(a,b), we illustrate the
+time series of Nu(K) for the HD run (dashed red curve) and the MHD runs
+(solid red curve) for K = 1 and K = 2. In Table 1, we list the average values
+of Nu(K) for all the runs. We observe that Nu(K) for the three MHD runs
+are smaller than Nu(K) for the HD counterpart. Hence, there is a reduction
+in ⟨|(u · ∇) u|⟩LS for MHD turbulence compared to HD turbulence, signalling
+TDR in MHD turbulence.
+After this, we compute the drag reduction coefficient ¯Cd2, which is defined
+in Eq. (44) as ⟨|(u · ∇)u|⟩LS /(U 2
+rms/L). The time series of ¯Cd2 for K = 1 and
+K = 2 are plotted in Figure 16, and their average values for their steady states
+
+1Springer Nature 2021 LATEX template
+26
+Turbulent Drag Reduction in MHD Turbulence
+0
+1
+2
+3
+4
+5
+0.025
+0.075
+0.125
+Nu
+(a): Pm = 1/3
+K = 1
+HD
+MHD
+0
+1
+2
+3
+4
+5
+0.1
+0.2
+0.3
+0.4
+(b): Pm = 1/3
+K = 2
+0
+10
+20
+30
+40
+0.025
+0.075
+0.125
+Nu
+(c): Pm = 1
+0
+10
+20
+30
+40
+0.1
+0.2
+0.3
+0.4
+(d): Pm = 1
+0
+1
+2
+3
+4
+5
+t
+0.025
+0.075
+0.125
+Nu
+(e): Pm = 10/3
+0
+1
+2
+3
+4
+5
+t
+0.1
+0.2
+0.3
+0.4
+(f): Pm = 10/3
+Fig. 15 (a,b,c) Plots of the time series of nonlinear term (Nu) for spheres of radii (a) K = 1
+and (b) K = 2 for the HD run (dashed red curve) and the MHD runs (solid red curve) with
+Pm = 1/3, 1, 10/3.
+are listed in Table 1. We observe that ¯Cd2(K = 1) for the MHD runs with
+Pm = 1/3 and 10/3 are smaller than that for the HD run for t ⪆ 2. For the
+other cases, ¯Cd2 for MHD runs are larger than those for the HD run.
+Thus, for 1/3 ≤ Pm ≤ 10/3, Πu and ⟨|(u · ∇)u|⟩ for the MHD runs are
+smaller than the corresponding values for the HD run. For K = 1, the drag
+coefficient ¯Cd2 exhibits similar behaviour for Pm = 1/3 and 10/3, but not for
+Pm = 1. This is in contrast to ¯Cd1, which is typically larger for MHD runs
+than that for the corresponding HD runs.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+27
+0
+1
+2
+3
+4
+5
+0.06
+0.10
+0.14
+0.18
+¯Cd2
+(a): Pm = 1/3
+K = 1
+HD
+MHD
+0
+1
+2
+3
+4
+5
+0.3
+0.4
+0.5
+0.6
+(b): Pm = 1/3
+K = 2
+0
+10
+20
+30
+40
+0.06
+0.10
+0.14
+0.18
+¯Cd2
+(c): Pm = 1
+0
+10
+20
+30
+40
+0.3
+0.4
+0.5
+0.6
+(d): Pm = 1
+0
+1
+2
+3
+4
+5
+t
+0.06
+0.10
+0.14
+0.18
+¯Cd2
+(e): Pm = 10/3
+0
+1
+2
+3
+4
+5
+t
+0.3
+0.4
+0.5
+0.6
+(f): Pm = 10/3
+Fig. 16 (a,b,c) Time evolution of drag reduction coefficient ¯Cd2 for sphere of radii (a)
+K = 1, and (b) K = 2 for HD turbulence (dashed red curve) and MHD turbulence (solid
+red curve) with Pm = 1/3, 1, 10/3.
+We will show in Section 8 that QSMHD turbulence, which corresponds
+to Pm = 0, exhibits larger U than the respective HD turbulence. Hence,
+we expect that MHD runs with very small Pm will yield larger U than the
+corresponding HD runs. This conjecture needs to be verified in future. In addi-
+tion, dynamo simulations exhibit enhancement in U on the emergence of a
+large-scale magnetic field (see Section 7). We will discuss these issues in later
+sections.
+
+Springer Nature 2021 LATEX template
+28
+Turbulent Drag Reduction in MHD Turbulence
+In summary, DNS of MHD turbulence exhibits reduction in Πu(k) and
+⟨|(u · ∇) u|⟩LS in comparison to HD turbulence. However, we do not observe
+enhancement in U in the MHD runs, at least for 1/3 ≤ Pm ≤ 10/3. We
+conjecture that MHD runs with very small Pm may exhibit enhancement in U.
+After the above discussion on DNS results on TDR in MHD turbulence, in
+the next subsection, we will discuss TDR in the shell model of MHD turbulence.
+6.2 Numerical verification of TDR in shell models of
+MHD turbulence
+In comparison to DNS, shell models have much fewer variables, hence they are
+computationally faster than DNS. Therefore, shell models are often used to
+study turbulence, especially for extreme parameters. Beginning with Gledzer-
+Ohkitani-Yamada (GOY) shell model for HD turbulence [67–69], researchers
+have developed several shell models for MHD turbulence [70–73]. In this sub-
+section, we report TDR in a shell model of MHD turbulence [11]. Verma et
+al. employed a revised version of GOY shell model and computed the drag
+forces and nonlinear terms for the HD and MHD runs. They showed that
+the turbulent drag in MHD turbulence is indeed reduced compared to HD
+turbulence.
+In a shell model of turbulence, all the Fourier modes in a wavenumber shell
+are represented by a single variable. A MHD shell model with N shells has
+N velocity and N magnetic shell variables that are coupled nonlinearly. The
+corresponding HD shell model has N velocity shell variables. In this subsection,
+we present the results of the shell model of Verma et al. [11].
+Verma et al. [11] employed a shell model with 36 shells, with random forcing
+employed at shells n = 1 and 2 such that the KE injection rate is maintained at
+a constant value [74]. They performed three sets of HD and MHD simulations
+with KE injection rates ϵinj = 0.1, 1.0 and 10.0, and ν = η = 10−6. For time
+integration, they used Runge-Kutta fourth order (RK4) scheme with a fixed
+∆t. For ϵinj = 0.1 and 1.0, they chose ∆t = 5 × 10−5, but for ϵinj = 10.0, they
+took ∆t = 1 × 10−5. The numerical results are summarized in Table 2. They
+carried out the HD and MHD simulations up to 1000 eddy turnover time. For
+further details on the model and the numerical method, refer to Verma et al.
+[11].
+Both HD and MHD simulations reached their respective steady states after
+approximately 200 eddy turnover time. Interestingly, Verma et al. [11] observed
+that for the same ϵinj, the KE and U for MHD turbulence are larger than those
+for HD turbulence (see Table 2). These observations clearly demonstrate an
+enhancement of U in MHD turbulence compared to HD turbulence, as is the
+case for turbulent flows with dilute polymers.
+The increase in U for the MHD runs compared to the HD runs has its origin
+in the energy spectra. Verma et al. [11] computed the average KE spectra
+Eu(k) for the HD and MHD runs. These spectra, shown in Fig. 17, exhibit
+Kolmogorov’s k−5/3 spectrum. For a given ϵinj, Eu(k) plots for the HD and
+MHD runs almost overlap with each other, except for small wavenumbers
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+29
+Table 2 For the shell model runs of HD and MHD turbulence with ϵinj = 0.1, 1.0, 10.0,
+numerical values of inertial-range KE flux Πu, rms velocity U,
+⟨|(u · ∇)u|⟩ = (�
+n|Nn[u, u]|2)1/2, ¯Cd1, and ¯Cd2. [11].
+ϵinj
+Πu
+U
+⟨|(u · ∇)u|⟩
+¯Cd1
+¯Cd2
+HD
+0.1
+0.1
+0.87
+8.77
+0.15
+11.6
+MHD
+0.1
+0.02
+0.92
+4.17
+0.026
+4.93
+HD
+1.0
+1.0
+1.88
+47.48
+0.15
+13.4
+MHD
+1.0
+0.21
+2.02
+23.79
+0.026
+5.83
+HD
+10.0
+10.0
+3.95
+271.88
+0.16
+17.4
+MHD
+10.0
+2.06
+4.33
+136.44
+0.025
+7.28
+100
+102
+104
+106
+k
+10-11
+10-7
+10-3
+101
+Eu(k)
+k −5/3
+Fig. 17 Plots of KE spectra Eu(k) for the shell model runs with ϵinj = 0.1 (red), ϵinj = 1.0
+(green) and ϵinj = 10.0 (blue). The dashed and solid curves represent the Eu(k) for the
+MHD and HD runs respectively. Kolmogorov’s −5/3 scaling (black) fits well in the inertial
+range for all the runs. From Verma et al. [11]. Reproduced with permission from AIP.
+where Eu(k) for the MHD runs are larger than the HD counterpart. Since the
+energy is concentrated at small wavenumbers, we observe that UMHD > UHD.
+This is in sharp contrast to DNS results of Section 6 where U and Eu(k) of
+the MHD runs with moderate Pm are smaller than the corresponding values
+for the HD runs. However, in dynamo simulations, we do observe that U of
+MHD turbulence could be larger than that for HD turbulence; this topic will
+be discussed in the next section.
+Next, using the numerical data of the shell model, Verma et al. [11]
+estimated the rms values of (u · ∇)u for the HD and MHD runs using
+⟨|(u · ∇)u|⟩ =
+��
+n
+|Nn[u, u]|2
+�1/2
+.
+(84)
+To suppress the fluctuations, averaging was performed over a large number
+of states. As listed in Table 2, ⟨|(u · ∇)u|⟩ for the MHD runs are suppressed
+
+Springer Nature 2021 LATEX template
+30
+Turbulent Drag Reduction in MHD Turbulence
+100
+102
+104
+106
+k
+10-5
+10-3
+10-1
+101
+Πu(k)
+Fig. 18 Plots of Πu(k) for ϵinj = 0.1 (red), ϵinj = 1.0 (green) and ϵinj = 10.0 (blue). The
+dashed curves represent Πu(k) for the HD runs, whereas the solid curves indicate the same
+for the MHD runs. From Verma et al. [11]. Reproduced with permission from AIP.
+compared to the corresponding HD runs. These results reinforce the fact that
+the nonlinearity ⟨|(u · ∇)u|⟩ depends critically on the phases of the Fourier
+modes; larger U does not necessarily imply larger ⟨|(u · ∇)u|⟩. We remark
+that averaging over the small n would have been more appropriate for the
+estimation of ⟨|(u · ∇)u|⟩, as was done for the DNS.
+Verma et al. [11] also computed the average KE fluxes for the HD and MHD
+runs [37, 73]. These fluxes are illustrated in Fig. 18, and their average values
+in the steady state are listed in Table 2. The figure illustrates that for a given
+ϵinj, the MHD run has a lower KE flux than corresponding HD run. This is
+consistent with the suppression of ⟨|(u · ∇)u|⟩; lower ⟨|(u · ∇)u|⟩ leads to lower
+KE flux. In addition, we compute ¯Cd1 and ¯Cd2 using the values of Table 2 and
+L = 1. Clearly, ¯Cd1 and ¯Cd2 for the MHD runs are lower than those for the
+corresponding HD runs, thus indicating TDR in MHD turbulence.
+Thus, DNS and the shell model results illustrate that MHD turbulence has
+lower ⟨|(u · ∇)u|⟩ and lower Πu(k) compared to HD turbulence. These results
+demonstrate TDR in MHD turbulence. Note, however, that in DNS, U for the
+MHD runs with 1/3 ≤ Pm ≤ 10/3 are smaller than the corresponding U for
+the HD runs, but it is other way round in the shell model. As argued in Section
+6, we expect that U for MHD runs with very small Pm would be larger than
+U for the HD runs.
+In the next section we will describe TDR in dynamos.
+7 TDR in Dynamos
+Magnetic field generation, or dynamo process, in astrophysical objects is an
+important subfield of MHD. In dynamo process, the velocity field is forced
+mechanically, or by convection induced via temperature and/or concentration
+gradients. Rotation too plays an important role in dynamo. There are many
+books and papers written on dynamo, see e.g. [24, 25]. In this section, we will
+discuss only a handful of dynamo studies that are related to TDR.
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+31
+Fig. 19 For the Taylor-Green dynamo with the forcing amplitude F0 = 15.2, (a) 3D plot
+of the spatially chaotic velocity field for a no-dynamo state; (b) ordered velocity field for a
+dynamo state arising due to the suppression of chaos in the presence of a finite mean magnetic
+field; (c) ordered magnetic field. From Yadav et al. [27]. Reprinted with the permission of
+APS.
+Yadav et al. [27] simulated Taylor-Green dynamo for magnetic Prandtl
+number Pm = 0.5. They reported many interesting properties, including sub-
+critical dynamo transition, as well as steady, periodic, quasi-periodic, and
+chaotic dynamo states. Let us focus on an interesting feature of this dynamo
+that is related to TDR. In Fig. 19 we exhibit the intensities of the magni-
+tudes of the velocity and magnetic fields for the forcing amplitude F0 = 15.2.
+Before the dynamo transition, the velocity field is quite turbulent, as shown
+in Fig. 19(a). However, after the dynamo transition or emergence of magnetic
+field, both the velocity and magnetic fields, shown in Fig. 19(b,c), become more
+ordered compared to the pure HD state of Fig. 19(a). Yadav et al. observed
+similar features at several other F0’s. For example, at F0 = 15.8, after the
+emergence of magnetic field, the velocity fluctuations are suppressed, and the
+velocity and magnetic fields become quite coherent (see Fig. 20). The emer-
+gence of ordered velocity field is akin to an enhancement of the mean velocity
+in a pipe flow with polymers.
+The aforementioned simulation of Yadav et al. [27] is somewhat idealized
+in comparison to spherical geo- and solar dynamos with rotation and thermal
+convection at extreme parameters. Interestingly, spherical dynamos share cer-
+tain common features with Taylor-Green dynamo. As shown in Fig. 21, the
+velocity field of spherical dynamo [28] is organized in vertical columns, which
+
+2.0
+6.0
+2.0
+.4.0
+6.0.
+.8.0
+(a)
+(b)
+z
+Z
+1.0
+2.0
+3.0
+(c)
+XSpringer Nature 2021 LATEX template
+32
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 20 Plots of the total KE (top panel) and the total ME (bottom panel) for Taylor-
+Green dynamo with F0 = 15.8. We observe ordered velocity and magnetic fields after the
+onset of dynamo (time > 3000 units). From Yadav et al. [27]. Reprinted with the permission
+of APS.
+Fig. 21 The radial component of the velocity field in a numerical simulation of geodynamo
+by Olson et al. [28]. From Olson et al. [28]. Reproduced with permission from John Wiley
+& Sons.
+is also a feature of rotating turbulence [29, 75]. It is possible that thermal con-
+vection and magnetic field too contribute to the structural organization of the
+flow; this feature however needs a careful examination.
+Even though ⟨|u · ∇u|⟩ and the energy fluxes for dynamos have been stud-
+ied widely (e.g., [25, 42, 58]), TDR in dynamos has not been analyzed in detail.
+It is hoped that a systematic study of TDR in dynamos would be performed
+in future.
+In the next section, we describe TDR in QSMHD turbulence.
+
+8
+7
+6
+5
+Fo = 15.8
+500
+1500
+2500
+3500
+4500
+2
+1
+Fo = 15.8
+0
+500
+1500
+2500
+3500
+4500
+TimeRADIALVELOCITYSpringer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+33
+8 TDR in QSMHD turbulence via energy flux
+Liquid metals have small magnetic Prandtl number (Pm), and they are
+described using QSMHD equations, which are a limiting case of MHD
+equations [20, 21, 76]. The equations for QSMHD with a strong external
+magnetic field B0 are [20, 21, 76]
+∂u
+∂t + (u · ∇)u = −∇(p/ρ) − σ
+ρ ∆−1[(B0 · ∇)2u] + ν∇2u + Fext,
+(85)
+∇ · u = 0,
+(86)
+where σ is the electrical conductivity, and ∆−1 is the inverse Laplacian oper-
+ator. In Fourier space, a nondimensionalized version of QSMHD equations
+is
+d
+dtu(k) = −i
+�
+p
+{k · u(q)}u(p) − ikp(k)/ρ − N(cos2 θ)u(k)
+−νk2u(k) + Fext(k),
+(87)
+k · u(k) = 0,
+(88)
+where N is the interaction parameter, and θ is the angle between the wavenum-
+ber k and B0. The interaction parameter N is the ratio of the Lorentz force
+and nonlinear term (u · ∇)u, or
+N = σB2
+0L
+ρU
+.
+(89)
+Using Eq. (87), we derive an equation for the modal energy as
+d
+dtEu(k) = Tu(k) − 2NEu(k) cos2 θ + Fext(k) − Du(k),
+(90)
+where Tu(k) is defined in Eq. (10), and the dissipation induced by Lorentz
+term is [21, 76]
+Fu(k) = −2NEu(k) cos2 θ < 0.
+(91)
+Hence, the magnetic field induces additional dissipation in QSMHD turbu-
+lence.
+Equation (91) represents the energy transfers from the velocity field to the
+magnetic field at a wavenumber k. A sum of Fu(k) over a wavenumber sphere
+of radius K yields the following expression for the energy flux ΠB(K):
+ΠB(K) = −
+�
+k≤K
+Fu(k) =
+�
+k≤K
+2NEu(k) cos2 θ > 0.
+(92)
+
+Springer Nature 2021 LATEX template
+34
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 22 From the numerical simulation of QSMHD turbulence by Reddy and Verma [22],
+the time series of the normalised KE, E(t)/E0, for N = 5.5, 11, 18, 27, 130, where E0 is the
+energy at the final state of N = 0 simulation. For each N, after an application of external
+magnetic field, the KE drops suddenly, and then it increases and reaches a statistically
+steady value. The asymptotic KE for all the runs with N > 18 are larger than E0. From
+Reddy and Verma [22]. Reproduced with permission from AIP.
+Thus, the Lorentz force transfers the kinetic energy to the magnetic energy,
+which is immediately dissipated by the Joule dissipation; this feature is due to
+Pm = 0. As a consequence, for an injection rate ϵinj, Πu(K) of a QSMHD run
+is suppressed compared to Πu(K) of the corresponding HD run. Hence, in the
+inertial range,
+Πu < ϵinj.
+(93)
+Therefore, following the same line arguments as in earlier sections, we deduce
+that turbulent drag is suppressed in QSMHD turbulence. In addition, the
+velocity fields of the MHD runs are less random (or more ordered) compared to
+the corresponding HD runs, thus suppressing ⟨|(u · ∇)u|⟩. Therefore, we expect
+the turbulent drag in QSMHD turbulence to be smaller than the corresponding
+HD counterpart. In the following discussion, we will describe numerical results
+that are consistent with the above predictions.
+Reddy and Verma [22] simulated QSMHD turbulence in a periodic box for
+N ranging from 1.7 to 220. They employed a constant KE injection rate of
+0.1 (in nondimensional units). In fact, the magnetic field B0 was switched on
+after the initial HD run was fully developed. After an introduction of B0, KE
+first decreases abruptly due to Joule dissipation, and then it increases due to
+reorganization of the flow. As shown in Fig. 22, for N > 18, the total KE is
+larger than its HD counterpart (N = 0). In this range of N, the flow becomes
+quasi two-dimensional with larger U and suppressed turbulent drag. This is
+counter-intuitive because we expect the KE to decrease with the increase of
+Joule dissipation. However, reorganization of the flow leads to enhancement of
+U and TDR in the flow.
+In Table 3, we list the rms velocity U as a function of N. Clearly, U increases
+monotonically with N because ⟨|(u · ∇)u|⟩ and turbulent drag decrease with
+
+3.0
+3.0r
+2.5
+N=130
+2.5
+2.0
+2.0
+1.5
+=27
+1.5
+N=27
+N=0
+1.0
+N=18
+N=11
+0.5
+N=5.5
+N=1.7
+0.0
+-
+0
+50
+100
+150
+200
+250
+300
+350
+400
+= t/T
+*Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+35
+Table 3 In numerical simulations of QSMHD
+turbulence by Verma and Reddy [77], rms
+velocity (U) for various N’s. Clearly, U
+increase with N.
+N
+1.7
+18
+27
+220
+U
+0.39
+0.51
+0.65
+0.87
+Fig. 23 From the numerical simulation of QSMHD turbulence by Reddy and Verma [22],
+the vorticity isosurfaces for (a) N = 0, (b) N = 5.5, and (c) N = 18. The flow field becomes
+anisotropic and ordered with the increase of N. We observe a vortex tube for N = 18. From
+Reddy and Verma [22]. Reproduced with permission from AIP.
+the increase of N. In Fig. 23 we exhibit the vorticity isosurfaces for N = 0, 5.5,
+and 18. As is evident in the figure, the flow becomes quasi-2D and more orderly
+with the increase of N.
+The above results again indicate that a large U does not necessarily
+imply large ⟨|(u · ∇)u|⟩ because the nonlinear term depends on U and the
+phase relations between the velocity modes. In QSMHD turbulence, two-
+dimensionalization leads to a reduction in ⟨|(u · ∇)u|⟩ even with large U. Note,
+however, that for a definitive demonstration of drag reduction in QSMHD tur-
+bulence, we still need to perform a comparative study of Πu and ⟨|(u · ∇)u|⟩
+for HD and QSMHD turbulence.
+Reduced turbulent flux is an important ingredient for drag reduction. Note
+that such a reduction does not occur in laminar QSMHD; here, the Lorentz
+force damps the flow further. We illustrate this claim for a channel flow. In a
+HD channel flow, the maximum velocity at the centre of the pipe is (see Fig. 2)
+[13, 39]
+UHD = − d2
+2νρ
+� dp
+dx
+�
+,
+(94)
+
+63.83
+14.89
+16.45
+47.88
+12.10
+12.34
+31.92
+(a)
+b)
+9.308
+8.227
+15.97
+6.516
+4.115
+0.015
+3.725
+0.0025Springer Nature 2021 LATEX template
+36
+Turbulent Drag Reduction in MHD Turbulence
+where d is half-width of the channel (see Fig. 2). However, in a laminar QSMHD
+flow, the corresponding velocity is [20, 76, 78]
+UQSMHD = −
+1
+σB2
+0
+� ∂p
+∂x
+�
+.
+(95)
+The ratio of the two velocities is
+UQSMHD
+UHD
+=
+2νρ
+σB2
+0d2 =
+1
+Ha2 ,
+(96)
+where Ha is the Hartmann number, which is much larger than unity for a
+QSMHD flow. Hence, the velocity in laminar QSMHD is much smaller than
+that in the HD channel. In comparison, U increases with N in QSMHD tur-
+bulence. Hence, drag reduction is a nonlinear phenomena, which is a visible in
+a turbulent flow.
+In the next section, we will cover several more examples of TDR.
+9 TDR in Miscellaneous Systems
+In this section, we briefly describe TDR in stably stratified turbulence, over
+smooth surfaces, and in turbulent convection.
+9.1 TDR in stably stratified turbulence
+Many natural and laboratory flows are stably stratified with lighter fluid
+above heavier fluid and gravity acting downwards. The governing equations
+for stably-stratified flows under Boussinesq approximation are [13, 29, 30, 79]
+∂u
+∂t + (u · ∇)u = −∇p − Ωρˆz + ν∇2u + FLS,
+(97)
+∂ρ
+∂t + (u · ∇)ρ = Ωuz + κ∇2ρ,
+(98)
+∇ · u = 0,
+(99)
+where p is the pressure, ρ is the density fluctuation in velocity units, −Ωρˆz is
+buoyancy, and Ω is the Brunt-V¨ais¨al¨a frequency, which is defined as [29, 79]
+Ω =
+�
+g
+ρm
+|d¯ρ
+dz |.
+(100)
+Here ρm is the mean density of the whole fluid, d¯ρ/dz is the average density
+gradient, and g is the acceleration due to gravity. We convert the density in
+velocity units using the transformation, ρ → ρg/(Ωρm). The ratio ν/κ is called
+Schmidt number, which is denoted by Sc. Richardson number, Ri, which is a
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+37
+nondimensional number, is employed to quantify the ratio of buoyancy and
+the nonlinear term (u · ∇)u.
+For periodic or vanishing boundary condition and in the absence of
+dissipative terms, the total energy,
+Eu + Eρ =
+�
+dr1
+2u2 +
+�
+dr1
+2ρ2,
+(101)
+is conserved [29, 40, 79, 80]. Here, Eρ can be interpreted as the total potential
+energy. It has been shown that in the inertial range, the associated energy
+fluxes obey the following conservation law [40, 81]:
+Πu + Πρ = const = ϵinj,
+(102)
+where Πρ is the potential energy flux, and ϵinj is the KE injection rate. Note
+that under steady state, Πρ equals the energy transfer rate from the velocity
+field to the density field. Using the stable nature of the flow, we can argue that
+Πρ > 0 [29, 30, 40, 81].
+Nature of the stably stratified turbulence depends quite critically on the
+density gradient or Richardson number. For moderate density gradient (Ri ≈
+1), Bolgiano [82] and Obukhov [83] argued that Πρ is positive and constant,
+whereas Πu(k) ∼ k−4/5. For small Richardson numbers, the scaling is closer to
+passive scalar turbulence [84], but the flow becomes quasi-2D for large Richard-
+son numbers [29, 30]. Here, we present only one numerical result. Kumar et
+al. [85] simulated stably stratified turbulence for Sc = 1 and Ri = 0.01, and
+observed that in the inertial range, Πρ(k) = const (> 0) and Πu(k) ∼ k−4/5.
+See Fig. 24 for an illustration. Researchers have observed that Πρ > 0 for small
+and large Ri’s as well [29, 80, 84].
+Using the fact that Πρ(k) > 0, following the arguments described in
+Section 3, we argue that the turbulent drag will be reduced in stably stratified
+turbulence. That is, for the same KE injection rate ϵinj, Πu(k) and ⟨u · ∇u⟩
+for stably stratified turbulence will be smaller than those for HD turbulence.
+We remark that the flux-based arguments presented above are consistent with
+the observations of Narasimha and Sreenivasan [38] who argued that stably
+stratified turbulence is relaminarized.
+In the next subsection, we will discuss TDR experienced by smooth bluff
+bodies.
+9.2 TDR over smooth bluff bodies
+As discussed in Section 2, bluff bodies experience turbulent drag at large
+Reynolds numbers. Models, experiments, and numerical simulations reveal
+that the turbulent drag on aerodynamic objects is a combination of the viscous
+drag and adverse pressure gradient [13–15]. Engineers have devised ingenious
+techniques to reduce this drag, which are beyond the scope of this article.
+
+Springer Nature 2021 LATEX template
+38
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 24 Stably stratified simulation with Sc = 1 and Ri = 0.01: plots of KE flux Πu(k),
+normalized KE flux Πu(k)k4/5, and potential energy flux Πρ(k) (presented as Πθ(k) in the
+figure). From Kumar et al. [85]. Reproduced with permission from APS.
+Equation (17) illustrates that the turbulent drag experienced by a bluff
+body is a combination of the inertial and viscous forces, and the adverse pres-
+sure gradient. However, for bluff bodies like aerofoils and automobiles, the
+dominant contributions come from the viscous drag and adverse pressure gra-
+dient [14, 15]. Note, however, that the bulk flow above the smooth surface is
+anisotropic, and it contains signatures of the surface properties. Hence, the
+nonlinear term ⟨|u · ∇u|⟩ and the drag coefficient ¯Cd2 could yield interesting
+insights into TDR over bluff bodies. Narasimha and Sreenivasan [38] performed
+such analysis for a variety of flows. In the following subsection, we will use the
+above idea to explain TDR in turbulent thermal convection.
+9.3 TDR in turbulent thermal convection
+Turbulent convection exhibits interesting properties related to TDR. In this
+subsection, we consider Rayleigh-B´enard convection (RBC), which is an ide-
+alized setup consisting of a thin fluid layer confined between two thermally
+conducting plates separated by a distance d. The temperatures of the bottom
+and top plates are Tb and Tt respectively, with Tb > Tt.
+The equations for thermal convection under Boussinesq approximation
+are [86]
+∂u
+∂t + (u · ∇)u = −1
+ρ∇p + αgTˆz + ν∇2u,
+(103)
+∂T
+∂t + (u · ∇)T = κ∇2T,
+(104)
+∇ · u = 0,
+(105)
+where T is the temperature field; α, κ are respectively the thermal expansion
+coefficient and thermal diffusivity of the fluid; and g is the acceleration due
+to gravity. The two important parameters of turbulent thermal convection are
+
+-
+102
+IIu (k), Ie(k)
+100
+Iu (k)
+10-2
+IIu (k)k4/5
+0.1IIe(k)
+10-4
+101
+102
+kSpringer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+39
+thermal Prandtl number, Pr = ν/κ, and Rayleigh number,
+Ra = αgd3(Tb − Tt)
+νκ
+.
+(106)
+In turbulent thermal convection, the velocity field receives energy from
+the temperature field via buoyancy. Note that thermal plumes drive thermal
+convection. This feature is opposite to what happens in polymeric, MHD,
+and stably stratified turbulence, where the velocity field loses energy to the
+secondary field. Yet, there are signatures of TDR in turbulent convection,
+which is due to the smooth thermal plates. Hence, the mechanism of TDR in
+turbulent thermal convection differs from that in polymeric, MHD, and stably
+stratified turbulence.
+In the following, we list some of the results related to TDR in thermal
+convection.
+1. Kraichnan [87] argued that turbulent thermal convection would become
+fully turbulent or reach ultimate regime at very large Rayleigh number. In
+this asymptotic state, the effects of walls are expected to vanish, similar to
+the vanishing of boundary effects in the bulk of HD turbulence [35, 36, 88].
+Kraichnan [87] predicted that Nu ∝ Ra1/2 in the ultimate regime. However,
+experimental observations and numerical simulations reveal that for Ra ⪅
+1013, Nu ∼ Raβ with β ranging from 0.29 to 0.33 [30, 89, 90]. This reduction
+in the Nu exponent from 1/2 to approximately 0.30 is attributed to the
+suppression of heat flux due to the smooth thermal plates, boundary layers,
+and other complex properties [30, 89–92].
+2. Pandey et al. [31] performed numerical simulations of RBC for Pr = 1 and
+Ra ranging from 106 to 5 × 108, and showed that
+Nonlinear term
+Viscous term
+= |u · ∇u|
+|ν∇2u| ∼ ReRa−0.14.
+(107)
+Note that the above ratio is Re for HD turbulence. Thus, nonlinearity
+(⟨|u · ∇u|⟩) is suppressed in turbulent thermal convection at large Ra.
+3. Pandey et al. [31] and Bhattacharya et al. [32, 93] showed that the viscous
+dissipation rate (ϵu) and thermal dissipation rate (ϵT ) depend on Rayleigh
+and Prandtl numbers, and that ϵu and ϵT are suppressed compared to HD
+turbulence. For moderate Pr and large Ra,
+ϵu ∼ U 3
+d Ra−0.2,
+(108)
+ϵT ∼ U(Tb − Tt)2
+d
+Ra−0.2.
+(109)
+Interestingly, for small Prandtl numbers, ϵu ∼ U 3/d with very small Ra-
+dependent correction [32, 93]. See Fig. 25 for an illustration.
+
+Springer Nature 2021 LATEX template
+40
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 25 Plots exhibiting the Ra and Pr dependence of the viscous and thermal dissipation
+rates. For moderate Pr, ϵu, ϵT ∼ Ra−0.20. From Bhattacharya et al. [32]. Reproduced with
+permission from AIP.
+Fig. 26 A LSC observed in 2D RBC by Sugiyama et al. [95]. The arrows represent the
+velocity field, whereas the colors represent the temperature of the fluid, with red as hot and
+blue as cold fluid. From Sugiyama et al. [95]. Reproduced with permission from APS.
+It is well known that a large-scale circulation (LSC) is present in turbu-
+lence convection (see Fig. 26) [94–98]. As we show below, the suppression of
+nonlinearity (⟨|u · ∇u|⟩) and turbulent drag in RBC is related to this LSC and
+the smooth walls.
+As shown in Fig. 26, the flows near the top and bottom plates have sim-
+ilarities with those near a flat plate. The LSC traverses vertically along the
+
+102
+(a)
+Ra
+(p / εn)/
+101
+Ra
+Eul
+100
+Ra
+10-1
+106
+108
+1010
+(b)
+10-1
+Pr = 0.02
+Pr = 0.1
+(p / zV)/L3
+Pr = 0.5
+Pr = 1
+Ra
+Pr = 6.8
+Pr = 50
+10-2
+Pr = 100
+106
+108
+1010
+Ra0.8
+0.6
+N
+0.4
+0.2Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+41
+Fig. 27 In numerical simulation of Zhu et al. [99], the velocity (a) and temperature (b)
+profiles in wall units for various Ra’s. The dashed lines illustrate the viscous sublayer and
+the log-layer. A log layer is observed for the velocity field, but not for the temperature field.
+From Zhu et al. [99]. Reproduced with permission from APS.
+vertical walls, but moves horizontally along the thermal plates. However, for
+a typical RBC flow, the horizontal extent of LSC is shorter than that in the
+flow past a flat plate. Researchers have argued that for large Rayleigh numbers
+(Ra ⪆ 1013), the boundary layers exhibit a transition to a log layer, which is
+a signature of transition from viscous to turbulent boundary layer, as in flow
+past a flat plate [12–14, 30, 89]. For example, Zhu et al. [99] simulated 2D RBC
+and showed that above the viscous layer, the normalized velocity field varies
+logarithmically with the normalized vertical distance. In particular, Zhu et al.
+[99] observed that u+ ∝ log(y+) for y+ ⪆ 10 (see Fig. 27). Note, however, that
+the thermal boundary layers do not show transition to log layer [99]. Several
+other experiments exhibit similar behaviour [100].
+Since the boundary layers of turbulent thermal convection have similar
+properties as those over a flat plate, we can argue that the nonlinearity ⟨u · ∇u⟩
+is suppressed in turbulent convection. This is the reason why the dissipa-
+tion rates and turbulent drag in turbulent convection are smaller than the
+corresponding quantities in HD turbulence. Verma et al. [101] studied the cor-
+relation ⟨uzθ⟩, where θ is the temperature fluctuation, and showed that for
+
+(a) 40
+Ra = 1011
+Ra = 1012
+30
+Ra = 1013
+K = 0.4
+Ra = 1014
++
+2 20
+10
+0
+10-1
+100
+101
+102
+103
+y+
+(b) 25
+Ra= 1011
+Ra = 1012
+20
+Ra= 1013
+Ra = 1014
+15
+T+
+10
+5
+0
+10-1
+100
+101
+102
+103Springer Nature 2021 LATEX template
+42
+Turbulent Drag Reduction in MHD Turbulence
+moderate Pr,
+⟨uzθ⟩ =
+�
+⟨u2z⟩
+�
+⟨θ2⟩(PrRa)−0.22.
+(110)
+Note that
+�
+⟨u2z⟩ ≈ Ra1/2 and
+�
+⟨θ2⟩ ≈ (∆T). Therefore, the correction
+(PrRa)−0.22 of the above equation leads to ⟨uzθ⟩ ∼ Ra0.28 or Nu ∼ Ra0.28.
+Verma et al. [30, 101] argued that at very large Ra, the corrections would dis-
+appear and the flow will approach the ultimate regime with ⟨uzθ⟩ ∼ Ra1/2 or
+Nu ∼ Ra1/2.
+Note, however, that no experiment and numerical simulation has been able
+to achieve the ultimate regime, thus the ultimate regime remains a conjecture
+at present [90, 99, 102, 103], even though several experiments and numerical
+simulation report a transition to the ultimate regime with the Nu exponent
+reaching up to 0.38 (but lower than 1/2) [99, 102], while some others argue
+against the transition to the ultimate regime [90, 103]. It is interesting to
+note that for rough thermal plates, the heat transport is enhanced because of
+increase in turbulence due to the roughness [104].
+RBC with periodic boundary condition exhibits Nu ∝ Ra1/2 due to the
+absence of boundary layers [101, 105]. In addition, RBC with small Prandtl
+numbers too exhibit properties similar to those of periodic boundary condition.
+This is because the temperature gradient is linear in the bulk in both these
+systems [93, 106].
+In summary, turbulent thermal convection exhibits suppression of nonlin-
+earity (⟨|u · ∇u|⟩) and KE flux compared to HD turbulence. This suppression,
+which occurs essentially due to the smooth walls, leads to TDR in thermal
+convection.
+10 Discussions and conclusions
+Experiments and numerical simulations show that turbulent flows with dilute
+polymers exhibit TDR. Many factors–boundary layers, polymer properties,
+bulk properties of the flow–are responsible for this phenomena [1–11]. There
+are many interesting works in this field, however, in this review, we focus
+on the role of bulk turbulence on TDR. The KE flux, Πu(k), is suppressed
+in the presence of polymers. This reduction in Πu(k) leads to suppression of
+nonlinearity ⟨u · ∇u⟩ and turbulent drag.
+MHD turbulence exhibits very similar behaviour as the polymeric tur-
+bulence [11]. Here too, Πu(k) is suppressed because a major fraction of the
+injected KE is transferred to the magnetic field. Consequently, ⟨u · ∇u⟩ and
+the turbulent drag are suppressed in MHD turbulence. For the same KE injec-
+tion rate at large scales, Πu(k) and ⟨u · ∇u⟩ for MHD turbulence are smaller
+than the respective quantities of HD turbulence. These properties are borne
+out in DNS and shell models.
+The KE flux Πu(k) of stably stratified turbulence too is suppressed com-
+pared to HD turbulence. Hence, we expect TDR in stably stratified turbulence.
+Narasimha and Sreenivasan [38] made a similar observation. We need detailed
+numerical simulations to verify the above statement. An interesting point to
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+43
+note that for the above three flows,
+Πu(k) + ΠB(k) = const = ϵinj,
+(111)
+where ΠB(k) represents the energy flux associated with the secondary field B,
+which could be polymer, magnetic field, or density. The constancy of the sum
+of fluxes in Eq. (111) arises due to the stable nature of system [29, 40, 81]. The
+above constancy also represents a redistribution of the injected kinetic energy
+at large scales to (a) the velocity field in the intermediate scales, and to (b) the
+secondary field. Positive ΠB implies that Πu(k) < ϵinj which leads to TDR in
+the flow. Thus, TDR is intimately related to the conservation law of Eq. (111).
+Another important feature of TDR is that the mean flow or large scale
+velocity (U) is enhanced in the presence of polymers or magnetic field. This is
+because the velocity field gets more ordered under TDR. Suppression of Πu(k)
+and ⟨u · ∇u⟩ even with strong U is due to the correlations in the velocity
+field. An emergence of ordered U is also observed in dynamo and QSMHD
+turbulence. Unfortunately, DNS of MHD turbulence with magnetic Prandtl
+number Pm = 1/3, 1, and 10/3 do not show enhancement in U compared to
+the respective HD turbulence. Based on the findings of QSMHD turbulence
+(Pm ≈ 0) and dynamo, we conjecture that U of MHD turbulence with very
+small Pm will be larger than that of corresponding HD turbulence.
+TDR is also observed in turbulent thermal convection. This observation is
+based on the suppression of viscous and thermal dissipation rates, and that of
+nonlinearity ⟨u · ∇u⟩ [31, 32, 37]. Note, however, that unlike MHD, polymeric,
+and stably-stratified turbulence, Πu(k) for turbulent thermal convection is not
+suppressed due to the unstable nature of thermal convection [40, 81]. Therefore,
+the mechanism for TDR in turbulent thermal convection differs from that for
+TDR in MHD, polymeric, and stably-stratified turbulence. In this review, we
+argue that TDR in turbulent thermal convection occurs due to the smooth
+thermal plates. Near the thermal plates, the large-scale circulation (LSC) are
+akin to the flow past a flat plate. This feature has important consequences on
+the possible transition to the ultimate regime in thermal convection.
+The enhancement of U under TDR is similar to the increase in the mean
+flow during relaminarization. Narasimha and Sreenivasan [38] showed rever-
+sion of flows from random to smooth profiles by relaminarizing agencies, which
+could be stably stratification, rotation, thermal convection, etc. Figure 28 illus-
+trates interactions between the mean flow and turbulence via a relaminarizing
+agency. In this figure, the channels 1, 2, and 3 represent complex interac-
+tions between the mean flow and fluctuations during relaminarization, whereas
+channel 0 represents these interactions in the HD turbulence. The arguments
+of Verma et al. [11] have certain similarities with those of Narasimha and
+Sreenivasan [38].
+In summary, this review discusses a general framework based on KE flux to
+explain TDR in a wide range of phenomena—polymeric, MHD, QSMHD, and
+stably stratified turbulence; dynamo; and turbulent thermal convection. This
+kind of study is relatively new, and it is hoped that it will be explored further
+
+Springer Nature 2021 LATEX template
+44
+Turbulent Drag Reduction in MHD Turbulence
+Fig. 28 Interactions between the mean flow and turbulence via relaminarizing agency. The
+interaction channels 1,2,3 relaminarize the flow in comparison to the HD turbulence where
+interactions occurs via channel 0. From Narasimha and Sreenivasan [38]. Reproduced with
+permission from K. R. Sreenivasan.
+in future. We also expect TDR to emerge in other systems, such as drift-wave
+turbulence, astrophysical MHD, rotating turbulence, etc. Such a study has an
+added benefit that TDR has practical applications in engineering flows, liquid
+metals, polymeric flows, etc.
+Acknowledgments.
+The authors thank Abhishek Kumar and Shashwat
+Bhattacharya for useful discussions. This project was supported by Indo-
+French project 6104-1 from CEFIPRA. S. Chatterjee is supported by INSPIRE
+fellowship (No. IF180094) of the Department of Science & Technology, India.
+Declarations
+Conflict of interest statement.
+The authors have no actual or potential
+conflicts of interest to declare in relation to this article.
+References
+[1] Lumley, J., Blossey, P.: Drag reduction by additives. Annu. Rev. Fluid
+Mech. 1(1), 367–384 (1969)
+[2] Tabor, M., de Gennes, P.G.: A cascade theory of drag reduction. EPL
+2(7), 519–522 (1986)
+[3] de Gennes, P.G.: Introduction to Polymer Dynamics. Cambridge Uni-
+versity Press, Cambridge (1990)
+[4] de Gennes, P.G.: Scaling Concepts in Polymer Physics. Cornell Univer-
+sity Press, Ithaca (1979)
+
+mean
+ftow
+12
+11
+relaminarizing
+agency
+3
+turbulenceSpringer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+45
+[5] Sreenivasan, K.R., White, C.M.: The onset of drag reduction by dilute
+polymer additives, and the maximum drag reduction asymptote. J. Fluid
+Mech. 409, 149–164 (2000)
+[6] L’vov, V.S., Pomyalov, A., Procaccia, I., Tiberkevich, V.: Drag reduction
+by polymers in wall bounded turbulence. Phys. Rev. Lett. 92(24), 244503
+(2004)
+[7] Benzi, R., De Angelis, E., Govindarajan, R., Procaccia, I.: Shell model
+for drag reduction with polymer additives in homogeneous turbulence.
+Phys. Rev. E 68(1), 016308 (2003)
+[8] White, C.M., Mungal, M.G.: Mechanics and prediction of turbulent drag
+reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256
+(2008)
+[9] Benzi, R.: A short review on drag reduction by polymers in wall bounded
+turbulence. Physica D 239(14), 1338–1345 (2010)
+[10] Benzi, R., Ching, E.S.C.: Polymers in Fluid Flows. Annu. Rev. Condens.
+Matter Phys. 9(1), 163–181 (2018)
+[11] Verma, M.K., Alam, S., Chatterjee, S.: Turbulent drag reduction in mag-
+netohydrodynamic and quasi-static magnetohydrodynamic turbulence.
+Phys. Plasmas 27, 052301 (2020)
+[12] Landau, L.D., Lifshitz, E.M.: Fluid Mechanics, 2nd edn. Course of
+Theoretical Physics. Elsevier, Oxford (1987)
+[13] Kundu, P.K., Cohen, I.M., Dowling, D.R.: Fluid Mechanics, 6th edn.
+Academic Press, San Diego (2015)
+[14] Anderson, J.D.: Fundamentals of Aerodynamics. McGraw-Hill Educa-
+tion, New York (2017)
+[15] Anderson Jr., J.D.: A History of Aerodynamics. Cambridge University
+Press, New York (1998)
+[16] Dar, G., Verma, M.K., Eswaran, V.: Energy transfer in two-dimensional
+magnetohydrodynamic turbulence: formalism and numerical results.
+Physica D 157(3), 207–225 (2001)
+[17] Mininni, P.D., Ponty, Y., Montgomery, D.C., Pinton, J.-F., Politano, H.,
+Pouquet, A.G.: Dynamo regimes with a nonhelical forcing. ApJ 626,
+853–863 (2005)
+[18] Valente, P.C., da Silva, C.B., Pinho, F.T.: The effect of viscoelasticity on
+the turbulent kinetic energy cascade. J. Fluid Mech. 760, 39–62 (2014)
+
+Springer Nature 2021 LATEX template
+46
+Turbulent Drag Reduction in MHD Turbulence
+[19] Valente, P.C., da Silva, C.B., Pinho, F.T.: Energy spectra in elasto-
+inertial turbulence. Phys. Fluids 28(7), 075108–17 (2016)
+[20] Moreau, R.J.: Magnetohydrodynamics. Springer, Berlin (1990)
+[21] Knaepen, B., Moreau, R.: Magnetohydrodynamic turbulence at low
+magnetic reynolds number. Annu. Rev. Fluid Mech. 40, 25–45 (2008)
+[22] Reddy, K.S., Verma, M.K.: Strong anisotropy in quasi-static magneto-
+hydrodynamic turbulence for high interaction parameters. Phys. Fluids
+26, 025109 (2014)
+[23] Reddy, K.S., Kumar, R., Verma, M.K.: Anisotropic energy transfers in
+quasi-static magnetohydrodynamic turbulence. Phys. Plasmas 21(10),
+102310 (2014)
+[24] Moffatt, H.K.: Magnetic Field Generation in Electrically Conducting
+Fluids. Cambridge University Press, Cambridge (1978)
+[25] Roberts, P.H., Glatzmaier, G.A.: Geodynamo theory and simulations.
+Rev. Mod. Phys. 72, 1081–1123 (2000)
+[26] Brandenburg, A., Subramanian, K.: Astrophysical magnetic fields and
+nonlinear dynamo theory. Phys. Rep. 417(1-4), 1–209 (2005)
+[27] Yadav, R.K., Verma, M.K., Wahi, P.: Bistability and chaos in the Taylor-
+Green dynamo. Phys. Rev. E 85(3), 036301 (2012)
+[28] Olson, P.L., Christensen, U.R., Glatzmaier, G.A.: Numerical modeling
+of the geodynamo: mechanisms of field generation and equilibration. J.
+Geophys. Res. B: Solid Earth 104(B5), 10383–10404 (1999)
+[29] Davidson, P.A.: Turbulence in Rotating, Stratified and Electrically
+Conducting Fluids. Cambridge University Press, Cambridge (2013)
+[30] Verma, M.K.: Physics of Buoyant Flows: From Instabilities to Turbu-
+lence. World Scientific, Singapore (2018)
+[31] Pandey, A., Verma, M.K.: Scaling of large-scale quantities in Rayleigh-
+B´enard convection. Phys. Fluids 28(9), 095105 (2016)
+[32] Bhattacharya, S., Verma, M.K., Samtaney, R.: Revisiting Reynolds and
+Nusselt numbers in turbulent thermal convection. Phys. Fluids 33,
+015113 (2021)
+[33] Kolmogorov, A.N.: Dissipation of Energy in Locally Isotropic Turbu-
+lence. Dokl Acad Nauk SSSR 32, 16–18 (1941)
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+47
+[34] Kolmogorov, A.N.: The local structure of turbulence in incompressible
+viscous fluid for very large Reynolds numbers. Dokl Acad Nauk SSSR
+30, 301–305 (1941)
+[35] Lesieur, M.: Turbulence in Fluids. Springer, Dordrecht (2008)
+[36] Frisch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge
+University Press, Cambridge (1995)
+[37] Verma, M.K.: Energy Transfers in Fluid Flows: Multiscale and Spectral
+Perspectives. Cambridge University Press, Cambridge (2019)
+[38] Narasimha, R., Sreenivasan, K.R.: Relaminarization of fluid flows. Adv.
+Appl. Mech. 19, 221–309 (1979)
+[39] Verma, M.K.: Introduction to Mechanics, 2nd edn. Universities Press,
+Hyderabad (2016)
+[40] Verma, M.K.: Variable energy flux in turbulence. Journal of Physics A:
+Mathematical and Theoretical 55(1), 013002 (2022) 2011.07291. https:
+//doi.org/10.1088/1751-8121/ac354e
+[41] Kraichnan, R.H.: The structure of isotropic turbulence at very high
+Reynolds numbers. J. Fluid Mech. 5, 497–543 (1959)
+[42] Verma, M.K.: Statistical theory of magnetohydrodynamic turbulence:
+recent results. Phys. Rep. 401(5), 229–380 (2004)
+[43] Sreenivasan, K.R.: An update on the energy dissipation rate in isotropic
+turbulence. Phys. Fluids 10(2), 528–529 (1998)
+[44] Onsager, L.: Statistical hydrodynamics. Il Nuovo Cimento 6(2), 279–287
+(1949)
+[45] Prandtl, L.: On the motion of fluids with very little friction. In: Krazer,
+A. (ed.) Verhandlungen des Dritten Internationalen Mathematiker-
+Kongresses in Heidelberg. Teubner, Leipzig (1905)
+[46] Fouxon, A., Lebedev, V.: Spectra of turbulence in dilute polymer
+solutions. Phys. Fluids 15(7), 2060–2072 (2003)
+[47] Perlekar, P., Mitra, D., Pandit, R.: Manifestations of drag reduction by
+polymer additives in decaying, homogeneous, isotropic turbulence. Phys.
+Rev. Lett. 97(26), 264501 (2006)
+[48] Sagaut, P., Cambon, C.: Homogeneous Turbulence Dynamics, 2nd edn.
+Cambridge University Press, Cambridge (2018)
+
+Springer Nature 2021 LATEX template
+48
+Turbulent Drag Reduction in MHD Turbulence
+[49] Ray, S.S., Vincenzi, D.: Elastic turbulence in a shell model of polymer
+solution. EPL 114, 44001 (2016)
+[50] Thais, L., Gatski, T.B., Mompean, G.: Analysis of polymer drag reduc-
+tion mechanisms from energy budgets. Int. J. Heat Mass Transfer 43(C),
+52–61 (2013)
+[51] Nguyen, M.Q., Delache, A., Simo¨ens, S., Bos, W.J.T., El Hajem, M.:
+Small scale dynamics of isotropic viscoelastic turbulence. Phys. Rev.
+Fluids 1(8), 083301 (2016)
+[52] L’vov, V.S., Pomyalov, A., Procaccia, I., Tiberkevich, V.: Drag Reduc-
+tion by Microbubbles in Turbulent Flows: The Limit of Minute Bubbles.
+Phys. Rev. Lett. 94(17), 174502 (2005)
+[53] Cowling, T.G.: Magnetohydrodynamics. Adam Hilger, London (1976)
+[54] Priest, E.R.: Magnetohydrodynamics of the Sun. Cambridge University
+Press, Cambridge (2014)
+[55] Goldstein, M.L., Roberts, D.A.: Magnetohydrodynamic turbulence in
+the solar wind. Annu. Rev. Astron. Astrophys. 33, 283–325 (1995)
+[56] Davidson, P.A.: Turbulence: An Introduction for Scientists and Engi-
+neers. Oxford University Press, Oxford (2004)
+[57] Debliquy, O., Verma, M.K., Carati, D.: Energy fluxes and shell-to-
+shell transfers in three-dimensional decaying magnetohydrodynamic
+turbulence. Phys. Plasmas 12(4), 042309 (2005)
+[58] Kumar, R., Verma, M.K., Samtaney, R.: Energy transfers and magnetic
+energy growth in small-scale dynamo. EPL 104(5), 54001 (2014)
+[59] Kumar, R., Verma, M.K., Samtaney, R.: Energy transfers in dynamos
+with small magnetic Prandtl numbers. J. of Turbulence 16(11), 1114–
+1134 (2015)
+[60] Verma, M.K.: Field theoretic calculation of renormalized viscosity,
+renormalized resistivity, and energy fluxes of magnetohydrodynamic
+turbulence. Phys. Rev. E 64(2), 026305 (2001)
+[61] Boyd, T.J.M., Sanderson, J.J.: The Physics of Plasmas. Cambridge
+University Press, Cambridge (2003)
+[62] Verma, M.K., Chatterjee, A.G., Yadav, R.K., Paul, S., Chandra, M.,
+Samtaney, R.: Benchmarking and scaling studies of pseudospectral code
+Tarang for turbulence simulations. Pramana-J. Phys. 81(4), 617–629
+(2013)
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+49
+[63] Chatterjee, A.G., Verma, M.K., Kumar, A., Samtaney, R., Hadri, B.,
+Khurram, R.: Scaling of a Fast Fourier Transform and a pseudo-spectral
+fluid solver up to 196608 cores. J. Parallel Distrib. Comput. 113, 77–91
+(2018)
+[64] Craya, A.: Contribution `a l’analyse de la turbulence associ´ee `a des
+vitesses moyennes. PhD thesis, Universit´e de Granoble (1958)
+[65] Herring, J.R.: Approach of axisymmetric turbulence to isotropy. Phys.
+Fluids 17(5), 859–872 (1974)
+[66] Sadhukhan, S., Verma, M.K., Stepanov, R., Plunian, F., Samtaney,
+R.: Kinetic helicity and enstrophy transfers in helical hydrodynamic
+turbulence. Phys. Rev. Fluids 4, 84607 (2019)
+[67] Gledzer, E.B.: System of hydrodynamic type allowing 2 quadratic
+integrals of motion . Dokl Acad Nauk SSSR 209, 1046–1048 (1973)
+[68] Yamada, M., Ohkitani, K.: Asymptotic formulas for the lyapunov spec-
+trum of fully developed shell model turbulence. Phys. Rev. E 57(6), 6257
+(1998)
+[69] Ditlevsen, P.D.: Turbulence and Shell Models. Cambridge University
+Press, Cambridge (2010)
+[70] Frick, P., Sokoloff, D.D.: Cascade and dynamo action in a shell model
+of magnetohydrodynamic turbulence. Phys. Rev. E 57(4), 4155–4164
+(1998)
+[71] Stepanov, R., Plunian, F.: Phenomenology of turbulent dynamo growth
+and saturation. ApJ 680(1), 809–815 (2008)
+[72] Plunian, F., Stepanov, R., Frick, P.: Shell models of magnetohydrody-
+namic turbulence. Phys. Rep. 523, 1–60 (2012)
+[73] Verma, M.K., Kumar, R.: Dynamos at extreme magnetic Prandtl num-
+bers: insights from shell models. J. Turbul. 17(12), 1112–1141 (2016)
+[74] Stepanov, R., Plunian, F.: Fully developed turbulent dynamo at low
+magnetic Prandtl numbers. J. Turbul. 7(39), 1–15 (2006)
+[75] Sharma, M.K., Kumar, A., Verma, M.K., Chakraborty, S.: Statistical
+features of rapidly rotating decaying turbulence: Enstrophy and energy
+spectra and coherent structures. Phys. Fluids 30(4), 045103 (2018)
+[76] Verma, M.K.: Anisotropy in Quasi-Static Magnetohydrodynamic Turbu-
+lence. Rep. Prog. Phys. 80(8), 087001 (2017)
+
+Springer Nature 2021 LATEX template
+50
+Turbulent Drag Reduction in MHD Turbulence
+[77] Verma, M.K., Reddy, K.S.: Modeling quasi-static magnetohydrodynamic
+turbulence with variable energy flux. Phys. Fluids 27(2), 025114 (2015)
+[78] M¨uller, U., B¨uhler, L.: Magnetofluiddynamics in Channels and Contain-
+ers. Springer, Berlin Heidelberg (2001)
+[79] Tritton, D.J.: Physical Fluid Dynamics. Clarendon Press, Oxord (1988)
+[80] Lindborg, E.: The energy cascade in a strongly stratified fluid. J. Fluid
+Mech. 550, 207–242 (2006)
+[81] Verma, M.K.: Contrasting turbulence in stably stratified flows and
+thermal convection. Phys. Scr. 94(6), 064003 (2019)
+[82] Bolgiano, R.: Turbulent spectra in a stably stratified atmosphere. J.
+Geophys. Res. 64(12), 2226–2229 (1959)
+[83] Obukhov, A.M.: On influence of buoyancy forces on the structure of
+temperature field in a turbulent flow. Dokl Acad Nauk SSSR 125, 1246
+(1959)
+[84] Yeung, P.K., Donzis, D.A., Sreenivasan, K.R.: High-Reynolds-number
+simulation of turbulent mixing. Phys. Fluids 17(8), 081703 (2005)
+[85] Kumar, A., Chatterjee, A.G., Verma, M.K.: Energy spectrum of
+buoyancy-driven turbulence. Phys. Rev. E 90(2), 023016 (2014)
+[86] Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Oxford
+University Press, Clarendon (1961)
+[87] Kraichnan, R.H.: Turbulent thermal convection at arbitrary prandtl
+number. Phys. Fluids 5(11), 1374–1389 (1962)
+[88] Verma, M.K., Ayyer, A., Debliquy, O., Kumar, S., Chandra, A.V.: Local
+shell-to-shell energy transfer via nonlocal interactions in fluid turbulence.
+Pramana-J. Phys. 65(2), 297–310 (2005)
+[89] Grossmann, S., Lohse, D.: Scaling in thermal convection: a unifying
+theory. J. Fluid Mech. 407, 27–56 (2000)
+[90] Niemela, J.J., Skrbek, L., Sreenivasan, K.R., Donnelly, R.J.: Turbulent
+convection at very high Rayleigh numbers. Nature 404, 837–840 (2000)
+[91] Shraiman, B.I., Siggia, E.D.: Heat transport in high-Rayleigh-number
+convection. Phys. Rev. A 42(6), 3650–3653 (1990)
+[92] Siggia, E.D.: High Rayleigh number convection. Annu. Rev. Fluid Mech.
+26(1), 137–168 (1994)
+
+Springer Nature 2021 LATEX template
+Turbulent Drag Reduction in MHD Turbulence
+51
+[93] Bhattacharya, S., Verma, M.K., Samtaney, R.: Prandtl number depen-
+dence of the small-scale properties in turbulent Rayleigh-B´enard convec-
+tion. Phys. Rev. Fluids 6, 063501 (2021)
+[94] Sreenivasan, K.R., Bershadskii, A., Niemela, J.J.: Mean wind and its
+reversal in thermal convection. Phys. Rev. E 65(5), 056306 (2002)
+[95] Sugiyama, K., Ni, R., Stevens, R.J.A.M., Chan, T.-S., Zhou, S.-Q., Xi,
+H.-D., Sun, C., Grossmann, S., Xia, K.-Q., Lohse, D.: Flow reversals in
+thermally driven turbulence. Phys. Rev. Lett. 105(3), 034503 (2010)
+[96] Chandra, M., Verma, M.K.: Dynamics and symmetries of flow reversals
+in turbulent convection. Phys. Rev. E 83, 067303 (2011)
+[97] Chandra, M., Verma, M.K.: Flow Reversals in Turbulent Convection via
+Vortex Reconnections. Phys. Rev. Lett. 110(11), 114503 (2013)
+[98] Verma, M.K., Ambhire, S.C., Pandey, A.: Flow reversals in turbulent
+convection with free-slip walls. Phys. Fluids 27(4), 047102 (2015)
+[99] Zhu, X., Mathai, V., Stevens, R.J.A.M., Verzicco, R., Lohse, D.: Tran-
+sition to the Ultimate Regime in Two-Dimensional Rayleigh-B´enard
+Convection. Phys. Rev. Lett. 120(14), 144502 (2018)
+[100] He, X., van Gils, D.P.M., Bodenschatz, E., Ahlers, G.: Logarithmic Spa-
+tial Variations and Universal Power Spectra of Temperature Fluctuations
+in Turbulent Rayleigh-B´enard Convection. Phys. Rev. Lett. 112(17),
+174501 (2014)
+[101] Verma, M.K., Mishra, P.K., Pandey, A., Paul, S.: Scalings of field corre-
+lations and heat transport in turbulent convection. Phys. Rev. E 85(1),
+016310 (2012)
+[102] He, X., Funfschilling, D., Nobach, H., Bodenschatz, E., Ahlers, G.: Tran-
+sition to the Ultimate State of Turbulent Rayleigh-B´enard Convection.
+Phys. Rev. Lett. 108(2), 024502 (2012)
+[103] Iyer, K.P., Scheel, J.D., Schumacher, J., Sreenivasan, K.R.: Classical 1/3
+scaling of convection holds up to ra = 1015. PNAS 117(14), 7594–7598
+(2020)
+[104] Roche, P.-E., Gauthier, F., Kaiser, R., Salort, J.: On the triggering of
+the ultimate regime of convection. New J. Phys. 12(8), 085014 (2010)
+[105] Lohse, D., Toschi, F.: Ultimate state of thermal convection. Phys. Rev.
+Lett. 90(3), 034502 (2003)
+[106] Mishra, P.K., Wahi, P., Verma, M.K.: Patterns and bifurcations in
+
+Springer Nature 2021 LATEX template
+52
+Turbulent Drag Reduction in MHD Turbulence
+low–Prandtl-number Rayleigh–B´enard convection. EPL 89(4), 44003
+(2010)
+
diff --git a/JNAzT4oBgHgl3EQfVPyV/content/tmp_files/load_file.txt b/JNAzT4oBgHgl3EQfVPyV/content/tmp_files/load_file.txt
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@@ -0,0 +1,1835 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf,len=1834
+page_content='Springer Nature 2021 LATEX template  Turbulent Drag Reduction in  Magnetohydrodynamic Turbulence and  Dynamo from Energy Flux Perspectives  Mahendra K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma1*, Manohar K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Sharma2  and Soumyadeep Chatterjee1  1*Department of physics, Indian institute of Technology Kanpur,  Kalyanpur, Kanpur, 208016, Uttar Pradesh, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2Department of Mathematics, University of Grenoble Aples ,  Gires, Grenoble, 38000, Grenoble, France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Corresponding author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E-mail(s): mkv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='iitk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='in;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Contributing authors:  manohar-kumar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='sharma@univ-grenoble-aples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='fr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  soumyade@iitk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='in;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Abstract  In this review, we describe turbulent drag reduction in a variety of  flows using a universal framework of energy flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In a turbulent flow  with dilute polymers and magnetic field, the kinetic energy injected  at large scales cascades to the velocity field at intermediate scales,  as well as to the polymers and magnetic field at all scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Conse-  quently, the kinetic energy flux, Πu(k), is suppressed in comparison  to the pure hydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We argue that the suppression  of Πu(k) is an important factor in the reduction of the inertial force  ⟨u · ∇u⟩ and turbulent drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This feature of turbulent drag reduction  is observed in polymeric, magnetohydrodynamic, quasi-static magne-  tohydrodynamic, and stably-stratified turbulence, and in dynamos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In  addition, it is shown that turbulent drag reduction in thermal con-  vection is due to the smooth thermal plates, similar to the turbulent  drag reduction over bluff bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In all these flows, turbulent drag  reduction often leads to a strong large-scale velocity in the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Keywords: Turbulent drag reduction, Magnetohydrodynamic turbulence,  Energy flux, Dynamo, Quasi-static magnetohydrodynamics, Turbulent thernal  convection  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01281v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='plasm-ph]  29 Dec 2022  Springer Nature 2021 LATEX template  2  Turbulent Drag Reduction in MHD Turbulence  1 Introduction  It has been observed that an introduction of polymers and magnetic field  to a turbulent flow reduces turbulent drag [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Turbulence drag is also  suppressed over bluff bodies with particular shapes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', aerofoils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This phe-  nomena, known as turbulent drag reduction, or TDR in short, depends on  many factors—properties of the boundaries and fluids, bulk turbulence, nature  of polymers, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this review, using energy flux, we describe a univer-  sal framework to explain TDR in polymeric, magnetohydrodynamic (MHD),  quasi-static MHD, and stably-stratified turbulence, and in dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  A pipe flow exhibits viscous drag at small Reynolds numbers, but it experi-  ences turbulent drag at large Reynolds numbers [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It has been observed  that an introduction of small amount of polymers in the flow suppresses the  turbulent drag up to 80% [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 1, we illustrate the mean normal-  ized velocity profiles (V +) as a function of normalized distance from the wall  (y+) in a hydrodynamic (HD) flow with and without polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The bottom  curve with green dots represents V + for pure HD turbulence and it exhibits  K´arman’s log layer, whereas the chained curve with red squares is for polymeric  turbulence and it shows TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' L’vov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [6] constructed a phenomenological  model for the maximum drag reduction asymptote (represented by the chained  curve in the figure) that matches with numerical and experimental data quite  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Study of TDR is particularly important due to its wide-ranging practical  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For example, firefighters mix polymers in water to increase the  range of fire-hoses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Also, polymers are used to increase the flow rates in oil  pipe, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 1 For a wall-bound flow, mean normalized velocity profiles (V +) as a function of  the normalized distance from the wall (y+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The bottom curve with green dots is for pure  HD turbulence, whereas the chained-curve with red squares is for the polymeric turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  From L’vov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Newtonian, Warholic, 1999  MDR, Rollin, 1972  Rudd, 1969  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Rollin, 1972  DNS, De Angelis, 2003  MDR, our theory  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Newtonian, our theory  30-  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Newtonian plugs  X+  20  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  0  10  100  +  ySpringer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  3  Bluff bodies too experience viscous and turbulent drag at small and large  Reynolds numbers respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Turbulent drag over bluff bodies depend on  the surface properties, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', smoothness and curvature [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Keeping these  factors in mind, airplanes, automobiles, missiles, and ships are designed to  minimize turbulent drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In a recent paper, Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] argued that TDR occurs in MHD  turbulence analogous to TDR in turbulent flows with dilute polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They  showed that the kinetic energy (KE) flux (Πu(k)) is suppressed in polymeric  and MHD turbulence due to the transfer of energy from the velocity field  to polymers and magnetic field respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The energy fluxes in polymeric  and MHD turbulence have been studied in a number of earlier works [1, 11,  16–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It was argued that the turbulent drag and the nonlinearity ⟨u · ∇u⟩  are proportional to Πu(k)/U, where u is the velocity field, U is the large-  scale velocity, and ⟨.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='⟩ represents averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus, Verma et al.’s [11] formalism  provides a general framework for TDR in variety of flows, including polymeric  and MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  An introduction of polymers or magnetic field in a turbulent flow enhances  the mean flow, but suppresses ⟨u · ∇u⟩ [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] observed the  above phenomena in a shell model of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that ⟨u · ∇u⟩  and Πu(k) depend critically on the phase relations between the Fourier modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] argued that the velocity correlations in polymeric and MHD  turbulence are enhanced compared to pure HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These correlations  lead to suppressed ⟨u · ∇u⟩ and Πu(k) in spite of amplification of U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus,  TDR, energy flux, and enhancement of U are related to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Based on past results, Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] argued for TDR in quasi-static  MHD (QSMHD) turbulence [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The Joule dissipation suppresses Πu(k) at  all wavenumbers [20–23], and hence Πu(k) for QSMHD turbulence is lower than  the corresponding flux for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, large-scale U increases  with the increase of interaction parameter, thus indicating TDR in QSMHD  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Generation of magnetic field in astrophysical objects, such as planets, stars,  and galaxies, are explained using dynamo mechanism [24–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Here, magnetic  field grows and saturates at some level due to the self-induced currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the  present review, we discuss TDR in dynamo using the energy flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Based on  earlier dynamo simulations (e,g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', [27, 28]), we show that the fluctuations in the  velocity and magnetic fields are suppressed when a large-scale magnetic field  emerges in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This feature signals TDR in dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Planetary and stellar atmospheres often exhibit stably stratified turbu-  lence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In such flows, lighter fluid is above the heavier fluid with gravity acting  downwards [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The KE flux in stably stratified turbulence is suppressed,  as in polymeric and MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Based on these observations, we argue  for TDR in stably stratified turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Researchers have reported that compared to HD turbulence, viscous dissi-  pation rate (ϵu) and thermal dissipation rate (ϵT ) are suppressed in turbulent  thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For example, Pandey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [31] and Bhattacharya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  4  Turbulent Drag Reduction in MHD Turbulence  [32] showed that ϵu ∼ (U 3/d)Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2 and ϵT ∼ (U(∆T)2/d)Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2, where ∆T  is the temperature difference between the top and bottom thermal plates sep-  arated by distance d, and Ra is the Rayleigh number, which is the ratio of  buoyancy and diffusion in thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, Pandey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [31]  observed that ⟨u · ∇u⟩ /(Ud/ν) ≈ ReRa−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='14, where Re is the Reynolds num-  ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus, nonlinearity is suppressed in turbulent thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this  review, we relate the above suppression of nonlinearity and dissipation rates  to TDR over bluff bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It has been argued that TDR in turbulent convec-  tion arises due to large-scale circulation (LSC) over thermal plates, and that  the smooth thermal plates affect bulk turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Thus, KE flux and ⟨u · ∇u⟩ provide valuable insights into the physics of  TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' TDR is also related to the enhanced correlations in the velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The present review focusses on these aspects for a variety of flows—polymeric,  MHD, QSMHD, and stably-stratified turbulence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' dynamo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and turbulent ther-  mal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Here, we focus on bulk turbulence, and avoid discussion on  boundary layers and smooth surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The latter aspects are covered in many  books and reviews, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', [3–5, 10, 14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We remark that the energy flux is a  well known quantity in turbulence literature [33–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, the connection  between the energy flux and TDR has been brought out only recently [11], and  the number of papers highlighting the above connection is relatively limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The increase in the mean velocity field during TDR is related to relami-  narization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Narasimha and Sreenivasan [38] studied relaminarization in stably  stratified turbulence, rotating turbulence, and thermal convection, and related  it to the reduction in ⟨u · ∇u⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus, the mechanism of relaminarization is  intimately related to the TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  An outline of this review is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Section 2 we briefly review viscous  and turbulent drag in a pipe flow and over a bluff body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Section 3 we describe  a general framework for TDR using energy fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Section 4 we review the  energy fluxes in a turbulent flow with dilute polymers and relate it to TDR  in the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Section 5 contains a framework of TDR in MHD turbulence via  energy fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Section 6 we describe signatures of TDR in direct numerical  simulations (DNS) and shell models of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Sections 7 and 8  deal with TDR in dynamos and in QSMHD turbulence respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Section  9 we describe TDR in stably stratified turbulence and in turbulent thermal  convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We conclude in Section 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2 Viscous and turbulent drag in hydrodynamic  turbulence  The equations for incompressible hydrodynamics are  ∂u  ∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fext,  (1)  ∇ · u = 0,  (2)  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  5  (a)  (b)  (c)  d  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 2 Schematic illustrations of (a) pipe flow and (b) its viscous flow profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (c) The profile  of the mean velocity in a turbulent pipe flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  where u, p are respectively the velocity and pressure fields;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ρ is the density  which is assumed to be unity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ν is the kinematic viscosity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and Fext is the  external force employed at large scales that helps maintain a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' An  important parameter for the fluid flows is Reynolds number, which is  Re = UL  ν ,  (3)  where L and U are the large-scale length and velocity respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For homo-  geneous and isotropic turbulence, Re is the ratio of the nonlinear term and  the viscous term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, in more complex flows like polymeric turbulence,  MHD turbulence, and turbulent convection,  Nonlinear term  Viscous term  = fRe,  (4)  where the prefactor f may differ from unity and may provide a signature  for TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For example, f ≈ Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2 for turbulent convection, where Ra is  the Rayleigh number [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We expect complex f for MHD and polymeric  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  A fluid moving in a pipe of radius d experiences drag (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' At low  Reynolds numbers, this drag is called viscous drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this case, under steady  state, the pressure gradient, −∇(p/ρ), which can be treated as Fext, matches  with the viscous term, ν∇2u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, we estimate the viscous drag as [13, 39]  Fdrag ≈ νU  d2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (5)  The proportionality constant is of the order of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' At large Reynolds  number, the nonlinear term becomes significant, and hence [12–15],  Fdrag ≈ U 2  d + νU  d2 ,  (6)  r=a  ZSpringer Nature 2021 LATEX template  6  Turbulent Drag Reduction in MHD Turbulence  apart from the proportionality constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the above formula, U 2/d is the  turbulent drag that is larger than the viscous drag by a factor of Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clearly,  the turbulent drag dominates the viscous drag at large Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that the above  drag force is in the units of force per unit mass;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' we will follow this convention  throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  A related problem is the frictional force experienced by a bluff body in a  flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Analogous to a pipe flow, a bluff body experiences viscous drag at small  Re, but turbulent drag at large Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In literature, the drag coefficient is defined  as [13, 14]  Cd = Fdrag  ρU 2A,  (7)  where A is the area of the bluff body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  It is customary to describe fluid flows in Fourier space, where Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (1, 2)  get transformed to [35–37]  d  dtu(k) = −i  �  p  {k · u(q)}u(p) − ikp(k) − νk2u(k) + Fext(k),  (8)  where k, p, q are the wavenumbers with k = p + q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and u(k), u(p), u(q) are  the corresponding velocity Fourier modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' An equation for the modal energy  Eu(k) = |u(k)|2/2 is [35–37, 40]  d  dtEu(k) = Tu(k) + Fext(k) − Du(k),  (9)  where  Tu(k) =  �  p  ℑ [{k · u(q)}{u(p) · u∗(k)}] ,  (10)  Fext(k) = ℜ[Fext(k) · u∗(k)],  (11)  Du(k) = 2νk2Eu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (12)  Here, ℜ, ℑ stand respectively for the real and imaginary parts of the argument;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Tu(k) is the nonlinear energy transfer to the mode u(k);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Du(k) is the energy  dissipation rate at wavenumber k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and Fext(k) is the KE injection rate to u(k)  by the external force Fext(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We assume that the external force injects KE at large scales, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', in a  wavenumber band (0, kf) with small kf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, the total KE injection rate,  ϵinj, is  � kf  0  dkFext(k) ≈ ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (13)  This injected KE cascades to intermediate and small scales as KE flux, Πu(K),  which is defined as the cumulative KE transfer rate from the velocity modes  inside the sphere of radius K to velocity modes outside the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 3,  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  7  ky  Force  Inertial  Dissip-  ative  Πu(K)  u<  u>  Πu(K)  u>  K F  Du  Du  kx  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 3 An illustration of KE flux Πu(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' KE is injected into the small red sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Πu(K)  is constant in the inertial range, and it is dissipated at small scales with a dissipation rate  of Du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  we illustrate the inner and outer modes as u< and u> respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In terms  of Fourier modes, the above flux is [16, 37, 41, 42]  Πu(K) = −  �  k≤K  Tu(k) =  �  p≤K  �  k>K  ℑ [{k · u(q)}{u(p) · u∗(k)}] ,  (14)  where q = k − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The above energy flux is dissipated in the dissipative range, with the total  viscous dissipation rate as  ϵu =  �  dkDu(k) =  �  dk2νk2Eu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (15)  At large Reynolds numbers, it has been shown that in the inertial range [33,  35, 36, 43, 44],  Πu(k) ≈ ϵinj ≈ ϵu ≈ U 3  d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (16)  That is, the inertial-range energy flux, the viscous dissipation rate, and the  energy injection rate are all equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that in the inertial range, Πu(k) = ϵinj  due to absence of external force and negligible viscous dissipation [33, 37, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We show later that the magnetic field and polymers, as well as smooth walls,  suppress the energy flux relative to ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We argue that this feature leads to  TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  8  Turbulent Drag Reduction in MHD Turbulence  For a steady state, an integration of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (1) over a bluff body yields the  following formula for the drag force:  Fdrag =  �  dr  �  (u · ∇)u + ∇(p/ρ) − ν∇2u  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (17)  The viscous force dominates the inertial term near the surface of a bluff body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Hence, for bluff bodies, the inertial term of the above equation is ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Prandtl [15, 45] was first to compute Fdrag for a bluff body as a sum of viscous  drag and adverse pressure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The drag forces for a cylinder and aerofoil  are computed in this manner [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Computation of Fdrag for a pipe flow is also quite complex involving many  factors—walls, fluid properties, bulk turbulence, Reynolds number, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the  present review, we focus on the turbulent drag in bulk where we can ignore  the effects of walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The above simplification enables us to compute turbulent  drag in many diverse flows—polymeric turbulence, MHD turbulence, dynamo,  liquid metals—using a common framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We focus on a turbulent flow within a periodic box for which  �  dr∇(p/ρ) =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' By ignoring the viscous drag, we deduce the turbulent drag as (see Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (1,  17))  Fdrag = Fext =  �  dr [(u · ∇)u] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (18)  Since the external force is active at large scales, under steady state,  ⟨Fdrag⟩LS ≈ ⟨|(u · ∇)u|⟩LS ≈ ⟨Fext⟩ ,  (19)  where ⟨.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='⟩LS represents ensemble averaging over large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' To estimate  ⟨Fdrag⟩LS, we perform a dot product of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (1) with u and integrate it over a  wavenumber sphere of radius kf (forcing wavenumber band) that leads to  �  LS  dr[Fext · u] =  �  LS  dr[Fdrag · u] = f1UFdrag,  (20)  with f1 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Under steady state, using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (9,14) we deduce that  �  LS  dr[Fext · u] = ⟨|[(u · ∇)u] · u|⟩LS = −  � kf  0  Tu(k′)dk′ = Πu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (21)  Therefore,  UFdrag ≈ Πu ≈ U 3  d ≈ ϵinj,  (22)  or  Fdrag ≈ Πu  U ≈ U 2  d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (23)  Note that the viscous dissipation can be ignored at large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  It has been observed that polymers and magnetic field suppress turbulent  drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We detail these phenomena in the subsequent sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  9  3 General framework for TDR using energy flux  In this section, we describe a general framework for TDR in a turbulent flow  with a secondary field B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' At present, for convenience, we assume B to be a  vector, however, it could also be a scalar or a tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The present formalism is  taken from Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The equations for the velocity and secondary fields are [11, 29, 37, 46]:  ∂u  ∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fu(u, B) + Fext,  (24)  ∂B  ∂t + (u · ∇)B = η∇2B + FB(u, B),  (25)  ∇ · u = 0,  (26)  where u, p are the velocity and pressure fields respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ρ is the density  which is assumed to be unity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ν is the kinematic viscosity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' η is the diffusion  coefficient for B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and Fu and FB are the force fields acting on u and B respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that Fu and FB typically represent interactions between u and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The external field Fext is employed at large scales of the velocity field to  maintain a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (24) we derive the following equation for the KE density u2/2  (with ρ = 1):  ∂  ∂t  u2  2 + ∇ ·  �u2  2 u  �  = −∇ · (pu) + [Fu + Fext] · u − νu · ∇2u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (27)  In Fourier space, the equation for the modal KE, Eu(k) = |u(k)|2/2, is  d  dtEu(k) = Tu(k) + Fu(k) + Fext(k) − Du(k),  (28)  where  Tu(k) =  �  p  ℑ [{k · u(q)}{u(p) · u∗(k)}] ,  (29)  Fu(k) = ℜ[Fu(k) · u∗(k)],  (30)  Fext(k) = ℜ[Fext(k) · u∗(k)],  (31)  Du(k) = −2νk2Eu(k),  (32)  with q = k − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We sum Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (28) over the u modes of the wavenumber sphere  of radius K that yields [37, 40]:  d  dt  �  k≤K  Eu(k) =  �  k≤K  Tu(k) +  �  k≤K  Fu(k) +  �  k≤K  Fext(k) −  �  k≤K  Du(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (33)  Springer Nature 2021 LATEX template  10  Turbulent Drag Reduction in MHD Turbulence  A physical interpretation of the terms in the right-hand side of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (33) are  as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' �  k≤K Tu(k) is the net KE transfer from the u modes outside the sphere to  the u modes inside the sphere due to the nonlinearity (u·∇)u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Equivalently,  �  k≤K Tu(k) = −Πu(K) of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' �  k≤K Fu(k) is the total energy transfer rate by the interaction force Fu(k)  to u(k) modes inside the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' �  k≤K Fext(k) is the net KE injected by the external force Fext (red sphere  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For K > kf, �  k≤K Fext(k) = ϵinj because Fext = 0 beyond  k = kf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The u< modes lose energy to u> and B modes via nonlinear interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The term − �  k≤K Fu(k) of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (33) represents the net energy transfer from  the u< modes (those inside the sphere) to all the B modes (B< and B>) via  the interaction force Fu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We define the corresponding flux ΠB(K) as  ΠB(K) = −  �  k≤K  Fu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (34)  Thus, u< modes lose energy to u> modes, as well as to B modes, via nonlinear  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, u< modes lose energy via viscous dissipation, which  is the last term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, under steady state, the kinetic energy  injected by Fext must match (statistically) with the sum of Πu(K), ΠB(K),  and the viscous dissipation rate [37, 40]1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' That is,  Πu(K) + ΠB(K) +  �  k≤K  Du(k) = ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (35)  In the inertial range where Du(k) ≈ 0, we obtain  Πu(K) + ΠB(K) ≈ ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (36)  In later sections, we show that ΠB(k) > 0 in MHD, QSMHD, polymeric,  and stably-stratified turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (36) we deduce that for  the same injection rate ϵinj, Πu(k) in the mixture (with field B) is lower than  that in HD turbulence, that is,  Πu,mix < Πu,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (37)  Now we estimate the drag force in the presence of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As discussed below,  there are several ways to estimate this drag force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  1In this paper we do not discuss the energetics of B field because TDR is related to the energy  fluxes associated with the velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  11  Πu(K) + ΠB(K) = ϵinj  Πu(K)  ΠB(K)  ΠB(K)  B<  u<  u>  B>  u>  B>  Πu(K)  ΠB(K)  K F  K  Du  Du  DB  DB  kx  kx  ky  ky  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 4 The external force injects KE into the small red sphere with the rate of ϵint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Πu(K)  is the KE flux for the velocity wavenumber sphere of radius K (yellow sphere), and ΠB(K) is  the net energy transfer from u modes inside the sphere to all the B modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The energy flux  Πu(K) is dissipated with dissipation rates Du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For small wavenumbers and inertial range,  Πu(K) + ΠB(K) ≈ ϵint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As discussed in Section 2, we average Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (24) over small wavenumbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Using  �  LS  dr[Fext · u] =  �  LS  dr[Fdrag · u] = f2UFdrag,mix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (38)  Under steady state, using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (9,14) we deduce that  �  LS  dr[Fext · u] = −  � kf  0  [Tu(k′) + Fu(k′)]dk′ = Πu(k) + ΠB(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (39)  Hence,  Fdrag,mix ≈ Πu + ΠB  f2U  ≈ ϵinj  f2U .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (40)  It is observed that in a mixture, U is typically larger than that in HD  turbulence [5, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Computation of f2 may be quite complex, and it is  difficult to compare f1 and f2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Still, considering Umix > UHD, we expect  Fdrag,mix to be weaker than the corresponding drag in HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This  is the origin of TDR in the bulk when B field (polymers or magnetic field)  is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Considering the uncertainties in f2, it is proposed that turbulent drag is  proportional to (u · ∇)u [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For MHD turbulence, the force Fu, which is  the Lorentz force, may be treated separately, and (u·∇)u may be considered  Springer Nature 2021 LATEX template  12  Turbulent Drag Reduction in MHD Turbulence  as the drag force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This assumption simplifies the calculation with  Fdrag,mix ≈ Πu  U .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (41)  In a typical scenario, Πu,mix < Πu,HD, and Umix > UHD [5, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore,  we expect that  Fdrag,mix < Fdrag,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (42)  Thus, turbulent drag is reduced in the presence of a secondary fields, such  as magnetic field and polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] adopted this scheme for  the computation of turbulent drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We will use this scheme throughout the  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 5, we present a schematic diagram illustrating TDR in a pipe flow  and in bulk turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' An introduction of polymers in a pipe flow weakens the  fluctuations and enhances the mean flow (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 5(a,b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Similarly, in bulk  turbulence, polymers and magnetic field can induce strong large-scale U and  weaken the fluctuations in comparison to HD turbulence (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 5(c,d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 5 (a) Mean velocity profile (D profile) and fluctuations (green arrows) in a pipe flow  without polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (b) With dilute polymers, the mean flow is enhanced, but the fluctuations  are suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (c) Velocity fluctuations in HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (d) With polymers and magnetic  field, the fluctuations (green arrows) are suppressed, but the large-scale U (black arrows) is  enhanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  13  We propose the following drag coefficients to quantify TDR in the bulk:  ¯Cd1 = ⟨Πu⟩  U 3/L,  (43)  ¯Cd2 = ⟨|(u · ∇)u|⟩  U 2/L  ,  (44)  where L is the integral length scale, and U is the large-scale velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We  obtain ¯Cd1 ≈ 1 and ¯Cd2 ≈ 1 for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, ¯Cd1 and ¯Cd2 for  a mixture are smaller than those for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In subsequent sections,  we will compute the above drag coefficients for a variety of flows, but with an  emphasis on MHD and QSMHD turbulence, and dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the next section, we provide a brief introduction to TDR in a turbulent  flow with dilute polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  4 TDR in flows with dilute polymers via  energy flux  An introduction of small amount of polymers in a turbulent flow suppresses  turbulent drag [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As discussed in Section 1, TDR in polymeric turbulence  depends on the boundaries, bulk turbulence, properties of fluids and polymers,  anisotropy, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, in this paper we focus on the TDR due to suppression  of KE flux in the presence of polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For detailed discussions on TDR due  to polymers, refer to the references [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  One of the popular models for polymers is finitely extensible nonlin-  ear elastic-Peterlin model (FENE-P) [9, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this model, the governing  equations for the velocity field u and configuration tensor C are [9, 46, 48]  ∂ui  ∂t + uj∂jui = −∂ip/ρ + ν∂jjui + µ  τp  ∂j(fCij) + Fext,i,  (45)  ∂Cij  ∂t + ul∂lCij = Cil∂luj + Cjl∂lui + 1  τp  [fCij − δij],  (46)  ∂iui = 0,  (47)  where ρ is the mean density of the solvent, ν is the kinematic viscosity, µ is an  additional viscosity parameter, τp is the polymer relaxation time, and f is the  renormalized Peterlin’s function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the above equations, the following forces  are associated with u and C (apart from constants) [3, 10, 37, 40, 47]:  Fu,i = ∂j(fCij),  (48)  Fu,i(k) =  �  p  [ikjf(q)Cij(p)] ,  (49)  Fu(k) = ℜ[Fu,i(k)u∗  i (k)] = −c1  �  p  ℑ [kjf(q)Cij(p)u∗  i (k)] ,  (50)  Springer Nature 2021 LATEX template  14  Turbulent Drag Reduction in MHD Turbulence  ∫  k  0  d k′  u  ∫  k  0  d k′  u<  ζ  ′  ′  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 6 For a polymeric flow with De = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2, the energy fluxes Πu(k) and ΠC(k) normalized  with the KE injection rate P, and dissipation rate Du(k) [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The injected KE, P, is  transferred to u> and C as Πu(k) and ΠC(k) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The rest of the injected energy is  dissipated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Adapted from a figure from Valente et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with the permission of  AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  where q = k − p, and c1 is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that the field C replaces B of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (24-26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Using the above equations, we derive the energy flux ΠC(K), which is  the net energy transfer rate from u< to C, as [37, 40]  ΠC(K) =  �  k≤K  �  p  −c1ℑ [kjf(q)Cij(p)u∗  i (k)]  (51)  with q = k − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Valente et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [18, 19] analysed the energy fluxes Πu(k) and ΠC(k) in a  turbulent flow with dilute polymers and observed that ΠC(k) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' One of  their figures illustrating Πu(k) and ΠC(k) is reproduced in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 6 [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As  shown in the figure, for De = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2, ΠC(k)/P (P = total injected power) peaks  at approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9 when kη ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1, where η is Kolmogorov’s wavenumber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  However, Πu(k)/P remains less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 for all kη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Valente et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [18, 19] also  reported that Πu(k) and ΠC(k) depend on the Deborah number, De, which  is the ratio of the relaxation time scale of the polymer and the characteristic  time scale for the energy cascade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Notably, ΠC(k) is maximum when De ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Thus, Valente et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [18, 19] showed that Πu(k) is reduced significantly from  ϵinj due to the energy transfer from the velocity field to polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' That is,  Πu(k) < ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  a  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  F(k)/P  I[pl(k)/P  A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='7  D(k)/P  / I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  / /  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  H(k)/P  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='05  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  kn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  1  2Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  15  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 7 KE spectra for pure HD turbulence (dashed line with circle) and polymeric turbu-  lence (solid line with squares).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' At small wavenumbers, Eu(k) with polymers is larger than  that without polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Benzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with permission from APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Benzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [7] and Ray and Vincenzi [49] showed that during TDR, the  large-scale KE is enhanced compared to HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Figure 7 illustrates  the energy spectra of Benzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' for pure HD and polymeric turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In  the figure we observe that at small wavenumbers, Eu(k) is larger for polymeric  turbulence than that for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, we deduce that large-scale U  is enhanced in the presence of polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thais et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [50] and Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [51]  arrived at similar conclusions using direct numerical simulation of polymeric  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Based on these observations, we deduce that  Πu,Polymeric < Πu,HD  and  UPolymeric > UHD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (52)  Therefore, using Fdrag = Πu/U, we deduce that  Fdrag,Polymeric < Fdrag,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (53)  Thus, reduction in KE flux leads to a decrease in nonlinearity, and hence, TDR  in polymeric turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  L’vov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [52] and others have observed TDR in flows with bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In a bubbly flow, the KE is transferred to the elastic energy of the bubbles  that leads to TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We also remark that in the laminar regime, the polymers  induce additional drag via the term µ∂j(fCij)/τp of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, polymers  enhance the drag in the viscous limit [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Also note that in the present review,  we focus on TDR in bulk turbulence and have avoided discussions on boundary  layers, anisotropy, effects of polymer concentration, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Earlier, Fouxon and Lebedev [46] had related the equations of a turbulent  flow with dilute polymers to those of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the next section, we  6  8  L  10  2  12  Q  14  16  18  0  2  4  6  8  10  nSpringer Nature 2021 LATEX template  16  Turbulent Drag Reduction in MHD Turbulence  will show that the energy transfers in MHD turbulence are similar to those in  polymeric turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  5 TDR in MHD turbulence via energy flux  Magnetofluid is quasi-neutral and highly conducting charged fluid, and its  dynamics is described by magnetohydrodynamics (MHD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Our universe is filled  with magnetofluids, with prime examples being solar wind, solar corona, stellar  convection zone, interstellar medium, and intergalactic medium [53–55] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The equations for incompressible MHD are [53, 54]  ∂u  ∂t + (u · ∇)u = −∇(p/ρ) + ν∇2u + Fu(B, B) + Fext,  (54)  ∂B  ∂t + (u · ∇)B = η∇2B + FB(B, u),  (55)  ∇ · u = 0,  (56)  ∇ · B = 0,  (57)  where u, B are the velocity and magnetic fields respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' p is the total  (thermal + magnetic) pressure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ρ is the density which is assumed to be unity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  ν is the kinematic viscosity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' η is the magnetic diffusivity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fext is the external  force employed at large scales;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and  Fu = (B · ∇)B,  (58)  FB = (B · ∇)u  (59)  represent respectively the Lorentz force and the stretching of the magnetic  field by the velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that Fu and FB induce energy exchange among  u and B modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the above equations, the magnetic field B is in velocity  units, which is achieved by Bcgs → Bcgs/√4πρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The evolution equation for the modal kinetic energy Eu(k) = |u(k)|2/2  is [16, 36, 37, 40–42, 56]  d  dtEu(k) = Tu(k) + Fu(k) + Fext(k) − Du(k),  (60)  where  Tu(k) =  �  p  ℑ [{k · u(q)}{u(p) · u∗(k)}] ,  (61)  Fu(k) = ℜ[Fu(k) · u∗(k)] =  �  p  −ℑ [{k · B(q)}{B(p) · u∗(k)}] ,  (62)  Fext(k) = ℜ[Fext(k) · u∗(k)],  (63)  Du(k) = 2νk2Eu(k),  (64)  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  17  with q = k − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Summing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (60) over the modes of the wavenumber sphere  of radius K yields [30, 48, 56]:  − d  dt  �  k≤K  Eu(k) = −  �  k≤K  Tu(k) −  �  k≤K  Fu(k) −  �  k≤K  Fext(k) +  �  k≤K  Du(k)  = Πu(K) + ΠB(K) − ϵinj + total viscous dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (65)  Note that  ΠB(K) = −  �  k≤K  Fu(k) =  �  k≤K  �  p  ℑ [{k · B(q)}{B(p) · u∗(k)}] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (66)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 4, we illustrate ΠB(K) using the red arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Under a steady state (dEu(k)/dt = 0),  Πu(K) + ΠB(K) +  �  k≤K  Du(k) = ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (67)  In the inertial range where Du(k) ≈ 0, we obtain  Πu(K) + ΠB(K) ≈ ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (68)  Following similar lines of arguments as in Section 3, we estimate the turbulent  drag in MHD turbulence as  ⟨Fdrag,MHD⟩ ≈ ⟨|(u · ∇)u|⟩LS ≈ Πu  U ≈ ϵinj − ΠB  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (69)  Researchers have studied the energy fluxes Πu and ΠB in detail for various  combinations of parameters—forcing functions, boundary condition, ν and η  (or their ratio Pm = ν/η, which is called the magnetic Prandtl number).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For  example, Dar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [16], Debliquy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [57], Mininni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [17], and Kumar  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [58, 59] computed the fluxes Πu and ΠB using numerical simulations  and observed that ΠB > 0 on most occasions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Using numerical simulations,  Mininni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [17] showed that Fu(k) < 0, and hence ΠB(k) > 0 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Hence, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (69) we deduce that  Πu,MHD < Πu,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (70)  That is, the KE flux in MHD turbulence is lower than the corresponding flux  in HD turbulence (without magnetic field).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, the speed U may  increase under the inclusion of magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, using Fdrag = Πu/U,  we deduce that  Fdrag,MHD < Fdrag,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (71)  In this next section, we will explore whether the above inequality holds in  numerical simulations of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  18  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 8  Numerically computed Fu(k) = ℜ[[J × B](k)·u∗(k)] by Mininni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clearly,  Fu(k) > 0, and hence ΠB(K) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Mininni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission  from ApJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  6 Numerical verification of TDR in MHD  turbulence  Many researchers have simulated MHD turbulence, but TDR in MHD turbu-  lence has not been explored in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this section, we will present numerical  results on TDR from direct numerical simulations (DNS) and shell models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  MHD turbulence exhibits six energy fluxes that are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These  fluxes represent energy transfers from u< and u> to b< and b> [16, 37, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  However, as we discussed in Section 3, the relevant fluxes for TDR are Πu and  ΠB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Also, TDR takes place at large scales, hence, we consider energy fluxes  from small wavenumber spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In terms of the fluxes of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 9,  Πu(K) = Πu<  u>(K),  (72)  ΠB(K) = Πu<  b< (K) + Πu<  b> (K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (73)  As discussed in Section 5, ΠB > 0 [16, 17, 57–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, Πu < ϵinj that leads  to TDR in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this section, we will report the energy fluxes  and ⟨|(u · ∇)u|⟩ for HD and MHD turbulence from DNS and shell models, and  compare them to quantify TDR in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  It is important to note that the velocity field receives parts of ΠB via the  energy fluxes Πb<  u> and Πb>  u>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, these transfers are effective at interme-  diate and large wavenumbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this review we focus on small wavenumbers,  hence we can ignore these energy transfers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the following subsection, we  discuss TDR in DNS of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='25  t=344  t=352  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='20  (jxB)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='Vk  t=360  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='15  t=368  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='05  2  4  6  8  10  12  14Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  19  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 9 Six energy fluxes of MHD turbulence: Πu<  u>, Πu<  b< , Πu<  b> , Πb<  b>, Πb<  u>, Πu>  b> .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From  Verma [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from Verma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 TDR in direct numerical simulation of MHD  turbulence  We solve the nondimensional MHD equations (54-57) using pseudo-spectral  code TARANG [61–63] in a cubic periodic box of size (2π)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We nondimension-  alize velocity, length, and time using the initial rms speed (U0), box size (2π),  and the initial eddy turnover time (2π/U0) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We employ the fourth-  order Runge-Kutta (RK4) scheme for time marching;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Courant-Friedrich-Lewis  (CFL) condition for computing the time step ∆t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and 2/3 rule for dealising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We perform our simulations on a 2563 grid for Pm = 1/3, 1, 10/3 (the details  in the following discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The mean magnetic field B0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that the  2563 grid resolution is sufficient for computing the large-scale Πu, ΠB, and  ⟨u · ∇u⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, the low grid resolution helps us carry out simulations  for many eddy turnover times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  For the initial condition, we employ random velocity and magnetic fields  at all wavenumbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For creating such fields, it is convenient to employ Craya-  Herring basis [64, 65], whose basis vectors for wavenumber k are  ˆe3(k) = ˆk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  ˆe1(k) = (ˆk × ˆn)/|ˆk × ˆn|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  ˆe2(k) = ˆk × ˆe1(k)  (74)  with ˆn along any arbitrary direction, and ˆk as the unit vector along k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We  choose 3D incompressible flow, hence,  u(k) = u1(k)ˆe1(k) + u2(k)ˆe2(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (75)  +y  Fext(k)  <n  Eu  (0x)≤nII  ur  II(k 0)  II(ko)  b<  Ib%(ko)  x  b>  EbSpringer Nature 2021 LATEX template  20  Turbulent Drag Reduction in MHD Turbulence  For random initial velocity with the total kinetic energy as Eu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' we employ  u1(k) =  �  (Eu/2N 3) i (exp(iφ1(k)) − exp(iφ2(k))) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (76)  u2(k) =  �  (Eu/2N 3) (exp(iφ1(k)) + exp(iφ2(k))) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (77)  where N 3 is the total number of modes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and the phases φ1(k) and φ2(k) are  chosen randomly from uniform distribution in the band [0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 2π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The above  formulas ensure that the kinetic helicity remains zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We employ Eu = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  for our simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' A similar scheme is adopted for the random magnetic field  with the initial magnetic energy as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We carry out the above run for ν =  η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, or Pm = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We employ random force to the velocity modes in a wavenumber shell (2, 3),  denoted by kf = 2, so as to achieve a steady state [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The kinetic-energy  injection rate ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We carry out the simulation till 29 eddy turnover  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note, however, that the flow reaches a steady state in approximately 15  eddy turnover times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  At the end of the above simulation, we perform four independent simula-  tions given below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We take the final state of the above run as the initial state  (t = 0) for the following simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' MHD1: ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='03, and hence Pm = 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' MHD2: ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, and hence Pm = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is continuation of the  run described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' MHD3: ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='003, and hence Pm = 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' HD: ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01 with magnetic field turned off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We carry out the HD and MHD2 simulations till 40 eddy turnover times,  whereas MHD1 and MHD3 runs till 5 eddy turnover times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Subsequently, we  compare the energy fluxes and ⟨|(u · ∇)u|⟩ of the four runs after they have  reached their respective steady states that occur in several eddy turnover times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The Reynolds number (Re = UL/ν) for the steady state of the HD run is 457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  For the steady state of the MHD runs with Pm = 1/3, 1, and 10/3, Re = 413,  347, and 338 respectively, while Rm = 137, 347 and 1127 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 10 (left column), we exhibit the time series of KE of the HD run,  and as well as KE, magnetic energies (ME), and the total energies of the  three MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The corresponding dissipation rates are exhibited in the  right column of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As shown in the figures, all the runs reach steady  states after several eddy turnover times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The KE dissipation rate for the  HD run increases rapidly to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4, which is the KE injection rate (ϵinj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The  KE for the MHD runs with Pm = 1/3, 1, and 10/3 saturate respectively to  approximate values of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='65, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='47 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='41, but the respective magnetic energies  saturate at approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='07, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that energies for the MHD  runs exhibit significant fluctuations, however, the dissipation rates of the total  energy remain at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  21  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  E  (a): Pm = 1/3  Eu,HD  Eu,MHD  Eb,MHD  Eu,MHD + Eb,MHD  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  ϵ  (b): Pm = 1/3  ϵu,HD  ϵu,MHD  ϵb,MHD  ϵu,MHD + ϵb,MHD  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  E  (c): Pm = 1  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  ϵ  (d): Pm = 1  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  E  (e): Pm = 10/3  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='9  ϵ  (f): Pm = 10/3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 10 Left column: (a,c,e) Time series of KE of the HD run (dashed red curve);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and  KE (solid red curve), magnetic energies (solid green curve), and total energies (solid blue  curve) of the MHD runs for Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Right column: (b,d,f) Corresponding energy  dissipation rates with the same notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Now, we report the energy spectra for the velocity and magnetic fields for  a wavenumber k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Numerically, we compute them using  Eu(k) = 1  2  �  k−1<|k′|≤k  |u(k′)|2,  (78)  Eb(k) = 1  2  �  k−1<|k′|≤k  |b(k′)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (79)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 11, we exhibit Eu(k) and Eb(k) for the MHD runs, along with Eu(k)  for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These quantities are averaged over several time frames in the  steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe that Eu(k) for the HD run is larger than those for  the MHD runs, except at several small wavenumbers for Pm = 1/3 where  Eb(k) > Eu(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  22  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 11 (a,b,c) For MHD runs with Pm = 1/3, 1, 10/3, the KE spectra (solid red curve)  and the magnetic energy spectra (solid green curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We also exhibit the plots of the KE  spectra of the HD run (dashed red curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Further, for the HD and MHD runs, we report the large-scale velocity U,  integral length scales L, and Reynolds numbers based on Taylor microscale,  Reλ = Uλ/ν, where Taylor microscale λ = (15νU 2/ϵ)1/2 [35, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Following  Sreenivasan [43], we compute U as the rms value for each component of the  velocity field, or  U =  �2  3  �  dkE(k)  �1/2  ,  (80)  whereas the integral length L is computed using  L =  �  dkk−1E(k)  �  dkE(k)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (81)  We quantify U in three ways: Urms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and U(K = 1) and U(K = 2), which are  computed using the KE in the wavenumber spheres of radii 1 and 2 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We list Urms in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 12, we exhibit the time series of Urms, U(K = 1),  U(K = 2), L, and Reλ for the four runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe that Urms, U(K = 1), and  U(K = 2) for the MHD runs are smaller than the corresponding quantities  for the HD run, except for MHD1 (Pm = 1/3) where U(K = 1) is comparable  to that for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Consequently, Reλ for MHD1 is close to that for the  HD run, but Reλ for the other two MHD runs are smaller than those for the  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  23  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  Urms  (a)  Pm = 1/3  HD  MHD  (b)  Pm = 1  (c)  Pm = 10/3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='16  U(K = 1)  (d)  (e)  (f)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='24  U(K = 2)  (g)  (h)  (i)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='70  L  (j)  (k)  (l)  0  1  2  3  4  t  20  25  30  35  Re∏  (m)  10  20  30  t  (n)  1  2  3  4  5  t  (o)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 12 Time evolution of rms velocity (Urms), U(K = 1), U(K = 2), integral length scale  (L), and Reλ for the HD run (dashed red curve) and the MHD runs (solid red curve) for  Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' U(K = 1) and U(K = 2) are computed using the KE contained in the  waveumber spheres of radii 1 and 2 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The integral lengths L for the three MHD runs are larger than the  corresponding L for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, the velocity fields are more ordered  in the MHD runs compared to the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Next, we compute Πu(K) for the HD and MHD runs, as well as ΠB(K) for  the MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These fluxes exhibit significant fluctuations, hence we average  over several time frames in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The fluxes, shown in Fig 13,  clearly show that ΠB > 0, indicating energy transfers from the velocity field  Springer Nature 2021 LATEX template  24  Turbulent Drag Reduction in MHD Turbulence  Table 1 For MHD runs with Pm = 1/3, 1, 10/3, numerical values of average KE flux  (⟨Πu⟩) in the inertial range, rms velocity (Urms), and  � ¯Cd1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We also list ⟨|(u · ∇)u|⟩ and  � ¯Cd2  �  for the wavenumber spheres of radii K = 1 and K = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The table contains the  corresponding quantities for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For all the runs, ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  K = 1  K = 2  Pm  ⟨Πu⟩  Urms  � ¯Cd1  �  ⟨|(u · ∇)u|⟩  � ¯Cd2  �  ⟨|(u · ∇)u|⟩  � ¯Cd2  �  HD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='37  MHD1  1/3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='46  MHD2  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='49  MHD3  10/3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='53  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='41  to magnetic field at all scales, and that  Πu,MHD < Πu,HD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (82)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 13 (a,b,c) Plots Πu(K) (solid red curve) and ΠB(K) (solid green curve) for the MHD  runs with Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Plots also illustrate Πu(K) (dashed red curve) for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We compute the drag coefficient ¯Cd1, which is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (43) as  ⟨Πu⟩ /(U 3  rms/L), and exhibit its time series in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Table 1, we list the  average values of ¯Cd1 for the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe that ¯Cd1 for the steady  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  25  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 14 (a,b,c) Time evolution of the drag reduction coefficient ¯Cd1 for the HD run (dashed  red curve) and the MHD runs (solid red curve) with Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  state of the HD run is consistent with the results of Sreenivasan [43], thus val-  idating our code and diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, ¯Cd1 for the steady states of the  three MHD runs are larger than that for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is because the  decrease in U 3  rms for the MHD runs overcompensates the decrease in Πu(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Now, we examine the nonlinear term Nu for the HD and MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Since  the drag force is effective at large scales, we estimate Nu by its rms value for  a small wavenumber sphere of radius K, that is,  ⟨|(u · ∇) u|⟩LS = Nu(K) =  � �  k≤K  |Nu(k)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (83)  In particular, we choose K = 1 and K = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 15(a,b), we illustrate the  time series of Nu(K) for the HD run (dashed red curve) and the MHD runs  (solid red curve) for K = 1 and K = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Table 1, we list the average values  of Nu(K) for all the runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe that Nu(K) for the three MHD runs  are smaller than Nu(K) for the HD counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, there is a reduction  in ⟨|(u · ∇) u|⟩LS for MHD turbulence compared to HD turbulence, signalling  TDR in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  After this, we compute the drag reduction coefficient ¯Cd2, which is defined  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (44) as ⟨|(u · ∇)u|⟩LS /(U 2  rms/L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The time series of ¯Cd2 for K = 1 and  K = 2 are plotted in Figure 16, and their average values for their steady states  1Springer Nature 2021 LATEX template  26  Turbulent Drag Reduction in MHD Turbulence  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='125  Nu  (a): Pm = 1/3  K = 1  HD  MHD  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  (b): Pm = 1/3  K = 2  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='125  Nu  (c): Pm = 1  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  (d): Pm = 1  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='125  Nu  (e): Pm = 10/3  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  (f): Pm = 10/3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 15 (a,b,c) Plots of the time series of nonlinear term (Nu) for spheres of radii (a) K = 1  and (b) K = 2 for the HD run (dashed red curve) and the MHD runs (solid red curve) with  Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe that ¯Cd2(K = 1) for the MHD runs with  Pm = 1/3 and 10/3 are smaller than that for the HD run for t ⪆ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For the  other cases, ¯Cd2 for MHD runs are larger than those for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Thus, for 1/3 ≤ Pm ≤ 10/3, Πu and ⟨|(u · ∇)u|⟩ for the MHD runs are  smaller than the corresponding values for the HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For K = 1, the drag  coefficient ¯Cd2 exhibits similar behaviour for Pm = 1/3 and 10/3, but not for  Pm = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is in contrast to ¯Cd1, which is typically larger for MHD runs  than that for the corresponding HD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  27  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='18  ¯Cd2  (a): Pm = 1/3  K = 1  HD  MHD  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  (b): Pm = 1/3  K = 2  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='18  ¯Cd2  (c): Pm = 1  0  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  (d): Pm = 1  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='18  ¯Cd2  (e): Pm = 10/3  0  1  2  3  4  5  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  (f): Pm = 10/3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 16 (a,b,c) Time evolution of drag reduction coefficient ¯Cd2 for sphere of radii (a)  K = 1, and (b) K = 2 for HD turbulence (dashed red curve) and MHD turbulence (solid  red curve) with Pm = 1/3, 1, 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We will show in Section 8 that QSMHD turbulence, which corresponds  to Pm = 0, exhibits larger U than the respective HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence,  we expect that MHD runs with very small Pm will yield larger U than the  corresponding HD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This conjecture needs to be verified in future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addi-  tion, dynamo simulations exhibit enhancement in U on the emergence of a  large-scale magnetic field (see Section 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We will discuss these issues in later  sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  28  Turbulent Drag Reduction in MHD Turbulence  In summary, DNS of MHD turbulence exhibits reduction in Πu(k) and  ⟨|(u · ∇) u|⟩LS in comparison to HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, we do not observe  enhancement in U in the MHD runs, at least for 1/3 ≤ Pm ≤ 10/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We  conjecture that MHD runs with very small Pm may exhibit enhancement in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  After the above discussion on DNS results on TDR in MHD turbulence, in  the next subsection, we will discuss TDR in the shell model of MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2 Numerical verification of TDR in shell models of  MHD turbulence  In comparison to DNS, shell models have much fewer variables, hence they are  computationally faster than DNS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, shell models are often used to  study turbulence, especially for extreme parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Beginning with Gledzer-  Ohkitani-Yamada (GOY) shell model for HD turbulence [67–69], researchers  have developed several shell models for MHD turbulence [70–73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this sub-  section, we report TDR in a shell model of MHD turbulence [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' employed a revised version of GOY shell model and computed the drag  forces and nonlinear terms for the HD and MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They showed that  the turbulent drag in MHD turbulence is indeed reduced compared to HD  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In a shell model of turbulence, all the Fourier modes in a wavenumber shell  are represented by a single variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' A MHD shell model with N shells has  N velocity and N magnetic shell variables that are coupled nonlinearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The  corresponding HD shell model has N velocity shell variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this subsection,  we present the results of the shell model of Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] employed a shell model with 36 shells, with random forcing  employed at shells n = 1 and 2 such that the KE injection rate is maintained at  a constant value [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They performed three sets of HD and MHD simulations  with KE injection rates ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0, and ν = η = 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For time  integration, they used Runge-Kutta fourth order (RK4) scheme with a fixed  ∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0, they chose ∆t = 5 × 10−5, but for ϵinj = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0, they  took ∆t = 1 × 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The numerical results are summarized in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They  carried out the HD and MHD simulations up to 1000 eddy turnover time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For  further details on the model and the numerical method, refer to Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Both HD and MHD simulations reached their respective steady states after  approximately 200 eddy turnover time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Interestingly, Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] observed  that for the same ϵinj, the KE and U for MHD turbulence are larger than those  for HD turbulence (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These observations clearly demonstrate an  enhancement of U in MHD turbulence compared to HD turbulence, as is the  case for turbulent flows with dilute polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The increase in U for the MHD runs compared to the HD runs has its origin  in the energy spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] computed the average KE spectra  Eu(k) for the HD and MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These spectra, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 17, exhibit  Kolmogorov’s k−5/3 spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For a given ϵinj, Eu(k) plots for the HD and  MHD runs almost overlap with each other, except for small wavenumbers  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  29  Table 2 For the shell model runs of HD and MHD turbulence with ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0,  numerical values of inertial-range KE flux Πu, rms velocity U,  ⟨|(u · ∇)u|⟩ = (�  n|Nn[u, u]|2)1/2, ¯Cd1, and ¯Cd2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  ϵinj  Πu  U  ⟨|(u · ∇)u|⟩  ¯Cd1  ¯Cd2  HD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='87  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='15  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  MHD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='92  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='026  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='93  HD  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='88  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='15  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  MHD  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='02  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='026  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='83  HD  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='95  271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='16  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  MHD  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='06  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='33  136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='025  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='28  100  102  104  106  k  10-11  10-7  10-3  101  Eu(k)  k −5/3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 17 Plots of KE spectra Eu(k) for the shell model runs with ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 (red), ϵinj = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  (green) and ϵinj = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0 (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The dashed and solid curves represent the Eu(k) for the  MHD and HD runs respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Kolmogorov’s −5/3 scaling (black) fits well in the inertial  range for all the runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  where Eu(k) for the MHD runs are larger than the HD counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Since the  energy is concentrated at small wavenumbers, we observe that UMHD > UHD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  This is in sharp contrast to DNS results of Section 6 where U and Eu(k) of  the MHD runs with moderate Pm are smaller than the corresponding values  for the HD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, in dynamo simulations, we do observe that U of  MHD turbulence could be larger than that for HD turbulence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' this topic will  be discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Next, using the numerical data of the shell model, Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11]  estimated the rms values of (u · ∇)u for the HD and MHD runs using  ⟨|(u · ∇)u|⟩ =  ��  n  |Nn[u, u]|2  �1/2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (84)  To suppress the fluctuations, averaging was performed over a large number  of states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As listed in Table 2, ⟨|(u · ∇)u|⟩ for the MHD runs are suppressed  Springer Nature 2021 LATEX template  30  Turbulent Drag Reduction in MHD Turbulence  100  102  104  106  k  10-5  10-3  10-1  101  Πu(k)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 18 Plots of Πu(k) for ϵinj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 (red), ϵinj = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0 (green) and ϵinj = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0 (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The  dashed curves represent Πu(k) for the HD runs, whereas the solid curves indicate the same  for the MHD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  compared to the corresponding HD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These results reinforce the fact that  the nonlinearity ⟨|(u · ∇)u|⟩ depends critically on the phases of the Fourier  modes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' larger U does not necessarily imply larger ⟨|(u · ∇)u|⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We remark  that averaging over the small n would have been more appropriate for the  estimation of ⟨|(u · ∇)u|⟩, as was done for the DNS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] also computed the average KE fluxes for the HD and MHD  runs [37, 73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These fluxes are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 18, and their average values  in the steady state are listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The figure illustrates that for a given  ϵinj, the MHD run has a lower KE flux than corresponding HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is  consistent with the suppression of ⟨|(u · ∇)u|⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' lower ⟨|(u · ∇)u|⟩ leads to lower  KE flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, we compute ¯Cd1 and ¯Cd2 using the values of Table 2 and  L = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clearly, ¯Cd1 and ¯Cd2 for the MHD runs are lower than those for the  corresponding HD runs, thus indicating TDR in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Thus, DNS and the shell model results illustrate that MHD turbulence has  lower ⟨|(u · ∇)u|⟩ and lower Πu(k) compared to HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These results  demonstrate TDR in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note, however, that in DNS, U for the  MHD runs with 1/3 ≤ Pm ≤ 10/3 are smaller than the corresponding U for  the HD runs, but it is other way round in the shell model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As argued in Section  6, we expect that U for MHD runs with very small Pm would be larger than  U for the HD runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the next section we will describe TDR in dynamos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  7 TDR in Dynamos  Magnetic field generation, or dynamo process, in astrophysical objects is an  important subfield of MHD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In dynamo process, the velocity field is forced  mechanically, or by convection induced via temperature and/or concentration  gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rotation too plays an important role in dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' There are many  books and papers written on dynamo, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this section, we will  discuss only a handful of dynamo studies that are related to TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  31  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19 For the Taylor-Green dynamo with the forcing amplitude F0 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2, (a) 3D plot  of the spatially chaotic velocity field for a no-dynamo state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (b) ordered velocity field for a  dynamo state arising due to the suppression of chaos in the presence of a finite mean magnetic  field;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (c) ordered magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with the permission of  APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [27] simulated Taylor-Green dynamo for magnetic Prandtl  number Pm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They reported many interesting properties, including sub-  critical dynamo transition, as well as steady, periodic, quasi-periodic, and  chaotic dynamo states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Let us focus on an interesting feature of this dynamo  that is related to TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19 we exhibit the intensities of the magni-  tudes of the velocity and magnetic fields for the forcing amplitude F0 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Before the dynamo transition, the velocity field is quite turbulent, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, after the dynamo transition or emergence of magnetic  field, both the velocity and magnetic fields, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19(b,c), become more  ordered compared to the pure HD state of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' observed  similar features at several other F0’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For example, at F0 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8, after the  emergence of magnetic field, the velocity fluctuations are suppressed, and the  velocity and magnetic fields become quite coherent (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The emer-  gence of ordered velocity field is akin to an enhancement of the mean velocity  in a pipe flow with polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The aforementioned simulation of Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [27] is somewhat idealized  in comparison to spherical geo- and solar dynamos with rotation and thermal  convection at extreme parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Interestingly, spherical dynamos share cer-  tain common features with Taylor-Green dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 21, the  velocity field of spherical dynamo [28] is organized in vertical columns, which  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  (a)  (b)  z  Z  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  (c)  XSpringer Nature 2021 LATEX template  32  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 20 Plots of the total KE (top panel) and the total ME (bottom panel) for Taylor-  Green dynamo with F0 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe ordered velocity and magnetic fields after the  onset of dynamo (time > 3000 units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reprinted with the permission  of APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 21 The radial component of the velocity field in a numerical simulation of geodynamo  by Olson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Olson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from John Wiley  & Sons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  is also a feature of rotating turbulence [29, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It is possible that thermal con-  vection and magnetic field too contribute to the structural organization of the  flow;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' this feature however needs a careful examination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Even though ⟨|u · ∇u|⟩ and the energy fluxes for dynamos have been stud-  ied widely (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', [25, 42, 58]), TDR in dynamos has not been analyzed in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  It is hoped that a systematic study of TDR in dynamos would be performed  in future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the next section, we describe TDR in QSMHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  8  7  6  5  Fo = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  500  1500  2500  3500  4500  2  1  Fo = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  0  500  1500  2500  3500  4500  TimeRADIALVELOCITYSpringer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  33  8 TDR in QSMHD turbulence via energy flux  Liquid metals have small magnetic Prandtl number (Pm), and they are  described using QSMHD equations, which are a limiting case of MHD  equations [20, 21, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The equations for QSMHD with a strong external  magnetic field B0 are [20, 21, 76]  ∂u  ∂t + (u · ∇)u = −∇(p/ρ) − σ  ρ ∆−1[(B0 · ∇)2u] + ν∇2u + Fext,  (85)  ∇ · u = 0,  (86)  where σ is the electrical conductivity, and ∆−1 is the inverse Laplacian oper-  ator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fourier space, a nondimensionalized version of QSMHD equations  is  d  dtu(k) = −i  �  p  {k · u(q)}u(p) − ikp(k)/ρ − N(cos2 θ)u(k)  −νk2u(k) + Fext(k),  (87)  k · u(k) = 0,  (88)  where N is the interaction parameter, and θ is the angle between the wavenum-  ber k and B0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The interaction parameter N is the ratio of the Lorentz force  and nonlinear term (u · ∇)u, or  N = σB2  0L  ρU  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (89)  Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (87), we derive an equation for the modal energy as  d  dtEu(k) = Tu(k) − 2NEu(k) cos2 θ + Fext(k) − Du(k),  (90)  where Tu(k) is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (10), and the dissipation induced by Lorentz  term is [21, 76]  Fu(k) = −2NEu(k) cos2 θ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (91)  Hence, the magnetic field induces additional dissipation in QSMHD turbu-  lence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Equation (91) represents the energy transfers from the velocity field to the  magnetic field at a wavenumber k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' A sum of Fu(k) over a wavenumber sphere  of radius K yields the following expression for the energy flux ΠB(K):  ΠB(K) = −  �  k≤K  Fu(k) =  �  k≤K  2NEu(k) cos2 θ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (92)  Springer Nature 2021 LATEX template  34  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 22 From the numerical simulation of QSMHD turbulence by Reddy and Verma [22],  the time series of the normalised KE, E(t)/E0, for N = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5, 11, 18, 27, 130, where E0 is the  energy at the final state of N = 0 simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For each N, after an application of external  magnetic field, the KE drops suddenly, and then it increases and reaches a statistically  steady value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The asymptotic KE for all the runs with N > 18 are larger than E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From  Reddy and Verma [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Thus, the Lorentz force transfers the kinetic energy to the magnetic energy,  which is immediately dissipated by the Joule dissipation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' this feature is due to  Pm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As a consequence, for an injection rate ϵinj, Πu(K) of a QSMHD run  is suppressed compared to Πu(K) of the corresponding HD run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, in the  inertial range,  Πu < ϵinj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (93)  Therefore, following the same line arguments as in earlier sections, we deduce  that turbulent drag is suppressed in QSMHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, the  velocity fields of the MHD runs are less random (or more ordered) compared to  the corresponding HD runs, thus suppressing ⟨|(u · ∇)u|⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, we expect  the turbulent drag in QSMHD turbulence to be smaller than the corresponding  HD counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the following discussion, we will describe numerical results  that are consistent with the above predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Reddy and Verma [22] simulated QSMHD turbulence in a periodic box for  N ranging from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='7 to 220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' They employed a constant KE injection rate of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 (in nondimensional units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In fact, the magnetic field B0 was switched on  after the initial HD run was fully developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' After an introduction of B0, KE  first decreases abruptly due to Joule dissipation, and then it increases due to  reorganization of the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 22, for N > 18, the total KE is  larger than its HD counterpart (N = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this range of N, the flow becomes  quasi two-dimensional with larger U and suppressed turbulent drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is  counter-intuitive because we expect the KE to decrease with the increase of  Joule dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, reorganization of the flow leads to enhancement of  U and TDR in the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In Table 3, we list the rms velocity U as a function of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clearly, U increases  monotonically with N because ⟨|(u · ∇)u|⟩ and turbulent drag decrease with  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0r  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  N=130  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  =27  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  N=27  N=0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0  N=18  N=11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  N=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  N=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0 0  50  100  150  200  250  300  350  400  = t/T  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  35  Table 3 In numerical simulations of QSMHD  turbulence by Verma and Reddy [77], rms  velocity (U) for various N’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clearly, U  increase with N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  N  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='7  18  27  220  U  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='87  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 23 From the numerical simulation of QSMHD turbulence by Reddy and Verma [22],  the vorticity isosurfaces for (a) N = 0, (b) N = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5, and (c) N = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The flow field becomes  anisotropic and ordered with the increase of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We observe a vortex tube for N = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From  Reddy and Verma [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  the increase of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 23 we exhibit the vorticity isosurfaces for N = 0, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5,  and 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As is evident in the figure, the flow becomes quasi-2D and more orderly  with the increase of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The above results again indicate that a large U does not necessarily  imply large ⟨|(u · ∇)u|⟩ because the nonlinear term depends on U and the  phase relations between the velocity modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In QSMHD turbulence, two-  dimensionalization leads to a reduction in ⟨|(u · ∇)u|⟩ even with large U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note,  however, that for a definitive demonstration of drag reduction in QSMHD tur-  bulence, we still need to perform a comparative study of Πu and ⟨|(u · ∇)u|⟩  for HD and QSMHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Reduced turbulent flux is an important ingredient for drag reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note  that such a reduction does not occur in laminar QSMHD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' here, the Lorentz  force damps the flow further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We illustrate this claim for a channel flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In a  HD channel flow, the maximum velocity at the centre of the pipe is (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 2)  [13, 39]  UHD = − d2  2νρ  � dp  dx  �  ,  (94)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='83  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='89  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='45  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='88  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='10  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='34  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='92  (a)  b)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='308  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='227  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='97  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='516  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='115  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='015  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='725  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='0025Springer Nature 2021 LATEX template  36  Turbulent Drag Reduction in MHD Turbulence  where d is half-width of the channel (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, in a laminar QSMHD  flow, the corresponding velocity is [20, 76, 78]  UQSMHD = −  1  σB2  0  � ∂p  ∂x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (95)  The ratio of the two velocities is  UQSMHD  UHD  =  2νρ  σB2  0d2 =  1  Ha2 ,  (96)  where Ha is the Hartmann number, which is much larger than unity for a  QSMHD flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, the velocity in laminar QSMHD is much smaller than  that in the HD channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In comparison, U increases with N in QSMHD tur-  bulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, drag reduction is a nonlinear phenomena, which is a visible in  a turbulent flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the next section, we will cover several more examples of TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  9 TDR in Miscellaneous Systems  In this section, we briefly describe TDR in stably stratified turbulence, over  smooth surfaces, and in turbulent convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1 TDR in stably stratified turbulence  Many natural and laboratory flows are stably stratified with lighter fluid  above heavier fluid and gravity acting downwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The governing equations  for stably-stratified flows under Boussinesq approximation are [13, 29, 30, 79]  ∂u  ∂t + (u · ∇)u = −∇p − Ωρˆz + ν∇2u + FLS,  (97)  ∂ρ  ∂t + (u · ∇)ρ = Ωuz + κ∇2ρ,  (98)  ∇ · u = 0,  (99)  where p is the pressure, ρ is the density fluctuation in velocity units, −Ωρˆz is  buoyancy, and Ω is the Brunt-V¨ais¨al¨a frequency, which is defined as [29, 79]  Ω =  �  g  ρm  |d¯ρ  dz |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (100)  Here ρm is the mean density of the whole fluid, d¯ρ/dz is the average density  gradient, and g is the acceleration due to gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We convert the density in  velocity units using the transformation, ρ → ρg/(Ωρm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The ratio ν/κ is called  Schmidt number, which is denoted by Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Richardson number, Ri, which is a  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  37  nondimensional number, is employed to quantify the ratio of buoyancy and  the nonlinear term (u · ∇)u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  For periodic or vanishing boundary condition and in the absence of  dissipative terms, the total energy,  Eu + Eρ =  �  dr1  2u2 +  �  dr1  2ρ2,  (101)  is conserved [29, 40, 79, 80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Here, Eρ can be interpreted as the total potential  energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It has been shown that in the inertial range, the associated energy  fluxes obey the following conservation law [40, 81]:  Πu + Πρ = const = ϵinj,  (102)  where Πρ is the potential energy flux, and ϵinj is the KE injection rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note  that under steady state, Πρ equals the energy transfer rate from the velocity  field to the density field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Using the stable nature of the flow, we can argue that  Πρ > 0 [29, 30, 40, 81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Nature of the stably stratified turbulence depends quite critically on the  density gradient or Richardson number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For moderate density gradient (Ri ≈  1), Bolgiano [82] and Obukhov [83] argued that Πρ is positive and constant,  whereas Πu(k) ∼ k−4/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For small Richardson numbers, the scaling is closer to  passive scalar turbulence [84], but the flow becomes quasi-2D for large Richard-  son numbers [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Here, we present only one numerical result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Kumar et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [85] simulated stably stratified turbulence for Sc = 1 and Ri = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01, and  observed that in the inertial range, Πρ(k) = const (> 0) and Πu(k) ∼ k−4/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 24 for an illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Researchers have observed that Πρ > 0 for small  and large Ri’s as well [29, 80, 84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Using the fact that Πρ(k) > 0, following the arguments described in  Section 3, we argue that the turbulent drag will be reduced in stably stratified  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' That is, for the same KE injection rate ϵinj, Πu(k) and ⟨u · ∇u⟩  for stably stratified turbulence will be smaller than those for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  We remark that the flux-based arguments presented above are consistent with  the observations of Narasimha and Sreenivasan [38] who argued that stably  stratified turbulence is relaminarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the next subsection, we will discuss TDR experienced by smooth bluff  bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2 TDR over smooth bluff bodies  As discussed in Section 2, bluff bodies experience turbulent drag at large  Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Models, experiments, and numerical simulations reveal  that the turbulent drag on aerodynamic objects is a combination of the viscous  drag and adverse pressure gradient [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Engineers have devised ingenious  techniques to reduce this drag, which are beyond the scope of this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  38  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 24 Stably stratified simulation with Sc = 1 and Ri = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='01: plots of KE flux Πu(k),  normalized KE flux Πu(k)k4/5, and potential energy flux Πρ(k) (presented as Πθ(k) in the  figure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Equation (17) illustrates that the turbulent drag experienced by a bluff  body is a combination of the inertial and viscous forces, and the adverse pres-  sure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, for bluff bodies like aerofoils and automobiles, the  dominant contributions come from the viscous drag and adverse pressure gra-  dient [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note, however, that the bulk flow above the smooth surface is  anisotropic, and it contains signatures of the surface properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, the  nonlinear term ⟨|u · ∇u|⟩ and the drag coefficient ¯Cd2 could yield interesting  insights into TDR over bluff bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Narasimha and Sreenivasan [38] performed  such analysis for a variety of flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In the following subsection, we will use the  above idea to explain TDR in turbulent thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='3 TDR in turbulent thermal convection  Turbulent convection exhibits interesting properties related to TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this  subsection, we consider Rayleigh-B´enard convection (RBC), which is an ide-  alized setup consisting of a thin fluid layer confined between two thermally  conducting plates separated by a distance d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The temperatures of the bottom  and top plates are Tb and Tt respectively, with Tb > Tt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The equations for thermal convection under Boussinesq approximation  are [86]  ∂u  ∂t + (u · ∇)u = −1  ρ∇p + αgTˆz + ν∇2u,  (103)  ∂T  ∂t + (u · ∇)T = κ∇2T,  (104)  ∇ · u = 0,  (105)  where T is the temperature field;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' α, κ are respectively the thermal expansion  coefficient and thermal diffusivity of the fluid;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and g is the acceleration due  to gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The two important parameters of turbulent thermal convection are 102  IIu (k), Ie(k)  100  Iu (k)  10-2  IIu (k)k4/5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1IIe(k)  10-4  101  102  kSpringer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  39  thermal Prandtl number, Pr = ν/κ, and Rayleigh number,  Ra = αgd3(Tb − Tt)  νκ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (106)  In turbulent thermal convection, the velocity field receives energy from  the temperature field via buoyancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note that thermal plumes drive thermal  convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This feature is opposite to what happens in polymeric, MHD,  and stably stratified turbulence, where the velocity field loses energy to the  secondary field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Yet, there are signatures of TDR in turbulent convection,  which is due to the smooth thermal plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, the mechanism of TDR in  turbulent thermal convection differs from that in polymeric, MHD, and stably  stratified turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In the following, we list some of the results related to TDR in thermal  convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Kraichnan [87] argued that turbulent thermal convection would become  fully turbulent or reach ultimate regime at very large Rayleigh number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In  this asymptotic state, the effects of walls are expected to vanish, similar to  the vanishing of boundary effects in the bulk of HD turbulence [35, 36, 88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Kraichnan [87] predicted that Nu ∝ Ra1/2 in the ultimate regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However,  experimental observations and numerical simulations reveal that for Ra ⪅  1013, Nu ∼ Raβ with β ranging from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='29 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='33 [30, 89, 90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This reduction  in the Nu exponent from 1/2 to approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='30 is attributed to the  suppression of heat flux due to the smooth thermal plates, boundary layers,  and other complex properties [30, 89–92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Pandey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [31] performed numerical simulations of RBC for Pr = 1 and  Ra ranging from 106 to 5 × 108, and showed that  Nonlinear term  Viscous term  = |u · ∇u|  |ν∇2u| ∼ ReRa−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (107)  Note that the above ratio is Re for HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus, nonlinearity  (⟨|u · ∇u|⟩) is suppressed in turbulent thermal convection at large Ra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Pandey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [31] and Bhattacharya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [32, 93] showed that the viscous  dissipation rate (ϵu) and thermal dissipation rate (ϵT ) depend on Rayleigh  and Prandtl numbers, and that ϵu and ϵT are suppressed compared to HD  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For moderate Pr and large Ra,  ϵu ∼ U 3  d Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2,  (108)  ϵT ∼ U(Tb − Tt)2  d  Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (109)  Interestingly, for small Prandtl numbers, ϵu ∼ U 3/d with very small Ra-  dependent correction [32, 93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 25 for an illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  40  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 25 Plots exhibiting the Ra and Pr dependence of the viscous and thermal dissipation  rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For moderate Pr, ϵu, ϵT ∼ Ra−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Bhattacharya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with  permission from AIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 26 A LSC observed in 2D RBC by Sugiyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The arrows represent the  velocity field, whereas the colors represent the temperature of the fluid, with red as hot and  blue as cold fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Sugiyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  It is well known that a large-scale circulation (LSC) is present in turbu-  lence convection (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 26) [94–98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' As we show below, the suppression of  nonlinearity (⟨|u · ∇u|⟩) and turbulent drag in RBC is related to this LSC and  the smooth walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 26, the flows near the top and bottom plates have sim-  ilarities with those near a flat plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The LSC traverses vertically along the  102  (a)  Ra  (p / εn)/  101  Ra  Eul  100  Ra  10-1  106  108  1010  (b)  10-1  Pr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='02  Pr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1  (p / zV)/L3  Pr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='5  Pr = 1  Ra  Pr = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  Pr = 50  10-2  Pr = 100  106  108  1010  Ra0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='6  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='2Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  41  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 27 In numerical simulation of Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [99], the velocity (a) and temperature (b)  profiles in wall units for various Ra’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The dashed lines illustrate the viscous sublayer and  the log-layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' A log layer is observed for the velocity field, but not for the temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  From Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with permission from APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  vertical walls, but moves horizontally along the thermal plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' However, for  a typical RBC flow, the horizontal extent of LSC is shorter than that in the  flow past a flat plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Researchers have argued that for large Rayleigh numbers  (Ra ⪆ 1013), the boundary layers exhibit a transition to a log layer, which is  a signature of transition from viscous to turbulent boundary layer, as in flow  past a flat plate [12–14, 30, 89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For example, Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [99] simulated 2D RBC  and showed that above the viscous layer, the normalized velocity field varies  logarithmically with the normalized vertical distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In particular, Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  [99] observed that u+ ∝ log(y+) for y+ ⪆ 10 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note, however, that  the thermal boundary layers do not show transition to log layer [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Several  other experiments exhibit similar behaviour [100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Since the boundary layers of turbulent thermal convection have similar  properties as those over a flat plate, we can argue that the nonlinearity ⟨u · ∇u⟩  is suppressed in turbulent convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is the reason why the dissipa-  tion rates and turbulent drag in turbulent convection are smaller than the  corresponding quantities in HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [101] studied the cor-  relation ⟨uzθ⟩, where θ is the temperature fluctuation, and showed that for  (a) 40  Ra = 1011  Ra = 1012  30  Ra = 1013  K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='4  Ra = 1014  +  2 20  10  0  10-1  100  101  102  103  y+  (b) 25  Ra= 1011  Ra = 1012  20  Ra= 1013  Ra = 1014  15  T+  10  5  0  10-1  100  101  102  103Springer Nature 2021 LATEX template  42  Turbulent Drag Reduction in MHD Turbulence  moderate Pr,  ⟨uzθ⟩ =  �  ⟨u2z⟩  �  ⟨θ2⟩(PrRa)−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  (110)  Note that  �  ⟨u2z⟩ ≈ Ra1/2 and  �  ⟨θ2⟩ ≈ (∆T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore, the correction  (PrRa)−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='22 of the above equation leads to ⟨uzθ⟩ ∼ Ra0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='28 or Nu ∼ Ra0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [30, 101] argued that at very large Ra, the corrections would dis-  appear and the flow will approach the ultimate regime with ⟨uzθ⟩ ∼ Ra1/2 or  Nu ∼ Ra1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Note, however, that no experiment and numerical simulation has been able  to achieve the ultimate regime, thus the ultimate regime remains a conjecture  at present [90, 99, 102, 103], even though several experiments and numerical  simulation report a transition to the ultimate regime with the Nu exponent  reaching up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='38 (but lower than 1/2) [99, 102], while some others argue  against the transition to the ultimate regime [90, 103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' It is interesting to  note that for rough thermal plates, the heat transport is enhanced because of  increase in turbulence due to the roughness [104].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  RBC with periodic boundary condition exhibits Nu ∝ Ra1/2 due to the  absence of boundary layers [101, 105].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In addition, RBC with small Prandtl  numbers too exhibit properties similar to those of periodic boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  This is because the temperature gradient is linear in the bulk in both these  systems [93, 106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In summary, turbulent thermal convection exhibits suppression of nonlin-  earity (⟨|u · ∇u|⟩) and KE flux compared to HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This suppression,  which occurs essentially due to the smooth walls, leads to TDR in thermal  convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  10 Discussions and conclusions  Experiments and numerical simulations show that turbulent flows with dilute  polymers exhibit TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Many factors–boundary layers, polymer properties,  bulk properties of the flow–are responsible for this phenomena [1–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' There  are many interesting works in this field, however, in this review, we focus  on the role of bulk turbulence on TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The KE flux, Πu(k), is suppressed  in the presence of polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This reduction in Πu(k) leads to suppression of  nonlinearity ⟨u · ∇u⟩ and turbulent drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  MHD turbulence exhibits very similar behaviour as the polymeric tur-  bulence [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Here too, Πu(k) is suppressed because a major fraction of the  injected KE is transferred to the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Consequently, ⟨u · ∇u⟩ and  the turbulent drag are suppressed in MHD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' For the same KE injec-  tion rate at large scales, Πu(k) and ⟨u · ∇u⟩ for MHD turbulence are smaller  than the respective quantities of HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' These properties are borne  out in DNS and shell models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The KE flux Πu(k) of stably stratified turbulence too is suppressed com-  pared to HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Hence, we expect TDR in stably stratified turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Narasimha and Sreenivasan [38] made a similar observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We need detailed  numerical simulations to verify the above statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' An interesting point to  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  43  note that for the above three flows,  Πu(k) + ΠB(k) = const = ϵinj,  (111)  where ΠB(k) represents the energy flux associated with the secondary field B,  which could be polymer, magnetic field, or density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The constancy of the sum  of fluxes in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (111) arises due to the stable nature of system [29, 40, 81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The  above constancy also represents a redistribution of the injected kinetic energy  at large scales to (a) the velocity field in the intermediate scales, and to (b) the  secondary field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Positive ΠB implies that Πu(k) < ϵinj which leads to TDR in  the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Thus, TDR is intimately related to the conservation law of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (111).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Another important feature of TDR is that the mean flow or large scale  velocity (U) is enhanced in the presence of polymers or magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This is  because the velocity field gets more ordered under TDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Suppression of Πu(k)  and ⟨u · ∇u⟩ even with strong U is due to the correlations in the velocity  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' An emergence of ordered U is also observed in dynamo and QSMHD  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Unfortunately, DNS of MHD turbulence with magnetic Prandtl  number Pm = 1/3, 1, and 10/3 do not show enhancement in U compared to  the respective HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Based on the findings of QSMHD turbulence  (Pm ≈ 0) and dynamo, we conjecture that U of MHD turbulence with very  small Pm will be larger than that of corresponding HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  TDR is also observed in turbulent thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This observation is  based on the suppression of viscous and thermal dissipation rates, and that of  nonlinearity ⟨u · ∇u⟩ [31, 32, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Note, however, that unlike MHD, polymeric,  and stably-stratified turbulence, Πu(k) for turbulent thermal convection is not  suppressed due to the unstable nature of thermal convection [40, 81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Therefore,  the mechanism for TDR in turbulent thermal convection differs from that for  TDR in MHD, polymeric, and stably-stratified turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this review, we  argue that TDR in turbulent thermal convection occurs due to the smooth  thermal plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Near the thermal plates, the large-scale circulation (LSC) are  akin to the flow past a flat plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This feature has important consequences on  the possible transition to the ultimate regime in thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The enhancement of U under TDR is similar to the increase in the mean  flow during relaminarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Narasimha and Sreenivasan [38] showed rever-  sion of flows from random to smooth profiles by relaminarizing agencies, which  could be stably stratification, rotation, thermal convection, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Figure 28 illus-  trates interactions between the mean flow and turbulence via a relaminarizing  agency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In this figure, the channels 1, 2, and 3 represent complex interac-  tions between the mean flow and fluctuations during relaminarization, whereas  channel 0 represents these interactions in the HD turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The arguments  of Verma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' [11] have certain similarities with those of Narasimha and  Sreenivasan [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  In summary, this review discusses a general framework based on KE flux to  explain TDR in a wide range of phenomena—polymeric, MHD, QSMHD, and  stably stratified turbulence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' dynamo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' and turbulent thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This  kind of study is relatively new, and it is hoped that it will be explored further  Springer Nature 2021 LATEX template  44  Turbulent Drag Reduction in MHD Turbulence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 28 Interactions between the mean flow and turbulence via relaminarizing agency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' The  interaction channels 1,2,3 relaminarize the flow in comparison to the HD turbulence where  interactions occurs via channel 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' From Narasimha and Sreenivasan [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Reproduced with  permission from K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Sreenivasan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  in future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' We also expect TDR to emerge in other systems, such as drift-wave  turbulence, astrophysical MHD, rotating turbulence, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Such a study has an  added benefit that TDR has practical applications in engineering flows, liquid  metals, polymeric flows, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The authors thank Abhishek Kumar and Shashwat  Bhattacharya for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' This project was supported by Indo-  French project 6104-1 from CEFIPRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Chatterjee is supported by INSPIRE  fellowship (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' IF180094) of the Department of Science & Technology, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Declarations  Conflict of interest statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  The authors have no actual or potential  conflicts of interest to declare in relation to this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  References  [1] Lumley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Blossey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Drag reduction by additives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid  Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 1(1), 367–384 (1969)  [2] Tabor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', de Gennes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : A cascade theory of drag reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' EPL  2(7), 519–522 (1986)  [3] de Gennes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Introduction to Polymer Dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge Uni-  versity Press, Cambridge (1990)  [4] de Gennes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Scaling Concepts in Polymer Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cornell Univer-  sity Press, Ithaca (1979)  mean  ftow  12  11  relaminarizing  agency  3  turbulenceSpringer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  45  [5] Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', White, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : The onset of drag reduction by dilute  polymer additives, and the maximum drag reduction asymptote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid  Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 409, 149–164 (2000)  [6] L’vov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pomyalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Procaccia, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Tiberkevich, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Drag reduction  by polymers in wall bounded turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 92(24), 244503  (2004)  [7] Benzi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', De Angelis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Govindarajan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Procaccia, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Shell model  for drag reduction with polymer additives in homogeneous turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 68(1), 016308 (2003)  [8] White, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Mungal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Mechanics and prediction of turbulent drag  reduction with polymer additives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 40, 235–256  (2008)  [9] Benzi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': A short review on drag reduction by polymers in wall bounded  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Physica D 239(14), 1338–1345 (2010)  [10] Benzi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ching, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Polymers in Fluid Flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 9(1), 163–181 (2018)  [11] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Alam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chatterjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulent drag reduction in mag-  netohydrodynamic and quasi-static magnetohydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Plasmas 27, 052301 (2020)  [12] Landau, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Lifshitz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Fluid Mechanics, 2nd edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Course of  Theoretical Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Elsevier, Oxford (1987)  [13] Kundu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Cohen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Dowling, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Fluid Mechanics, 6th edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Academic Press, San Diego (2015)  [14] Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Fundamentals of Aerodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' McGraw-Hill Educa-  tion, New York (2017)  [15] Anderson Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : A History of Aerodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University  Press, New York (1998)  [16] Dar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Eswaran, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Energy transfer in two-dimensional  magnetohydrodynamic turbulence: formalism and numerical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Physica D 157(3), 207–225 (2001)  [17] Mininni, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ponty, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Montgomery, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pinton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Politano, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=',  Pouquet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Dynamo regimes with a nonhelical forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ApJ 626,  853–863 (2005)  [18] Valente, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', da Silva, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pinho, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : The effect of viscoelasticity on  the turbulent kinetic energy cascade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 760, 39–62 (2014)  Springer Nature 2021 LATEX template  46  Turbulent Drag Reduction in MHD Turbulence  [19] Valente, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', da Silva, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pinho, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Energy spectra in elasto-  inertial turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 28(7), 075108–17 (2016)  [20] Moreau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Magnetohydrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Springer, Berlin (1990)  [21] Knaepen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Moreau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Magnetohydrodynamic turbulence at low  magnetic reynolds number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 40, 25–45 (2008)  [22] Reddy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Strong anisotropy in quasi-static magneto-  hydrodynamic turbulence for high interaction parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids  26, 025109 (2014)  [23] Reddy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Anisotropic energy transfers in  quasi-static magnetohydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Plasmas 21(10),  102310 (2014)  [24] Moffatt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Magnetic Field Generation in Electrically Conducting  Fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University Press, Cambridge (1978)  [25] Roberts, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Glatzmaier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Geodynamo theory and simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 72, 1081–1123 (2000)  [26] Brandenburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Subramanian, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Astrophysical magnetic fields and  nonlinear dynamo theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 417(1-4), 1–209 (2005)  [27] Yadav, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Wahi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Bistability and chaos in the Taylor-  Green dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 85(3), 036301 (2012)  [28] Olson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Christensen, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Glatzmaier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Numerical modeling  of the geodynamo: mechanisms of field generation and equilibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' B: Solid Earth 104(B5), 10383–10404 (1999)  [29] Davidson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Turbulence in Rotating, Stratified and Electrically  Conducting Fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University Press, Cambridge (2013)  [30] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Physics of Buoyant Flows: From Instabilities to Turbu-  lence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' World Scientific, Singapore (2018)  [31] Pandey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Scaling of large-scale quantities in Rayleigh-  B´enard convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 28(9), 095105 (2016)  [32] Bhattacharya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Revisiting Reynolds and  Nusselt numbers in turbulent thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 33,  015113 (2021)  [33] Kolmogorov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Dissipation of Energy in Locally Isotropic Turbu-  lence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Dokl Acad Nauk SSSR 32, 16–18 (1941)  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  47  [34] Kolmogorov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : The local structure of turbulence in incompressible  viscous fluid for very large Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Dokl Acad Nauk SSSR  30, 301–305 (1941)  [35] Lesieur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulence in Fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Springer, Dordrecht (2008)  [36] Frisch, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulence: The Legacy of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Kolmogorov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge  University Press, Cambridge (1995)  [37] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Energy Transfers in Fluid Flows: Multiscale and Spectral  Perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University Press, Cambridge (2019)  [38] Narasimha, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Relaminarization of fluid flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 19, 221–309 (1979)  [39] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Introduction to Mechanics, 2nd edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Universities Press,  Hyderabad (2016)  [40] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Variable energy flux in turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Journal of Physics A:  Mathematical and Theoretical 55(1), 013002 (2022) 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='07291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='1088/1751-8121/ac354e  [41] Kraichnan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': The structure of isotropic turbulence at very high  Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 5, 497–543 (1959)  [42] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Statistical theory of magnetohydrodynamic turbulence:  recent results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 401(5), 229–380 (2004)  [43] Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : An update on the energy dissipation rate in isotropic  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 10(2), 528–529 (1998)  [44] Onsager, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Statistical hydrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Il Nuovo Cimento 6(2), 279–287  (1949)  [45] Prandtl, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': On the motion of fluids with very little friction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' In: Krazer,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=') Verhandlungen des Dritten Internationalen Mathematiker-  Kongresses in Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Teubner, Leipzig (1905)  [46] Fouxon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Lebedev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Spectra of turbulence in dilute polymer  solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 15(7), 2060–2072 (2003)  [47] Perlekar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Mitra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pandit, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Manifestations of drag reduction by  polymer additives in decaying, homogeneous, isotropic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 97(26), 264501 (2006)  [48] Sagaut, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Cambon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Homogeneous Turbulence Dynamics, 2nd edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Cambridge University Press, Cambridge (2018)  Springer Nature 2021 LATEX template  48  Turbulent Drag Reduction in MHD Turbulence  [49] Ray, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Vincenzi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Elastic turbulence in a shell model of polymer  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' EPL 114, 44001 (2016)  [50] Thais, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Gatski, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Mompean, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Analysis of polymer drag reduc-  tion mechanisms from energy budgets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Heat Mass Transfer 43(C),  52–61 (2013)  [51] Nguyen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Delache, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Simo¨ens, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Bos, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', El Hajem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=':  Small scale dynamics of isotropic viscoelastic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Fluids 1(8), 083301 (2016)  [52] L’vov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pomyalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Procaccia, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Tiberkevich, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Drag Reduc-  tion by Microbubbles in Turbulent Flows: The Limit of Minute Bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 94(17), 174502 (2005)  [53] Cowling, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Magnetohydrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Adam Hilger, London (1976)  [54] Priest, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Magnetohydrodynamics of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University  Press, Cambridge (2014)  [55] Goldstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Roberts, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Magnetohydrodynamic turbulence in  the solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 33, 283–325 (1995)  [56] Davidson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Turbulence: An Introduction for Scientists and Engi-  neers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Oxford University Press, Oxford (2004)  [57] Debliquy, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Carati, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Energy fluxes and shell-to-  shell transfers in three-dimensional decaying magnetohydrodynamic  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Plasmas 12(4), 042309 (2005)  [58] Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Energy transfers and magnetic  energy growth in small-scale dynamo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' EPL 104(5), 54001 (2014)  [59] Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Energy transfers in dynamos  with small magnetic Prandtl numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' of Turbulence 16(11), 1114–  1134 (2015)  [60] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Field theoretic calculation of renormalized viscosity,  renormalized resistivity, and energy fluxes of magnetohydrodynamic  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 64(2), 026305 (2001)  [61] Boyd, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sanderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': The Physics of Plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge  University Press, Cambridge (2003)  [62] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chatterjee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Yadav, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Paul, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chandra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=',  Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Benchmarking and scaling studies of pseudospectral code  Tarang for turbulence simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Pramana-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 81(4), 617–629  (2013)  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  49  [63] Chatterjee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Hadri, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=',  Khurram, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Scaling of a Fast Fourier Transform and a pseudo-spectral  fluid solver up to 196608 cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Parallel Distrib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 113, 77–91  (2018)  [64] Craya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Contribution `a l’analyse de la turbulence associ´ee `a des  vitesses moyennes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' PhD thesis, Universit´e de Granoble (1958)  [65] Herring, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Approach of axisymmetric turbulence to isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Fluids 17(5), 859–872 (1974)  [66] Sadhukhan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Stepanov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Plunian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Kinetic helicity and enstrophy transfers in helical hydrodynamic  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 4, 84607 (2019)  [67] Gledzer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : System of hydrodynamic type allowing 2 quadratic  integrals of motion .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Dokl Acad Nauk SSSR 209, 1046–1048 (1973)  [68] Yamada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ohkitani, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Asymptotic formulas for the lyapunov spec-  trum of fully developed shell model turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 57(6), 6257  (1998)  [69] Ditlevsen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Turbulence and Shell Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Cambridge University  Press, Cambridge (2010)  [70] Frick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sokoloff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Cascade and dynamo action in a shell model  of magnetohydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 57(4), 4155–4164  (1998)  [71] Stepanov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Plunian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Phenomenology of turbulent dynamo growth  and saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' ApJ 680(1), 809–815 (2008)  [72] Plunian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Stepanov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Frick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Shell models of magnetohydrody-  namic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 523, 1–60 (2012)  [73] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Dynamos at extreme magnetic Prandtl num-  bers: insights from shell models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Turbul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 17(12), 1112–1141 (2016)  [74] Stepanov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Plunian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Fully developed turbulent dynamo at low  magnetic Prandtl numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Turbul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 7(39), 1–15 (2006)  [75] Sharma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chakraborty, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Statistical  features of rapidly rotating decaying turbulence: Enstrophy and energy  spectra and coherent structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 30(4), 045103 (2018)  [76] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Anisotropy in Quasi-Static Magnetohydrodynamic Turbu-  lence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 80(8), 087001 (2017)  Springer Nature 2021 LATEX template  50  Turbulent Drag Reduction in MHD Turbulence  [77] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Reddy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Modeling quasi-static magnetohydrodynamic  turbulence with variable energy flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 27(2), 025114 (2015)  [78] M¨uller, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', B¨uhler, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Magnetofluiddynamics in Channels and Contain-  ers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Springer, Berlin Heidelberg (2001)  [79] Tritton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Physical Fluid Dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Clarendon Press, Oxord (1988)  [80] Lindborg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': The energy cascade in a strongly stratified fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid  Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 550, 207–242 (2006)  [81] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Contrasting turbulence in stably stratified flows and  thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Scr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 94(6), 064003 (2019)  [82] Bolgiano, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulent spectra in a stably stratified atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 64(12), 2226–2229 (1959)  [83] Obukhov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': On influence of buoyancy forces on the structure of  temperature field in a turbulent flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Dokl Acad Nauk SSSR 125, 1246  (1959)  [84] Yeung, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Donzis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : High-Reynolds-number  simulation of turbulent mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 17(8), 081703 (2005)  [85] Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chatterjee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Energy spectrum of  buoyancy-driven turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 90(2), 023016 (2014)  [86] Chandrasekhar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Hydrodynamic and Hydromagnetic Stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Oxford  University Press, Clarendon (1961)  [87] Kraichnan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulent thermal convection at arbitrary prandtl  number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 5(11), 1374–1389 (1962)  [88] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ayyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Debliquy, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chandra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Local  shell-to-shell energy transfer via nonlocal interactions in fluid turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Pramana-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 65(2), 297–310 (2005)  [89] Grossmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Lohse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Scaling in thermal convection: a unifying  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 407, 27–56 (2000)  [90] Niemela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Skrbek, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Donnelly, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Turbulent  convection at very high Rayleigh numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Nature 404, 837–840 (2000)  [91] Shraiman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Siggia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Heat transport in high-Rayleigh-number  convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' A 42(6), 3650–3653 (1990)  [92] Siggia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : High Rayleigh number convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  26(1), 137–168 (1994)  Springer Nature 2021 LATEX template  Turbulent Drag Reduction in MHD Turbulence  51  [93] Bhattacharya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Samtaney, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Prandtl number depen-  dence of the small-scale properties in turbulent Rayleigh-B´enard convec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Fluids 6, 063501 (2021)  [94] Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Bershadskii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Niemela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Mean wind and its  reversal in thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 65(5), 056306 (2002)  [95] Sugiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ni, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Stevens, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Chan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Zhou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Xi,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Grossmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Xia, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 105(3), 034503 (2010)  [96] Chandra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=' E 83, 067303 (2011)  [97] Chandra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=', Mathai, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Stevens, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=', Lohse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Tran-  sition to the Ultimate Regime in Two-Dimensional Rayleigh-B´enard  Convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 120(14), 144502 (2018)  [100] He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', van Gils, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=', Bodenschatz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ahlers, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Logarithmic Spa-  tial Variations and Universal Power Spectra of Temperature Fluctuations  in Turbulent Rayleigh-B´enard Convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 112(17),  174501 (2014)  [101] Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Mishra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Pandey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Paul, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Scalings of field corre-  lations and heat transport in turbulent convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' E 85(1),  016310 (2012)  [102] He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Funfschilling, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Nobach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Bodenschatz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Ahlers, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Tran-  sition to the Ultimate State of Turbulent Rayleigh-B´enard Convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 108(2), 024502 (2012)  [103] Iyer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Scheel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Schumacher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Classical 1/3  scaling of convection holds up to ra = 1015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' PNAS 117(14), 7594–7598  (2020)  [104] Roche, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Gauthier, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Kaiser, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Salort, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': On the triggering of  the ultimate regime of convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 12(8), 085014 (2010)  [105] Lohse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Toschi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=': Ultimate state of thermal convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' 90(3), 034502 (2003)  [106] Mishra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Wahi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
+page_content=' : Patterns and bifurcations in  Springer Nature 2021 LATEX template  52  Turbulent Drag Reduction in MHD Turbulence  low–Prandtl-number Rayleigh–B´enard convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAzT4oBgHgl3EQfVPyV/content/2301.01281v1.pdf'}
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+A Generic Topological Criterion for Flat Bands in Two Dimensions
+Alireza Parhizkar1 and Victor Galitski1, 2
+1Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA
+2Center for Computational Quantum Physics, The Flatiron Institute, New York, NY 10010, United States
+(Dated: January 4, 2023)
+Mutually distorted layers of graphene give rise to a moir´e pattern and a variety of non-trivial
+phenomena. We show that the continuum limit of this class of models is equivalent to a (2 + 1)-
+dimensional field theory of Dirac fermions coupled to two classical gauge fields. We further show
+that the existence of a flat band implies an effective dimensional reduction in the field theory, where
+the time dimension is “removed.”
+The resulting two-dimensional Euclidean theory contains the
+chiral anomaly. The associated Atiyah-Singer index theorem provides a self-consistency condition
+for the existence of flat bands. In particular, it reproduces a series of quantized magic angles known
+to exist in twisted bilayer graphene in the chiral limit where there is a particle-hole symmetry. We
+also use this criterion to prove that an external magnetic field splits this series into pairs of magnetic
+field-dependent magic angles associated with flat moir´e-Landau bands. The topological criterion we
+derive provides a generic practical method for finding flat bands in a variety of material systems
+including but not limited to moir´e bilayers.
+Moir´e phenomena in twisted bilayer graphene [1–10]
+and other systems [11, 12] have been an active topic of
+research in recent years. Of particular interest for the
+former are flat bands, where localized electrons exhibit a
+variety of strongly-correlated phases. In this Letter we
+draw a universal picture for the occurrence of the flat
+bands through emergent gauge fields and the anomaly.
+Consider a bilayer graphene system with a small twist
+and/or strain applied to the layers. As emphasized in
+Ref. [11], both can be described in terms of a diffeomor-
+phism: ξω ≡ ϵω(r)r for strain and ξθ ≡ ϵθ(r)ˆz × r for
+a twist (parameterized by ϵ ≪ 1). With ξω and ξθ be-
+ing orthogonal to each other and thus forming a basis, all
+possible flows in two dimensions can be described as a lin-
+ear combination of these two fields. Therefore, a bilayer
+system with a general infinitesimal deformation can be
+achieved by applying the diffeomorphism r → r + ξω,θ/2
+to one layer and r → r−ξω,θ/2 to the other, as in Fig. 1.
+A finite deformation is reached by successively applying
+such diffeomorphisms. The time dependent moir´e fields
+ω(t, r) and θ(t, r) can be further looked at as bosonic
+phonon-like degrees of freedom for the bilayer system.
+Focusing on only one valley, K, in the Brillouin zone,
+an electron that hops from the K-point of one layer to
+that of the other, can do so along three different momen-
+tum vectors that will form the moir´e reciprocal lattice
+vectors of the bilayer system. This is because the defor-
+mation has separated the equivalent K-points in three
+different ways (along qθ
+1,2,3 for twist and qω
+1,2,3 for strain
+as depicted in Fig. 1) that are related to each other by a
+2π/3 rotation. For the general deformation these vectors
+are given by q1 ≡ 2KD(sinh ω
+2 ˆx − sin θ
+2 ˆy) with q2,3 de-
+rived by successive 2π/3 rotations of q1, while KD is the
+distance between K-points of the undeformed Brillouin
+zone and its center.
+The characteristic length of the superstructure, i.e.
+the moir´e lattice constant, L, can be read off of the
+FIG. 1.
+Each blue hexagon designates the Brillouin zone
+of a single layer of graphene that has gone under either a
+strain, ξω, or a twist, ξθ. In (a) the Brillouin zones are ex-
+panded/shrunken with respect to the undeformed Brillouin
+zone (green dotted hexagon), where as in (b) they are rotated
+with respect to each other. Each pair gives rise to its moir´e
+reciprocal lattice (shown by red hexagonals). Also K points
+are designated by black dots.
+magnitude of the moir´e reciprocal lattice vectors, |q| =
+2KD(sinh2 ω
+2 + sin2 θ
+2)1/2, which is equal to the distance
+between the corresponding K-points (denoted by k and
+k′ in Fig. 1): L = 4π/3|q|. If the electron hops from
+one layer to the other without changing its position, it
+acquires a phase determined only by the moir´e reciprocal
+lattice vectors. The dynamics of this electron is given by
+the following Hamiltonian density [8],
+h(r)=
+� −iν /∂
+T(r)
+T †(r) −iν /∂
+�
+, T(r)≡
+� vV (r) uU ∗(−r)
+uU(r)
+vV (r)
+�
+,
+(1)
+where −iν /∂ is the Hamiltonian density for a single layer
+of graphene with /∂ ≡ σi∂i, and T(r) is the inter-
+layer tunneling matrix and encodes the periodic pro-
+file of the moir´e pattern, Fig.
+3.
+V (x) = �
+j e−iqj·r
+takes the electron from one sublattice (either A or B)
+to the same sublattice on the other layer, while U(x) =
+�
+j e−iqj·rei(j−1)2π/3 takes it to the opposing sublattice,
+arXiv:2301.00824v1  [cond-mat.mes-hall]  2 Jan 2023
+
+(a)
+(b)
+K
+k
+k2
+with v and u being the corresponding tunneling ampli-
+tudes and j = 1, 2, 3.
+Using the algebra of gamma matrices, {γµ, γν} = 2ηµν,
+with ηµν as the metric, and the unitary transformation,
+h(r) → Ωh(r)Ω†
+with
+Ω =
+1
+√
+2
+� −1
+1
+σz
+σz
+�
+,
+(2)
+we can write the Hamiltonian density (1) in terms of
+Dirac fermions coupled to non-fluctuating gauge fields as
+follows
+H =
+�
+d2x
+�
+¯ψiνγa (∂a + iAaγ5 + iSaiγ3) ψ
+− ¯ψγ0A0γ5ψ − ¯ψγ0S0iγ3ψ
+�
+,
+(3)
+with ¯ψ ≡ ψ†γ0. Or in the even tidier action formulation,
+S =
+�
+d3x ¯ψi /Dψ,
+/D ≡ γµ (∂µ + iAµγ5 + iSµiγ3) , (4)
+where a = 1, 2, µ = 0, 1, 2 and the field components are,
+A0 = −v
+ν Re[V (r)],
+S0 = v
+ν Im[V (r)],
+(5)
+A1 = u
+2ν Re[U(r) + U(−r)], A2 = u
+2ν Im[U(r) + U(−r)],
+S1 = u
+2ν Im[U(r) − U(−r)], S2 = u
+2ν Re[U(−r) − U(r)].
+The total field strength associated with /D is given by
+Fµν = γ5F A
+µν + iγ3F S
+µν + 2iγ5γ3AµSν, with F A,S
+µν
+being
+the field strengths generated by Aµ and Sµ respectively.
+Looking at the action (4), we see that the bilayer prob-
+lem has transformed into that of Dirac fermions moving
+in a (2 + 1) dimensional spacetime and acted upon by
+two axial-vector fields: A chiral gauge field, Aµ, and a
+spin field, Sµ. Note that γ3 measures the spin along the
+direction normal to the material plane. The gauge fields,
+(5), are periodic with periodicity
+√
+3L, hence their cor-
+responding field strengths are proportional to 1/L and
+also periodic with the same period, while the distance
+between each minimum and its neighboring maximum is
+L (see Fig. 2 for example). In particular the spatial part
+of the field strength F A
+12 = ∂2A1 − ∂1A2 is given by
+B(r) ≡ F A
+12 = u
+ν
+�
+j
+ˆqθ
+j · ∇(qj · r) sin(qj · r) ,
+(6)
+where ˆqθ
+j · ∇ is the derivative along the unit vector ˆqθ
+j ≡
+qθ
+j/|qθ
+j |. That of Sa is given by �
+j ˆqθ
+j·∇(qj·r) cos(qj · r).
+Consider the following chiral transformations associ-
+ated with action (4)
+� ¯ψ → ¯ψeiαγ5
+ψ → eiαγ5ψ
+�
+,
+� ¯ψ → ¯ψeiαiγ3
+ψ → eiαiγ3ψ
+�
+,
+� ¯ψ → ¯ψeiαΓ
+ψ → eiαΓψ
+�
+, (7)
+with Γ ≡ γ0γ3γ5. Each one of the above chiral trans-
+formations can become a symmetry of the action (4) un-
+der additional constraints: ψ → eiαγ5ψ, ψ → eiαiγ3ψ,
+and ψ → eiαΓψ are promoted to symmetries if Sµ = 0,
+Aµ = 0, and A0 = S0 = 0 respectively. Chiral particles
+can be defined with respect to each of these symmetries
+by using projection operators, e.g.
+ψ± ≡
+1
+2(1 ± γ5)ψ.
+Since γ5 and γ3 do not commute we cannot simultane-
+ously create fermions with definite γ5 and γ3 handedness,
+in contrast to Γ which commutes with both. So we can,
+for example, have ψ⟳,⟲
+↑↓
+≡ 1
+4(1 ± iγ3)(1 ± Γ)ψ.
+Our interest here is focused, more than anything else,
+on flat bands, which can be looked at as a class of modes
+covering the whole Brillouin zone at constant energy,
+¯ψkγ0∂0ψk = µψ†
+kψk, within which the electrons are there-
+fore localized ∂Ek/∂k = 0. If we only consider this class,
+we eliminate the time dependence from the action en-
+tirely and reduce the (2 + 1) dimensional theory to its
+(2 + 0) dimensional version. Specifically, in the case of
+v = 0, which supports exact flat bands [4], we have
+I =
+�
+D ¯ψψ exp
+��
+d2x ¯ψiγa (∂a + iAaγ5 + iSaiγ3) ψ
+�
+.
+(8)
+Using any of the chiral projections, ψ⟳,⟲
+± or ↑↓, we can break
+the above path-integral further down, for instance, to
+I =
+�
+D ¯ψ±ψ± exp
+� �
+d2x
+�
+¯ψ±iγa (∂a ± iAa) ψ±
++ ¯ψ∓γaϵabSbψ±
+��
+,
+(9)
+where the path-integral is over the four field variables ¯ψ±
+and ψ±, while ψ± fermions are coupled to ±Aa.
+In this form the anomaly residing in the theory given
+by the path integral (8) takes the familiar shape of the
+chiral anomaly in two dimensional Euclideanized space-
+time. In a path integral such as above the gauge field Aa
+has an index associated with it that is directly given by
+the chiral anomaly [13, 14]. But the index must be an
+integer number which as we will see is only possible for
+certain values of θ and ω that coincide with the magic
+angle. This consistency condition can therefore tell us
+whether a flat band exists or not. Before proceeding to a
+more detailed investigation, it is worth mentioning that
+this reasoning, following the reduction from Eq. (4) to
+Eq. (9), is generalizable to other more complicated sys-
+tems such as multilayer graphene in which case we should
+use higher dimensional gamma matrices to accommodate
+for the additional layers.
+Since the gauge potentials are periodic the path in-
+tegral can be divided into equivalent patches sewn to-
+gether by an integration over all field configurations on
+the boundaries.
+I =
+� �
+▽
+D ¯ψ∂▽ψ∂▽ I▽
+� ¯ψ∂▽, ψ∂▽
+�
+,
+(10)
+with
+I▽
+� ¯ψ∂▽, ψ∂▽
+�
+=
+�
+¯
+ψ∂▽,ψ∂▽
+D ¯ψ▽ψ▽eiS▽ ,
+(11)
+
+3
+FIG. 2. (a) The magnetic field B created by Aa felt by ψ+ while its negative is exerted upon the ψ−. (b) The field strength
+associated with the spin field. (c) Vector fields Aa (blue) and Sa (red). The black line designates two magnetic regions related
+by parity. Parallel sides are identified with each other and the whole system can be reconstructed by sewing these together.
+The Sa field is zero everywhere on the green dashed hexagon. (d) The chiral scalar potential A0 as experienced by ψ+ and (e)
+that of S0. Except for (c) the fields are zero on the black curves. Note how S0 coincides with the magnetic field in (a) and
+also how A0 coincides with field strength in (b), in particular S0 vanishes on edge of each magnetic region. Also note that a
+fermion configuration localized on the edge of each magnetic region will be perpendicular to Sa (see (c) for example).
+where ∂▽ designates the boundary of the patches and
+the configuration residing on it, while ▽ designates the
+patch itself. I▽ is the path-integral over all configura-
+tions on one patch, [ ¯ψ▽, ψ▽], that go to [ ¯ψ∂▽, ψ∂▽] on the
+boundary. Also S▽ is the same action before but with
+an integral only over ▽. The patches are chosen so that
+the action S▽ is the same in all I▽. While satisfying this
+property, we choose ▽ so that Sa will either vanish on
+or be perpendicular to ∂▽. This way the edge configura-
+tions along ∂▽ will have an additional chiral symmetry
+with respect to eiαγ5 and the edge mode residing on ∂▽
+will obtain no phase from Sa.
+If the fermions remain confined within one patch,
+which should be the case when they are localized, we can
+exclude from the path-integration those configurations
+that connect different patches together. The probability
+density and current are here given by ψ†ψ and ja ≡ ¯ψγµψ
+respectively. We expect the excluded configurations to be
+those with a nonzero flow of probability current, ja, out
+of ▽:
+�
+▽ ∂0ψ†ψ =
+�
+▽ ∂aja =
+�
+∂▽ ˆna
+∂▽·ja ̸= 0. In that case
+the problem is reduced, from the initial path-integral I,
+to segregated path-integrals of I▽ =
+�
+D ¯ψ▽ψ▽ exp{iS▽}.
+If, moreover, there is a flat-band then the transition am-
+plitude and therefore the path-integral, from any state
+to any other state within the flat-band would be time
+independent
+⟨ζ| eiHt |χ⟩ ≡
+� ζ
+χ
+D ¯ψψeiS = ⟨ζ | χ⟩ .
+(12)
+This allows us to reduce the theory to (2+0) dimensions
+as in Eq. (4) to Eq. (9):
+I▽ =
+�
+▽
+D ¯ψ±ψ± exp
+� �
+▽
+d2x
+�
+¯ψ±iγa (∂a ± iAa) ψ±
++ ¯ψ∓γaϵabSbψ±
+��
+, (13)
+where we have removed the ▽ sign from the fermionic
+field variables (and brought it under the path-integral
+sign instead) in order to avoid clutter.
+Focusing only on I▽, we see however, that not all gauge
+field configurations fit within the boundaries ∂▽; only
+those with a complete integer index, n⟳ − n⟲ ∈ Z. One
+way to observe this is first to notice that a continuous chi-
+ral rotation of ψ+ → ei2πΓψ+ = ψ+ takes the spinor field
+to itself while leaving the action unchanged. However,
+the theory (13) is subject to chiral anomaly, namely, the
+Jacobian of our chiral transformation, J5, is non-trivial,
+I▽ =
+�
+▽
+�
+D ¯ψ+ψ+
+�
+D ¯ψ−ψ−eiS▽ −→
+(14)
+�
+▽
+�
+D ¯ψ+ψ+J5
+�
+D ¯ψ−ψ−eiS▽ = I▽ei2π(n⟳−n⟲) .
+The last equality above comes from knowing that the
+Jacobian of chiral transformation is connected to the
+Atiyah-Singer index [13–15]. Chiral transformation dis-
+criminates between right and left handed modes, n⟳−n⟲,
+hence the path-integral (which yields the determinant of
+the Dirac operator) obtains a phase associated with this
+difference. This phase encodes the winding number of
+the gauge field associated with the Dirac operator—an
+integer number which in two dimensional spacetime is
+written as,
+1
+2π
+�
+▽
+d2x ϵab∂aAb = n⟳ − n⟲ .
+(15)
+But since the field variables do not change by a com-
+plete rotation, in Eq.
+(14), the path integral must
+also remain the same: I▽ = I▽ei2π(n⟳−n⟲).
+Thus, if
+ei2π(n⟳−n⟲) ̸= 1, then the only way that the initial and
+the transformed path-integrals can be equal is for them
+to vanish, I▽ = 0. This zero valued partition function
+means that the state is unrealizable.
+In contrast, the
+flat-band can be realized if n⟳,⟲ ∈ Z.
+
+(a)
+(b)4
+What we have discussed so far applies generally to
+all deformations of any bilayer system that shares the
+symmetries of graphene. Let us now focus on uniform
+twist for which q1 = qθ
+1 = qθ(−1, 0) and q2,3 = qθ
+2,3 =
+qθ(±
+√
+3/2, 1/2) with qθ = 2KD sin(θ/2) = 4π/3L. The
+gauge fields Aa and Sa generated by uniform twist are
+divergenceless with their corresponding field strengths
+proportional to u/νL.
+The gauge potentials and field
+strengths are shown in Fig. 2. We need to calculate the
+minimum value of L corresponding to n⟳ = 1. Using
+Fujikawa’s method of calculating anomalies [13] we find,
+n⟳ = 1
+4π
+�
+▽
+d2x ϵab∂aAb = 1
+4π
+�
+▽
+d2x B = 3
+√
+3u
+4πν L , (16)
+which is equal to 1 for L = L0 ≡ 4πν/3
+√
+3u. Consider-
+ing L = a/2 sin(θ/2), where a = 2.46˚A is the graphene
+lattice constant, the first magic angle is given by θ ≈
+3
+√
+3au/4πv ≈ 1.1◦ with u = 0.11eV and νKD = 9.9eV.
+To develop semi-classical intuition, let us first assume
+that the spin current term Sa ¯ψγaγ3ψ is disregardable.
+Then we are left with only a magnetic field with strength
+proportional to u/νL acting with opposite signs on ψ±
+fermions that are completely decoupled from each other.
+If the magnetic field was constant across the material
+then the electrons would have been subject to Landau
+localization rotating around a fixed center, in a semi-
+classical picture, and forming Landau levels. Since the
+moir´e effective magnetic field is inhomogeneous, the semi-
+classical picture changes to that of drifting fermions—
+rotating around a cycling center. See Fig. 3. For lo-
+calization to be possible, the drifting fermion should be
+able to fit into one magnetic region. The smallest rotat-
+ing fermion, according to the uncertainty principle, has
+a size of ℓB ∝ 1/
+√ ¯B and, since here the average mag-
+netic field ¯B is proportional to 1/L, it expands with
+√
+L.
+But the size of the magnetic regions, or ▽, is propor-
+tional to L which grows faster than ℓB ∝
+√
+L. Thus ▽
+gets bigger faster than the smallest possible electron and
+eventually can catch one, at which moment one electron
+has just been trapped inside the magnetic region and can
+complete a cycle there without getting out of it.
+At that exact moment we expect to have an edge mode
+on the boundary of the magnetic region. Appropriately,
+for this mode the spin current term is indeed disregard-
+able since Sa and ¯ψγaγ3ψ are perpendicular to each other
+at ∂▽. But if there is an edge mode it means that the
+number of right or left handed fermions that reside in
+the magnetic region must at least be one, n⟳,⟲ = 1. This
+again leads us to Eq. (16) and the magic angle. This also
+can be seen in terms of unit of flux and a restricted type
+of Landau quantization. The size of the unit flux is given
+by ℓB =
+�
+Lν/u. Therefore, n = L2/2πℓ2
+B = uL/2πν
+will be the degeneracy of the restricted Landau level, at
+least for large n ∈ Z. Thus we expect a series of magic
+angles connected to each other by steps of δL ≈ 2πν/u.
+FIG. 3. On the left, a generic electron (red trajectory) drift-
+ing in the magnetic region while another electron (green tra-
+jectory) is moving close to the edge of one magnetic region.
+A right or left handed fermion belongs only to either of the
+magnetic regions but since the sides are identified a right
+handed fermion in one region is the left handed fermion in
+the other. Having one electron in both regions is similar to
+having two electrons in one region and forgetting about the
+other. On the right the twisted bilayer graphene at first magic
+angle with blue dots denoting AA stacking and yellow/green
+dots AB/BA stacking. The distance between the neighboring
+equivalent dots is equal to L.
+Reformulating the theory in terms of Dirac fermions
+(4) has other merits as well. For example, the applica-
+tion of an external electromagnetic field yields the same
+theory (4) but now with the Dirac operator carrying an
+additional external gauge field, Aµ,
+/D ≡ γµ (∂µ + iAµ + iAµγ5 + iSµiγ3) .
+Upon projecting the Dirac fermions into ψ± ≡ 1
+2(1±γ5)ψ
+as before, we see that the chiral fermions are now coupled
+to the shifted gauge fields Aa ± Aa. For example, if Aa
+is due to a constant magnetic field H, Eq. (16) reads
+n⟳ = 1
+4π
+�
+▽
+d2x (H ± B) = H
+4π
+3
+√
+3
+4 L2 ± 3
+√
+3u
+4πν L . (17)
+For u2/ν2 > 4πH/3
+√
+3, the requirement n⟳ = ±1 has
+more than one solution in contrast to Eq. (16). Thus, an
+external magnetic field splits each magic angle into
+L = ±u
+ν
+2
+H ±
+��u
+ν
+2
+H
+�2
+±
+16π
+3
+√
+3H ,
+(18)
+with the magic angles given by θ = 2 arcsin(L/2), while
+each combination of pluses and minuses above yields a
+solution to Eq. (17). For a small external magnetic field
+H ≪ (3
+√
+3/4π)u2/ν2 ≈ 140mT the positive solutions
+can be written as,
+L±
+1 = L0± 4π2
+27
+ν3
+u3 H , L±
+2 = 4
+H
+u
+ν ±L0− 4π2
+27
+ν3
+u3 H . (19)
+with L0 ≡ 4πν/3
+√
+3u, being the magic angle in the ab-
+sence of the external magnetic field. In the limit H → 0
+we regain the previous magic angle from L±
+1 , in addition
+to having L±
+2 → ∞ that happens when the bilayer is un-
+twisted, θ → 0, and the moir´e reciprocal lattice, which
+would have a vanishing size, is in fact flat.
+
+5
+Let us also consider applying a uniform strain on top
+of the already existing uniform twist. The moir´e pattern
+will rotate by arccos(qθ/|q|) and its length, L, will shrink
+accordingly. In this case, using Eq. (6), the magnetic
+field generated by Aa and its corresponding index are
+given by B = qθ u
+ν
+�
+j sin(qj · r) and n⟳ = (qθ/|q|)L/L0
+respectively. Comparing this with Eq. (16) we see that
+the flat-band now happens at,
+L = L0
+�
+1 + sinh2(ω/2)
+sin2(θ/2) .
+(20)
+Now consider the case of finite AA hoppings by grad-
+ually increasing v from zero. This is equivalent to rein-
+troducing S0 and A0 to the Lagrangian.
+The former
+vanishes on the edges of magnetic regions (see Fig. 2)
+and therefore will have no effect on the edge mode. On
+the other hand, the A0 term acts as an electric potential
+for either ψ±.
+An edge mode trajectory is perpendic-
+ular to constant A0 curves, so even though A0 might
+redistribute the density of the mode along the edge, it
+will do little to deviate it out of the edge.
+Therefore,
+the first magic angle is robust against a non-vanishing
+v. Like a mass term, γ0A0 does not anti-commute with
+the generator of the chiral transformation, Γ. Since we
+have { /D, Γ} ∝ v the v → 0 ensures that the action
+is invariant under ψ → eiαΓψ and that for each pos-
+itive eigenvalue of /D there is a negative one with the
+same magnitude. Deviating form the v = 0 limit breaks
+particle-hole symmetry, shifts the eigenvalues of /D, dis-
+connects the number of left- and right-handed zero modes
+n⟳,⟲ from the Jacobian of the transformation, and gives
+the formerly flat-band a curvature. In this situation we
+can define the magic angle, where the flatness of the
+band is approximate, through the flux felt by ψ±, e.g.
+�
+▽ F12/4π =
+�
+▽ Aa ¯ψ∂▽γaψ∂▽ = 1, but this implies an
+exact flat-band upon the existence of a well-defined n⟳,⟲
+which can be found only at v = 0.
+As we have seen in this Letter, although anomalies are
+not present in all dimensions, it is still possible to con-
+jure them in specific situations. In particular, a flat band
+can be described through an anomaly in the timeless ver-
+sion of its hosting theory. We saw that the dimensionally
+reduced theory and thus the flat band are not always re-
+alizable. In the case of bilayer graphene, the obstruction
+comes from the chiral anomaly and the need to satisfy
+an index condition, which in turn confirms the topologi-
+cal nature of the flat band. The Dirac field theory form,
+Eq. (4), of the bilayer moir´e lattice problem allows many
+generalizations including the finite temperature case, the
+presence of complex inhomogeneous external fields and
+general deformations, and interaction effects in the spirit
+of Refs. [16, 17] where the interplay of anomaly with in-
+teractions are discussed. Of particular interest are quan-
+tum Hall phenomena and unconventional superconduct-
+ing pairing associated with the moir´e gauge fields.
+This
+work
+was
+supported
+by
+the
+National
+Sci-
+ence Foundation under Grant No.
+DMR-2037158,
+the U.S. Army Research Office under Contract No.
+W911NF1310172, and the Simons Foundation.
+[1] J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H.
+Castro Neto, Graphene bilayer with a twist: Electronic
+structure, Phys. Rev. Lett. 99, 256802 (2007).
+[2] R.
+Bistritzer and A. H. MacDonald, Moir´e bands
+in twisted double-layer graphene, Proceedings of the
+National
+Academy
+of
+Sciences
+108,
+12233
+(2011),
+https://www.pnas.org/content/108/30/12233.full.pdf.
+[3] P. San-Jose, J. Gonz´alez, and F. Guinea, Non-abelian
+gauge potentials in graphene bilayers, Phys. Rev. Lett.
+108, 216802 (2012).
+[4] G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Ori-
+gin of magic angles in twisted bilayer graphene, Phys.
+Rev. Lett. 122, 106405 (2019).
+[5] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi,
+E. Kaxiras, and P. Jarillo-Herrero, Unconventional super-
+conductivity in magic-angle graphene superlattices, Na-
+ture 556, 43 (2018).
+[6] Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken,
+J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe,
+T. Taniguchi, E. Kaxiras, et al., Correlated insulator be-
+haviour at half-filling in magic-angle graphene superlat-
+tices, Nature 556, 80 (2018).
+[7] E. Y. Andrei and A. H. MacDonald, Graphene bilayers
+with a twist, Nature materials 19, 1265 (2020).
+[8] L. Balents, General continuum model for twisted bilayer
+graphene and arbitrary smooth deformations, SciPost
+Phys. 7, 48 (2019).
+[9] A. O. Sboychakov, A. L. Rakhmanov, A. V. Rozhkov,
+and F. Nori, Electronic spectrum of twisted bilayer
+graphene, Phys. Rev. B 92, 075402 (2015).
+[10] L. Zou, H. C. Po, A. Vishwanath, and T. Senthil, Band
+structure of twisted bilayer graphene: Emergent symme-
+tries, commensurate approximants, and wannier obstruc-
+tions, Phys. Rev. B 98, 085435 (2018).
+[11] A. Parhizkar and V. Galitski, Strained bilayer graphene,
+emergent energy scales, and moir´e gravity, Phys. Rev.
+Research 4, L022027 (2022).
+[12] A. Parhizkar and V. Galitski, Moir´e gravity and cosmol-
+ogy (2022).
+[13] K. Fujikawa and H. Suzuki, Path integrals and quantum
+anomalies, 122 (Oxford University Press on Demand,
+2004).
+[14] M. F. Atiyah and I. M. Singer, The index of elliptic op-
+erators on compact manifolds, Bulletin of the American
+Mathematical Society 69, 422 (1963).
+[15] K. Fujikawa, Path-integral measure for gauge-invariant
+fermion theories, Phys. Rev. Lett. 42, 1195 (1979).
+[16] C. Rylands, A. Parhizkar, A. A. Burkov, and V. Galitski,
+Chiral anomaly in interacting condensed matter systems,
+Phys. Rev. Lett. 126, 185303 (2021).
+[17] C. Rylands, A. Parhizkar, and V. Galitski, Non-abelian
+bosonization in a (3+1)-d kondo semimetal via quantum
+anomalies, Phys. Rev. B 105, 195108 (2022).
+
diff --git a/LtAyT4oBgHgl3EQf6frG/content/tmp_files/load_file.txt b/LtAyT4oBgHgl3EQf6frG/content/tmp_files/load_file.txt
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@@ -0,0 +1,307 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf,len=306
+page_content='A Generic Topological Criterion for Flat Bands in Two Dimensions  Alireza Parhizkar1 and Victor Galitski1, 2  1Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA  2Center for Computational Quantum Physics, The Flatiron Institute, New York, NY 10010, United States  (Dated: January 4, 2023)  Mutually distorted layers of graphene give rise to a moir´e pattern and a variety of non-trivial  phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We show that the continuum limit of this class of models is equivalent to a (2 + 1)-  dimensional field theory of Dirac fermions coupled to two classical gauge fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We further show  that the existence of a flat band implies an effective dimensional reduction in the field theory, where  the time dimension is “removed.”  The resulting two-dimensional Euclidean theory contains the  chiral anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The associated Atiyah-Singer index theorem provides a self-consistency condition  for the existence of flat bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In particular, it reproduces a series of quantized magic angles known  to exist in twisted bilayer graphene in the chiral limit where there is a particle-hole symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We  also use this criterion to prove that an external magnetic field splits this series into pairs of magnetic  field-dependent magic angles associated with flat moir´e-Landau bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The topological criterion we  derive provides a generic practical method for finding flat bands in a variety of material systems  including but not limited to moir´e bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Moir´e phenomena in twisted bilayer graphene [1–10]  and other systems [11, 12] have been an active topic of  research in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Of particular interest for the  former are flat bands, where localized electrons exhibit a  variety of strongly-correlated phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In this Letter we  draw a universal picture for the occurrence of the flat  bands through emergent gauge fields and the anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Consider a bilayer graphene system with a small twist  and/or strain applied to the layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' As emphasized in  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' [11], both can be described in terms of a diffeomor-  phism: ξω ≡ ϵω(r)r for strain and ξθ ≡ ϵθ(r)ˆz × r for  a twist (parameterized by ϵ ≪ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' With ξω and ξθ be-  ing orthogonal to each other and thus forming a basis, all  possible flows in two dimensions can be described as a lin-  ear combination of these two fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Therefore, a bilayer  system with a general infinitesimal deformation can be  achieved by applying the diffeomorphism r → r + ξω,θ/2  to one layer and r → r−ξω,θ/2 to the other, as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  A finite deformation is reached by successively applying  such diffeomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The time dependent moir´e fields  ω(t, r) and θ(t, r) can be further looked at as bosonic  phonon-like degrees of freedom for the bilayer system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Focusing on only one valley, K, in the Brillouin zone,  an electron that hops from the K-point of one layer to  that of the other, can do so along three different momen-  tum vectors that will form the moir´e reciprocal lattice  vectors of the bilayer system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This is because the defor-  mation has separated the equivalent K-points in three  different ways (along qθ  1,2,3 for twist and qω  1,2,3 for strain  as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 1) that are related to each other by a  2π/3 rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' For the general deformation these vectors  are given by q1 ≡ 2KD(sinh ω  2 ˆx − sin θ  2 ˆy) with q2,3 de-  rived by successive 2π/3 rotations of q1, while KD is the  distance between K-points of the undeformed Brillouin  zone and its center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The characteristic length of the superstructure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  the moir´e lattice constant, L, can be read off of the  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Each blue hexagon designates the Brillouin zone  of a single layer of graphene that has gone under either a  strain, ξω, or a twist, ξθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In (a) the Brillouin zones are ex-  panded/shrunken with respect to the undeformed Brillouin  zone (green dotted hexagon), where as in (b) they are rotated  with respect to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Each pair gives rise to its moir´e  reciprocal lattice (shown by red hexagonals).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Also K points  are designated by black dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  magnitude of the moir´e reciprocal lattice vectors, |q| =  2KD(sinh2 ω  2 + sin2 θ  2)1/2, which is equal to the distance  between the corresponding K-points (denoted by k and  k′ in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 1): L = 4π/3|q|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' If the electron hops from  one layer to the other without changing its position, it  acquires a phase determined only by the moir´e reciprocal  lattice vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The dynamics of this electron is given by  the following Hamiltonian density [8],  h(r)=  � −iν /∂  T(r)  T †(r) −iν /∂  �  , T(r)≡  � vV (r) uU ∗(−r)  uU(r)  vV (r)  �  ,  (1)  where −iν /∂ is the Hamiltonian density for a single layer  of graphene with /∂ ≡ σi∂i, and T(r) is the inter-  layer tunneling matrix and encodes the periodic pro-  file of the moir´e pattern, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  V (x) = �  j e−iqj·r  takes the electron from one sublattice (either A or B)  to the same sublattice on the other layer, while U(x) =  �  j e−iqj·rei(j−1)2π/3 takes it to the opposing sublattice,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='00824v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='mes-hall]  2 Jan 2023  (a)  (b)  K  k  k2  with v and u being the corresponding tunneling ampli-  tudes and j = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Using the algebra of gamma matrices, {γµ, γν} = 2ηµν,  with ηµν as the metric, and the unitary transformation,  h(r) → Ωh(r)Ω†  with  Ω =  1  √  2  � −1  1  σz  σz  �  ,  (2)  we can write the Hamiltonian density (1) in terms of  Dirac fermions coupled to non-fluctuating gauge fields as  follows  H =  �  d2x  �  ¯ψiνγa (∂a + iAaγ5 + iSaiγ3) ψ  − ¯ψγ0A0γ5ψ − ¯ψγ0S0iγ3ψ  �  ,  (3)  with ¯ψ ≡ ψ†γ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Or in the even tidier action formulation,  S =  �  d3x ¯ψi /Dψ,  /D ≡ γµ (∂µ + iAµγ5 + iSµiγ3) , (4)  where a = 1, 2, µ = 0, 1, 2 and the field components are,  A0 = −v  ν Re[V (r)],  S0 = v  ν Im[V (r)],  (5)  A1 = u  2ν Re[U(r) + U(−r)], A2 = u  2ν Im[U(r) + U(−r)],  S1 = u  2ν Im[U(r) − U(−r)], S2 = u  2ν Re[U(−r) − U(r)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The total field strength associated with /D is given by  Fµν = γ5F A  µν + iγ3F S  µν + 2iγ5γ3AµSν, with F A,S  µν  being  the field strengths generated by Aµ and Sµ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Looking at the action (4), we see that the bilayer prob-  lem has transformed into that of Dirac fermions moving  in a (2 + 1) dimensional spacetime and acted upon by  two axial-vector fields: A chiral gauge field, Aµ, and a  spin field, Sµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Note that γ3 measures the spin along the  direction normal to the material plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The gauge fields,  (5), are periodic with periodicity  √  3L, hence their cor-  responding field strengths are proportional to 1/L and  also periodic with the same period, while the distance  between each minimum and its neighboring maximum is  L (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 2 for example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In particular the spatial part  of the field strength F A  12 = ∂2A1 − ∂1A2 is given by  B(r) ≡ F A  12 = u  ν  �  j  ˆqθ  j · ∇(qj · r) sin(qj · r) ,  (6)  where ˆqθ  j · ∇ is the derivative along the unit vector ˆqθ  j ≡  qθ  j/|qθ  j |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' That of Sa is given by �  j ˆqθ  j·∇(qj·r) cos(qj · r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Consider the following chiral transformations associ-  ated with action (4)  � ¯ψ → ¯ψeiαγ5  ψ → eiαγ5ψ  �  ,  � ¯ψ → ¯ψeiαiγ3  ψ → eiαiγ3ψ  �  ,  � ¯ψ → ¯ψeiαΓ  ψ → eiαΓψ  �  , (7)  with Γ ≡ γ0γ3γ5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Each one of the above chiral trans-  formations can become a symmetry of the action (4) un-  der additional constraints: ψ → eiαγ5ψ, ψ → eiαiγ3ψ,  and ψ → eiαΓψ are promoted to symmetries if Sµ = 0,  Aµ = 0, and A0 = S0 = 0 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Chiral particles  can be defined with respect to each of these symmetries  by using projection operators, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  ψ± ≡  1  2(1 ± γ5)ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Since γ5 and γ3 do not commute we cannot simultane-  ously create fermions with definite γ5 and γ3 handedness,  in contrast to Γ which commutes with both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' So we can,  for example, have ψ⟳,⟲  ↑↓  ≡ 1  4(1 ± iγ3)(1 ± Γ)ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Our interest here is focused, more than anything else,  on flat bands, which can be looked at as a class of modes  covering the whole Brillouin zone at constant energy,  ¯ψkγ0∂0ψk = µψ†  kψk, within which the electrons are there-  fore localized ∂Ek/∂k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' If we only consider this class,  we eliminate the time dependence from the action en-  tirely and reduce the (2 + 1) dimensional theory to its  (2 + 0) dimensional version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Specifically, in the case of  v = 0, which supports exact flat bands [4], we have  I =  �  D ¯ψψ exp  ��  d2x ¯ψiγa (∂a + iAaγ5 + iSaiγ3) ψ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (8)  Using any of the chiral projections, ψ⟳,⟲  ± or ↑↓, we can break  the above path-integral further down, for instance, to  I =  �  D ¯ψ±ψ± exp  � �  d2x  �  ¯ψ±iγa (∂a ± iAa) ψ±  + ¯ψ∓γaϵabSbψ±  ��  ,  (9)  where the path-integral is over the four field variables ¯ψ±  and ψ±, while ψ± fermions are coupled to ±Aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  In this form the anomaly residing in the theory given  by the path integral (8) takes the familiar shape of the  chiral anomaly in two dimensional Euclideanized space-  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In a path integral such as above the gauge field Aa  has an index associated with it that is directly given by  the chiral anomaly [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' But the index must be an  integer number which as we will see is only possible for  certain values of θ and ω that coincide with the magic  angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This consistency condition can therefore tell us  whether a flat band exists or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Before proceeding to a  more detailed investigation, it is worth mentioning that  this reasoning, following the reduction from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (4) to  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (9), is generalizable to other more complicated sys-  tems such as multilayer graphene in which case we should  use higher dimensional gamma matrices to accommodate  for the additional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Since the gauge potentials are periodic the path in-  tegral can be divided into equivalent patches sewn to-  gether by an integration over all field configurations on  the boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  I =  � �  ▽  D ¯ψ∂▽ψ∂▽ I▽  � ¯ψ∂▽, ψ∂▽  �  ,  (10)  with  I▽  � ¯ψ∂▽, ψ∂▽  �  =  �  ¯  ψ∂▽,ψ∂▽  D ¯ψ▽ψ▽eiS▽ ,  (11)  3  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (a) The magnetic field B created by Aa felt by ψ+ while its negative is exerted upon the ψ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (b) The field strength  associated with the spin field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (c) Vector fields Aa (blue) and Sa (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The black line designates two magnetic regions related  by parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Parallel sides are identified with each other and the whole system can be reconstructed by sewing these together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The Sa field is zero everywhere on the green dashed hexagon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (d) The chiral scalar potential A0 as experienced by ψ+ and (e)  that of S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Except for (c) the fields are zero on the black curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Note how S0 coincides with the magnetic field in (a) and  also how A0 coincides with field strength in (b), in particular S0 vanishes on edge of each magnetic region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Also note that a  fermion configuration localized on the edge of each magnetic region will be perpendicular to Sa (see (c) for example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  where ∂▽ designates the boundary of the patches and  the configuration residing on it, while ▽ designates the  patch itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' I▽ is the path-integral over all configura-  tions on one patch, [ ¯ψ▽, ψ▽], that go to [ ¯ψ∂▽, ψ∂▽] on the  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Also S▽ is the same action before but with  an integral only over ▽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The patches are chosen so that  the action S▽ is the same in all I▽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' While satisfying this  property, we choose ▽ so that Sa will either vanish on  or be perpendicular to ∂▽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This way the edge configura-  tions along ∂▽ will have an additional chiral symmetry  with respect to eiαγ5 and the edge mode residing on ∂▽  will obtain no phase from Sa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  If the fermions remain confined within one patch,  which should be the case when they are localized, we can  exclude from the path-integration those configurations  that connect different patches together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The probability  density and current are here given by ψ†ψ and ja ≡ ¯ψγµψ  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We expect the excluded configurations to be  those with a nonzero flow of probability current, ja, out  of ▽:  �  ▽ ∂0ψ†ψ =  �  ▽ ∂aja =  �  ∂▽ ˆna  ∂▽·ja ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In that case  the problem is reduced, from the initial path-integral I,  to segregated path-integrals of I▽ =  �  D ¯ψ▽ψ▽ exp{iS▽}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  If, moreover, there is a flat-band then the transition am-  plitude and therefore the path-integral, from any state  to any other state within the flat-band would be time  independent  ⟨ζ| eiHt |χ⟩ ≡  � ζ  χ  D ¯ψψeiS = ⟨ζ | χ⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (12)  This allows us to reduce the theory to (2+0) dimensions  as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (4) to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (9):  I▽ =  �  ▽  D ¯ψ±ψ± exp  � �  ▽  d2x  �  ¯ψ±iγa (∂a ± iAa) ψ±  + ¯ψ∓γaϵabSbψ±  ��  , (13)  where we have removed the ▽ sign from the fermionic  field variables (and brought it under the path-integral  sign instead) in order to avoid clutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Focusing only on I▽, we see however, that not all gauge  field configurations fit within the boundaries ∂▽;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' only  those with a complete integer index, n⟳ − n⟲ ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' One  way to observe this is first to notice that a continuous chi-  ral rotation of ψ+ → ei2πΓψ+ = ψ+ takes the spinor field  to itself while leaving the action unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' However,  the theory (13) is subject to chiral anomaly, namely, the  Jacobian of our chiral transformation, J5, is non-trivial,  I▽ =  �  ▽  �  D ¯ψ+ψ+  �  D ¯ψ−ψ−eiS▽ −→  (14)  �  ▽  �  D ¯ψ+ψ+J5  �  D ¯ψ−ψ−eiS▽ = I▽ei2π(n⟳−n⟲) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The last equality above comes from knowing that the  Jacobian of chiral transformation is connected to the  Atiyah-Singer index [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Chiral transformation dis-  criminates between right and left handed modes, n⟳−n⟲,  hence the path-integral (which yields the determinant of  the Dirac operator) obtains a phase associated with this  difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This phase encodes the winding number of  the gauge field associated with the Dirac operator—an  integer number which in two dimensional spacetime is  written as,  1  2π  �  ▽  d2x ϵab∂aAb = n⟳ − n⟲ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (15)  But since the field variables do not change by a com-  plete rotation, in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (14), the path integral must  also remain the same: I▽ = I▽ei2π(n⟳−n⟲).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Thus, if  ei2π(n⟳−n⟲) ̸= 1, then the only way that the initial and  the transformed path-integrals can be equal is for them  to vanish, I▽ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This zero valued partition function  means that the state is unrealizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  In contrast, the  flat-band can be realized if n⟳,⟲ ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (a)  (b)4  What we have discussed so far applies generally to  all deformations of any bilayer system that shares the  symmetries of graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Let us now focus on uniform  twist for which q1 = qθ  1 = qθ(−1, 0) and q2,3 = qθ  2,3 =  qθ(±  √  3/2, 1/2) with qθ = 2KD sin(θ/2) = 4π/3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The  gauge fields Aa and Sa generated by uniform twist are  divergenceless with their corresponding field strengths  proportional to u/νL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The gauge potentials and field  strengths are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We need to calculate the  minimum value of L corresponding to n⟳ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Using  Fujikawa’s method of calculating anomalies [13] we find,  n⟳ = 1  4π  �  ▽  d2x ϵab∂aAb = 1  4π  �  ▽  d2x B = 3  √  3u  4πν L , (16)  which is equal to 1 for L = L0 ≡ 4πν/3  √  3u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Consider-  ing L = a/2 sin(θ/2), where a = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='46˚A is the graphene  lattice constant, the first magic angle is given by θ ≈  3  √  3au/4πv ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='1◦ with u = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='11eV and νKD = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='9eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  To develop semi-classical intuition, let us first assume  that the spin current term Sa ¯ψγaγ3ψ is disregardable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Then we are left with only a magnetic field with strength  proportional to u/νL acting with opposite signs on ψ±  fermions that are completely decoupled from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  If the magnetic field was constant across the material  then the electrons would have been subject to Landau  localization rotating around a fixed center, in a semi-  classical picture, and forming Landau levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Since the  moir´e effective magnetic field is inhomogeneous, the semi-  classical picture changes to that of drifting fermions—  rotating around a cycling center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' For lo-  calization to be possible, the drifting fermion should be  able to fit into one magnetic region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The smallest rotat-  ing fermion, according to the uncertainty principle, has  a size of ℓB ∝ 1/  √ ¯B and, since here the average mag-  netic field ¯B is proportional to 1/L, it expands with  √  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  But the size of the magnetic regions, or ▽, is propor-  tional to L which grows faster than ℓB ∝  √  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Thus ▽  gets bigger faster than the smallest possible electron and  eventually can catch one, at which moment one electron  has just been trapped inside the magnetic region and can  complete a cycle there without getting out of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  At that exact moment we expect to have an edge mode  on the boundary of the magnetic region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Appropriately,  for this mode the spin current term is indeed disregard-  able since Sa and ¯ψγaγ3ψ are perpendicular to each other  at ∂▽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' But if there is an edge mode it means that the  number of right or left handed fermions that reside in  the magnetic region must at least be one, n⟳,⟲ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This  again leads us to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (16) and the magic angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This also  can be seen in terms of unit of flux and a restricted type  of Landau quantization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The size of the unit flux is given  by ℓB =  �  Lν/u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Therefore, n = L2/2πℓ2  B = uL/2πν  will be the degeneracy of the restricted Landau level, at  least for large n ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Thus we expect a series of magic  angles connected to each other by steps of δL ≈ 2πν/u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' On the left, a generic electron (red trajectory) drift-  ing in the magnetic region while another electron (green tra-  jectory) is moving close to the edge of one magnetic region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  A right or left handed fermion belongs only to either of the  magnetic regions but since the sides are identified a right  handed fermion in one region is the left handed fermion in  the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Having one electron in both regions is similar to  having two electrons in one region and forgetting about the  other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' On the right the twisted bilayer graphene at first magic  angle with blue dots denoting AA stacking and yellow/green  dots AB/BA stacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The distance between the neighboring  equivalent dots is equal to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Reformulating the theory in terms of Dirac fermions  (4) has other merits as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' For example, the applica-  tion of an external electromagnetic field yields the same  theory (4) but now with the Dirac operator carrying an  additional external gauge field, Aµ,  /D ≡ γµ (∂µ + iAµ + iAµγ5 + iSµiγ3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Upon projecting the Dirac fermions into ψ± ≡ 1  2(1±γ5)ψ  as before, we see that the chiral fermions are now coupled  to the shifted gauge fields Aa ± Aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' For example, if Aa  is due to a constant magnetic field H, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (16) reads  n⟳ = 1  4π  �  ▽  d2x (H ± B) = H  4π  3  √  3  4 L2 ± 3  √  3u  4πν L .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (17)  For u2/ν2 > 4πH/3  √  3, the requirement n⟳ = ±1 has  more than one solution in contrast to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Thus, an  external magnetic field splits each magic angle into  L = ±u  ν  2  H ±  ��u  ν  2  H  �2  ±  16π  3  √  3H ,  (18)  with the magic angles given by θ = 2 arcsin(L/2), while  each combination of pluses and minuses above yields a  solution to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' For a small external magnetic field  H ≪ (3  √  3/4π)u2/ν2 ≈ 140mT the positive solutions  can be written as,  L±  1 = L0± 4π2  27  ν3  u3 H , L±  2 = 4  H  u  ν ±L0− 4π2  27  ν3  u3 H .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (19)  with L0 ≡ 4πν/3  √  3u, being the magic angle in the ab-  sence of the external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In the limit H → 0  we regain the previous magic angle from L±  1 , in addition  to having L±  2 → ∞ that happens when the bilayer is un-  twisted, θ → 0, and the moir´e reciprocal lattice, which  would have a vanishing size, is in fact flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  5  Let us also consider applying a uniform strain on top  of the already existing uniform twist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The moir´e pattern  will rotate by arccos(qθ/|q|) and its length, L, will shrink  accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In this case, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (6), the magnetic  field generated by Aa and its corresponding index are  given by B = qθ u  ν  �  j sin(qj · r) and n⟳ = (qθ/|q|)L/L0  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Comparing this with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (16) we see that  the flat-band now happens at,  L = L0  �  1 + sinh2(ω/2)  sin2(θ/2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  (20)  Now consider the case of finite AA hoppings by grad-  ually increasing v from zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' This is equivalent to rein-  troducing S0 and A0 to the Lagrangian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  The former  vanishes on the edges of magnetic regions (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 2)  and therefore will have no effect on the edge mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' On  the other hand, the A0 term acts as an electric potential  for either ψ±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  An edge mode trajectory is perpendic-  ular to constant A0 curves, so even though A0 might  redistribute the density of the mode along the edge, it  will do little to deviate it out of the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Therefore,  the first magic angle is robust against a non-vanishing  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Like a mass term, γ0A0 does not anti-commute with  the generator of the chiral transformation, Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Since we  have { /D, Γ} ∝ v the v → 0 ensures that the action  is invariant under ψ → eiαΓψ and that for each pos-  itive eigenvalue of /D there is a negative one with the  same magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Deviating form the v = 0 limit breaks  particle-hole symmetry, shifts the eigenvalues of /D, dis-  connects the number of left- and right-handed zero modes  n⟳,⟲ from the Jacobian of the transformation, and gives  the formerly flat-band a curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In this situation we  can define the magic angle, where the flatness of the  band is approximate, through the flux felt by ψ±, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  �  ▽ F12/4π =  �  ▽ Aa ¯ψ∂▽γaψ∂▽ = 1, but this implies an  exact flat-band upon the existence of a well-defined n⟳,⟲  which can be found only at v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  As we have seen in this Letter, although anomalies are  not present in all dimensions, it is still possible to con-  jure them in specific situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In particular, a flat band  can be described through an anomaly in the timeless ver-  sion of its hosting theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' We saw that the dimensionally  reduced theory and thus the flat band are not always re-  alizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' In the case of bilayer graphene, the obstruction  comes from the chiral anomaly and the need to satisfy  an index condition, which in turn confirms the topologi-  cal nature of the flat band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' The Dirac field theory form,  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' (4), of the bilayer moir´e lattice problem allows many  generalizations including the finite temperature case, the  presence of complex inhomogeneous external fields and  general deformations, and interaction effects in the spirit  of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' [16, 17] where the interplay of anomaly with in-  teractions are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Of particular interest are quan-  tum Hall phenomena and unconventional superconduct-  ing pairing associated with the moir´e gauge fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  This  work  was  supported  by  the  National  Sci-  ence Foundation under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  DMR-2037158,  the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Army Research Office under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  W911NF1310172, and the Simons Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lopes dos Santos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Peres, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Castro Neto, Graphene bilayer with a twist: Electronic  structure, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 99, 256802 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [2] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Bistritzer and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' MacDonald, Moir´e bands  in twisted double-layer graphene, Proceedings of the  National  Academy  of  Sciences  108,  12233  (2011),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='org/content/108/30/12233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' San-Jose, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Gonz´alez, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Guinea, Non-abelian  gauge potentials in graphene bilayers, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  108, 216802 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Tarnopolsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Kruchkov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Vishwanath, Ori-  gin of magic angles in twisted bilayer graphene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 122, 106405 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Cao, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fatemi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Taniguchi,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Kaxiras, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Jarillo-Herrero, Unconventional super-  conductivity in magic-angle graphene superlattices, Na-  ture 556, 43 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [6] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Cao, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fatemi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Demir, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Tomarken,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Sanchez-Yamagishi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Watanabe,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Taniguchi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Kaxiras, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=', Correlated insulator be-  haviour at half-filling in magic-angle graphene superlat-  tices, Nature 556, 80 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Andrei and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' MacDonald, Graphene bilayers  with a twist, Nature materials 19, 1265 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Balents, General continuum model for twisted bilayer  graphene and arbitrary smooth deformations, SciPost  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 7, 48 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Sboychakov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rakhmanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rozhkov,  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Nori, Electronic spectrum of twisted bilayer  graphene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' B 92, 075402 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Zou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Po, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Vishwanath, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Senthil, Band  structure of twisted bilayer graphene: Emergent symme-  tries, commensurate approximants, and wannier obstruc-  tions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' B 98, 085435 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Parhizkar and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Galitski, Strained bilayer graphene,  emergent energy scales, and moir´e gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  Research 4, L022027 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Parhizkar and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Galitski, Moir´e gravity and cosmol-  ogy (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fujikawa and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Suzuki, Path integrals and quantum  anomalies, 122 (Oxford University Press on Demand,  2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Atiyah and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Singer, The index of elliptic op-  erators on compact manifolds, Bulletin of the American  Mathematical Society 69, 422 (1963).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [15] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Fujikawa, Path-integral measure for gauge-invariant  fermion theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 42, 1195 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rylands, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Parhizkar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Burkov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Galitski,  Chiral anomaly in interacting condensed matter systems,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' 126, 185303 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content='  [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rylands, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Parhizkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Galitski, Non-abelian  bosonization in a (3+1)-d kondo semimetal via quantum  anomalies, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
+page_content=' B 105, 195108 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtAyT4oBgHgl3EQf6frG/content/2301.00824v1.pdf'}
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+Virtual physics laboratory courses: An evaluation of students’ self-efficacy and
+intelligence mindset
+Meg Foster,∗ Philip von Doetinchem,† and Sandra von Doetinchem‡
+University of Hawai‘i at M¯anoa
+(Dated: January 10, 2023)
+Following the emergence of COVID-19 in Spring 2020, undergraduate in-person physics laboratory
+courses at a R1 public university were adapted for remote learning to accommodate the subsequent
+campus closure. Video lectures and web-based virtual experiments were utilized to provide students
+enrolled in these laboratories with required learning materials on a weekly basis. During the fall
+semester of the 2021–2022 academic year, optional Kahoot! quizzes were offered in addition, serv-
+ing to incentivize participation and to provide self-efficacy opportunities to students. This study
+sought to explore the intersection of self-efficacy growth, self-regulatory behaviors, and intelligence
+mindsets (i.e., having fixed or growth mindsets) for students and to examine the impact of these
+remote learning methods. Using a modified version of the Colorado Learning Attitudes About Sci-
+ence Survey (CLASS), students’ physics self-efficacy was measured at the beginning and end of the
+semester. The analysis revealed that participation in Kahoot! alone did not correspond to greater
+self-efficacy scores or greater self-efficacy change. However, a strong correlation was observed be-
+tween intelligence mindset and self-efficacy for both pre-and post-surveys. Pre-survey intelligence
+mindset scores were not related to average Kahoot! performance, while post- survey intelligence
+mindsets were. Finally, positive self-efficacy change ⟨c⟩ was measured for the class, but was not
+statistically significant.
+Keywords: remote learning, game-based learning, self-efficacy, intelligence mindsets, physics education re-
+search
+I.
+INTRODUCTION
+Faced with the initial outbreak of COVID-19 in March 2020, higher education institutions worldwide were forced to
+modify countless aspects of their operations. In an effort to accommodate health and safety guidelines, many institu-
+tions opted for a transition to online teaching-learning methods. The urgency of the situation and lack of preparedness
+at both the institutional and national levels bore a sense of responsibility for educators and administrations to usher
+in a new era of teaching and learning, practically overnight. In the following two and a half years, the merits of
+distance education and remote learning have given rise to a new outlook on teaching-learning methods and created a
+new perspective surrounding classroom technology. In a 2020 publication, Mishra et al. [1] stated that the integration
+of technology and other pivotal online tools in higher education will enable instructors to teach with methods that
+students not only feel comfortable with, but which match the demands of the 21st century; and many agree [2–7].
+As technology integrates more fully into classrooms and a new era of mobile learning [8] emerges, a focus on
+constructivist teaching methods and a shift toward learner-centered instruction seems apparent [9–11]. These methods
+not only allow, but encourage students to construct their own understanding of the learning content [12] through
+lessons that support self-paced learning. For example, the Flipped Classroom (FC) model has been growing widely
+in higher education science courses, embraced for its unique ability to produce active learning environments in large
+lecture courses, cultivate self-paced learning, motivate further learning, and for its popularity among students [13–15].
+This model for teaching equips students with online tools and resources and is driven by self-paced learning outside
+the classroom.
+The proliferation of online learning and incorporation of classroom technology (such as virtual labs) has coincided
+with and educational landscape that brings more learner-centered methods to the table. In response, educational
+researchers have sought to understand how instructional approaches (e.g., flipped classrooms, virtual labs, etc.) might
+impact students’ attitudes and beliefs. In general, the study of personal attitudes and beliefs is examined through
+the framework of self-efficacy.
+The framework of self-efficacy was developed by Bandura [16] in 1977 and is defined as the confidence one has
+in their own ability to perform a particular task. It is developed and moderated by personal attitudes, beliefs, and
+experiences, and is understood to have four main sources. Identified by Bandura [17], these are mastery experiences,
+∗ mfoster3@hawaii.edu
+† philipvd@hawaii.edu
+‡ sandravd@hawaii.edu
+arXiv:2301.02699v1  [physics.ed-ph]  6 Jan 2023
+
+2
+vicarious experiences, social persuasion, and emotional states. Mastery experiences reflect perceptions of personal
+task performance (e.g. “I did well on the exam, so I understand this topic well”), whereas vicarious experiences
+reflect perceptions based on the task performance of others (e.g. “My study group did well on the exam, so I expect
+to do well too.”). Self-efficacy perceptions are also influenced by social persuasion (e.g. receiving a pep talk) or
+by an individual’s emotional state (e.g. experiencing anxiety or an adrenaline rush). In the classroom, a student’s
+self-efficacy will inform decisions about how to prepare for an exam, whether or not to ask a question in class, or what
+kind of goals to set for a course. Furthermore, the utility of understanding the role of self-efficacy in academia lies
+in the expectation that students with high academic self-efficacy are more likely to succeed in school, choose career
+paths that require success in academia, and choose majors that align with their self-beliefs about personal capabilities
+[18–22].
+From high school to university, physics classrooms have been designed and equipped to help students understand
+the world around them. Unfortunately, few students ever attain a strong personal conviction that they have achieved
+this goal. Moreover, it is not uncommon for undergraduate students to report negative attitudinal shifts towards
+the subject after completing an introductory physics course [23–25]. This means that students tend to have more
+expert-like beliefs at the beginning, rather than the end, of an introductory physics course. Given that physics is a
+discipline of curiosity and investigation, many have speculated why this occurs. Knight [26] suspects that this issue
+stems from the fact that students do not attend their first physics lecture as blank slates, but are rather filled with
+experiences and ideas about the world around them [27–29]. These beliefs and conceptions from day-to-day life guide
+their understanding of the natural world, but are not necessarily correct [26–30]. Responses that differ substantially
+from the views of physicists are called pre- or misconceptions. Students use these strongly held beliefs, whether true
+or not, to explain and predict physical processes [31] and are incredibly difficult to change [26–28, 32]. McDermott
+[33] supports this observation with her statement summarizing the constructivist view, “all individuals must construct
+their own concepts, and the knowledge they already have (or think they have) significantly affects what they learn.” It
+appears that developing positive self-efficacy is not the result of known ledge alone, but rather knowledge acquisition
+accompanied by a belief that this knowledge is accessible and understood.
+As digital transformations sweep the educational landscape, institutions must develop reliable technology-enabled
+learning for students. These adaptations will ensure quality educational outcomes in the wake of future unforeseen
+academic disruptions and assist in addressing pre-pandemic educational disparities [1]. In examining physics self-
+efficacy, the goal of research is not just to understand the way students feel towards physics but also their impressions
+on the relevance of physics to the real world, connections between mathematical equations and physical reality, and
+the coherence of physics concepts. This study aims to examine how instructional methods applied to a remotely
+taught undergraduate physics laboratory course at a R1 public university impact the self-efficacy of students and to
+explore what beliefs and behaviors inform these opinions. An online survey was used to probe physics self-efficacy,
+online learning attitudes, and the intelligence mindsets held by these students.
+II.
+PREVIOUS RESEARCH
+Over the last three decades, researchers have identified a variety of student attitudes and beliefs that shape and
+are shaped by classroom experiences [30, 34–40]. To better understand these experiences in the physics classroom,
+instruments such as the Maryland Physics Expectations Survey (MPEX) [23], the Epistemological Beliefs Assessment
+for Physical Science (EBAPS) [41], the Colorado Learning Attitudes about Science Survey (CLASS)[24], along with
+others, have been developed and used to probe student perspectives and epistemological beliefs in physics. In addition,
+intelligence mindsets have recently been explored, particularly in fields that are generally male-dominated. These
+findings, discussed below, provide important insight into why certain fields, such as physics, have persistent gender
+disparities.
+A.
+The Colorado Learning Attitudes About Science Survey
+As an evaluation tool, the CLASS has assisted researchers in reforming educational practices to improve students’
+attitudes toward science [42, 43]. Developed by Adams et al. [24] at the University of Colorado Boulder (CU Boulder),
+the CLASS was specifically designed to probe students’ beliefs about physics and learning physics and to distinguish the
+beliefs of experts from those of novices and has been used widely used as a tool for evaluating instructional techniques
+[43, 44]. In this way, expert beliefs refers to answers consistently chosen by expert physicists to questions on the
+CLASS survey. Aside from physics, the CLASS has been modified for use in biology, chemistry, astronomy, and math
+[45, 46] and translated for use in several languages [47].
+
+3
+Composed of forty-two Likert-style questions, the CLASS allows respondents to answer on a scale ranging from
+strongly disagree (1) to strongly agree (5) to statements such as “I study physics to learn knowledge that will be useful
+in my life outside of school.” For scoring purposes, the responses strongly (dis)agree and (dis)agree are collapsed
+and student responses are coded as agree, disagree, or neutral. Neutral answers are not scored as they do not agree
+or disagree with the view consistently held by experts. A student’s self-efficacy score is reflected by the number
+of favorable (expert-like) responses chosen and is referred to as the percent favorable.
+Based on factor analysis,
+Adams et al. [24] also determined that twenty-six of the forty-two questions are grouped into eight overlapping
+categories, characterizing different aspects of student thinking: Real World Connections (RCW), Personal Interest
+(PI), Sense Making and Effort (SME), Conceptual Connections (CC), Applied Conceptual Understanding (ACU),
+Problem Solving General (PSG), Problem Solving Confidence (PSC), and Problem Solving Sophistication (PSS).
+B.
+Self-Efficacy Development
+Self-efficacy represents a consequential component of understanding the academic outcomes of students. Studies
+have shown that self-efficacy can predict a student’s persistence in the face of difficulty, effort and performance, course
+enrollment [48], and choice of career [49]. Consequently, individuals with high self-efficacy are more likely to persist
+at tasks and preserve in the face of challenging or adverse experiences [16, 19, 20, 50–52]. Examining students’ self-
+efficacy beliefs puts deliberate attention to the perceptions of students and can help educators be more effective. A
+study by Hall and Webb [53] found that autonomy-supportive instructors (who acknowledge students’ perspectives
+and feelings) can positively impact the motivation and performance of students and is positively correlated with
+student interest and enjoyment in learning physic.
+When it comes to self-efficacy development, research has revealed differences in the role that the four sources of self-
+efficacy (mastery experiences, vicarious experiences, social persuasion, and emotional states) have on influencing the
+personal beliefs of male and female students [54]. A study published by Zeldin and Pajares [55] revealed that verbal
+persuasions and vicarious experiences were critical sources of women’s self-efficacy beliefs and found that the perceived
+importance of these sources may be stronger for women in male-dominated domains. A later study by Zeldin et al. [56]
+added to this claim with the following conclusion: “The self-efficacy beliefs of men in these male-dominated domains
+are created primarily as a result of the interpretations they make of their ongoing achievements and successes. Women,
+on the other hand, rely on relational episodes in their lives to create and buttress the confidence that they can succeed
+in male-dominated domains.” A similar study of high school students by Britner [57] reported that interpretations of
+self-efficacy sources are gendered and also vary by field of science. In a 2012 study, Sawtelle et al. [58] found that
+predicting the probability of passing an introductory calculus-based physics course for women relies primarily on the
+vicarious learning experiences source, with no significant contribution from the social persuasion experiences, while
+predicting the probability of passing for men requires only the mastery experiences source.
+These findings underscore how instructional techniques can significantly impact the outcomes of students, par-
+ticularly in STEM fields. Exposing these gender differences through instruments such as the CLASS have equipped
+educators in their positions of power to facilitate better classroom experiences and to teach in a way that acknowledges
+the perspectives and beliefs of students. Measures like this have been shown to significantly improve the experiences
+of female students, specifically in laboratory settings and in science classrooms [53].
+C.
+Instructional Pedagogy: A Shift toward Learner-Center Approaches
+The learner-centered pedagogy broadly implies that students are given the opportunity to participate in the learning
+process. This can also be understood through a constructivist lens as summarized by McDermott [33] when she stated
+that “meaningful learning, which connotes the ability to interpret and use knowledge in situations not identical to
+those in which it was initially acquired, requires a deep mental engagement by the learner.” That is, students engaged
+with the material and cognitively involved in the learning process are participating in meaningful learning.
+In an effort to provide more self-efficacy enriching experiences to students, science educators have examined several
+aspects regarding the way students learn and understand scientific ideas. In fact, factors such as gender [59–61],
+field of study [62], prior instruction [61], perceptions of belonging [63], parenting styles [64], participation, sense of
+autonomy [53], instructional pedagogy [25, 65], and ethnicity have all been examined by researchers for their role in
+influencing student attitudes and beliefs in the physics classroom. Furthermore, sufficient research has shown that
+classroom experiences and student self-efficacy are strongly correlated [66]. For instance, in a study comparing physics
+laboratory pedagogy, Wilcox and Lewandowski [38] found that physics labs that focused on developing lab skills led
+to more expert-like post-instruction self-efficacy scores than did those that focused on reinforcing concepts developed
+in lecture. Likewise, in a comparison of interactive-engagement (IE) and traditional physics instruction methods,
+
+4
+Hake [40] revealed that “conceptual and problems-solving test results strongly suggest that the classroom use of
+IE methods can increase mechanics-course effectiveness well beyond that obtained in traditional practice.” In this
+manner, traditional teaching implies that students play a passive role in the learning process. In the literature, this is
+also referred to by phrases such as “transmissive lecture style”, “unidirectional instruction”, and “teacher-centered.”
+These methods have been shown by researchers to have little effect on students’ personal development [67] and have
+been shown to “impart little conceptual understanding of Newtonian mechanics.” [40]
+Attempts to remedy the shift away from expert-like beliefs in introductory physics courses have been met with
+intermittent success. For instance, IE, capable of producing significant conceptual gains in physics, falls short of
+producing significant improvements in physics self-efficacy. Similarly, interactive lecture experiments were shown by
+Moll and Milner-Bolotin [68] to be insufficient at significantly improving student attitudes toward physics. On the
+other hand, physics curricula such as Physics by Inquiry [69], Physics for Everyday Thinking [70], and Modeling
+Instruction [42, 43, 71] have found success at improving student attitudes and beliefs in physics as measured by
+instruments such as the CLASS. Lindsey et al. [72] credits the epistemological focus of these curricula for their
+success across multiple implementations. By placing an intentional focus on students’ conceptual development, these
+curricula are forced to reckon with student misconceptions and, to be successful, must nurture and inspire meaningful
+learning. In developing instructional techniques that cater to epistemological development, successful curricula have
+come to reflect the learner.
+Other learner-centered teaching approaches can be achieved through active learning methodologies (ALM), which
+strive to engage and motivate students in the learning process. For example, the FC model, characterized by its ability
+to allow self-paced learning outside of the classroom, affords more time to be spent in the classroom cultivating qualita-
+tive reasoning skills, addressing common misconceptions, and reviewing challenging topics. Furthermore, research has
+identified that flipped approaches can help students manage cognitive loads more effectively as self-paced preparatory
+work might better manage working memory compared with traditional methods (i.e., face-to-face, teacher-centered)
+[67]. In addition to FC models, Problem/Project/Practiced-Based Learning (P3BL) [73], team-based learning, peer
+instruction [29], guided-discovery [74, 75], and recently, gamification [76–82] have been explored for their ability to
+positively impact student learning outcomes and science perceptions. These so-called blended methodologies show
+promise in physics education, as shown by Forndran and Zacharias [79] in their study examining the effects of gami-
+fication in a course on electric resistors, which reported high engagement and acceptance by students.
+The broadly used learning platform Kahoot! was designed to engage students through interactive quizzes and has
+become a popular tool for classroom feedback and assessment since its release in 2013. Students participate on their
+own devices (computer, tablet, phone, etc.) and compete with peers using game-generated nicknames, typically all
+while in the classroom. A student-paced challenge mode was launched in 2018 [83], allowing students to play at
+their own pace. Research suggests that using Kahoot! as a classroom tool can lead to many positive outcomes for
+students [84, 85]. For example, in addition to real-time feedback, studies have reported that using Kahoot! as a
+classroom tool can increase student engagement [35, 36], clarify misunderstandings [6], motivate further learning [86],
+and increase enjoyment in the learning process [80, 84, 85]. For a literature review of Kahoot!’s effect on learning,
+see Wang and Tahir [37]. While Kahoots!’s effect on physics self-efficacy has not been studied, a recent paper by
+Shyr et al. [87] found that the use of Kahoot! in a remedial math course led to improved self-efficacy outcomes for
+a group of middle school students. The paper did not identify which self-efficacy sources were responsible for these
+changes, so it remains unclear how this tool influences self-efficacy perceptions. However, given typical classroom use,
+it is reasonable to hypothesize that mastery and vicarious experiences are the primary influencers. By completing
+a Kahoot! quiz, students are able to evaluate their individual performance (i.e. Kahoot! as a mastery experience),
+as well as the performance of others, which in turn, also impacts their self-efficacy perceptions (i.e. Kahoot! as
+a vicarious experience). Because female students generally cite vicarious experiences, not mastery experiences, as
+having more influence on self-efficacy perceptions (especially in male-dominated fields), successful experiences with
+Kahoot! in physics classrooms is hypothesized to support the self-efficacy development of female students more than
+male students.
+In a similar manner, interactive web-based learning environments, such as virtual laboratories (VL), can provide
+better learning environments for students to develop an understanding of scientific outcomes [88] and may support
+students’ mastery of concepts [89] compared to traditional face-to-face methods. In a recent study exploring the
+effectiveness of virtual experiments on physics laboratory students’ learning, Hamed and Ahmad [90] came to the
+conclusion that “substituting face-to-face theoretical preparation in the general physics lab is at least as effective as
+using virtual experiments.” The authors further state, “students with virtual components acquired deeper understand-
+ing of physics concepts and were better prepared for carrying out real experiments.” Like FC models, this approach
+afforded students more time and flexibility in the learning process. In a similar study, researchers at CU Boulder
+found that students who used computer simulations to carry out experiments outperformed their peers (who had used
+real equipment) on both a conceptual survey and in the coordinated task of assembling a real circuit and describing
+how it worked [91].
+
+5
+D.
+Mindsets and Motivation
+In addition to examining the self-efficacy beliefs of physics students, researchers have recently explored the nature
+of intelligence mindsets and their influence on student attitudes and beliefs. Identified by Dweck [92] as two primary
+implicit theories of intelligence, “fixed mindset” and “growth mindset” have been examined by physics education
+researchers for their role in aspects ranging from academic achievement [60, 93] to departmental decision-making
+[94]. These studies found that personal beliefs about intelligence inform student motivation and persistence and can
+moderate the impact of self-efficacy sources on self-efficacy development.
+On an individual level, those with a fixed mindset see intelligence as immutable, something which cannot be
+improved; they interpret difficult cognitive tasks or academic settings as potentially revealing the limits of their
+intelligence and, therefore, may choose to avoid them [92, 95, 96]. Alternatively, those with a growth mindset believe
+that intelligence is a capacity that can improve incrementally with increased knowledge and effort; they interpret
+difficult intellectual tasks as opportunities for learning and may seek them out [92, 95, 96]. A study by Scherr et al.
+[94] made two significant observations on the topic. One, that most individuals do not adhere strictly to a “fixed” or
+a “growth” mindset, but some combination of both, and two, that having a “fixed mindset” (also called an “entity
+theory of intelligence”) is consistent with research identifying physics as a “brilliance required” field. In such fields,
+members tend to believe that raw, innate talent is a primary requirement for success in the discipline.
+Studies such as those by Gray et al. [32] and Marshman et al. [97] have shown that gender plays a consistent
+role in contributing to students’ beliefs about physics and learning physics. For example, using the CLASS, Gray
+et al. [32] compared responses for which students answered once for themselves and once for how they thought a
+physicist would respond. The study revealed that introductory physics students tend to have a surprisingly accurate
+understanding of the beliefs held by expert physicists (regardless of prior physics exposure) and that female students
+report much greater differences between these two sets of responses than their male counterparts. This suggests that
+students, female students in particular, understand what physicists believe but do not identify with these beliefs.
+Likewise, Marshman et al. [97] found that female students with A grades have similar physics self-efficacy beliefs as
+male students with C grades in introductory physics courses [97]. These findings suggest that gendered stereotypes
+may play a significant role in the development of self-efficacy. Another troubling finding was revealed through a study
+by Bian et al. [98], which found that beginning at the age of six, girls start to avoid activities said to be for children
+who are “really, really smart” [98] suggesting that beliefs about intellectual abilities are endorsed by children very
+early on. These deep-rooted stereotypes, along with the maintenance that physics is a “brilliance required” discipline,
+likely contribute to the under-representation of women in physics [99]. Unfortunately, women and underrepresented
+ethnic or racial minorities have remained severely underrepresented in physics, accounting for just 19% and 7% of all
+PhDs awarded in the U.S., respectively [100].
+III.
+THE STUDY
+A.
+Pandemic Related Course Modifications
+Following the emergence of COVID-19 in the spring of 2020, all physics laboratory courses at this R1 university
+were modified for online instruction. In this regard, three substantial modifications were made to the undergraduate
+physics laboratory course and were still in place at the time of this study.
+1.
+Laboratory Videos
+Given that the transition from face-to-face to remote learning occurred in a matter of one week, finding a way to
+fulfill laboratory course objectives without needing students to come on campus became an urgent responsibility for
+the course’s teaching assistants (TAs). As a solution, the TAs performed the experiments and collected experimental
+data on behalf of the students. For each experiment, data were stored in a separate Google sheets document. TAs
+also recorded the experimental setup procedures and documented the process of collecting data. Clipped together
+and narrated, these videos came to be called “experiment videos.” Additionally, videos explaining the theoretical
+motivation for these experiments were put together as “theory videos.” Experiment videos ranged in length from four
+to eight minutes and theory videos ranged from six to ten minutes. During each of the twelve experiment weeks,
+data and videos pertaining to that experiment were uploaded to the class website. Worksheet assignments were used
+to tie all learning materials together.
+
+6
+TABLE I. An outline of the laboratory experiments carried out during the semester. The first Kahoot! was played during
+Week 3 for the Electric Deflection experiment. The pre-CLASS was offered during Weeks 4 and 12.
+Week
+Experiment
+1
+Simple Electric Circuit with LED
+2
+Electric Field Mapping
+3
+Measuring Electric Deflection with a CRT
+4
+Operation of an Oscilloscope
+5
+Ohm’s and Kirchhoff’s Laws
+6
+Capacitors
+7
+Magnetic Field Mapping
+8
+Charge-to-Mass Ratio of Electrons
+9
+Inductors
+10
+Natural Oscillations with RLC Circuit
+11
+Driven Oscillations with RLC Circuit
+12
+Snell’s Law and the Lensmaker Equation
+2.
+Virtual Experimentation
+The second modification was the addition of web-based virtual laboratories. For most experiments, the Physics
+Education Technology (PhET) [101] platform was utilized, though other platforms such as GeoGebra [102], NTNU
+Java Virtual Physics Laboratory [103], and MIT Mathlets [104] were also utilized. These free online platforms provided
+high-quality science simulations and allowed students to simulate nearly identical experiments to the ones performed
+by TAs. For the “Virtual Experiment” portion of the laboratory worksheets, students followed instructions for setting
+up the simulated experiment, inputting the necessary parameters, and conducting the experiment. Students also
+collected data, performed error analysis, and drew conclusions from the simulations. This component was included to
+give students experience with laboratory equipment and procedures, to gain practical knowledge, and to foster their
+experimental physics self-efficacy.
+3.
+Game Based Learning
+Another modification was the incorporation of the online game-based learning (GBL) platform Kahoot!. At the
+beginning of the 2021 fall semester, ten Kahoot!
+quizzes were created to align with the laboratory experiments
+for Weeks 3 through 12.
+These quizzes are publicly available on Kahoot!
+[105].
+All quizzes were composed of
+nine questions aimed to probe students’ understanding of the physics concepts underlying each experiment, their
+understanding of the experimental setup, and the potential outcomes of the experiment. In general, the design of
+each Kahoot! reflected the intention to motivate student engagement, expose misconceptions, and foster conceptual
+growth. The answers could always be found in at least two of the following student materials: the laboratory manual,
+the theory video, or the experiment video. Questions varied from multiple choice to multiple select to fill in the blank.
+B.
+Methods
+The goal of this study was to document how COVID-19-related course modifications, particularly the incorporation
+of FC methods and the supplement of optional GBL Kahoot! quizzes, affected the self-efficacy beliefs of introductory
+physics students’ enrolled in a remote laboratory course. During the 2021 fall semester, students enrolled in the
+General Physics II laboratory sections attended weekly 50-minute online lectures held by TAs as a means to tie all of
+the learning materials together. Utilizing Zoom, all online meetings were held synchronously and offered throughout
+the week for various lab sections. During these lectures, TAs discussed the motivation behind the experiment, reviewed
+relevant equations and derivations, and although students did not collect data in person, experimental setup and data
+collection procedures were reviewed. All laboratory materials, including the laboratory manual, worksheets, theory
+videos, experiment videos, virtual experiments, and Kahoot! access codes were provided to students via the class
+website on a weekly basis and prior to all meetings.
+
+7
+1.
+Data Collection
+For the purpose of this study, an abbreviated version of the CLASS was utilized. This modification was implemented
+to increase participation by means of a shorter survey. In the end, twenty-one questions were selected from the twenty-
+six questions belonging to the self-efficacy subcategories mentioned prior. The questions retained for this study can
+be found in Table VII in the Appendix.
+During Week 3 of the semester, students opting to participate in the study played the first Kahoot! quiz and received
+their game-generated nickname (which they were encouraged to write down). In the following weeks, students who
+remembered their nicknames played weekly Kahoot! games under the same alias, establishing a way to anonymously
+track students’ participation and to establish a way for comparing individuals’ pre- and post-survey results. Students
+who forgot their nickname or did not participate in the first Kahoot! quiz still had the option to participate in
+future Kahoot! quizzes and the abbreviated CLASS survey. During Week 4, the abbreviated CLASS was offered
+to students electronically via a Google form. To maximize participation in the study, students were offered extra
+credit for completing it outside of class time. No identifying information was collected by the form aside from the
+game-generated nickname.
+In addition to the twenty-one CLASS questions, the Google form asked for the student’s gender identity and
+included six questions on intelligence mindsets, two questions on test-related anxiety, and five questions regarding
+online learning. These questions were included to investigate their relation to self-efficacy or participation. Each
+week, students were provided with a Kahoot! code and a one-week window of time to play.
+2.
+Data Analysis
+The objective of this analysis was two-fold. First, data was analyzed to measure the impact of pandemic-related
+physics laboratory modifications on students’ physics self-efficacy over the course of one semester of instruction. Then,
+an analysis was carried out to understand what attitudes and beliefs (physics self-efficacy or intelligence mindset
+related) tend to be successful for improving physics self-efficacy. This was examined by comparing students’ percent-
+favorable (hereby “self-efficacy”) scores at the beginning and end of the semester. Before statistical analysis was
+performed, data cleaning was carried out for both pre- and post- surveys. First, individual surveys were eliminated if
+the moderating CLASS question, Question 13 (see Table VII), was answered incorrectly. Other data cleaning measures
+included removing surveys for which students made the same selection for every question or completed less than half
+of the survey (this did not apply to any students in this study).
+Data obtained from both pre-and post-surveys followed approximately normal distributions with roughly equal
+variance in both pre- and post-scores. For this reason, parametric statistical tests were utilized to compare paired
+and unpaired sample means with paired t-tests and independent t-tests, respectively. An α significance level of 0.05
+was applied to all statistical tests, and following the recommendations of Day et al. [106], for statistically significant
+outcomes, Cohen’s d is report to represent effect size. Changes in self-efficacy for this study were examined using the
+average normalized change c,
+c =
+�
+�
+�
+�
+�
+(post − pre)/(max − pre)
+if post > pre
+0
+if post = pre
+(post − pre)/(pre)
+if post < pre
+(1)
+defined as the ratio of the gain to the maximum possible gain (or as the loss to the maximum possible loss), where gain
+is measured by taking the difference between post- and pre- (modified) CLASS scores. To measure c for individual
+students, game-generated nicknames were used to pair pre- and post-survey scores. For non-participating students
+and to measure change for the entire student sample, normalized change ⟨c⟩,
+⟨c⟩ = ⟨post⟩ − ⟨pre⟩
+max − ⟨pre⟩
+(2)
+was computed using class averaged ⟨pre⟩ and ⟨post⟩ (modified) CLASS scores. After dropping the moderating question,
+the max self-efficacy score was twenty.
+
+8
+IV.
+RESULTS AND DISCUSSION
+A.
+Attitudes toward Online Learning
+In addition to exploring the intelligence mindsets and self-efficacy beliefs of introductory physics students, the
+primary aspect of this study aimed to evaluate how pandemic-related course modifications might influence students’
+self-efficacy perceptions. These course modifications reflected a shift toward learner-center pedagogy and included
+aspects of flipped learning, such as laboratory and theory videos to be watched outside of class, the addition of virtual
+experiments for all labs, and elements of game-based learning through optional weekly Kahoot! quizzes. The five
+additional survey questions used to measure student beliefs toward online learning are shown in Table II.
+TABLE II. This table gives the results from the attitudes toward online learning portion of the survey. Mean scores for each
+of the five questions are shown for both pre- and post- surveys.
+Question
+⟨pre⟩
+⟨post⟩
+1. Virtual learning encourages me to learn independently.
+3.6 ± 0.2
+3.5 ± 0.1
+2. I prefer to learn in person.
+3.7 ± 0.2
+3.9 ± 0.1
+3. I am satisfied with the online resources developed for this course.
+3.5 ± 0.1
+3.5 ± 0.1
+4. Interactions with classmates help me learn.
+3.5 ± 0.1
+3.8 ± 0.1
+5. Virtual classrooms modernize education.
+3.1 ± 0.2
+3.2 ± 0.1
+At the start of the Fall 2021 semester, attitudes toward online learning varied. Nearly 40% of respondents selected
+the neutral answer for Question 4, with about 15% of students selecting disagree or strongly disagree. Most students
+believed that virtual learning encourages independent learning, yet 35% of students strongly agreed with the statement
+in Question 2, preferring to learn in person. Answers to Question 3 indicated that by Week 4 of the semester, there
+was a general attitude of satisfaction regarding the online resources developed for the course. Interestingly, students
+were undecided on the notion that virtual classrooms modernize education, with nearly 40% preferring to stay neutral
+on the topic.
+By the end of the semester, students were still split on the topic of Question 5, with nearly an identical breakdown
+of responses reported on the post-survey. Interestingly, the belief that interactions with classmates aid in the learning
+process shifted significantly toward strongly agree, with only 26% remaining neutral and over 60% selecting either
+agree or strongly agree. The number of respondents strongly agreeing with Question 3 rose 10% while those in strong
+disagreement increased from 4% to 9%. Students became slightly more polarized in preferring to learn in person, with
+10% more students in strong agreement and 3% more percent in strong disagreement. Finally, the mean response to
+Question 1 remained relatively unchanged.
+Of the five online learning questions (See Table II) included in the survey, only one revealed a statistically significant
+difference between genders. This question, Question 3, weighed students’ satisfaction with online resources developed
+for the course. Female students reported a mean response of 3.9 ± 0.1, whereas males reported a mean of 3.0 ± 0.2
+(p = 0.005). Further analysis revealed that female students were twice more likely to report satisfaction with the
+course’s online materials than male students. Seventy percent of female students agreed or strongly agreed with this
+statement, compared to just 35% of male students. This sentiment increased for male students by the end of the
+semester to 52% while female students’ approval remained at 70%. Question 5 also garnered different means from
+each gender, but it was not enough to be significant. At the beginning of the semester, about half of all male students
+agreed or strongly agreed with the statement, virtual learning encourages me to learn independently, compared to
+70% of female students. This sentiment persisted to the end of the semester for males, but dropped from 70% to 60%
+for female students coinciding with a 22% increase in females answering strongly agree to the statement, interactions
+with classmates help me learn, and a 17% increase in females answering strongly agree to I prefer to learn in person
+at the end of the semester.
+At the beginning of the semester, male students were more likely than female students to believe that interactions
+with classmates help them learn. Around 1 in 5 females chose strongly disagree for the statement in Question 4,
+whereas 1 in 10 males did. At the same time, 35% of female students agreed or strongly agreed with this statement
+compared to 60% of male students. At the end of the semester, this percentage was around 60% for both genders.
+B.
+Self-Efficacy
+Pretest scores from the modified CLASS survey revealed an average self-efficacy score of 8.3 ± 0.5 (n = 65) out
+of a possible twenty. This “percent favorable” score (41%) is lower than average according to Adams et al. [24] who
+
+9
+cites scores in the 60-70% range as typical for a calculus-based Physics I course at a large state research university
+(LSRU). In this study, calculus-based and algebra-based sections reported slightly different pretest averages with
+the calculus-based sections outscoring the algebra-based sections. Students in the calculus-based laboratory had an
+average pretest score of 8.7 ± 0.6, whereas students in the algebra-based laboratory had an average of 7.7 ± 0.6.
+Interestingly, females outscored males in the algebra-based sections, while the reverse was true for the calculus-based
+sections. Overall, differences between male and female pretest scores were not statistically significant, with males
+reporting an average of 8.5 ± 0.6 and females 8.3 ± 0.6.
+Post-test scores revealed an average self-efficacy of 9.3 ± 0.4 (n = 110) corresponding to a 5% increase in “percent
+favorable” for the class. This increase corresponded to a class-averaged normalized change ⟨c⟩ of 0.09 and an effect size
+of 0.27. Mean post-test scores for the calculus-based and algebra-based sections were 10.2 ± 0.5 (n = 58) and 8.3 ±
+0.5 (n = 52), respectively. Unlike the pretest, the difference in means between these groups was significant (p < 0.01).
+Female students in the calculus-based course had significantly (p < 0.05) more expert-like beliefs at the end of the
+semester compared to the beginning, with a final self-efficacy score of 10.9 ± 0.9 and a positive normalized change
+of 0.25. On the other hand, female students in the algebra-based sections were the only group to report negative
+normalized change (see Table III).
+TABLE III. Pre- and post- survey results for the calculus-based and algebra-based laboratory sections. p-values measure the
+significance of each groups’ mean score change. The * indicates a significant result.
+Group
+⟨pre⟩
+⟨post⟩
+⟨c⟩
+p
+Calculus-Based
+All
+8.7±0.6
+10.2±0.5
+0.10
+p > 0.05
+Female*
+7.9±1.2
+10.9±0.9
+0.30
+p < 0.05
+Male
+9.3±0.7
+9.6±0.6
+0.03
+p > 0.05
+Algebra-Based
+All
+7.7±0.6
+8.3±0.5
+0.04
+p > 0.05
+Female
+8.6±0.7
+8.5±0.7
+–0.01
+p > 0.05
+Male
+6.5±1.2
+8.1±0.8
+0.12
+p > 0.05
+C.
+Optional Game Quizzes
+During Week 3 of the semester, 157 students obtained anonymous nickname identities by participating in the first
+Kahoot! quiz. In Week 4, 71 opted to complete the pre-survey and 65 were retained for correctly answering the
+moderating question (see Table VII). These students are referred to as the Initial Participants. Students who took
+both pre- and post-surveys, as identified by their game-generated Kahoot! nicknames, make up the Players group
+(n = 26). Over the course of the semester, a group of consistent players emerged from the Initial Participants group.
+These students who played five or more Kahoot! quizzes are the Regular Players (n = 18). Students who participated
+in all ten Kahoot! quizzes are called the Ultra Players (n = 7). To assess aspects of mastery and vicarious learning
+experiences related to Kahoot!, students who scored in the top three each week were also considered. Nicknamed the
+Podium Players, these students were recognized in a weekly email shout-out and, over the course of the semester,
+accounted for n = 6 of the pre-survey takers and n = 9 of the post-survey takers. During Week 13, around one-third
+of the class completed the post-survey and are referred to as Final Participants (n = 110). Finally, students who
+took either survey, but did not report a nickname, are called the Non-Players. However, it is possible that these
+students played and forgot their initial game-generated nicknames on the survey. To reduce the odds of potential
+players being included in this group, another question asked students directly if they played a Kahoot! or not. Using
+this question, it was determined that the Non-Players accounted for eleven of the pre-survey takers and twenty-one
+of the post-survey takers. For a summary of these groups, see Table IV.
+To explore the nature of optional participation as a means to modify physics attitudes and beliefs, the aforemen-
+tioned groups of students were examined for significant differences in attitude change. To analyze the significance
+of different group self-efficacy mean scores, t-tests were used. Paired t-tests were utilized for groups with matched
+datasets (paired pre- and post-test scores), while independent t-tests were utilized for groups with unmatched datasets.
+Participation in Kahoot! quizzes was not required, and a steep decline was initially observed in the number of
+students who opted to play (see Figure 1). While the first Kahoot! drew 157 participants, these students played an
+average of 2.47 more times, with half playing zero additional games. Just over 10% of them played all ten Kahoots!.
+Further analysis revealed that the Players group had positive and significant gains (p = 0.002), while the Non-Players
+did not. Though the Non-Players did show improvement in mean self-efficacy as a group, the difference in means from
+pre- to post-survey was not statistically significant (p = 0.18). Like the Players, the Regular Players also reported
+significant and positive gains. The Ultra Players, who had the lowest pretest average of all groups also reported
+
+10
+TABLE IV. This table summarizes the groups of students considered in the analysis of Kahoot! participation and self-efficacy.
+Group Name
+Attributes
+Initial Participants
+Students who opted to take the pre-
+survey (n = 65).
+Final Participants
+Students who opted to take the post-
+survey (n = 110).
+Players
+Students who participated in the first
+Kahoot! and who took the both pre-
+and post- surveys (n = 26).
+Regular Players
+Players who participated in five or
+more Kahoot! quizzes (n = 18).
+Ultra Players
+Players who participated in all ten
+Kahoot! quizzes (n = 7)
+Podium Players
+Players who earned a podiums spot
+during one more Kahoot! (n = 6).
+FIG. 1. A decline in participation was observed during the semester.
+positive gains but, due to a limited sample size (n = 7), could not be deemed statistically significant. These results
+can be found in Table V
+While participating in Kahoot! did correspond to positive c measurements, it remains unclear whether greater
+participation leads to greater self-efficacy gains. Furthermore, students with high physics self-efficacy were not likelier
+to play than those with low physics self-efficacy.
+As stated earlier, gender can influence the effects of mastery and vicarious experiences. Based on previous findings
+(see [55, 56]), males in male-dominated fields are more likely to benefit from mastery experiences (doing well per-
+sonally), whereas females in male-dominated fields are more likely to benefit from vicarious experiences (doing well
+compared to others). To test this hypothesis, the self-efficacy scores of Podium Players were examined to see if gender
+was a moderating factor for self-efficacy change. Only five students from the Podium Players group took both surveys
+and therefore, had a measured change, c. For male podium players, the average change ⟨c⟩ was 0.348, and for females
+was 0.063. This result seems to contradict the hypothesis that doing well compared to others (as measured by Kahoot!
+performance) corresponds to greater increases in self-efficacy perceptions for females compared to males. Although
+Kahoot! quizzes represent opportunities for self-efficacy development through both vicarious and mastery experiences,
+the vicarious aspect is potentially lessened due to the anonymous nature of the game. Vicarious experiences are most
+influential when an individual compares themselves to a peer perceived as equally capable; because students don’t
+know the identity of their opponents, the impact of vicarious experiences through Kahoot! may be lessened.
+Due to limited statistics, it is not possible to draw conclusions about the impact of optional Kahoot!
+quizzes
+on physics students’ attitudes and beliefs.
+However, it can be stated that students with high pretest scores are
+more likely to reach the quiz podium based on the high pretest average of Podium Players. This supports previous
+
+160
+140 
+8
+78
+Week11
+TABLE V. Results from pre- and post- (modified) CLASS surveys reveal significant gains for only two groups (indicated by
+*). Cohen’s d is reported to represent effect size.
+Pre-
+Post-
+⟨ c ⟩
+p
+Cohen’s d
+N
+µ
+σ
+N
+µ
+σ
+Players*
+26
+8.46
+3.74
+26
+10.04
+4.32
+0.14
+≪ 0.05
+0.39
+Regular Players*
+18
+8.50
+3.90
+18
+9.72
+4.13
+0.12
+< 0.05
+0.30
+Ultra Players
+7
+7.00
+4.43
+7
+8.43
+4.43
+0.09
+> 0.05
+0.32
+Podium Players
+6
+11.33
+5.39
+9
+11.00
+4.90
+–0.03
+≫ 0.05
+0.07
+Non-Players
+11
+7.27
+2.90
+21
+9.24
+4.19
+0.15
+≫ 0.05
+0.52
+Participants
+65
+8.26
+3.62
+110
+9.31
+3.93
+0.09
+> 0.05
+0.27
+TABLE VI. This table lists the Likert style survey questions and scoring guidelines for the intelligence mindset portion of
+the survey. These questions were used to asses the intelligence mindsets of students as either “growth” and “fixed”. Neutral
+answers were not scored.
+Question
+Growth Mindset
+Fixed Mindset
+1. Reviewing mistakes is a big part of how I learn.
+≥4
+≤ 2
+2. Even when I do poorly on a test I try to learn from my mistakes.
+≥4
+≤ 2
+3. A significant problem in learning physics is being able to
+memorize all the information I need to know (Q1).
+≤ 2
+≥4
+4. I cannot learn physics if the teacher does not explain things well (Q5).
+≤ 2
+≥4
+5. Nearly everyone is capable of understanding physics if they work at it (Q8).
+≥4
+≤ 2
+6. Learning physics changes my ideas about how the world works (Q20).
+≥4
+≤ 2
+findings that self-efficacy and achievement are correlated. Furthermore, students who participated in all ten Kahoot!
+quizzes reported the lowest mean scores on both surveys out of all groups. This could indicate that Kahoot! does
+not adequately inspire meaningful learning and may not lead to significant gains, particularly for students with low
+self-efficacy.
+D.
+Intelligence Mindsets and Self-Efficacy
+In addition to exploring optional participation and self-efficacy, another aspect of this study aimed to explore how
+intelligence mindsets might be related to students’ willingness to participate in self-efficacy opportunities or experience
+positive self-efficacy change. Specifically, total participation and self-efficacy scores were compared for students who
+reported “fixed” or “growth” mindsets.
+These comparisons were additionally observed through a gender lens to
+explore the mindsets of male and female introductory physics students.
+Six survey questions were used to compute intelligence mindsets, four of which were taken from the CLASS (see
+Table VI). Answers that reflected a willingness to participate in the learning process or which aligned with the belief
+that intelligence is flexible and something which can be achieved through time and practice were labeled growth
+mindset and scored as “1”. Answers reflecting a belief that intelligence is finite or unchanging were deemed fixed
+mindset and scored as “0”. Neutral answers were not scored. For each student, these answers were then tallied;
+students with strong growth mindsets had a score of 5 or 6, and those with strong fixed mindsets had a score of 0 or
+1.
+At the beginning of the semester, 4.6% of respondents reported strong growth mindsets, while 15.4% reported strong
+fixed mindsets. Because intelligence mindset studies are relatively new to the PER community, follow up studies are
+needed to properly reflect on these results. At the conclusion of the semester, the percentage of students reporting
+strong growth mindsets rose to 9.1%, while the percentage of fixed mindset students dropped to 8.2%. Applying an
+independent t-test revealed these groups to be statistically distinct (p ≪ 0.001) at both times of the semester.
+Minor differences in participation were reported for the two groups. Students scoring in the upper quartile of self-
+efficacy scores played an average of 4.4 ± 0.8 games, while students scoring in the lower quartile played an average of
+3.3 ± 0.9 games. This suggests that participation in Kahoot! does not align with intelligence mindsets. On the other
+hand, the analysis did show a correlation between intelligence mindset and average Kahoot! performance, as shown
+in Figure 2. Compared to the beginning of the semester, intelligence mindsets and average Kahoot! scores became
+more strongly related at the end of the semester, suggesting that students with high quiz averages developed stronger
+growth mindsets than students with low quiz averages.
+Further analysis revealed a correlation between intelligence mindsets and self-efficacy scores. The initial self-efficacy
+
+12
+FIG. 2. The relationship between intelligence mindsets and Kahoot! performance according pre- and post- survey results for
+the group Participants (n = 26).
+averages for the “growth” and “fixed” mindset groups were 16.3 ± 0.7 and 5.9 ± 0.8, respectively. Both an independent
+t-test and Cohen’s d indicate these means to be statistically significant (p ≪ 0.001 and d = 4.27). Additionally, at the
+end of the semester, the self-efficacy averages were 15.2 ± 0.70 and 4.7 ± 1.0, respectively also with strong significance
+(p ≪ 0.001 and d = 4.11).
+FIG. 3. Intelligence mindset beliefs relative to self-efficacy scores as measured by the pre-survey (left) and post-survey (right).
+No male students reported strong growth mindsets on the pre-survey.
+The previously mentioned research by Kalender et al. [60] showed differences between males and females regarding
+intelligence mindsets, particularly in male-dominated fields such as physics. To explore the nature of this finding,
+male and female students with fixed, neutral, and growth mindsets were compared at both points during the semester.
+Self-efficacy scores were also compared for the groups to see if self-efficacy and intelligence mindsets reflect gender.
+Initially, the group of students with strong initial growth mindsets comprised three females (and no males) with an
+average self-efficacy of 16.3 ± 0.7. By the end of the semester, this group was comprised of six females and four males,
+with an average self-efficacy of 16.2 ± 0.8 for the female students and 13.8 ± 0.9 for the male students.
+The observation that male students consistently outperform female students on various physics inventories should
+be examined on the basis of intelligence mindsets. In this study, male and female students with similar intelligence
+mindsets reported similar self-efficacy scores. Figure 3 shows the relationship between intelligence mindsets and self-
+efficacy as measured by both pre- and post-surveys, broken down by gender. Only in the growth mindset group was
+there a sizeable difference (p = 0.09) in self-efficacy averages for males and females, with females outscoring males.
+Females also have higher reported self-efficacy in the fixed mindset group, but overlapping error bars make this result
+less meaningful. Only in the neutral mindset range, where roughly 80% of students lie, do we see male students with
+
+7400
+壬 Pre
+王- Post
+T
+T4DO
+ Kahoot! Score
+G600
+200
+Average I
+58D0
+54D0
+5000
+Neutral
+Grwth
+Pre- Intelligence Mindset ScoreWomen (n=35)
+TI
+Women (n=52)
+16
+Men (n=28)
+16
+Men (n=55)
+14 
+Eficac
+1
+Initial
+8
+中
+8
+6
+6-
+4
+Foxed
+Neutral
+Growth
+Foxed
+Neutral
+Growth
+Pre- Intelligence Mindset Score
+Post- Intelligence Mindset Score13
+higher self-efficacy scores than female students. Again, follow up studies will be necessary to clarify the nature of this
+finding.
+V.
+CONCLUSION
+The (modified) CLASS measured positive gains over the course of one semester for students enrolled in the remotely
+taught introductory physics laboratory. However, due to limited statistics, conclusions regarding the different effects
+of intermittent versus regular Kahoot! participation could not be made. Perhaps classroom games like Kahoot! are
+more effective for students who participate intermittently (possibly on a need-to-need basis) and become less effective
+for students who play for other reasons, perhaps for consistency or out of habit (not for meaningful learning). This was
+potentially the case for the Ultra Players, who, having participated in all optional quizzes throughout the semester,
+was the only group of students to report negative self-efficacy change, ⟨c⟩.
+Results from the online learning attitudes portion of the survey demonstrated that while male and female students
+generally hold similar attitudes toward online learning, distinction between the genders can be made. Social interac-
+tions play an important role in formulating perceptions of belonging [63], and further research should be carried out
+to understand how remote classrooms shape and modify these perceptions, particularly in male-dominated fields like
+physics. Furthermore, intelligence mindsets and self-efficacy beliefs may influence attitudes toward online learning,
+though not enough data was collected in this study to examine this hypothesis thoroughly. However, it does not
+seem unlikely, given that women typically cite social interactions as informing self-efficacy perceptions the most, that
+remote learning may limit the scope of self-efficacy development.
+The COVID-19 pandemic provided an opportunity for higher education communities to reflect on current teaching-
+learning methods and to adapt novel ones. The pandemic also paved the way for flexible teaching-learning methods and
+inspired institutions to develop robust educational techniques. In the past two years, many adaptations have helped
+to protect and fortify these institutions against future unforeseen disruptions. In successful cases, these adaptations
+have increased accessibility for students’ in a way that nurtures their self-efficacy and long-term success.
+[1] L. Mishra, T. Gupta, and A. Shree, International Journal of Educational Research Open 1, 100012 (2020).
+[2] G. M. Novak, E. T. Patterson, A. D. Gavrin, and W. Christian, Just in time teaching (1999).
+[3] J. Bransford, S. Brophy, and S. Williams, Journal of Applied Developmental Psychology 21, 59 (2000).
+[4] V. K. Otero and D. E. Meltzer, Physics Today 70, 50 (2017).
+[5] K. Perkins and B. Moore, in 2017 Physics Education Research Conference Proceedings (American Association of Physics
+Teachers, 2018) pp. 296–299.
+[6] M. Prieto, L. Orcos, P. Blazquez, and F. Le´on, Education Sciences 9, 55 (2019).
+[7] Y. Zhao, A. M. Pinto Llorente, and M. C. S´anchez G´omez, Computers & Education 168, 104212 (2021).
+[8] M. L. Bernacki, J. A. Greene, and H. Crompton, Contemporary Educational Psychology 60, 101827 (2020).
+[9] S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, and M. P. Wenderoth, Proceedings of the
+National Academy of Sciences 111, 8410 (2014).
+[10] E. Brewe and V. Sawtelle, European Journal of Physics 39, 054001 (2018).
+[11] H. C¸elik, H. M. Pektas, and O. Karamustafaoglu, Electronic Journal for Research in Science & Mathematics Education
+25, 47 (2021).
+[12] I. Hussain, Creative Education 3, 179 (2012).
+[13] S. Bryans Bongey, G. Cizadlo, and L. Kalnbach, Campus-Wide Information Systems 22, 252 (2005).
+[14] H. J. Cho, K. Zhao, C. R. Lee, D. Runshe, and C. Krousgrill, International Journal of STEM Education 8, 1 (2021).
+[15] E. Sointu, M. Hyypi¨a, M. C. Lambert, L. Hirsto, M. Saarelainen, and T. Valtonen, Higher Education (2022).
+[16] A. Bandura, Psychological Review 84, 191 (1977).
+[17] A. Bandura, Self-Efficacy: The Exercise of Control, edited by C. H. S.F. Brennan (W.H. Freeman and Company, 1997).
+[18] S. Andrew, Journal of Advanced Nursing 27, 596 (1998).
+[19] R. W. Lent, S. D. Brown, and K. C. Larkin, Journal of Counseling Psychology 31, 356 (1984).
+[20] R. W. Lent, S. D. Brown, and K. C. Larkin, Journal of Counseling Psychology 34, 293 (1987).
+[21] K. D. Multon, S. D. Brown, and R. W. Lent, Journal of Counseling Psychology 38, 30 (1991).
+[22] J. Pietsch, R. Walker, and E. Chapman, Journal of Educational Psychology 95, 589 (2003).
+[23] E. F. Redish, J. M. Saul, and R. N. Steinberg, American Journal of Physics 66, 212 (1998).
+[24] W. K. Adams, K. K. Perkins, N. S. Podolefsky, M. Dubson, N. D. Finkelstein, and C. E. Wieman, Physical Review
+Special Topics-physics Education Research 2, 010101 (2006).
+[25] A. Madsen, S. B. McKagan, and E. C. Sayre, Phys. Rev. ST Phys. Educ. Res. 11, 010115 (2015).
+[26] R. Knight, Five Easy Lessons: Strategies for Successful Physics Teaching, Pearson Educational Innovation (Addison
+Wesley, 2002).
+
+14
+[27] I. A. Halloun and D. Hestenes, American Journal of Physics 53, 1043 (1985).
+[28] J. Clement, American Journal of Physics 50, 66 (1982).
+[29] E. Mazur, Peer Instruction: A User’s Manual, Series in Educational Innovation (Prentice Hall, 1997) pp. 3–7.
+[30] A. Van Heuvelen, American Journal of Physics 59, 891 (1991).
+[31] D. Hammer, American Journal of Physics 64, 1316 (1996).
+[32] K. E. Gray, W. K. Adams, C. E. Wieman, and K. K. Perkins, Physical Review Special Topics-Physics Education Research
+4, 020106 (2008).
+[33] L. C. McDermott, American Journal of Physics 59, 301 (1991).
+[34] I. Halloun and D. Hestenes, Science & Education 7, 553 (1998).
+[35] S. A. Licorish, H. E. Owen, B. Daniel, and J. L. George, Rearch and Practice in Technology Enhanced Learning 13
+(2018).
+[36] K. White and L. P. McCoy, Networks: An Online Journal for Teacher Research 21 (2019).
+[37] A. I. Wang and R. Tahir, Computers & Education 149, 103818 (2020).
+[38] B. R. Wilcox and H. J. Lewandowski, Phys. Rev. Phys. Educ. Res. 13, 010108 (2017).
+[39] O. Oymak and F. Ogan-Bekiroglu (2017).
+[40] R. R. Hake, American Journal of Physics 66, 64 (1998).
+[41] E. A. Davis, in Annual Meeting of the American Educational Research Association (ERIC, 1997).
+[42] E. Brewe, L. Kramer, and G. O’Brien, Phys. Rev. ST Phys. Educ. Res. 5, 013102 (2009).
+[43] E. Brewe, A. Traxler, J. de la Garza, and L. H. Kramer, Phys. Rev. ST Phys. Educ. Res. 9, 020116 (2013).
+[44] N. D. Finkelstein and S. J. Pollock, Phys. Rev. ST Phys. Educ. Res. 1, 010101 (2005).
+[45] K. Semsar, J. K. Knight, G. Birol, and M. K. Smith, CBE—Life Sciences Education 10, 268 (2011).
+[46] J. Barbera, W. Adams, C. Wieman, and K. Perkins, Journal of Chemical Education - J CHEM EDUC 85 (2008).
+[47] Colorado Learning Attitudes About Science Survey (CLASS) (2022).
+[48] G. Hackett and N. E. Betz, Journal for Research in Mathematics Education 20, 261 (1989).
+[49] G. Hackett and N. E. Betz, Journal of Vocational Behavior 18, 326 (1981).
+[50] R. W. Lent, S. D. Brown, and K. C. Larkin, Journal of Counseling Psychology 33, 265 (1986).
+[51] S. D. Brown, R. W. Lent, and K. C. Larkin, Journal of Vocational Behavior 35, 64 (1989).
+[52] D. A. Luzzo, P. Hasper, K. A. Albert, M. A. Bibby, and E. A. Martinelli Jr., Journal of Counseling Psychology 46, 233
+(1999).
+[53] N. Hall and D. Webb, Phys. Rev. ST Phys. Educ. Res. 10, 020116 (2014).
+[54] M. A. Hutchison, D. K. Follman, M. Sumpter, and G. M. Bodner, Journal of Engineering Education 95, 39 (2006).
+[55] A. L. Zeldin and F. Pajares, American Educational Research Journal 37, 215 (2000).
+[56] A. L. Zeldin, S. L. Britner, and F. Pajares, Journal of Research in Science Teaching 45, 1036 (2008).
+[57] S. L. Britner, Journal of Research in Science Teaching 45, 955–970 (2008).
+[58] V. Sawtelle, E. Brewe, and L. H. Kramer, Journal of Research in Science Teaching 49, 1096 (2012).
+[59] A. Madsen, S. B. McKagan, and E. C. Sayre, Phys. Rev. ST Phys. Educ. Res. 9, 020121 (2013).
+[60] Z. Y. Kalender, E. Marshman, C. D. Schunn, T. J. Nokes-Malach, and C. Singh, Phys. Rev. Phys. Educ. Res. 18, 010116
+(2022).
+[61] C. Lindstrøm and M. Sharma, Int. J. Innov. Sci. Math. Educ. 19, 1 (2011).
+[62] B. R. Wilcox and H. J. Lewandowski, American Journal of Physics 86, 212 (2018).
+[63] T. Dobbins, Bulletin of the American Physical Society (2020).
+[64] H. Masud, M. S. Ahmad, F. A. Jan, and A. Jamil, Asia Pacific Education Review 17, 121 (2016).
+[65] K. K. Perkins, W. K. Adams, S. J. Pollock, N. D. Finkelstein, and C. E. Wieman, AIP Conference Proceedings 790, 61
+(2005).
+[66] D. H. Schunk, Educational psychology review 1, 173 (1989).
+[67] L. Abeysekera and P. Dawson, Higher Education Research & Development 34, 1 (2015).
+[68] R. F. Moll and M. Milner-Bolotin, Canadian Journal of Physics 87, 917 (2009).
+[69] L. C. McDermott et al., Physics by Inquiry: An Introduction to Physics and the Physical Sciences, Volume 1 (John Wiley
+& Sons, 1995).
+[70] V. K. Otero and K. E. Gray, Phys. Rev. ST Phys. Educ. Res. 4, 020104 (2008).
+[71] L. L. Liang, G. W. Fulmer, D. M. Majerich, R. Clevenstine, and R. Howanski, Journal of Science Education and Technology
+21, 114 (2012).
+[72] B. A. Lindsey, L. Hsu, H. Sadaghiani, J. W. Taylor, and K. Cummings, Phys. Rev. ST Phys. Educ. Res. 8, 010102 (2012).
+[73] A. N. R. Silva, in Proceedings of the PBL 2010 International Conference-Problem-Based Learning and Active Learning
+Methodologies (2010).
+[74] G. Abdisa and T. Getinet, Journal of Physics Education 4, 530 (2012).
+[75] I. G. A. P. A. Wulandari, C. Sa’dijah, A. R. As’ari, and S. Rahardjo, Journal of Physics: Conference Series 1028, 012153
+(2018).
+[76] K. M. Kapp, The gamification of learning and instruction: game-based methods and strategies for training and education
+(John Wiley & Sons, 2012).
+[77] S. Subhash and E. A. Cudney, Computers in Human Behavior 87, 192 (2018).
+[78] G. A¸sıksoy, Quality & Quantity: International Journal of Methodology 52, 129 (2018).
+[79] F. Forndran and C. R. Zacharias, European Journal of Physics 40, 045702 (2019).
+[80] H. D. Ahmed and G. Asiksoy, Sustainability 13 (2021).
+
+15
+[81] M. Kalogiannakis, S. Papadakis, and A.-I. Zourmpakis, Education Sciences 11 (2021).
+[82] I. Bouchrika, N. Harrati, V. Wanick, and G. Wills, Interactive Learning Environments 29, 1244 (2021).
+[83] Kahoot! (2022).
+[84] M. Gebbels, Compass: Journal of Learning and Teaching 11 (2018).
+[85] M. Boeker, P. Andel, W. Vach, and A. Frankenschmidt, PLOS ONE 8 (2013).
+[86] F. Kilickaya, A Journal of Language Teaching and Learning 53 (2017).
+[87] W.-J. Shyr, Y.-M. Hsieh, and C.-H. Chen, Sustainability 13 (2021).
+[88] V. K. Kolil, S. Muthupalani, and K. Achuthan, International Journal of Educational Technology in Higher Education 17
+(2020).
+[89] M. C. Linn, E. A. Davis, and P. E. Bell, Internet environments for science education (Lawrence Erlbaum Associates
+Publishers, 2004).
+[90] G. Hamed and A. Ahmad, Journal of Information Technology Education: Research 19, 976 (2020).
+[91] N. D. Finkelstein, W. K. Adams, C. J. Keller, P. B. Kohl, K. K. Perkins, N. S. Podolefsky, S. Reid, and R. LeMaster,
+Phys. Rev. ST Phys. Educ. Res. 1, 010103 (2005).
+[92] C. S. Dweck, Mindset: The new psychology of success (Random House, 2006).
+[93] D. S. Yeager, P. Hanselman, G. M. Walton, J. S. Murray, R. Crosnoe, C. Muller, E. Tipton, B. Schneider, C. S. Hulleman,
+C. P. Hinojosa, et al., Nature 573, 364 (2019).
+[94] R. E. Scherr, M. Plisch, K. E. Gray, G. Potvin, and T. Hodapp, Phys. Rev. Phys. Educ. Res. 13, 020133 (2017).
+[95] C. S. Dweck, Self-theories: Their role in motivation, personality, and development (Psychology press, 2013).
+[96] E. S. Elliott and C. S. Dweck, Journal of personality and social psychology 54, 5 (1988).
+[97] E. M. Marshman, Z. Y. Kalender, T. Nokes-Malach, C. Schunn, and C. Singh, Phys. Rev. Phys. Educ. Res. 14, 020123
+(2018).
+[98] L. Bian, S.-J. Leslie, and A. Cimpian, Science 355, 389 (2017).
+[99] S.-J. Leslie, A. Cimpian, M. Meyer, and E. Freeland, Science 347, 262 (2015).
+[100] APS, American physical society, percentage of underrepresented minorities, Available at https://www.aps.org/
+programs/education/statistics/urm.cfm (10/06/2022) (2020).
+[101] PhET, PhET simulations, Available at https://phet.colorado.edu (10/06/2022) (2004).
+[102] GeoGebra, GeoGebra, Available at https://www.geogebra.org (10/06/2022) (2001).
+[103] F.-K. Hwang, Basic function of an oscilloscope, Available at https://www.phy.ntnu.edu.tw/ntnujava/ (10/06/2022)
+(2004).
+[104] Mathlets, MIT Mathlets, Available at https://mathlets.org/activities/ (10/06/2022) (2009).
+[105] M.
+Foster,
+UH
+Manoa
+Physics
+Lab
+Quizzes,
+https://create.kahoot.it/course/
+205fca5e-c5e3-47ff-b587-c2aeec664328/edit (2021).
+[106] J. Day, J. B. Stang, N. G. Holmes, D. Kumar, and D. A. Bonn, Phys. Rev. Phys. Educ. Res. 12, 020104 (2016).
+
+16
+Appendix: Modifications to the CLASS
+The questions used in this study for the purpose of measuring self-efficacy are appended below. Twenty-one of the
+original forty-two Colorado Learning Attitudes About Science Survey (CLASS) questions were incorporated, including
+the moderating question.
+TABLE VII. This table includes the CLASS questions used in this study. Corresponding question numbers, expert responses,
+and categorical assignments are included.
+Survey Question
+Number
+CLASS Question
+Number
+Question
+Expert
+Response
+Category
+1
+1
+A significant problem in learning physics is being able to
+memorize all the information I need to know.
+D
+CC, ACU
+2
+2
+When I am solving a physics problem, I try to decide what
+would be a reasonable value for the answer.
+A
+No category
+3
+5
+After I study a topic in physics and feel that I understand
+it, I have difficulty solving problems on the same topic.
+D
+CC, ACU, PSS
+4
+6
+Knowledge in physics consists of many disconnected topics.
+D
+CC, ACU
+5
+12
+I cannot learn physics if the teacher does not explain
+things well in class.
+D
+No category
+6
+13
+I do not expect physics equations to help my understanding
+of the ideas; they are just for doing calculations.
+D
+CC, PSG
+7
+14
+I study physics to learn knowledge that will be useful in my
+life outside of school.
+A
+PI
+8
+16
+Nearly everyone is capable of understanding physics if they
+work at it.
+A
+PSG, PSC
+9
+18
+There could be two different correct values to a physics
+problem if I use two different approaches.
+D
+No category
+10
+23
+In doing a physics problem, if my calculation gives a
+result very different from what I’d expected, I’d trust the
+calculation rather than going back through the problem.
+D
+SME
+11
+25
+I enjoy solving physics problems.
+A
+PI, PSG, PSS
+12
+26
+In physics, mathematical formulas express meaningful
+relationships among measurable quantities.
+A
+PSG
+13
+31
+We use this statement to discard the survey of people
+who are not reading the questions. Please select
+agree-option 4 (no strongly agree) for this question to
+preserve your answers.
+A only
+No category
+14
+32
+Spending a lot of time understanding where formulas come
+from is a waste of time.
+D
+CC, SME
+15
+34
+I can usually figure out a way to solve physics problems.
+A
+PSG, PSC, PSS
+16
+35
+The subject of physics has little relation to what I
+experience in the real world.
+D
+RWC
+17
+39
+When I solve a physics problem, I explicitly think about
+which physics ideas apply to the problem.
+A
+SME
+18
+40
+If I get stuck on a physics problem, there is no chance I’ll
+figure it out on my own.
+D
+ACU, PSG, PSC, PSS
+19
+42
+When studying physics, I relate the important information
+to what I already know rather than just memorizing
+it the way it was presented.
+A
+SME, PSG
+20
+28
+Learning physics changes my ideas about how the world
+works.
+A
+RWC, PI,
+21
+30
+Reasoning skills used to understand physics can be
+helpful to me in my everyday life.
+A
+RWC, PI
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf,len=1295
+page_content='Virtual physics laboratory courses: An evaluation of students’ self-efficacy and  intelligence mindset  Meg Foster,∗ Philip von Doetinchem,† and Sandra von Doetinchem‡  University of Hawai‘i at M¯anoa  (Dated: January 10, 2023)  Following the emergence of COVID-19 in Spring 2020, undergraduate in-person physics laboratory  courses at a R1 public university were adapted for remote learning to accommodate the subsequent  campus closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Video lectures and web-based virtual experiments were utilized to provide students  enrolled in these laboratories with required learning materials on a weekly basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During the fall  semester of the 2021–2022 academic year, optional Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes were offered in addition, serv-  ing to incentivize participation and to provide self-efficacy opportunities to students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This study  sought to explore the intersection of self-efficacy growth, self-regulatory behaviors, and intelligence  mindsets (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', having fixed or growth mindsets) for students and to examine the impact of these  remote learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Using a modified version of the Colorado Learning Attitudes About Sci-  ence Survey (CLASS), students’ physics self-efficacy was measured at the beginning and end of the  semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The analysis revealed that participation in Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' alone did not correspond to greater  self-efficacy scores or greater self-efficacy change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' However, a strong correlation was observed be-  tween intelligence mindset and self-efficacy for both pre-and post-surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pre-survey intelligence  mindset scores were not related to average Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' performance, while post- survey intelligence  mindsets were.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finally, positive self-efficacy change ⟨c⟩ was measured for the class, but was not  statistically significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Keywords: remote learning, game-based learning, self-efficacy, intelligence mindsets, physics education re-  search  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  INTRODUCTION  Faced with the initial outbreak of COVID-19 in March 2020, higher education institutions worldwide were forced to  modify countless aspects of their operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In an effort to accommodate health and safety guidelines, many institu-  tions opted for a transition to online teaching-learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The urgency of the situation and lack of preparedness  at both the institutional and national levels bore a sense of responsibility for educators and administrations to usher  in a new era of teaching and learning, practically overnight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the following two and a half years, the merits of  distance education and remote learning have given rise to a new outlook on teaching-learning methods and created a  new perspective surrounding classroom technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In a 2020 publication, Mishra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [1] stated that the integration  of technology and other pivotal online tools in higher education will enable instructors to teach with methods that  students not only feel comfortable with, but which match the demands of the 21st century;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' and many agree [2–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  As technology integrates more fully into classrooms and a new era of mobile learning [8] emerges, a focus on  constructivist teaching methods and a shift toward learner-centered instruction seems apparent [9–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These methods  not only allow, but encourage students to construct their own understanding of the learning content [12] through  lessons that support self-paced learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For example, the Flipped Classroom (FC) model has been growing widely  in higher education science courses, embraced for its unique ability to produce active learning environments in large  lecture courses, cultivate self-paced learning, motivate further learning, and for its popularity among students [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  This model for teaching equips students with online tools and resources and is driven by self-paced learning outside  the classroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The proliferation of online learning and incorporation of classroom technology (such as virtual labs) has coincided  with and educational landscape that brings more learner-centered methods to the table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In response, educational  researchers have sought to understand how instructional approaches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', flipped classrooms, virtual labs, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=') might  impact students’ attitudes and beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In general, the study of personal attitudes and beliefs is examined through  the framework of self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The framework of self-efficacy was developed by Bandura [16] in 1977 and is defined as the confidence one has  in their own ability to perform a particular task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' It is developed and moderated by personal attitudes, beliefs, and  experiences, and is understood to have four main sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Identified by Bandura [17], these are mastery experiences,  ∗ mfoster3@hawaii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='edu  † philipvd@hawaii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='edu  ‡ sandravd@hawaii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='edu  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='02699v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='ed-ph]  6 Jan 2023  2  vicarious experiences, social persuasion, and emotional states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Mastery experiences reflect perceptions of personal  task performance (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' “I did well on the exam, so I understand this topic well”), whereas vicarious experiences  reflect perceptions based on the task performance of others (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' “My study group did well on the exam, so I expect  to do well too.”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Self-efficacy perceptions are also influenced by social persuasion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' receiving a pep talk) or  by an individual’s emotional state (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' experiencing anxiety or an adrenaline rush).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the classroom, a student’s  self-efficacy will inform decisions about how to prepare for an exam, whether or not to ask a question in class, or what  kind of goals to set for a course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, the utility of understanding the role of self-efficacy in academia lies  in the expectation that students with high academic self-efficacy are more likely to succeed in school, choose career  paths that require success in academia, and choose majors that align with their self-beliefs about personal capabilities  [18–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  From high school to university, physics classrooms have been designed and equipped to help students understand  the world around them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Unfortunately, few students ever attain a strong personal conviction that they have achieved  this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Moreover, it is not uncommon for undergraduate students to report negative attitudinal shifts towards  the subject after completing an introductory physics course [23–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This means that students tend to have more  expert-like beliefs at the beginning, rather than the end, of an introductory physics course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Given that physics is a  discipline of curiosity and investigation, many have speculated why this occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Knight [26] suspects that this issue  stems from the fact that students do not attend their first physics lecture as blank slates, but are rather filled with  experiences and ideas about the world around them [27–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These beliefs and conceptions from day-to-day life guide  their understanding of the natural world, but are not necessarily correct [26–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Responses that differ substantially  from the views of physicists are called pre- or misconceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students use these strongly held beliefs, whether true  or not, to explain and predict physical processes [31] and are incredibly difficult to change [26–28, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McDermott  [33] supports this observation with her statement summarizing the constructivist view, “all individuals must construct  their own concepts, and the knowledge they already have (or think they have) significantly affects what they learn.” It  appears that developing positive self-efficacy is not the result of known ledge alone, but rather knowledge acquisition  accompanied by a belief that this knowledge is accessible and understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  As digital transformations sweep the educational landscape, institutions must develop reliable technology-enabled  learning for students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These adaptations will ensure quality educational outcomes in the wake of future unforeseen  academic disruptions and assist in addressing pre-pandemic educational disparities [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In examining physics self-  efficacy, the goal of research is not just to understand the way students feel towards physics but also their impressions  on the relevance of physics to the real world, connections between mathematical equations and physical reality, and  the coherence of physics concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This study aims to examine how instructional methods applied to a remotely  taught undergraduate physics laboratory course at a R1 public university impact the self-efficacy of students and to  explore what beliefs and behaviors inform these opinions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' An online survey was used to probe physics self-efficacy,  online learning attitudes, and the intelligence mindsets held by these students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  PREVIOUS RESEARCH  Over the last three decades, researchers have identified a variety of student attitudes and beliefs that shape and  are shaped by classroom experiences [30, 34–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To better understand these experiences in the physics classroom,  instruments such as the Maryland Physics Expectations Survey (MPEX) [23], the Epistemological Beliefs Assessment  for Physical Science (EBAPS) [41], the Colorado Learning Attitudes about Science Survey (CLASS)[24], along with  others, have been developed and used to probe student perspectives and epistemological beliefs in physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In addition,  intelligence mindsets have recently been explored, particularly in fields that are generally male-dominated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These  findings, discussed below, provide important insight into why certain fields, such as physics, have persistent gender  disparities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The Colorado Learning Attitudes About Science Survey  As an evaluation tool, the CLASS has assisted researchers in reforming educational practices to improve students’  attitudes toward science [42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Developed by Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [24] at the University of Colorado Boulder (CU Boulder),  the CLASS was specifically designed to probe students’ beliefs about physics and learning physics and to distinguish the  beliefs of experts from those of novices and has been used widely used as a tool for evaluating instructional techniques  [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In this way, expert beliefs refers to answers consistently chosen by expert physicists to questions on the  CLASS survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Aside from physics, the CLASS has been modified for use in biology, chemistry, astronomy, and math  [45, 46] and translated for use in several languages [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3  Composed of forty-two Likert-style questions, the CLASS allows respondents to answer on a scale ranging from  strongly disagree (1) to strongly agree (5) to statements such as “I study physics to learn knowledge that will be useful  in my life outside of school.” For scoring purposes, the responses strongly (dis)agree and (dis)agree are collapsed  and student responses are coded as agree, disagree, or neutral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Neutral answers are not scored as they do not agree  or disagree with the view consistently held by experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A student’s self-efficacy score is reflected by the number  of favorable (expert-like) responses chosen and is referred to as the percent favorable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Based on factor analysis,  Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [24] also determined that twenty-six of the forty-two questions are grouped into eight overlapping  categories, characterizing different aspects of student thinking: Real World Connections (RCW), Personal Interest  (PI), Sense Making and Effort (SME), Conceptual Connections (CC), Applied Conceptual Understanding (ACU),  Problem Solving General (PSG), Problem Solving Confidence (PSC), and Problem Solving Sophistication (PSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Self-Efficacy Development  Self-efficacy represents a consequential component of understanding the academic outcomes of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Studies  have shown that self-efficacy can predict a student’s persistence in the face of difficulty, effort and performance, course  enrollment [48], and choice of career [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Consequently, individuals with high self-efficacy are more likely to persist  at tasks and preserve in the face of challenging or adverse experiences [16, 19, 20, 50–52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Examining students’ self-  efficacy beliefs puts deliberate attention to the perceptions of students and can help educators be more effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A  study by Hall and Webb [53] found that autonomy-supportive instructors (who acknowledge students’ perspectives  and feelings) can positively impact the motivation and performance of students and is positively correlated with  student interest and enjoyment in learning physic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  When it comes to self-efficacy development, research has revealed differences in the role that the four sources of self-  efficacy (mastery experiences, vicarious experiences, social persuasion, and emotional states) have on influencing the  personal beliefs of male and female students [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A study published by Zeldin and Pajares [55] revealed that verbal  persuasions and vicarious experiences were critical sources of women’s self-efficacy beliefs and found that the perceived  importance of these sources may be stronger for women in male-dominated domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A later study by Zeldin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [56]  added to this claim with the following conclusion: “The self-efficacy beliefs of men in these male-dominated domains  are created primarily as a result of the interpretations they make of their ongoing achievements and successes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Women,  on the other hand, rely on relational episodes in their lives to create and buttress the confidence that they can succeed  in male-dominated domains.” A similar study of high school students by Britner [57] reported that interpretations of  self-efficacy sources are gendered and also vary by field of science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In a 2012 study, Sawtelle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [58] found that  predicting the probability of passing an introductory calculus-based physics course for women relies primarily on the  vicarious learning experiences source, with no significant contribution from the social persuasion experiences, while  predicting the probability of passing for men requires only the mastery experiences source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  These findings underscore how instructional techniques can significantly impact the outcomes of students, par-  ticularly in STEM fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Exposing these gender differences through instruments such as the CLASS have equipped  educators in their positions of power to facilitate better classroom experiences and to teach in a way that acknowledges  the perspectives and beliefs of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Measures like this have been shown to significantly improve the experiences  of female students, specifically in laboratory settings and in science classrooms [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Instructional Pedagogy: A Shift toward Learner-Center Approaches  The learner-centered pedagogy broadly implies that students are given the opportunity to participate in the learning  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This can also be understood through a constructivist lens as summarized by McDermott [33] when she stated  that “meaningful learning, which connotes the ability to interpret and use knowledge in situations not identical to  those in which it was initially acquired, requires a deep mental engagement by the learner.” That is, students engaged  with the material and cognitively involved in the learning process are participating in meaningful learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  In an effort to provide more self-efficacy enriching experiences to students, science educators have examined several  aspects regarding the way students learn and understand scientific ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In fact, factors such as gender [59–61],  field of study [62], prior instruction [61], perceptions of belonging [63], parenting styles [64], participation, sense of  autonomy [53], instructional pedagogy [25, 65], and ethnicity have all been examined by researchers for their role in  influencing student attitudes and beliefs in the physics classroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, sufficient research has shown that  classroom experiences and student self-efficacy are strongly correlated [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For instance, in a study comparing physics  laboratory pedagogy, Wilcox and Lewandowski [38] found that physics labs that focused on developing lab skills led  to more expert-like post-instruction self-efficacy scores than did those that focused on reinforcing concepts developed  in lecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Likewise, in a comparison of interactive-engagement (IE) and traditional physics instruction methods,  4  Hake [40] revealed that “conceptual and problems-solving test results strongly suggest that the classroom use of  IE methods can increase mechanics-course effectiveness well beyond that obtained in traditional practice.” In this  manner, traditional teaching implies that students play a passive role in the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the literature, this is  also referred to by phrases such as “transmissive lecture style”, “unidirectional instruction”, and “teacher-centered.”  These methods have been shown by researchers to have little effect on students’ personal development [67] and have  been shown to “impart little conceptual understanding of Newtonian mechanics.” [40]  Attempts to remedy the shift away from expert-like beliefs in introductory physics courses have been met with  intermittent success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For instance, IE, capable of producing significant conceptual gains in physics, falls short of  producing significant improvements in physics self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Similarly, interactive lecture experiments were shown by  Moll and Milner-Bolotin [68] to be insufficient at significantly improving student attitudes toward physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' On the  other hand, physics curricula such as Physics by Inquiry [69], Physics for Everyday Thinking [70], and Modeling  Instruction [42, 43, 71] have found success at improving student attitudes and beliefs in physics as measured by  instruments such as the CLASS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lindsey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [72] credits the epistemological focus of these curricula for their  success across multiple implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' By placing an intentional focus on students’ conceptual development, these  curricula are forced to reckon with student misconceptions and, to be successful, must nurture and inspire meaningful  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In developing instructional techniques that cater to epistemological development, successful curricula have  come to reflect the learner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Other learner-centered teaching approaches can be achieved through active learning methodologies (ALM), which  strive to engage and motivate students in the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For example, the FC model, characterized by its ability  to allow self-paced learning outside of the classroom, affords more time to be spent in the classroom cultivating qualita-  tive reasoning skills, addressing common misconceptions, and reviewing challenging topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, research has  identified that flipped approaches can help students manage cognitive loads more effectively as self-paced preparatory  work might better manage working memory compared with traditional methods (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', face-to-face, teacher-centered)  [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In addition to FC models, Problem/Project/Practiced-Based Learning (P3BL) [73], team-based learning, peer  instruction [29], guided-discovery [74, 75], and recently, gamification [76–82] have been explored for their ability to  positively impact student learning outcomes and science perceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These so-called blended methodologies show  promise in physics education, as shown by Forndran and Zacharias [79] in their study examining the effects of gami-  fication in a course on electric resistors, which reported high engagement and acceptance by students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The broadly used learning platform Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' was designed to engage students through interactive quizzes and has  become a popular tool for classroom feedback and assessment since its release in 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students participate on their  own devices (computer, tablet, phone, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=') and compete with peers using game-generated nicknames, typically all  while in the classroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A student-paced challenge mode was launched in 2018 [83], allowing students to play at  their own pace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Research suggests that using Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' as a classroom tool can lead to many positive outcomes for  students [84, 85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For example, in addition to real-time feedback, studies have reported that using Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' as a  classroom tool can increase student engagement [35, 36], clarify misunderstandings [6], motivate further learning [86],  and increase enjoyment in the learning process [80, 84, 85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For a literature review of Kahoot!’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='s effect on learning,  see Wang and Tahir [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' While Kahoots!’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='s effect on physics self-efficacy has not been studied, a recent paper by  Shyr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [87] found that the use of Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' in a remedial math course led to improved self-efficacy outcomes for  a group of middle school students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The paper did not identify which self-efficacy sources were responsible for these  changes, so it remains unclear how this tool influences self-efficacy perceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' However, given typical classroom use,  it is reasonable to hypothesize that mastery and vicarious experiences are the primary influencers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' By completing  a Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quiz, students are able to evaluate their individual performance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' as a mastery experience),  as well as the performance of others, which in turn, also impacts their self-efficacy perceptions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' as  a vicarious experience).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Because female students generally cite vicarious experiences, not mastery experiences, as  having more influence on self-efficacy perceptions (especially in male-dominated fields), successful experiences with  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' in physics classrooms is hypothesized to support the self-efficacy development of female students more than  male students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  In a similar manner, interactive web-based learning environments, such as virtual laboratories (VL), can provide  better learning environments for students to develop an understanding of scientific outcomes [88] and may support  students’ mastery of concepts [89] compared to traditional face-to-face methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In a recent study exploring the  effectiveness of virtual experiments on physics laboratory students’ learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hamed and Ahmad [90] came to the  conclusion that “substituting face-to-face theoretical preparation in the general physics lab is at least as effective as  using virtual experiments.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The authors further state,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' “students with virtual components acquired deeper understand-  ing of physics concepts and were better prepared for carrying out real experiments.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Like FC models,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' this approach  afforded students more time and flexibility in the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In a similar study, researchers at CU Boulder  found that students who used computer simulations to carry out experiments outperformed their peers (who had used  real equipment) on both a conceptual survey and in the coordinated task of assembling a real circuit and describing  how it worked [91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  5  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Mindsets and Motivation  In addition to examining the self-efficacy beliefs of physics students, researchers have recently explored the nature  of intelligence mindsets and their influence on student attitudes and beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Identified by Dweck [92] as two primary  implicit theories of intelligence, “fixed mindset” and “growth mindset” have been examined by physics education  researchers for their role in aspects ranging from academic achievement [60, 93] to departmental decision-making  [94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These studies found that personal beliefs about intelligence inform student motivation and persistence and can  moderate the impact of self-efficacy sources on self-efficacy development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  On an individual level, those with a fixed mindset see intelligence as immutable, something which cannot be  improved;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' they interpret difficult cognitive tasks or academic settings as potentially revealing the limits of their  intelligence and, therefore, may choose to avoid them [92, 95, 96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Alternatively, those with a growth mindset believe  that intelligence is a capacity that can improve incrementally with increased knowledge and effort;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' they interpret  difficult intellectual tasks as opportunities for learning and may seek them out [92, 95, 96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A study by Scherr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [94] made two significant observations on the topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' One, that most individuals do not adhere strictly to a “fixed” or  a “growth” mindset, but some combination of both, and two, that having a “fixed mindset” (also called an “entity  theory of intelligence”) is consistent with research identifying physics as a “brilliance required” field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In such fields,  members tend to believe that raw, innate talent is a primary requirement for success in the discipline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Studies such as those by Gray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [32] and Marshman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [97] have shown that gender plays a consistent  role in contributing to students’ beliefs about physics and learning physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For example, using the CLASS, Gray  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [32] compared responses for which students answered once for themselves and once for how they thought a  physicist would respond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The study revealed that introductory physics students tend to have a surprisingly accurate  understanding of the beliefs held by expert physicists (regardless of prior physics exposure) and that female students  report much greater differences between these two sets of responses than their male counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This suggests that  students, female students in particular, understand what physicists believe but do not identify with these beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Likewise, Marshman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [97] found that female students with A grades have similar physics self-efficacy beliefs as  male students with C grades in introductory physics courses [97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These findings suggest that gendered stereotypes  may play a significant role in the development of self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Another troubling finding was revealed through a study  by Bian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [98], which found that beginning at the age of six, girls start to avoid activities said to be for children  who are “really, really smart” [98] suggesting that beliefs about intellectual abilities are endorsed by children very  early on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These deep-rooted stereotypes, along with the maintenance that physics is a “brilliance required” discipline,  likely contribute to the under-representation of women in physics [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Unfortunately, women and underrepresented  ethnic or racial minorities have remained severely underrepresented in physics, accounting for just 19% and 7% of all  PhDs awarded in the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', respectively [100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  THE STUDY  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Pandemic Related Course Modifications  Following the emergence of COVID-19 in the spring of 2020, all physics laboratory courses at this R1 university  were modified for online instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In this regard, three substantial modifications were made to the undergraduate  physics laboratory course and were still in place at the time of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Laboratory Videos  Given that the transition from face-to-face to remote learning occurred in a matter of one week, finding a way to  fulfill laboratory course objectives without needing students to come on campus became an urgent responsibility for  the course’s teaching assistants (TAs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' As a solution, the TAs performed the experiments and collected experimental  data on behalf of the students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For each experiment, data were stored in a separate Google sheets document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' TAs  also recorded the experimental setup procedures and documented the process of collecting data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Clipped together  and narrated, these videos came to be called “experiment videos.” Additionally, videos explaining the theoretical  motivation for these experiments were put together as “theory videos.” Experiment videos ranged in length from four  to eight minutes and theory videos ranged from six to ten minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During each of the twelve experiment weeks,  data and videos pertaining to that experiment were uploaded to the class website.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Worksheet assignments were used  to tie all learning materials together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  6  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' An outline of the laboratory experiments carried out during the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The first Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' was played during  Week 3 for the Electric Deflection experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The pre-CLASS was offered during Weeks 4 and 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Week  Experiment  1  Simple Electric Circuit with LED  2  Electric Field Mapping  3  Measuring Electric Deflection with a CRT  4  Operation of an Oscilloscope  5  Ohm’s and Kirchhoff’s Laws  6  Capacitors  7  Magnetic Field Mapping  8  Charge-to-Mass Ratio of Electrons  9  Inductors  10  Natural Oscillations with RLC Circuit  11  Driven Oscillations with RLC Circuit  12  Snell’s Law and the Lensmaker Equation  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Virtual Experimentation  The second modification was the addition of web-based virtual laboratories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For most experiments, the Physics  Education Technology (PhET) [101] platform was utilized, though other platforms such as GeoGebra [102], NTNU  Java Virtual Physics Laboratory [103], and MIT Mathlets [104] were also utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These free online platforms provided  high-quality science simulations and allowed students to simulate nearly identical experiments to the ones performed  by TAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For the “Virtual Experiment” portion of the laboratory worksheets, students followed instructions for setting  up the simulated experiment, inputting the necessary parameters, and conducting the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students also  collected data, performed error analysis, and drew conclusions from the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This component was included to  give students experience with laboratory equipment and procedures, to gain practical knowledge, and to foster their  experimental physics self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Game Based Learning  Another modification was the incorporation of the online game-based learning (GBL) platform Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='. At the  beginning of the 2021 fall semester, ten Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  quizzes were created to align with the laboratory experiments  for Weeks 3 through 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  These quizzes are publicly available on Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [105].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  All quizzes were composed of  nine questions aimed to probe students’ understanding of the physics concepts underlying each experiment, their  understanding of the experimental setup, and the potential outcomes of the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In general, the design of  each Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' reflected the intention to motivate student engagement, expose misconceptions, and foster conceptual  growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The answers could always be found in at least two of the following student materials: the laboratory manual,  the theory video, or the experiment video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Questions varied from multiple choice to multiple select to fill in the blank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Methods  The goal of this study was to document how COVID-19-related course modifications, particularly the incorporation  of FC methods and the supplement of optional GBL Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes, affected the self-efficacy beliefs of introductory  physics students’ enrolled in a remote laboratory course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During the 2021 fall semester, students enrolled in the  General Physics II laboratory sections attended weekly 50-minute online lectures held by TAs as a means to tie all of  the learning materials together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Utilizing Zoom, all online meetings were held synchronously and offered throughout  the week for various lab sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During these lectures, TAs discussed the motivation behind the experiment, reviewed  relevant equations and derivations, and although students did not collect data in person, experimental setup and data  collection procedures were reviewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' All laboratory materials, including the laboratory manual, worksheets, theory  videos, experiment videos, virtual experiments, and Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' access codes were provided to students via the class  website on a weekly basis and prior to all meetings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Data Collection  For the purpose of this study, an abbreviated version of the CLASS was utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This modification was implemented  to increase participation by means of a shorter survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the end, twenty-one questions were selected from the twenty-  six questions belonging to the self-efficacy subcategories mentioned prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The questions retained for this study can  be found in Table VII in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  During Week 3 of the semester, students opting to participate in the study played the first Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quiz and received  their game-generated nickname (which they were encouraged to write down).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the following weeks, students who  remembered their nicknames played weekly Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' games under the same alias, establishing a way to anonymously  track students’ participation and to establish a way for comparing individuals’ pre- and post-survey results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students  who forgot their nickname or did not participate in the first Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quiz still had the option to participate in  future Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes and the abbreviated CLASS survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During Week 4, the abbreviated CLASS was offered  to students electronically via a Google form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To maximize participation in the study, students were offered extra  credit for completing it outside of class time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' No identifying information was collected by the form aside from the  game-generated nickname.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  In addition to the twenty-one CLASS questions, the Google form asked for the student’s gender identity and  included six questions on intelligence mindsets, two questions on test-related anxiety, and five questions regarding  online learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These questions were included to investigate their relation to self-efficacy or participation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Each  week, students were provided with a Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' code and a one-week window of time to play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Data Analysis  The objective of this analysis was two-fold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' First, data was analyzed to measure the impact of pandemic-related  physics laboratory modifications on students’ physics self-efficacy over the course of one semester of instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Then,  an analysis was carried out to understand what attitudes and beliefs (physics self-efficacy or intelligence mindset  related) tend to be successful for improving physics self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This was examined by comparing students’ percent-  favorable (hereby “self-efficacy”) scores at the beginning and end of the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Before statistical analysis was  performed, data cleaning was carried out for both pre- and post- surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' First, individual surveys were eliminated if  the moderating CLASS question, Question 13 (see Table VII), was answered incorrectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Other data cleaning measures  included removing surveys for which students made the same selection for every question or completed less than half  of the survey (this did not apply to any students in this study).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Data obtained from both pre-and post-surveys followed approximately normal distributions with roughly equal  variance in both pre- and post-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For this reason, parametric statistical tests were utilized to compare paired  and unpaired sample means with paired t-tests and independent t-tests, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' An α significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  was applied to all statistical tests, and following the recommendations of Day et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [106], for statistically significant  outcomes, Cohen’s d is report to represent effect size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Changes in self-efficacy for this study were examined using the  average normalized change c,  c =  �  �  �  �  �  (post − pre)/(max − pre)  if post > pre  0  if post = pre  (post − pre)/(pre)  if post < pre  (1)  defined as the ratio of the gain to the maximum possible gain (or as the loss to the maximum possible loss), where gain  is measured by taking the difference between post- and pre- (modified) CLASS scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To measure c for individual  students, game-generated nicknames were used to pair pre- and post-survey scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For non-participating students  and to measure change for the entire student sample, normalized change ⟨c⟩,  ⟨c⟩ = ⟨post⟩ − ⟨pre⟩  max − ⟨pre⟩  (2)  was computed using class averaged ⟨pre⟩ and ⟨post⟩ (modified) CLASS scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' After dropping the moderating question,  the max self-efficacy score was twenty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  8  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Attitudes toward Online Learning  In addition to exploring the intelligence mindsets and self-efficacy beliefs of introductory physics students, the  primary aspect of this study aimed to evaluate how pandemic-related course modifications might influence students’  self-efficacy perceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These course modifications reflected a shift toward learner-center pedagogy and included  aspects of flipped learning, such as laboratory and theory videos to be watched outside of class, the addition of virtual  experiments for all labs, and elements of game-based learning through optional weekly Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The five  additional survey questions used to measure student beliefs toward online learning are shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This table gives the results from the attitudes toward online learning portion of the survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Mean scores for each  of the five questions are shown for both pre- and post- surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Question  ⟨pre⟩  ⟨post⟩  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Virtual learning encourages me to learn independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' I prefer to learn in person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' I am satisfied with the online resources developed for this course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Interactions with classmates help me learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Virtual classrooms modernize education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1  At the start of the Fall 2021 semester, attitudes toward online learning varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Nearly 40% of respondents selected  the neutral answer for Question 4, with about 15% of students selecting disagree or strongly disagree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Most students  believed that virtual learning encourages independent learning, yet 35% of students strongly agreed with the statement  in Question 2, preferring to learn in person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Answers to Question 3 indicated that by Week 4 of the semester, there  was a general attitude of satisfaction regarding the online resources developed for the course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Interestingly, students  were undecided on the notion that virtual classrooms modernize education, with nearly 40% preferring to stay neutral  on the topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  By the end of the semester, students were still split on the topic of Question 5, with nearly an identical breakdown  of responses reported on the post-survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Interestingly, the belief that interactions with classmates aid in the learning  process shifted significantly toward strongly agree, with only 26% remaining neutral and over 60% selecting either  agree or strongly agree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The number of respondents strongly agreeing with Question 3 rose 10% while those in strong  disagreement increased from 4% to 9%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students became slightly more polarized in preferring to learn in person, with  10% more students in strong agreement and 3% more percent in strong disagreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finally, the mean response to  Question 1 remained relatively unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Of the five online learning questions (See Table II) included in the survey, only one revealed a statistically significant  difference between genders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This question, Question 3, weighed students’ satisfaction with online resources developed  for the course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Female students reported a mean response of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1, whereas males reported a mean of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Further analysis revealed that female students were twice more likely to report satisfaction with the  course’s online materials than male students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Seventy percent of female students agreed or strongly agreed with this  statement, compared to just 35% of male students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This sentiment increased for male students by the end of the  semester to 52% while female students’ approval remained at 70%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Question 5 also garnered different means from  each gender, but it was not enough to be significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' At the beginning of the semester, about half of all male students  agreed or strongly agreed with the statement, virtual learning encourages me to learn independently, compared to  70% of female students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This sentiment persisted to the end of the semester for males, but dropped from 70% to 60%  for female students coinciding with a 22% increase in females answering strongly agree to the statement, interactions  with classmates help me learn, and a 17% increase in females answering strongly agree to I prefer to learn in person  at the end of the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  At the beginning of the semester, male students were more likely than female students to believe that interactions  with classmates help them learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Around 1 in 5 females chose strongly disagree for the statement in Question 4,  whereas 1 in 10 males did.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' At the same time, 35% of female students agreed or strongly agreed with this statement  compared to 60% of male students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' At the end of the semester, this percentage was around 60% for both genders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Self-Efficacy  Pretest scores from the modified CLASS survey revealed an average self-efficacy score of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 (n = 65) out  of a possible twenty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This “percent favorable” score (41%) is lower than average according to Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [24] who  9  cites scores in the 60-70% range as typical for a calculus-based Physics I course at a large state research university  (LSRU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In this study, calculus-based and algebra-based sections reported slightly different pretest averages with  the calculus-based sections outscoring the algebra-based sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students in the calculus-based laboratory had an  average pretest score of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6, whereas students in the algebra-based laboratory had an average of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Interestingly, females outscored males in the algebra-based sections, while the reverse was true for the calculus-based  sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Overall, differences between male and female pretest scores were not statistically significant, with males  reporting an average of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6 and females 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Post-test scores revealed an average self-efficacy of 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='4 (n = 110) corresponding to a 5% increase in “percent  favorable” for the class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This increase corresponded to a class-averaged normalized change ⟨c⟩ of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='09 and an effect size  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Mean post-test scores for the calculus-based and algebra-based sections were 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 (n = 58) and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5 (n = 52), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Unlike the pretest, the difference in means between these groups was significant (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Female students in the calculus-based course had significantly (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05) more expert-like beliefs at the end of the  semester compared to the beginning, with a final self-efficacy score of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 and a positive normalized change  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' On the other hand, female students in the algebra-based sections were the only group to report negative  normalized change (see Table III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pre- and post- survey results for the calculus-based and algebra-based laboratory sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' p-values measure the  significance of each groups’ mean score change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The * indicates a significant result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Group  ⟨pre⟩  ⟨post⟩  ⟨c⟩  p  Calculus-Based  All  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='10  p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  Female*  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='30  p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  Male  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='03  p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  Algebra-Based  All  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='04  p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  Female  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7  –0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='01  p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  Male  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='5±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='12  p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Optional Game Quizzes  During Week 3 of the semester, 157 students obtained anonymous nickname identities by participating in the first  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In Week 4, 71 opted to complete the pre-survey and 65 were retained for correctly answering the  moderating question (see Table VII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These students are referred to as the Initial Participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students who took  both pre- and post-surveys, as identified by their game-generated Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' nicknames, make up the Players group  (n = 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Over the course of the semester, a group of consistent players emerged from the Initial Participants group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  These students who played five or more Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes are the Regular Players (n = 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students who participated  in all ten Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes are called the Ultra Players (n = 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To assess aspects of mastery and vicarious learning  experiences related to Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', students who scored in the top three each week were also considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Nicknamed the  Podium Players, these students were recognized in a weekly email shout-out and, over the course of the semester,  accounted for n = 6 of the pre-survey takers and n = 9 of the post-survey takers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' During Week 13, around one-third  of the class completed the post-survey and are referred to as Final Participants (n = 110).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finally, students who  took either survey, but did not report a nickname, are called the Non-Players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' However, it is possible that these  students played and forgot their initial game-generated nicknames on the survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To reduce the odds of potential  players being included in this group, another question asked students directly if they played a Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Using  this question, it was determined that the Non-Players accounted for eleven of the pre-survey takers and twenty-one  of the post-survey takers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For a summary of these groups, see Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  To explore the nature of optional participation as a means to modify physics attitudes and beliefs, the aforemen-  tioned groups of students were examined for significant differences in attitude change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To analyze the significance  of different group self-efficacy mean scores, t-tests were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Paired t-tests were utilized for groups with matched  datasets (paired pre- and post-test scores), while independent t-tests were utilized for groups with unmatched datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Participation in Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes was not required, and a steep decline was initially observed in the number of  students who opted to play (see Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' While the first Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' drew 157 participants, these students played an  average of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='47 more times, with half playing zero additional games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Just over 10% of them played all ten Kahoots!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='.  Further analysis revealed that the Players group had positive and significant gains (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='002), while the Non-Players  did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Though the Non-Players did show improvement in mean self-efficacy as a group, the difference in means from  pre- to post-survey was not statistically significant (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Like the Players, the Regular Players also reported  significant and positive gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The Ultra Players, who had the lowest pretest average of all groups also reported  10  TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This table summarizes the groups of students considered in the analysis of Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' participation and self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Group Name  Attributes  Initial Participants  Students who opted to take the pre-  survey (n = 65).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Final Participants  Students who opted to take the post-  survey (n = 110).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Players  Students who participated in the first  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' and who took the both pre-  and post- surveys (n = 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Regular Players  Players who participated in five or  more Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes (n = 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Ultra Players  Players who participated in all ten  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes (n = 7)  Podium Players  Players who earned a podiums spot  during one more Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' (n = 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A decline in participation was observed during the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  positive gains but, due to a limited sample size (n = 7), could not be deemed statistically significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These results  can be found in Table V  While participating in Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' did correspond to positive c measurements, it remains unclear whether greater  participation leads to greater self-efficacy gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, students with high physics self-efficacy were not likelier  to play than those with low physics self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  As stated earlier, gender can influence the effects of mastery and vicarious experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Based on previous findings  (see [55, 56]), males in male-dominated fields are more likely to benefit from mastery experiences (doing well per-  sonally), whereas females in male-dominated fields are more likely to benefit from vicarious experiences (doing well  compared to others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To test this hypothesis, the self-efficacy scores of Podium Players were examined to see if gender  was a moderating factor for self-efficacy change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Only five students from the Podium Players group took both surveys  and therefore, had a measured change, c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For male podium players, the average change ⟨c⟩ was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='348, and for females  was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This result seems to contradict the hypothesis that doing well compared to others (as measured by Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  performance) corresponds to greater increases in self-efficacy perceptions for females compared to males.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Although  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' quizzes represent opportunities for self-efficacy development through both vicarious and mastery experiences,  the vicarious aspect is potentially lessened due to the anonymous nature of the game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Vicarious experiences are most  influential when an individual compares themselves to a peer perceived as equally capable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' because students don’t  know the identity of their opponents, the impact of vicarious experiences through Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' may be lessened.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Due to limited statistics, it is not possible to draw conclusions about the impact of optional Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  quizzes  on physics students’ attitudes and beliefs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  However, it can be stated that students with high pretest scores are  more likely to reach the quiz podium based on the high pretest average of Podium Players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This supports previous  160  140  8  78  Week11  TABLE V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Results from pre- and post- (modified) CLASS surveys reveal significant gains for only two groups (indicated by  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cohen’s d is reported to represent effect size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Pre-  Post-  ⟨ c ⟩  p  Cohen’s d  N  µ  σ  N  µ  σ  Players*  26  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='46  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='74  26  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='04  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='14  ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='39  Regular Players*  18  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='50  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='90  18  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='72  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='12  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='30  Ultra Players  7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='00  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='43  7  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='43  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='09  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='32  Podium Players  6  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='33  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='39  9  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='00  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='90  –0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='03  ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='07  Non-Players  11  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='90  21  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='24  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='15  ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='52  Participants  65  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='26  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='62  110  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='09  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='27  TABLE VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This table lists the Likert style survey questions and scoring guidelines for the intelligence mindset portion of  the survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' These questions were used to asses the intelligence mindsets of students as either “growth” and “fixed”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Neutral  answers were not scored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Question  Growth Mindset  Fixed Mindset  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Reviewing mistakes is a big part of how I learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≥4  ≤ 2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Even when I do poorly on a test I try to learn from my mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≥4  ≤ 2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A significant problem in learning physics is being able to  memorize all the information I need to know (Q1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≤ 2  ≥4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' I cannot learn physics if the teacher does not explain things well (Q5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≤ 2  ≥4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Nearly everyone is capable of understanding physics if they work at it (Q8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≥4  ≤ 2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Learning physics changes my ideas about how the world works (Q20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  ≥4  ≤ 2  findings that self-efficacy and achievement are correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, students who participated in all ten Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  quizzes reported the lowest mean scores on both surveys out of all groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This could indicate that Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' does  not adequately inspire meaningful learning and may not lead to significant gains, particularly for students with low  self-efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Intelligence Mindsets and Self-Efficacy  In addition to exploring optional participation and self-efficacy, another aspect of this study aimed to explore how  intelligence mindsets might be related to students’ willingness to participate in self-efficacy opportunities or experience  positive self-efficacy change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Specifically, total participation and self-efficacy scores were compared for students who  reported “fixed” or “growth” mindsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  These comparisons were additionally observed through a gender lens to  explore the mindsets of male and female introductory physics students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Six survey questions were used to compute intelligence mindsets, four of which were taken from the CLASS (see  Table VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Answers that reflected a willingness to participate in the learning process or which aligned with the belief  that intelligence is flexible and something which can be achieved through time and practice were labeled growth  mindset and scored as “1”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Answers reflecting a belief that intelligence is finite or unchanging were deemed fixed  mindset and scored as “0”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Neutral answers were not scored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' For each student, these answers were then tallied;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  students with strong growth mindsets had a score of 5 or 6, and those with strong fixed mindsets had a score of 0 or  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  At the beginning of the semester, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='6% of respondents reported strong growth mindsets, while 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='4% reported strong  fixed mindsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Because intelligence mindset studies are relatively new to the PER community, follow up studies are  needed to properly reflect on these results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' At the conclusion of the semester, the percentage of students reporting  strong growth mindsets rose to 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='1%, while the percentage of fixed mindset students dropped to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Applying an  independent t-test revealed these groups to be statistically distinct (p ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='001) at both times of the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Minor differences in participation were reported for the two groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Students scoring in the upper quartile of self-  efficacy scores played an average of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8 games, while students scoring in the lower quartile played an average of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This suggests that participation in Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' does not align with intelligence mindsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' On the other  hand, the analysis did show a correlation between intelligence mindset and average Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' performance, as shown  in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Compared to the beginning of the semester, intelligence mindsets and average Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' scores became  more strongly related at the end of the semester, suggesting that students with high quiz averages developed stronger  growth mindsets than students with low quiz averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Further analysis revealed a correlation between intelligence mindsets and self-efficacy scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The initial self-efficacy  12  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The relationship between intelligence mindsets and Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' performance according pre- and post- survey results for  the group Participants (n = 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  averages for the “growth” and “fixed” mindset groups were 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Both an independent  t-test and Cohen’s d indicate these means to be statistically significant (p ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='001 and d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Additionally, at the  end of the semester, the self-efficacy averages were 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='70 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='0, respectively also with strong significance  (p ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='001 and d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Intelligence mindset beliefs relative to self-efficacy scores as measured by the pre-survey (left) and post-survey (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  No male students reported strong growth mindsets on the pre-survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The previously mentioned research by Kalender et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' [60] showed differences between males and females regarding  intelligence mindsets, particularly in male-dominated fields such as physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' To explore the nature of this finding,  male and female students with fixed, neutral, and growth mindsets were compared at both points during the semester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Self-efficacy scores were also compared for the groups to see if self-efficacy and intelligence mindsets reflect gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Initially, the group of students with strong initial growth mindsets comprised three females (and no males) with an  average self-efficacy of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' By the end of the semester, this group was comprised of six females and four males,  with an average self-efficacy of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8 for the female students and 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='9 for the male students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The observation that male students consistently outperform female students on various physics inventories should  be examined on the basis of intelligence mindsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In this study, male and female students with similar intelligence  mindsets reported similar self-efficacy scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Figure 3 shows the relationship between intelligence mindsets and self-  efficacy as measured by both pre- and post-surveys, broken down by gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Only in the growth mindset group was  there a sizeable difference (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='09) in self-efficacy averages for males and females, with females outscoring males.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Females also have higher reported self-efficacy in the fixed mindset group, but overlapping error bars make this result  less meaningful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Only in the neutral mindset range, where roughly 80% of students lie, do we see male students with  7400  壬 Pre  王- Post  T  T4DO  Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Score  G600  200  Average I  58D0  54D0  5000  Neutral  Grwth  Pre- Intelligence Mindset ScoreWomen (n=35)  TI  Women (n=52)  16  Men (n=28)  16  Men (n=55)  14  Eficac  1  Initial  8  中  8  6  6-  4  Foxed  Neutral  Growth  Foxed  Neutral  Growth  Pre- Intelligence Mindset Score  Post- Intelligence Mindset Score13  higher self-efficacy scores than female students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Again, follow up studies will be necessary to clarify the nature of this  finding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  CONCLUSION  The (modified) CLASS measured positive gains over the course of one semester for students enrolled in the remotely  taught introductory physics laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' However, due to limited statistics, conclusions regarding the different effects  of intermittent versus regular Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' participation could not be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perhaps classroom games like Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' are  more effective for students who participate intermittently (possibly on a need-to-need basis) and become less effective  for students who play for other reasons, perhaps for consistency or out of habit (not for meaningful learning).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This was  potentially the case for the Ultra Players, who, having participated in all optional quizzes throughout the semester,  was the only group of students to report negative self-efficacy change, ⟨c⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Results from the online learning attitudes portion of the survey demonstrated that while male and female students  generally hold similar attitudes toward online learning, distinction between the genders can be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Social interac-  tions play an important role in formulating perceptions of belonging [63], and further research should be carried out  to understand how remote classrooms shape and modify these perceptions, particularly in male-dominated fields like  physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Furthermore, intelligence mindsets and self-efficacy beliefs may influence attitudes toward online learning,  though not enough data was collected in this study to examine this hypothesis thoroughly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' However, it does not  seem unlikely, given that women typically cite social interactions as informing self-efficacy perceptions the most, that  remote learning may limit the scope of self-efficacy development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  The COVID-19 pandemic provided an opportunity for higher education communities to reflect on current teaching-  learning methods and to adapt novel ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' The pandemic also paved the way for flexible teaching-learning methods and  inspired institutions to develop robust educational techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In the past two years, many adaptations have helped  to protect and fortify these institutions against future unforeseen disruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' In successful cases, these adaptations  have increased accessibility for students’ in a way that nurtures their self-efficacy and long-term success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Mishra, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gupta, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Shree, International Journal of Educational Research Open 1, 100012 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Novak, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Patterson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gavrin, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Christian, Just in time teaching (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bransford, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brophy, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Williams, Journal of Applied Developmental Psychology 21, 59 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Otero and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Meltzer, Physics Today 70, 50 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Moore, in 2017 Physics Education Research Conference Proceedings (American Association of Physics  Teachers, 2018) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 296–299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Prieto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Orcos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Blazquez, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Le´on, Education Sciences 9, 55 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zhao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pinto Llorente, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S´anchez G´omez, Computers & Education 168, 104212 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bernacki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Greene, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Crompton, Contemporary Educational Psychology 60, 101827 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Freeman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Eddy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McDonough, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Smith, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Okoroafor, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Jordt, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wenderoth, Proceedings of the  National Academy of Sciences 111, 8410 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [10] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brewe and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sawtelle, European Journal of Physics 39, 054001 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C¸elik, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pektas, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Karamustafaoglu, Electronic Journal for Research in Science & Mathematics Education  25, 47 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [12] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hussain, Creative Education 3, 179 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bryans Bongey, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cizadlo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kalnbach, Campus-Wide Information Systems 22, 252 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cho, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zhao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Runshe, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Krousgrill, International Journal of STEM Education 8, 1 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [15] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sointu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hyypi¨a, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lambert, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hirsto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Saarelainen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Valtonen, Higher Education (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bandura, Psychological Review 84, 191 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bandura, Self-Efficacy: The Exercise of Control, edited by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brennan (W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Freeman and Company, 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Andrew, Journal of Advanced Nursing 27, 596 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brown, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Larkin, Journal of Counseling Psychology 31, 356 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brown, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Larkin, Journal of Counseling Psychology 34, 293 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Multon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brown, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lent, Journal of Counseling Psychology 38, 30 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pietsch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Walker, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Chapman, Journal of Educational Psychology 95, 589 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Redish, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Saul, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Steinberg, American Journal of Physics 66, 212 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [24] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Adams, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Podolefsky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dubson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finkelstein, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wieman, Physical Review  Special Topics-physics Education Research 2, 010101 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Madsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McKagan, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sayre, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 11, 010115 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Knight, Five Easy Lessons: Strategies for Successful Physics Teaching, Pearson Educational Innovation (Addison  Wesley, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  14  [27] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Halloun and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hestenes, American Journal of Physics 53, 1043 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Clement, American Journal of Physics 50, 66 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [29] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Mazur, Peer Instruction: A User’s Manual, Series in Educational Innovation (Prentice Hall, 1997) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 3–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [30] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Van Heuvelen, American Journal of Physics 59, 891 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hammer, American Journal of Physics 64, 1316 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gray, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Adams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wieman, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins, Physical Review Special Topics-Physics Education Research  4, 020106 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [33] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McDermott, American Journal of Physics 59, 301 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [34] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Halloun and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hestenes, Science & Education 7, 553 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Licorish, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Owen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Daniel, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' George, Rearch and Practice in Technology Enhanced Learning 13  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [36] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' White and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McCoy, Networks: An Online Journal for Teacher Research 21 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wang and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Tahir, Computers & Education 149, 103818 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [38] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wilcox and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lewandowski, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 13, 010108 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [39] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Oymak and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Ogan-Bekiroglu (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [40] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hake, American Journal of Physics 66, 64 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [41] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Davis, in Annual Meeting of the American Educational Research Association (ERIC, 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [42] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brewe, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kramer, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' O’Brien, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 5, 013102 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [43] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brewe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Traxler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' de la Garza, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kramer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 9, 020116 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [44] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finkelstein and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pollock, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 1, 010101 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [45] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Semsar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Knight, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Birol, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Smith, CBE—Life Sciences Education 10, 268 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Barbera, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Adams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wieman, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins, Journal of Chemical Education - J CHEM EDUC 85 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [47] Colorado Learning Attitudes About Science Survey (CLASS) (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [48] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hackett and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Betz, Journal for Research in Mathematics Education 20, 261 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [49] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hackett and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Betz, Journal of Vocational Behavior 18, 326 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [50] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brown, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Larkin, Journal of Counseling Psychology 33, 265 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brown, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lent, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Larkin, Journal of Vocational Behavior 35, 64 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [52] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Luzzo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hasper, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Albert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bibby, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Martinelli Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', Journal of Counseling Psychology 46, 233  (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [53] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hall and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Webb, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 10, 020116 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [54] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hutchison, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Follman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sumpter, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bodner, Journal of Engineering Education 95, 39 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zeldin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pajares, American Educational Research Journal 37, 215 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [56] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zeldin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Britner, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pajares, Journal of Research in Science Teaching 45, 1036 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [57] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Britner, Journal of Research in Science Teaching 45, 955–970 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [58] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sawtelle, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Brewe, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kramer, Journal of Research in Science Teaching 49, 1096 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Madsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McKagan, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sayre, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 9, 020121 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [60] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kalender, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Marshman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Schunn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Nokes-Malach, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Singh, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 18, 010116  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [61] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lindstrøm and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sharma, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Innov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 19, 1 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [62] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wilcox and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lewandowski, American Journal of Physics 86, 212 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [63] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dobbins, Bulletin of the American Physical Society (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [64] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Masud, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Ahmad, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Jan, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Jamil, Asia Pacific Education Review 17, 121 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [65] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Adams, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Pollock, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finkelstein, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wieman, AIP Conference Proceedings 790, 61  (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [66] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Schunk, Educational psychology review 1, 173 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [67] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Abeysekera and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dawson, Higher Education Research & Development 34, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [68] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Moll and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Milner-Bolotin, Canadian Journal of Physics 87, 917 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [69] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' McDermott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', Physics by Inquiry: An Introduction to Physics and the Physical Sciences, Volume 1 (John Wiley  & Sons, 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [70] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Otero and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gray, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 4, 020104 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [71] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Liang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Fulmer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Majerich, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Clevenstine, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Howanski, Journal of Science Education and Technology  21, 114 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [72] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Lindsey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sadaghiani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Taylor, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cummings, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 8, 010102 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [73] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Silva, in Proceedings of the PBL 2010 International Conference-Problem-Based Learning and Active Learning  Methodologies (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [74] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Abdisa and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Getinet, Journal of Physics Education 4, 530 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [75] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wulandari, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Sa’dijah, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' As’ari, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rahardjo, Journal of Physics: Conference Series 1028, 012153  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [76] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kapp, The gamification of learning and instruction: game-based methods and strategies for training and education  (John Wiley & Sons, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [77] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Subhash and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cudney, Computers in Human Behavior 87, 192 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [78] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A¸sıksoy, Quality & Quantity: International Journal of Methodology 52, 129 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [79] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Forndran and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zacharias, European Journal of Physics 40, 045702 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [80] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Ahmed and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Asiksoy, Sustainability 13 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  15  [81] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kalogiannakis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Papadakis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Zourmpakis, Education Sciences 11 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [82] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bouchrika, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Harrati, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wanick, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Wills, Interactive Learning Environments 29, 1244 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [83] Kahoot!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [84] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gebbels, Compass: Journal of Learning and Teaching 11 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [85] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Boeker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Andel, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Vach, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Frankenschmidt, PLOS ONE 8 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [86] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kilickaya, A Journal of Language Teaching and Learning 53 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [87] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Shyr, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hsieh, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Chen, Sustainability 13 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [88] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kolil, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Muthupalani, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Achuthan, International Journal of Educational Technology in Higher Education 17  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [89] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Linn, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Davis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bell, Internet environments for science education (Lawrence Erlbaum Associates  Publishers, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [90] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hamed and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Ahmad, Journal of Information Technology Education: Research 19, 976 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [91] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Finkelstein, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Adams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Keller, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kohl, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Perkins, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Podolefsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Reid, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' LeMaster,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' ST Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 1, 010103 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [92] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dweck, Mindset: The new psychology of success (Random House, 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [93] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Yeager, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hanselman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Walton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Murray, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Crosnoe, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Muller, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Tipton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Schneider, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hulleman,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hinojosa, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=', Nature 573, 364 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [94] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Scherr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Plisch, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Gray, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Potvin, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hodapp, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 13, 020133 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [95] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dweck, Self-theories: Their role in motivation, personality, and development (Psychology press, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [96] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Elliott and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Dweck, Journal of personality and social psychology 54, 5 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [97] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Marshman, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kalender, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Nokes-Malach, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Schunn, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Singh, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 14, 020123  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [98] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Leslie, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cimpian, Science 355, 389 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [99] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Leslie, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Cimpian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Meyer, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Freeland, Science 347, 262 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [100] APS, American physical society, percentage of underrepresented minorities, Available at https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='org/  programs/education/statistics/urm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='cfm (10/06/2022) (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [101] PhET, PhET simulations, Available at https://phet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='colorado.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='edu (10/06/2022) (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [102] GeoGebra, GeoGebra, Available at https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='geogebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='org (10/06/2022) (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [103] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Hwang, Basic function of an oscilloscope, Available at https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='phy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='ntnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='tw/ntnujava/ (10/06/2022)  (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [104] Mathlets, MIT Mathlets, Available at https://mathlets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='org/activities/ (10/06/2022) (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [105] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Foster,  UH  Manoa  Physics  Lab  Quizzes,  https://create.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='kahoot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='it/course/  205fca5e-c5e3-47ff-b587-c2aeec664328/edit (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  [106] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Day, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Stang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Holmes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Kumar, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Bonn, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' 12, 020104 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  16  Appendix: Modifications to the CLASS  The questions used in this study for the purpose of measuring self-efficacy are appended below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Twenty-one of the  original forty-two Colorado Learning Attitudes About Science Survey (CLASS) questions were incorporated, including  the moderating question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  TABLE VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' This table includes the CLASS questions used in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Corresponding question numbers, expert responses,  and categorical assignments are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  Survey Question  Number  CLASS Question  Number  Question  Expert  Response  Category  1  1  A significant problem in learning physics is being able to  memorize all the information I need to know.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  CC, ACU  2  2  When I am solving a physics problem, I try to decide what  would be a reasonable value for the answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  No category  3  5  After I study a topic in physics and feel that I understand  it, I have difficulty solving problems on the same topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  CC, ACU, PSS  4  6  Knowledge in physics consists of many disconnected topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  CC, ACU  5  12  I cannot learn physics if the teacher does not explain  things well in class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  No category  6  13  I do not expect physics equations to help my understanding  of the ideas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' they are just for doing calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  CC, PSG  7  14  I study physics to learn knowledge that will be useful in my  life outside of school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  PI  8  16  Nearly everyone is capable of understanding physics if they  work at it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  PSG, PSC  9  18  There could be two different correct values to a physics  problem if I use two different approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  No category  10  23  In doing a physics problem, if my calculation gives a  result very different from what I’d expected, I’d trust the  calculation rather than going back through the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  SME  11  25  I enjoy solving physics problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  PI, PSG, PSS  12  26  In physics, mathematical formulas express meaningful  relationships among measurable quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  PSG  13  31  We use this statement to discard the survey of people  who are not reading the questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content=' Please select  agree-option 4 (no strongly agree) for this question to  preserve your answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A only  No category  14  32  Spending a lot of time understanding where formulas come  from is a waste of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  CC, SME  15  34  I can usually figure out a way to solve physics problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  PSG, PSC, PSS  16  35  The subject of physics has little relation to what I  experience in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  RWC  17  39  When I solve a physics problem, I explicitly think about  which physics ideas apply to the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  SME  18  40  If I get stuck on a physics problem, there is no chance I’ll  figure it out on my own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  D  ACU, PSG, PSC, PSS  19  42  When studying physics, I relate the important information  to what I already know rather than just memorizing  it the way it was presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  SME, PSG  20  28  Learning physics changes my ideas about how the world  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
+page_content='  A  RWC, PI,  21  30  Reasoning skills used to understand physics can be  helpful to me in my everyday life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Q9E0T4oBgHgl3EQf1gIp/content/2301.02699v1.pdf'}
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+Learning Symbolic Representations for
+Reinforcement Learning of Non-Markovian Behavior
+Phillip J.K. Christoffersen, Andrew C. Li, Rodrigo Toro Icarte, Sheila A. McIlraith
+University of Toronto & Vector Institute for Artificial Intelligence, Toronto, Canada
+{phill,andrewli,rntoro,sheila}@cs.toronto.edu
+Abstract
+Many real-world reinforcement learning (RL) problems necessitate learning com-
+plex, temporally extended behavior that may only receive reward signal when the
+behavior is completed. If the reward-worthy behavior is known, it can be specified
+in terms of a non-Markovian reward function—a function that depends on aspects
+of the state-action history, rather than just the current state and action. Such reward
+functions yield sparse rewards, necessitating an inordinate number of experiences
+to find a policy that captures the reward-worthy pattern of behavior. Recent work
+has leveraged Knowledge Representation (KR) to provide a symbolic abstraction
+of aspects of the state that summarize reward-relevant properties of the state-action
+history and support learning a Markovian decomposition of the problem in terms
+of an automaton over the KR. Providing such a decomposition has been shown to
+vastly improve learning rates, especially when coupled with algorithms that exploit
+automaton structure. Nevertheless, such techniques rely on a priori knowledge
+of the KR. In this work, we explore how to automatically discover useful state
+abstractions that support learning automata over the state-action history. The result
+is an end-to-end algorithm that can learn optimal policies with significantly fewer
+environment samples than state-of-the-art RL on simple non-Markovian domains.
+1
+Introduction
+Deep RL has shown promise at learning complex behavior in many settings, including game-playing
+[1], robotics [2], and control systems [3]. These algorithms typically take advantage of a Markov
+assumption — that it is enough to consider only the current state when deciding which action to take.
+However, many real-world tasks are inherently temporally extended. The pattern of behavior the
+RL agent must learn depends not only upon the current state but also on past states and actions. For
+example, an agent that needs to get through a locked door to get high reward must have previously
+located and acquired the key. Unfortunately, learning such temporally extended behavior can be
+incredibly challenging since the agent must learn to discern relevant features from its state-action
+history; these can be arbitrarily far removed from the present state, and may depend on this history in
+complex ways and without intermediate reward signal to aid learning. The standard deep RL solution
+to learning such temporally extended behavior is to use a recurrent neural network (RNN), which
+learns an abstract hidden state in order to summarize environment histories, but RNNs require much
+data to train, and are difficult to tune.
+By contrast, in recent work, an algorithm for learning temporally extended behavior is proposed,
+where the RNN hidden states are replaced with an augmentation of the current state in terms of
+hand-designed propositional symbols, which incorporate domain knowledge and point the agent
+towards potentially reward-relevant properties of the state-action history (e.g. [4, 5, 6, 7]). In the
+previous example, one can augment the agent with the propositional symbol have_keys, indicating
+whether the agent has acquired the keys to the door in the past. Markovian policies on this state
+4th Knowledge Representation and Reasoning Meets Machine Learning Workshop (KR2ML 2020), at NeurIPS.
+arXiv:2301.02952v1  [cs.LG]  8 Jan 2023
+
+space now become vastly more expressive: if one can additionally condition on the truth state of
+have_keys when deciding an action, we can perform the following temporally extended behavior: go
+towards the keys when have_keys is false, then go towards the door when have_keys is true. But
+how did we know to augment the agent with have_keys in the first place? While this example seems
+simple, this is only because we contrived the reward: it is not in general clear which propositional
+symbols to augment an agent with, in order to achieve high performance. To address this, we propose
+the use of automata learning within the RL framework to automatically yield such propositional
+symbols, rather than relying on domain knowledge. We demonstrate that the trained automata
+dramatically accelerate policy learning, with our end-to-end approach outperforming a state-of-the-art
+RL algorithm (Recurrent-PPO) on several non-Markovian reward domains.
+2
+Related Work
+Recently, the idea of specifying non-Markovian reward functions in RL via formal languages such as
+Linear Temporal Logic (LTL) (e.g., ( [8, 9, 10, 11, 12, 13, 5, 14]) or automata (e.g., [7, 4, 15, 16])
+has garnered significant attention. While these approaches rely on domain knowledge and a domain-
+specific vocabulary for specification of the reward function, we consider a black-box non-Markovian
+reward and present an automated approach to uncover the reward structure. In this approach, we
+train automata offline using a reward-prediction heuristic, and augment the environment states with
+the states of the learned automaton, as opposed to hand-designed features. An alternate black-box
+approach to ours is to first train an RNN, with a standard deep (recurrent) RL algorithm, and then
+"quantize" the hidden state of the RNN, but this learned transition model is not a direct function of
+the state-action history [17].
+Previous work by Toro Icarte et al. [4] and Xu et al. [18] share many of the motivations of our work
+but perform poorly in noisy environments. The work most similar to ours is by Gaon & Brafman [6],
+which we build on in several key ways. First, the (off-the-shelf) automata-learning approaches they
+employ are sensitive to noisy data and often learn large, sample-sensitive automata even when the
+reward structure is simple. We make use of recent advances in automata-learning which are robust to
+noise and regularize the size of the automaton, which we demonstrate in Section 5. Furthermore, [6]
+lacked experimental comparisons against state-of-the-art RL. In our experiments with non-Markovian
+goals, we outperform state-of-the-art RL based on RNNs.
+3
+Preliminaries
+An MDP is a tuple M = (S, A, P, R, γ), where S is a set of states, A a set of actions, P : S×A×S →
+[0, 1] the state-action transition function, R : S → R the reward, and 0 ≤ γ ≤ 1 the discounting
+factor [19]. In such a setup, the reward R is considered Markovian, due to its dependence only
+on the most recent state. We will consider the following extension of the MDP: an NMRDP [20]
+(non-Markovian Reward Decision Process) N = (S, A, P, R, γ) is as before, but where the reward
+R : H → R, where H = (S × A)∗ is the set of finite histories with states S and actions A: in
+other words, the agent can be rewarded for behavior which is arbitrarily far removed from its current
+experience. Further, we define a proposition as a function P : H → {True, False}, in an NMRDP.
+Intuitively, propositions correspond to facts about the state-action history in a given episode, such as
+"the agent has at some point reached the top right corner" or "within the 3 most recent timesteps, the
+agent took action x". While the number of possible propositions grows double-exponentially in the
+length of the episode, domain knowledge is often used to specify a relevant set of such propositions,
+under which the reward is Markovian. The RL domains we consider have non-Markovian goals, i.e.
+there exists G ⊂ H where R(g) = 1 for g ∈ G, and R(h) = 0 for h ∈ H − G. Intuitively, we want to
+create a policy which makes the agent attain a goal history as soon as possible.
+4
+Algorithm
+We use the algorithm described in Algorithm 1 named AutRL. Following each period of Markovian
+learning, the sampled traces are used to train (offline) a deterministic finite automaton (DFA) M to
+predict whether a given sequence achieves reward 0 or 1. We leverage the DFA-learning approach
+from [21] due to its efficiency, its propensity to learn small DFAs with few transitions, and its
+robustness to noise. Tabular Q-learning is used for markov_learn. Intuitively, a DFA with state
+2
+
+Algorithm 1: AutRL
+1 dfa ← empty_automata;
+2 π ← uniform_random_policy;
+3 traces ← ∅ ;
+4 while true do
+5
+sample_traces ← sample(π, N) ;
+6
+append traces with sample_traces;
+7
+if sample_traces inconsistent with dfa then
+8
+dfa ← aut_learn(traces);
+9
+end
+10
+π ← markov_learn(sample_traces × dfa);
+11 end
+space Q that accurately discriminates reward 1 traces from reward 0 traces (which we define as
+consistent) must model all parts of the state-action history relevant to the goal, and therefore the
+augmented state space S × Q must make the problem Markovian. We remark that the resultant DFAs
+are functions H → Q and are learned end-to-end without domain knowledge. Examples of this can
+be seen in Section 5. We also provide a convergence guarantee for this algorithm in Appendix A.
+We note that our implementation using Q-learning converges to an optimal policy as the number
+of environment samples approaches infinity (assuming G is regular, as above) due to the optimal
+convergence guarantees of Q-learning on MDPs [19]). Note that while we search for consistent
+DFAs, this condition is not necessary to make the learning problem Markovian. For this reason, we
+relax the inconsistency condition analyzed above, replacing the DFA only under weak performance
+(i.e. low average reward) at the end of a given epoch of markov_learn.
+5
+Experimental Results
+The purpose of our experiments was to evaluate our AutRL algorithm, which leverages a learned
+symbolic representation, relative to a state-of-the-art RNN-based deep RL algorithm. The two metrics
+were the quality of the policies in terms of maximizing reward, and their sample efficiency. We tested
+on four non-Markovian domains, similar to those used in the experiments of [6] as follows.
+Multi-Armed Bandit: A single-state environment with two actions (left, right) and episodes
+of length 6.
+A reward of 1 is obtained only if the 6 actions performed are precisely
+left, right, right, left, right, left in that order.
+Hallway: A 1 × 10 grid, aligned left-to-right, with actions left, right, and with episodes of length 30.
+The agent spawns at a random location on the left half of the grid and must first reach the right-most
+square, and then reach the left-most square to obtain a reward of 1. Before reaching the right-most
+square, the optimal action in every state is right, but after reaching the right-most square, the optimal
+action becomes left in every state.
+Gridworld: A 5 × 5 gridworld (with x, y-coordinates from 0 to 4) with an episode length of 20 and
+actions up, down, left, right. The agent must first reach (4, 0) and then the opposite corner (0, 4)
+to collect a reward of 1. We also tested a noisy version of this environment where the reward was
+randomly withheld in 10% of successful traces, and actions had a random outcome 10% of the time.
+We compared AutRL against Recurrent-PPO ([22]) (with an LSTM policy) using the OpenAI
+Baselines implementation [23]. As shown in all of the below environments, AutRL converges to high
+reward policies in fewer environment samples than Recurrent-PPO does. Notice that AutRL, despite
+being automata-based, outperforms Recurrent-PPO even on the Stochastic Gridworld, showing that
+AutRL is robust to noisy environments. In Figure 2 are two such examples of learned automata on
+two different runs of the Hallway environment.
+3
+
+1000000
+2000000
+3000000
+4000000
+Environment Samples
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Average Reward
+Multi-Armed Bandit
+1000000
+2000000
+3000000
+4000000
+Environment Samples
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Average Reward
+Hallway
+1000000
+2000000
+3000000
+4000000
+Environment Samples
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Average Reward
+Gridworld
+1000000
+2000000
+3000000
+4000000
+Environment Samples
+0.0
+0.2
+0.4
+0.6
+0.8
+Average Reward
+Stochastic Gridworld
+Legend:
+PPO + LSTM
+AutRL + Q-Learning (ours)
+Figure 1: The results from the conducted experiments. The error bars are 95% confidence intervals over 30
+runs. AutRL learns a superior policy to the LSTM-based PPO in a way that is, at most, over order of magnitude
+more sample-efficient. Learning is far more stable across runs with AutRL: the error bars for AutRL are far
+tighter than those for PPO, indicating very little variation in the learning trajectory across runs.
+q0
+q2
+q1
+o/w
+o/w
+always
+Right side
+Left side
+q0
+q2
+q1
+o/w
+o/w
+always
+Right side
+4th square from left
+Figure 2: Two distinct DFAs learned from the Hallway environment. Both are enough to make the domain
+Markovian: however, the one on the right is not a perfect classifier of G for this domain. This shows that the
+condition in the statement of AutRL above is strictly stronger than necessary: there are automata which do
+not perfectly decide G, but which discern enough relevant information to learn optimal, temporally extended
+behavior in non-Markovian settings.
+6
+Concluding Remarks
+In this work, we show how to learn a KR that provides a useful symbolic abstraction in support of
+realizing temporally extended behavior in standard RL agents which rely on a Markov assumption. We
+provide an end-to-end RL algorithm which, in deterministic and stochastic domains, is demonstrably
+more sample-efficient than the state of the art. We further provide theoretical guarantees of optimal
+convergence for our approach (under conditions outlined in the theorem of Appendix A), along with
+insight into the structure of DFAs which are learned by this method.
+This work reveals several promising directions for future research. While we considered environments
+where the reward function is non-Markovian, learning in the more general setting of POMDPs is
+an important problem related to this work, to which the DFA methods leveraged here do not apply.
+Further, AutRL leverages DFAs, which can only represent regular languages, thus learning efficiently
+when G is not a regular language in S ×A, as well as learning KR in high-dimensional and continuous
+state spaces, remain major open challenges to this methodology.
+4
+
+Acknowledgments and Disclosure of Funding
+We gratefully acknowledge funding from the Natural Sciences and Engineering Research Council of
+Canada (NSERC), the Canada CIFAR AI Chairs Program, and Microsoft Research. The third author
+also acknowledges funding from ANID (Becas Chile). Resources used in preparing this research
+were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR,
+and companies sponsoring the Vector Institute for Artificial Intelligence (www.vectorinstitute.
+ai/partners). Finally, we thank the Schwartz Reisman Institute for Technology and Society for
+providing a rich multi-disciplinary research environment.
+References
+[1] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur
+Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, et al. A general
+reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science,
+362(6419):1140–1144, 2018.
+[2] Jan Peters, Sethu Vijayakumar, and Stefan Schaal. Reinforcement learning for humanoid
+robotics. In Proceedings of the Third IEEE-RAS International Conference On Humanoid
+Robots, pages 1–20, 2003.
+[3] Robert H Crites and Andrew G Barto. Improving elevator performance using reinforcement
+learning. In Proceedings of the 9th Conference on Advances in Neural Information Processing
+Systems (NIPS), pages 1017–1023, 1996.
+[4] Rodrigo Toro Icarte, Ethan Waldie, Toryn Klassen, Rick Valenzano, Margarita Castro, and
+Sheila McIlraith. Learning reward machines for partially observable reinforcement learning. In
+Proceedings of the 32nd Conference on Advances in Neural Information Processing Systems
+(NeurIPS), pages 15523–15534, 2019.
+[5] Alberto Camacho, Rodrigo Toro Icarte, Toryn Q Klassen, Richard Anthony Valenzano, and
+Sheila A McIlraith. LTL and beyond: Formal languages for reward function specification in
+reinforcement learning. In Proceedings of the 28th International Joint Conference on Artificial
+Intelligence (IJCAI), volume 19, pages 6065–6073, 2019.
+[6] Maor Gaon and Ronen Brafman. Reinforcement learning with non-Markovian rewards. In
+Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), volume 34, pages
+3980–3987, 2020.
+[7] Rodrigo Toro Icarte, Toryn Q. Klassen, Richard Valenzano, and Sheila A. McIlraith. Using
+reward machines for high-level task specification and decomposition in reinforcement learning.
+In Proceedings of the 35th International Conference on Machine Learning (ICML), pages
+2112–2121, 2018.
+[8] Bruno Lacerda, David Parker, and Nick Hawes. Optimal and dynamic planning for Markov
+decision processes with co-safe ltl specifications.
+In Proceedings of the 2014 IEEE/RSJ
+International Conference on Intelligent Robots and Systems (IROS), volume 13, pages 1511—-
+1516, 2014.
+[9] Michael L. Littman, Ufuk Topcu, Jie Fu, Charles Isbell, Min Wen, and James MacGlashan.
+Environment-independent task specifications via GLTL. arXiv preprint arXiv:1704.04341,
+2017.
+[10] Alberto Camacho, Oscar Chen, Scott Sanner, and Sheila McIlraith. Decision-making with
+non-Markovian rewards: From LTL to automata-based reward shaping. In Proceedings of the
+Tenth International Symposium on Combinatorial Search (SoCS 2017), pages 279—-283, 2017.
+[11] Xiao Li, Yao Ma, and Calin Belta. A policy search method for temporal logic specified
+reinforcement learning tasks. In 2018 Annual American Control Conference (ACC), pages
+240–245, 2018.
+[12] Rodrigo Toro Icarte, Toryn Q Klassen, Richard Valenzano, and Sheila A McIlraith. Teaching
+multiple tasks to an RL agent using LTL. In Proceedings of the 17th International Conference
+on Autonomous Agents and Multiagent Systems (AAMAS), pages 452–461, 2018.
+5
+
+[13] Ronen Brafman, Giuseppe De Giacomo, and Fabio Patrizi. LTLf/LDLf non-Markovian rewards.
+In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI), pages 1771–1778,
+2018.
+[14] Mohammadhosein Hasanbeig, Yiannis Kantaros, Alessandro Abate, Daniel Kroening, George J
+Pappas, and Insup Lee. Reinforcement learning for temporal logic control synthesis with
+probabilistic satisfaction guarantees. In 2019 IEEE 58th Conference on Decision and Control
+(CDC), pages 5338–5343. IEEE, 2019.
+[15] Ronen I Brafman and Giuseppe De Giacomo. Regular decision processes: A model for non-
+Markovian domains. In Proceedings of the 28th International Joint Conference on Artificial
+Intelligence (IJCAI), pages 5516–5522, 2019.
+[16] Mohammadhosein Hasanbeig, Alessandro Abate, and Daniel Kroening. Logically-constrained
+reinforcement learning. arXiv preprint arXiv:1801.08099v8, 2019.
+[17] Anurag Koul, Sam Greydanus, and Alan Fern. Learning finite state representations of recurrent
+policy networks. International Conference on Learning Representations, 2019.
+[18] Zhe Xu, Ivan Gavran, Yousef Ahmad, Rupak Majumdar, Daniel Neider, Ufuk Topcu, and Bo Wu.
+Joint inference of reward machines and policies for reinforcement learning. In Proceedings
+of the International Conference on Automated Planning and Scheduling, volume 30, pages
+590–598, 2020.
+[19] Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press,
+2018.
+[20] Faheim Bacchus, Craig Boutilier, and Adam Grove. Rewarding behaviors. In Proceedings
+of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), volume 13, pages
+1160–1161, 1996.
+[21] Maayan Shvo, Andrew C Li, Rodrigo Toro Icarte, and Sheila A McIlraith. Interpretable
+sequence classification via discrete optimization. arXiv preprint arXiv:2010.02819, 2020.
+[22] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal
+policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.
+[23] Prafulla Dhariwal, Christopher Hesse, Oleg Klimov, Alex Nichol, Matthias Plappert, Alec
+Radford, John Schulman, Szymon Sidor, Yuhuai Wu, and Peter Zhokhov. Openai baselines.
+https://github.com/openai/baselines, 2017.
+Appendix A: Convergence Guarantee + Proof
+Theorem 1. Let N be an NMRDP. Under the following (realistic) conditions, AutRL converges to
+an optimal policy in the sample limit.
+1. sample_traces visits every reachable history within N i.o.a.s. (infinitely often, almost
+surely) (exploration)
+2. For any regular language L, when sampling traces using sample_traces, that aut_learn
+eventually returns an automaton perfectly deciding L w.p.1. (consistency of aut_learn)
+3. markov_learn converges to the optimal policy in the sample limit for an MDP (consistency
+of markov_learn)
+4. {h : R(h) = 1} = G ⊂ H forms a regular language with alphabet Σ = S × A (regularity)
+Proof. Fix an NMRDP N = (S, A, P, R, γ), and assume all conditions are met in the theorem
+statement. Then, since G is a regular language, we have that the variable dfa is, with probability
+1, eventually set to an automaton, with state space Q, which perfectly decides G. At such a point,
+then we have that the states of the automaton perfectly predict the reward R: thus, the problem
+M = (S × Q, A, P, R, γ), simply defined as N but with a state space augmented with the automaton
+states of dfa, is actually an MDP. Further, dfa is never thereafter reset, since no inconsistent trace can
+possibly be sampled from the environment subsequently. Thus, M is simply an MDP being trained
+with Markovian learning algorithm markov_learn, and thus the appropriate convergence conditions
+apply.
+6
+
+Appendix B: Baseline Hyperparameter Tuning
+For the tabular Q-learning for our approach (AutRL), we used a learning rate of 0.1 on the determin-
+istic environment, 0.001 on the stochastic environment. Further, an exploration parameter of 0.01
+was used on the deterministic environments, and 0.05 with a decaying exponential schedule (with
+factor 0.99) was used for the stochastic environments. The automaton learning method was set at a
+maximum state threshold of 5 for all environments but the multi-armed bandit (which had 14), a loop
+penalty of 0.01 in all environments, and a transition penalty of 0.01 for the Multi-Armed Bandit, 0.3
+for both gridworlds, and 0.6 for the hallway. Further, the timeout was set to 250.
+For the Recurrent-PPO baseline, we used the OpenAI Baselines [23] implementation with an LSTM
+policy network, an entropy coefficient of 0.001, a learning rate of 0.0003, a discounting factor of
+0.99, a batch size of 16384 (with 8 minibatches per update), and all other hyperparameters set to
+default. We followed standard practice in tuning these hyperparameters and found that these settings
+consistently performed best across our domains.
+7
+
diff --git a/XtE1T4oBgHgl3EQfJgNL/content/tmp_files/load_file.txt b/XtE1T4oBgHgl3EQfJgNL/content/tmp_files/load_file.txt
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@@ -0,0 +1,255 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf,len=254
+page_content='Learning Symbolic Representations for  Reinforcement Learning of Non-Markovian Behavior  Phillip J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Christoffersen, Andrew C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Li, Rodrigo Toro Icarte, Sheila A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' McIlraith  University of Toronto & Vector Institute for Artificial Intelligence, Toronto, Canada  {phill,andrewli,rntoro,sheila}@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='toronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='edu  Abstract  Many real-world reinforcement learning (RL) problems necessitate learning com-  plex, temporally extended behavior that may only receive reward signal when the  behavior is completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' If the reward-worthy behavior is known, it can be specified  in terms of a non-Markovian reward function—a function that depends on aspects  of the state-action history, rather than just the current state and action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Such reward  functions yield sparse rewards, necessitating an inordinate number of experiences  to find a policy that captures the reward-worthy pattern of behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Recent work  has leveraged Knowledge Representation (KR) to provide a symbolic abstraction  of aspects of the state that summarize reward-relevant properties of the state-action  history and support learning a Markovian decomposition of the problem in terms  of an automaton over the KR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Providing such a decomposition has been shown to  vastly improve learning rates, especially when coupled with algorithms that exploit  automaton structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Nevertheless, such techniques rely on a priori knowledge  of the KR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In this work, we explore how to automatically discover useful state  abstractions that support learning automata over the state-action history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The result  is an end-to-end algorithm that can learn optimal policies with significantly fewer  environment samples than state-of-the-art RL on simple non-Markovian domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  1  Introduction  Deep RL has shown promise at learning complex behavior in many settings, including game-playing  [1], robotics [2], and control systems [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' These algorithms typically take advantage of a Markov  assumption — that it is enough to consider only the current state when deciding which action to take.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  However, many real-world tasks are inherently temporally extended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The pattern of behavior the  RL agent must learn depends not only upon the current state but also on past states and actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' For  example, an agent that needs to get through a locked door to get high reward must have previously  located and acquired the key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Unfortunately, learning such temporally extended behavior can be  incredibly challenging since the agent must learn to discern relevant features from its state-action  history;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' these can be arbitrarily far removed from the present state, and may depend on this history in  complex ways and without intermediate reward signal to aid learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The standard deep RL solution  to learning such temporally extended behavior is to use a recurrent neural network (RNN), which  learns an abstract hidden state in order to summarize environment histories, but RNNs require much  data to train, and are difficult to tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  By contrast, in recent work, an algorithm for learning temporally extended behavior is proposed,  where the RNN hidden states are replaced with an augmentation of the current state in terms of  hand-designed propositional symbols, which incorporate domain knowledge and point the agent  towards potentially reward-relevant properties of the state-action history (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' [4, 5, 6, 7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In the  previous example, one can augment the agent with the propositional symbol have_keys, indicating  whether the agent has acquired the keys to the door in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Markovian policies on this state  4th Knowledge Representation and Reasoning Meets Machine Learning Workshop (KR2ML 2020), at NeurIPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='02952v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='LG]  8 Jan 2023  space now become vastly more expressive: if one can additionally condition on the truth state of  have_keys when deciding an action, we can perform the following temporally extended behavior: go  towards the keys when have_keys is false, then go towards the door when have_keys is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' But  how did we know to augment the agent with have_keys in the first place?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' While this example seems  simple, this is only because we contrived the reward: it is not in general clear which propositional  symbols to augment an agent with, in order to achieve high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' To address this, we propose  the use of automata learning within the RL framework to automatically yield such propositional  symbols, rather than relying on domain knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We demonstrate that the trained automata  dramatically accelerate policy learning, with our end-to-end approach outperforming a state-of-the-art  RL algorithm (Recurrent-PPO) on several non-Markovian reward domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  2  Related Work  Recently, the idea of specifying non-Markovian reward functions in RL via formal languages such as  Linear Temporal Logic (LTL) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=', ( [8, 9, 10, 11, 12, 13, 5, 14]) or automata (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=', [7, 4, 15, 16])  has garnered significant attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' While these approaches rely on domain knowledge and a domain-  specific vocabulary for specification of the reward function, we consider a black-box non-Markovian  reward and present an automated approach to uncover the reward structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In this approach, we  train automata offline using a reward-prediction heuristic, and augment the environment states with  the states of the learned automaton, as opposed to hand-designed features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' An alternate black-box  approach to ours is to first train an RNN, with a standard deep (recurrent) RL algorithm, and then  "quantize" the hidden state of the RNN, but this learned transition model is not a direct function of  the state-action history [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Previous work by Toro Icarte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' [4] and Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' [18] share many of the motivations of our work  but perform poorly in noisy environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The work most similar to ours is by Gaon & Brafman [6],  which we build on in several key ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' First, the (off-the-shelf) automata-learning approaches they  employ are sensitive to noisy data and often learn large, sample-sensitive automata even when the  reward structure is simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We make use of recent advances in automata-learning which are robust to  noise and regularize the size of the automaton, which we demonstrate in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Furthermore, [6]  lacked experimental comparisons against state-of-the-art RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In our experiments with non-Markovian  goals, we outperform state-of-the-art RL based on RNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  3  Preliminaries  An MDP is a tuple M = (S, A, P, R, γ), where S is a set of states, A a set of actions, P : S×A×S →  [0, 1] the state-action transition function, R : S → R the reward, and 0 ≤ γ ≤ 1 the discounting  factor [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In such a setup, the reward R is considered Markovian, due to its dependence only  on the most recent state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We will consider the following extension of the MDP: an NMRDP [20]  (non-Markovian Reward Decision Process) N = (S, A, P, R, γ) is as before, but where the reward  R : H → R, where H = (S × A)∗ is the set of finite histories with states S and actions A: in  other words, the agent can be rewarded for behavior which is arbitrarily far removed from its current  experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Further, we define a proposition as a function P : H → {True, False}, in an NMRDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Intuitively, propositions correspond to facts about the state-action history in a given episode, such as  "the agent has at some point reached the top right corner" or "within the 3 most recent timesteps, the  agent took action x".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' While the number of possible propositions grows double-exponentially in the  length of the episode, domain knowledge is often used to specify a relevant set of such propositions,  under which the reward is Markovian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The RL domains we consider have non-Markovian goals, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  there exists G ⊂ H where R(g) = 1 for g ∈ G, and R(h) = 0 for h ∈ H − G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Intuitively, we want to  create a policy which makes the agent attain a goal history as soon as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  4  Algorithm  We use the algorithm described in Algorithm 1 named AutRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Following each period of Markovian  learning, the sampled traces are used to train (offline) a deterministic finite automaton (DFA) M to  predict whether a given sequence achieves reward 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We leverage the DFA-learning approach  from [21] due to its efficiency, its propensity to learn small DFAs with few transitions, and its  robustness to noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Tabular Q-learning is used for markov_learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Intuitively, a DFA with state  2  Algorithm 1: AutRL  1 dfa ← empty_automata;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  2 π ← uniform_random_policy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  3 traces ← ∅ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  4 while true do  5  sample_traces ← sample(π, N) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  6  append traces with sample_traces;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  7  if sample_traces inconsistent with dfa then  8  dfa ← aut_learn(traces);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  9  end  10  π ← markov_learn(sample_traces × dfa);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  11 end  space Q that accurately discriminates reward 1 traces from reward 0 traces (which we define as  consistent) must model all parts of the state-action history relevant to the goal, and therefore the  augmented state space S × Q must make the problem Markovian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We remark that the resultant DFAs  are functions H → Q and are learned end-to-end without domain knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Examples of this can  be seen in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We also provide a convergence guarantee for this algorithm in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  We note that our implementation using Q-learning converges to an optimal policy as the number  of environment samples approaches infinity (assuming G is regular, as above) due to the optimal  convergence guarantees of Q-learning on MDPs [19]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Note that while we search for consistent  DFAs, this condition is not necessary to make the learning problem Markovian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' For this reason, we  relax the inconsistency condition analyzed above, replacing the DFA only under weak performance  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' low average reward) at the end of a given epoch of markov_learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  5  Experimental Results  The purpose of our experiments was to evaluate our AutRL algorithm, which leverages a learned  symbolic representation, relative to a state-of-the-art RNN-based deep RL algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The two metrics  were the quality of the policies in terms of maximizing reward, and their sample efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We tested  on four non-Markovian domains, similar to those used in the experiments of [6] as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Multi-Armed Bandit: A single-state environment with two actions (left, right) and episodes  of length 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  A reward of 1 is obtained only if the 6 actions performed are precisely  left, right, right, left, right, left in that order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Hallway: A 1 × 10 grid, aligned left-to-right, with actions left, right, and with episodes of length 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  The agent spawns at a random location on the left half of the grid and must first reach the right-most  square, and then reach the left-most square to obtain a reward of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Before reaching the right-most  square, the optimal action in every state is right, but after reaching the right-most square, the optimal  action becomes left in every state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Gridworld: A 5 × 5 gridworld (with x, y-coordinates from 0 to 4) with an episode length of 20 and  actions up, down, left, right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The agent must first reach (4, 0) and then the opposite corner (0, 4)  to collect a reward of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We also tested a noisy version of this environment where the reward was  randomly withheld in 10% of successful traces, and actions had a random outcome 10% of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  We compared AutRL against Recurrent-PPO ([22]) (with an LSTM policy) using the OpenAI  Baselines implementation [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' As shown in all of the below environments, AutRL converges to high  reward policies in fewer environment samples than Recurrent-PPO does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Notice that AutRL, despite  being automata-based, outperforms Recurrent-PPO even on the Stochastic Gridworld, showing that  AutRL is robust to noisy environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Figure 2 are two such examples of learned automata on  two different runs of the Hallway environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  3  1000000  2000000  3000000  4000000  Environment Samples  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  Average Reward  Multi-Armed Bandit  1000000  2000000  3000000  4000000  Environment Samples  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  Average Reward  Hallway  1000000  2000000  3000000  4000000  Environment Samples  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  Average Reward  Gridworld  1000000  2000000  3000000  4000000  Environment Samples  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='8  Average Reward  Stochastic Gridworld  Legend:  PPO + LSTM  AutRL + Q-Learning (ours)  Figure 1: The results from the conducted experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The error bars are 95% confidence intervals over 30  runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' AutRL learns a superior policy to the LSTM-based PPO in a way that is, at most, over order of magnitude  more sample-efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Learning is far more stable across runs with AutRL: the error bars for AutRL are far  tighter than those for PPO, indicating very little variation in the learning trajectory across runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  q0  q2  q1  o/w  o/w  always  Right side  Left side  q0  q2  q1  o/w  o/w  always  Right side  4th square from left  Figure 2: Two distinct DFAs learned from the Hallway environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Both are enough to make the domain  Markovian: however, the one on the right is not a perfect classifier of G for this domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' This shows that the  condition in the statement of AutRL above is strictly stronger than necessary: there are automata which do  not perfectly decide G, but which discern enough relevant information to learn optimal, temporally extended  behavior in non-Markovian settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  6  Concluding Remarks  In this work, we show how to learn a KR that provides a useful symbolic abstraction in support of  realizing temporally extended behavior in standard RL agents which rely on a Markov assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We  provide an end-to-end RL algorithm which, in deterministic and stochastic domains, is demonstrably  more sample-efficient than the state of the art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We further provide theoretical guarantees of optimal  convergence for our approach (under conditions outlined in the theorem of Appendix A), along with  insight into the structure of DFAs which are learned by this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  This work reveals several promising directions for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' While we considered environments  where the reward function is non-Markovian, learning in the more general setting of POMDPs is  an important problem related to this work, to which the DFA methods leveraged here do not apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Further, AutRL leverages DFAs, which can only represent regular languages, thus learning efficiently  when G is not a regular language in S ×A, as well as learning KR in high-dimensional and continuous  state spaces, remain major open challenges to this methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  4  Acknowledgments and Disclosure of Funding  We gratefully acknowledge funding from the Natural Sciences and Engineering Research Council of  Canada (NSERC), the Canada CIFAR AI Chairs Program, and Microsoft Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The third author  also acknowledges funding from ANID (Becas Chile).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Resources used in preparing this research  were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR,  and companies sponsoring the Vector Institute for Artificial Intelligence (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='vectorinstitute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  ai/partners).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Finally, we thank the Schwartz Reisman Institute for Technology and Society for  providing a rich multi-disciplinary research environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  References  [1] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur  Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' A general  reinforcement learning algorithm that masters chess, shogi, and go through self-play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Science,  362(6419):1140–1144, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [2] Jan Peters, Sethu Vijayakumar, and Stefan Schaal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Reinforcement learning for humanoid  robotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the Third IEEE-RAS International Conference On Humanoid  Robots, pages 1–20, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [3] Robert H Crites and Andrew G Barto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Improving elevator performance using reinforcement  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the 9th Conference on Advances in Neural Information Processing  Systems (NIPS), pages 1017–1023, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [4] Rodrigo Toro Icarte, Ethan Waldie, Toryn Klassen, Rick Valenzano, Margarita Castro, and  Sheila McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Learning reward machines for partially observable reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In  Proceedings of the 32nd Conference on Advances in Neural Information Processing Systems  (NeurIPS), pages 15523–15534, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [5] Alberto Camacho, Rodrigo Toro Icarte, Toryn Q Klassen, Richard Anthony Valenzano, and  Sheila A McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' LTL and beyond: Formal languages for reward function specification in  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the 28th International Joint Conference on Artificial  Intelligence (IJCAI), volume 19, pages 6065–6073, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [6] Maor Gaon and Ronen Brafman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Reinforcement learning with non-Markovian rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In  Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), volume 34, pages  3980–3987, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [7] Rodrigo Toro Icarte, Toryn Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Klassen, Richard Valenzano, and Sheila A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Using  reward machines for high-level task specification and decomposition in reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  In Proceedings of the 35th International Conference on Machine Learning (ICML), pages  2112–2121, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [8] Bruno Lacerda, David Parker, and Nick Hawes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Optimal and dynamic planning for Markov  decision processes with co-safe ltl specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  In Proceedings of the 2014 IEEE/RSJ  International Conference on Intelligent Robots and Systems (IROS), volume 13, pages 1511—-  1516, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [9] Michael L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Littman, Ufuk Topcu, Jie Fu, Charles Isbell, Min Wen, and James MacGlashan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Environment-independent task specifications via GLTL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' arXiv preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='04341,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [10] Alberto Camacho, Oscar Chen, Scott Sanner, and Sheila McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Decision-making with  non-Markovian rewards: From LTL to automata-based reward shaping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the  Tenth International Symposium on Combinatorial Search (SoCS 2017), pages 279—-283, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [11] Xiao Li, Yao Ma, and Calin Belta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' A policy search method for temporal logic specified  reinforcement learning tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In 2018 Annual American Control Conference (ACC), pages  240–245, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [12] Rodrigo Toro Icarte, Toryn Q Klassen, Richard Valenzano, and Sheila A McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Teaching  multiple tasks to an RL agent using LTL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the 17th International Conference  on Autonomous Agents and Multiagent Systems (AAMAS), pages 452–461, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  5  [13] Ronen Brafman, Giuseppe De Giacomo, and Fabio Patrizi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' LTLf/LDLf non-Markovian rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI), pages 1771–1778,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [14] Mohammadhosein Hasanbeig, Yiannis Kantaros, Alessandro Abate, Daniel Kroening, George J  Pappas, and Insup Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Reinforcement learning for temporal logic control synthesis with  probabilistic satisfaction guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In 2019 IEEE 58th Conference on Decision and Control  (CDC), pages 5338–5343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [15] Ronen I Brafman and Giuseppe De Giacomo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Regular decision processes: A model for non-  Markovian domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings of the 28th International Joint Conference on Artificial  Intelligence (IJCAI), pages 5516–5522, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [16] Mohammadhosein Hasanbeig, Alessandro Abate, and Daniel Kroening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Logically-constrained  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' arXiv preprint arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='08099v8, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [17] Anurag Koul, Sam Greydanus, and Alan Fern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Learning finite state representations of recurrent  policy networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' International Conference on Learning Representations, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [18] Zhe Xu, Ivan Gavran, Yousef Ahmad, Rupak Majumdar, Daniel Neider, Ufuk Topcu, and Bo Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Joint inference of reward machines and policies for reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings  of the International Conference on Automated Planning and Scheduling, volume 30, pages  590–598, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [19] Richard S Sutton and Andrew G Barto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Reinforcement learning: An introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' MIT press,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [20] Faheim Bacchus, Craig Boutilier, and Adam Grove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Rewarding behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' In Proceedings  of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), volume 13, pages  1160–1161, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [21] Maayan Shvo, Andrew C Li, Rodrigo Toro Icarte, and Sheila A McIlraith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Interpretable  sequence classification via discrete optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='02819, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [22] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Proximal  policy optimization algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='06347, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  [23] Prafulla Dhariwal, Christopher Hesse, Oleg Klimov, Alex Nichol, Matthias Plappert, Alec  Radford, John Schulman, Szymon Sidor, Yuhuai Wu, and Peter Zhokhov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Openai baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='com/openai/baselines, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  Appendix A: Convergence Guarantee + Proof  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Let N be an NMRDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Under the following (realistic) conditions, AutRL converges to  an optimal policy in the sample limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' sample_traces visits every reachable history within N i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' (infinitely often, almost  surely) (exploration)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' For any regular language L, when sampling traces using sample_traces, that aut_learn  eventually returns an automaton perfectly deciding L w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' (consistency of aut_learn)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' markov_learn converges to the optimal policy in the sample limit for an MDP (consistency  of markov_learn)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' {h : R(h) = 1} = G ⊂ H forms a regular language with alphabet Σ = S × A (regularity)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Fix an NMRDP N = (S, A, P, R, γ), and assume all conditions are met in the theorem  statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Then, since G is a regular language, we have that the variable dfa is, with probability  1, eventually set to an automaton, with state space Q, which perfectly decides G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' At such a point,  then we have that the states of the automaton perfectly predict the reward R: thus, the problem  M = (S × Q, A, P, R, γ), simply defined as N but with a state space augmented with the automaton  states of dfa, is actually an MDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Further, dfa is never thereafter reset, since no inconsistent trace can  possibly be sampled from the environment subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Thus, M is simply an MDP being trained  with Markovian learning algorithm markov_learn, and thus the appropriate convergence conditions  apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  6  Appendix B: Baseline Hyperparameter Tuning  For the tabular Q-learning for our approach (AutRL), we used a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='1 on the determin-  istic environment, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='001 on the stochastic environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Further, an exploration parameter of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='01  was used on the deterministic environments, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='05 with a decaying exponential schedule (with  factor 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='99) was used for the stochastic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' The automaton learning method was set at a  maximum state threshold of 5 for all environments but the multi-armed bandit (which had 14), a loop  penalty of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='01 in all environments, and a transition penalty of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='01 for the Multi-Armed Bandit, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='3  for both gridworlds, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='6 for the hallway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' Further, the timeout was set to 250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  For the Recurrent-PPO baseline, we used the OpenAI Baselines [23] implementation with an LSTM  policy network, an entropy coefficient of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='001, a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='0003, a discounting factor of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='99, a batch size of 16384 (with 8 minibatches per update), and all other hyperparameters set to  default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content=' We followed standard practice in tuning these hyperparameters and found that these settings  consistently performed best across our domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
+page_content='  7' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtE1T4oBgHgl3EQfJgNL/content/2301.02952v1.pdf'}
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+A Polymorphic Electro-Optic Logic Gate for
+High-Speed Reconfigurable Computing Circuits
+Venkata Sai Praneeth Karempudi
+Department of ECE
+University of Kentucky
+Lexington, Kentucky, USA
+kvspraneeth@uky.edu
+Sairam Sri Vatsavai
+Department of ECE
+University of Kentucky
+Lexington, Kentucky, USA
+Sairam Srivatsavai@uky.edu
+Ishan Thakkar
+Department of ECE
+University of Kentucky
+Lexington, Kentucky, USA
+igthakkar@uky.edu
+Jeffrey Todd Hastings
+Department of ECE
+University of Kentucky
+Lexington, Kentucky, USA
+todd.hastings@uky.edu
+Abstract—In the wake of dwindling Moore’s law, integrated
+electro-optic (E-O) computing circuits have shown revolutionary
+potential to provide progressively faster and more efficient
+hardware for computing. The E-O circuits for computing from
+the literature can operate with minimal latency at high bit-
+rates. However, they face shortcomings due to their operand
+handling complexity, non-amortizable high area and static power
+overheads, and general unsuitability for large-scale integration
+on reticle-limited chips. To alleviate these shortcomings, in this
+paper, we present a microring resonator (MRR) based polymor-
+phic E-O logic gate (MRR-PEOLG) that can be dynamically
+programmed to implement different logic functions at different
+times. Our MRR-PEOLG can provide compactness and polymor-
+phism to E-O circuits, to consequently improve their operand
+handling and amortization of area and static power overheads.
+We model our MRR-PEOLG using photonics foundry-validated
+tools to perform frequency and time-domain analysis of its
+polymorphic logic functions. Our evaluation shows that the use
+of our MRR-PEOLG in two E-O circuits from prior works can
+reduce their area-energy-delay product by up to 82.6×. A tutorial
+on the modeling and simulation of our MRR-PEOLG, along with
+related codes and files, is available on https://github.com/uky-
+UCAT/MRR-PEOLG.
+Index Terms—Polymorphic, Microring Resonator, Tempera-
+ture, Bit-rate.
+I. INTRODUCTION
+Moore’s law has been steering the advancement of comput-
+ing hardware since its inception. But unfortunately, in recent
+years, it has faced fatal challenges as the nanofabrication
+technology is experiencing physical limitations due to the
+exceedingly small size of transistors [1]. This has forced
+researchers in industry and academia to develop new more-
+than-Moore technologies that can continue to provide per-
+sistently faster and more efficient computing hardware [1].
+Fortunately, silicon photonics (SiP) enabled electro-optic (E-
+O) circuit integration has been identified as one such promising
+technology [2]. The SiP-based E-O circuits are generally
+CMOS compatible and provide several advantages over their
+purely electrical counterparts. These advantages include sub-
+picosecond speeds, low dynamic power consumption and
+distance-independent bit-rate [2]. Due to these advantages
+compared to the CMOS-based electrical circuits, the early
+This research is supported by a grant from NSF (CNS-2139167)
+prototypes of SiP-based E-O circuits for computing (e.g., [2]–
+[8]) have been shown to provide up to two orders of magnitude
+improvements in performance and energy efficiency [9] [2].
+The SiP-based E-O circuits for computing, which have been
+demonstrated in prior works (e.g., [2]–[8]) are typically used
+to implement the following four types of logical and arithmetic
+functions: (I) Basic logic-gate functions. For instance, a
+microring resonator (MRR) integrated phase change memory
+(PCM) device based XNOR gate is employed in [3] to
+enable acceleration of binary neural networks. Similarly, in
+[4] and [5], an add-drop MRR based AND gate is employed
+to enable partial multiplications of two binary operands, to
+aid the acceleration of deep neural networks. (II) Arbitrary
+combinational logic functions. For example, the directed
+logic based MRR-enabled reconfigurable E-O circuits are
+demonstrated in [6] and [7]. These can work as the direct
+optical replacement of field programmable gate arrays (FP-
+GAs). (III) Two-operand arithmetic functions. High-speed
+E-O circuits for partial sum accumulation and two-operand
+addition have been demonstrated (e.g., [8], [2]) with various
+designs supporting custom precision [8] and full-precision
+polymorphic operation [2]. (IV) Multi-operand linear arith-
+metic functions. Several analog and digital E-O circuits based
+on MRRs and/or Mach-Zehnder Interferometers (MZIs) have
+been demonstrated to implement Multiply-Accumulate (MAC)
+and Vector Dot Product (VDP) operations (e.g., [3], [4],
+[9], [10]) for deep learning workloads. These logical and
+arithmetic functions implemented using E-O circuits typically
+fulfill the requirements of ultra-fast, highly-parallel general
+purpose computing or deep learning acceleration.
+However, we observe that these SiP-based E-O circuits from
+prior works face three major shortcomings. First, the E-O
+circuits for simple logic-gate functions intake the two input
+operands differently; one operand is typically applied optically
+and the other operand is applied electrically. For instance, in
+the E-O XNOR gate from [3] and the E-O AND gate from [4],
+one of the two operands has to be modulated onto the incoming
+optical wavelengths, for which an additional optical modulator
+device per gate function is required, assuming that the utilized
+laser sources provide unmodulated optical power. Having to
+provide one of the operands optically through an additional
+modulator device increases the hardware area overhead and
+arXiv:2301.13626v1  [cs.ET]  30 Jan 2023
+
+the operand handling complexity in the E-O circuits. Instead,
+there is a need to design a simpler hardware, which can be
+achieved by promoting all electrical provisioning of both the
+operands. Second, the E-O circuits for arithmetic functions
+occupy very large areas compared to CMOS implementations.
+For instance, the E-O MAC circuit used in [5] occupies up
+to 100× more area compared to the all-electric MAC circuit
+[5]. Moreover, such E-O circuits for arithmetic functions can
+hardly achieve more than 60% hardware utilization [4]. This
+is because these circuits typically belong to larger processing
+units where they occupy only part of the entire end-to-end
+datapath [3], [9], [10]. Such low hardware utilization often
+leads to high idle time and consequently very high, non-
+amortizable area and static power overheads. This in turn
+motivates the need for more flexible E-O circuits that can
+adapt to different arithmetic/logic functions at different times,
+to increase the amortization of their high area and static power
+overheads by reducing their total idle time. Third, the high area
+overhead of E-O circuits makes them less suitable for highly-
+parallel Single-Instruction-Multiple-Data (SIMD), Multiple-
+Instruction-Multiple-Data (MIMD), and Systolic Array (SA)
+based processing architectures. This is because SIMD, MIMD
+and SA architectures typically employ thousands of streaming
+processing units, with each processing unit requiring multiple
+copies of basic logical and arithmetic functions. Implementing
+these functions using bulky E-O circuits with 100× more area
+can drastically reduce the number of processing units that can
+be integrated on a single chip whose area is typically limited
+by the reticle size (<=900 mm2 [11]). Since SIMD, MIMD,
+and SA based processing units have become extremely popular
+for executing modern Euclidean as well as non-Euclidean
+data workloads (i.e., workloads with grid and graph structured
+data), it becomes crucial to alleviate the unsuitability of E-O
+circuits for SIMD, MIMD and SA based designs by forging
+new E-O circuits with relatively low area overheads.
+To address these shortcomings, in this paper, we present
+a single MRR based Polymorphic E-O Logic Gate (MRR-
+PEOLG). Our MRR-PEOLG can accept both input operands
+electrically, and its drop-port (through-port) optical response
+can be thermo-optically programmed to make it dynamically
+follow the truth table of different logic functions, such as
+AND, OR and XOR (NAND, NOR, and XNOR), at different
+times. Consequently, the E-O circuits built using our MRR-
+PEOLG can address the above-described shortcomings by pro-
+viding (1) the ability of all-electrical application of the input
+operands, (2) compactness through a single-MRR structure of
+the E-O gate, and (3) high flexibility through the introduced
+polymorphism, and consequently, low idle time and improved
+suitability for use with SIMD/MIMD/SA based architectures.
+The key contributions of this paper are summarized below:
+• We
+model
+our
+MRR-PEOLG
+using
+the
+photonics
+foundry-validated tools from Ansys/Lumerical [12], and
+then, perform the frequency, time-domain transient, and
+thermal analysis for different logic-gate functions. A
+tutorial on the modeling and simulation of our MRR-
+PEOLG, along with related codes and files, is available
+on https://github.com/uky-UCAT/MRR-PEOLG;
+• Based on our analysis, we evaluate the performance of
+our MRR-PEOLG, from which we determine the max-
+imum achievable bit-rate and thermal tuning power for
+each logic-gate function supported by our MRR-PEOLG;
+• We show that the use of our MRR-PEOLG in two E-
+O circuits from prior works can provide improvement in
+area-energy-delay product of up to 82.6×;
+• We also discuss how MRR-PEOLG can be used to realize
+E-O reconfigurable SIMD/MIMD architectures.
+Fig. 1. Structure and cross-section of our MRR based polymorphic E-O logic
+gate (MRR-PEOLG).
+II. MRR-BASED POLYMORPHIC ELECTRO-OPTIC LOGIC
+GATE (MRR-PEOLG)
+A. Structure
+Our MRR-PEOLG is basically an add-drop MRR [13] with
+four quarter-sized phase-shifting sections embedded in it, as
+shown in Fig. 1(a). Two quarter-sized sections of the MRR
+are two PN junctions which are operated in the forward bias
+condition, whereas the remaining two quarter-sized sections
+integrate micro-heaters. The cross-section of a PN-junction
+based section of our MRR-PEOLG is shown in the right hand
+side of Fig. 1(a), which consists of a ridge waveguide with
+an embedded lateral PN junction, fabricated on the top of a
+buried oxide layer. The dimensions of the P-type and N-type
+regions, and their corresponding carrier concentrations are also
+provided in Fig. 1(a). The PN junction based sections of our
+MRR-PEOLG work as the input terminals where the input
+logic signals/operand bits are applied. On the other hand, the
+microheaters integrated sections of our MRR-PEOLG work
+as the programming terminals that are used to program the
+MRR-PEOLG to perform specific logic-gate functions.
+Applying a voltage to the microheaters based programming
+terminals can increase the temperature of the MRR, which in
+turn can shift (red shift) the resonance of the MRR towards the
+longer wavelength. This is because of the thermo-optic effect
+in silicon ( [14]). To program MRR-PEOLG to implement
+a specific logic-gate function, the operand-independent MRR
+resonance (i.e., the programmed MRR resonance) is adjusted
+to a specific spectral position with respect to the input optical
+
+n
+p
+220nm
+n+ 100nml
+1μm1.75μm1.75μm1μm
+BOX (SiO2)wavelength, by applying a voltage to the programming termi-
+nals. Then, the electrical input logic signals or input operand
+bits (x and w) are applied to the PN junctions based input ter-
+minals of the MRR. Upon doing so, the resonance of the MRR
+shifts (blue shifts) towards the shorter wavelength depending
+on the combination of the applied input operand bits. This is
+because of the free-carrier plasma dispersion effect in silicon
+( [15]). Applying the input operand bits to the input terminals
+makes the through-port and drop-port optical responses of our
+MRR-PEOLG follow the truth-table of the logic-gate functions
+for which the MRR-PEOLG is programmed. In this manner,
+our MRR-PEOLG can perform different logic-gate functions
+at different times. At any given time, the through-port optical
+response of the MRR-PEOLG follows logical complement
+of the drop-port optical response. Therefore, AND, OR and
+XOR functions can be realized (one function at a time) at
+the drop port of the MRR-PEOLG. Concurrently, the through
+port of the MRR-PEOLG can provide complementary logic-
+gate functions such as NAND, NOR and XNOR as discussed
+below.
+B. Modeling
+We model our MRR-PEOLG using the photonics foundry-
+validated simulation tools from Ansys/Lumerical [12]. We
+break down our MRR-PEOLG design into a set of primitive
+elements. Fig. 2(a) shows a schematic of our MRR-PEOLG,
+whose breakdown into the primitive elements is shown in
+Fig. 2(b). We use different solvers in the Ansys/Lumerical
+tools [12] to model each primitive element. From these
+models, we extract various parameters for each primitive
+element. Later, we combine all of the extracted parameters
+in Ansys/Lumerical’s INTERCONNECT tool [12] (tool for
+the modeling and simulations of photonic integrated circuits)
+to create our MRR-PEOLG in Fig. 2(b). Finally, we perform
+the frequency-domain and time-domain transient simulations
+of our MRR-PEOLG. Different steps for the modeling and
+simulation of our MRR-PEOLG using the ANSYS/Lumerical
+tools/solvers are summarized below.
+Step-1 - modeling MRR-waveguide coupling sections:
+First, create coupling sections in the finite difference time
+domain (FDTD) solver and extract the power coupling co-
+efficients as a function of wavelength for the fundamental TE
+mode. Import these coefficients in the coupling elements C 1
+and C 2 (Fig. 2(b)).
+Step-2 - modeling straight waveguide sections: First,
+characterize the passive, straight, channel waveguides of the
+MRR-PEOLG using the finite difference eigenmode (FDE)
+solver. Extract the effective index, group index, and dispersion
+for the waveguides as functions of wavelength. Load this
+information into the primitive elements WGD 1, WGD 2,
+WGD 7, and WGD 8 (Fig. 2(b)).
+Step-3 - modeling PN-junction based input terminals:
+First, create a quarter ring with an embedded lateral PN-
+junction in the CHARGE tool. Perform the simulation to
+extract the spatial distribution of the charge carriers as a
+function of the bias voltage. Then, export this data into the
+FDE solver and calculate the perturbations in the refractive
+index of the waveguides connected to the input terminals.
+Then, calculate the change in the effective index and resonance
+of the entire MRR-PEOLG as a function of the bias voltage.
+Import this information into the primitive elements WGD 6
+(connected to OM 1) and WGD 5 (connected to OM 2) (Fig.
+2(b)).
+Step-4 - modeling microheaters based programming ter-
+minals: Extract the temperature profile of the MRR-PEOLG
+as a function of the applied microheater voltage. Then, import
+this data into the FDE solver to calculate the change in the
+effective index of the MRR-PEOLG as a function of its tem-
+perature. Import this information into the primitive elements
+WGD 3 (connected to OM 4) and WGD 4 (connected to
+OM 5) (Fig. 2(b)).
+Step-5 - preparing for simulations: Connect the primitive-
+elements based model of the MRR-PEOLG (Fig. 2(b)) with
+other testing and characterization apparatus in the INTER-
+CONNECT tool, as shown in Fig. 2(c) and Fig. 2(d).
+Fig. 2. (a) Step-1 to Step-4, and (b) Step-5 of the procedure used for modeling
+our MRR-PEOLG. The schematic simulation setup in ANSYS/Lumerical’s
+INTERCONNECT tool for (c) frequency-domain and (d) time-domain tran-
+sient analysis of our MRR-PEOLG.
+C. Operation
+To explain the operation of our MRR-PEOLG, we per-
+formed frequency-domain simulations using the INTERCON-
+NECT tool [12]. Our simulation setup for this frequency-
+domain analysis is shown in Fig. 2(c). Accordingly, we
+connected an optical network analyzer (ONA) to our MRR-
+PEOLG to extract the transmission spectra at its drop and
+through ports. We extracted the transmission spectra for dif-
+ferent values of the detuning of the operand-independent MRR
+resonance position κ with respect to the input wavelength λin.
+As mentioned earlier, these detuning values correspond to dif-
+ferent logic-gate functions that the MRR-PEOLG can perform.
+In addition, we also extracted transmission spectra for different
+combinations of the input operand bits. All of these transmis-
+sion spectra for different logic-gate and complementary logic-
+gate functions are shown in Figs. 3(a) to 3(f). Transmission
+
+WGD ‘2
+WGD_1
+C 1
+1O
+0M
+0M_2
+WGD 6
+WGD 5
+WGD_3
+WGD_4
+0M 5
+OM
+DC
+WGD_ 8
+WGDspectra corresponding to logic-gate functions AND, OR and
+XOR are shown in Figs. 3(a), 3(b), and 3(c) respectively.
+These transmission spectra are drop-port transmission spectra
+(Lorentzian lineshape passbands). Similarly, the transmission
+spectra corresponding to complementary logic-gate functions
+NAND, NOR and XNOR are shown in Figs. 3(d), 3(e), and
+3(f) respectively. These transmission spectra are through-port
+transmission spectra (inverse Lorentzian lineshape passbands).
+As we can see in Fig. 3, the drop port and through port
+transmission exhibits two clearly distinguishable levels. The
+full transmission range at the drop port and through port of
+our MRR-PEOLG is divided into two areas, in which the
+lower part of the full transmission range is indicated with
+shaded gray whereas the upper part is indicated with shaded
+blue. If the drop port (DT(λin)) and through port (TT(λin))
+transmission at λin falls in the lower part of the full transmis-
+sion range (i.e., in the gray-shaded area), then it is referred
+to as logic ‘0’ transmission. On the other hand, if the drop
+port and through port transmission at λin falls in the upper
+part of the full transmission range (i.e., in the blue-shaded
+area), then it is referred to as logic ‘1’ transmission. However,
+the vertical spans of the two distinguishable transmission
+levels differ between the drop port and through port. This is
+because, similar to the transmission spectra (Fig. 3), the spans
+of transmission levels at the drop port also complement the
+spans of transmission levels at the through port. The difference
+between the minimum supported logic ‘1’ transmission and the
+maximum supported logic ‘0’ transmission is the sensitivity of
+optical modulation amplitude (SOMA). SOMA is a property
+of the photodetector based receiver circuit, and it affects the
+performance of the MRR-PEOLG (as will be discussed in
+Sections III and IV).
+To clearly understand the operation of our MRR-PEOLG,
+let us consider the example of AND function, as shown in
+Fig. 3(a). To program our MRR-PEOLG to implement AND
+function, a 0.9 V voltage (3.52 mW power) is applied to
+the programming terminals of the MRR-PEOLG. This shifts
+the resonance from the initial position, η, to the programmed
+position, κ, where κ has the programmed detuning of 0.7 nm
+with respect to λin. Then, the input operand bits x and w
+are applied to the input terminals of the device. Doing so
+induces a blueshift in the MRR resonance, the magnitude of
+which depends on the specific combination of the applied input
+operand bits (x and w, as shown in Fig. 3(a)). If the applied
+bit-combination (x,w) is (0,0), the resonance position of the
+MRR stays at κ (magenta colored passband in Fig. 3(a)) and
+the drop port transmission at λin provides logic ’0’ level (the
+bottom red dot on the Y-axis). If the applied bit-combination
+(x,w) is (0,1) or (1,0), the position of the MRR resonance
+changes (red/orange colored passband in Fig. 3(a)), but the
+blueshift is the same for both (0,1) and (1,0) bit combinations,
+and the drop port transmission at λin still remains at logic ’0’
+level (the top red dot on the Y-axis). On the other hand, if the
+applied bit-combination (x,w) is (1,1), the MRR resonance
+undergoes a larger blueshift (blue colored passband in Fig.
+3(a)), and the position of the passband with respect to λin
+TABLE I
+POWER CONSUMED IN THE MICROHEATERS, PROGRAMMED DETUNING,
+AND REQUIRED RESONANCE SHIFTING, USED TO PROGRAM OUR
+MRR-PEOLG FOR IMPLEMENTING DIFFERENT LOGIC FUNCTIONS.
+Logic-Gate
+Functions
+Microheater
+Power (mW)
+Programmed
+Detuning
+(κ-λin) (nm)
+Required
+Shifting
+(η-κ) (nm)
+AND / NAND
+3.52
+0.7
+-1.1
+OR / NOR
+2.93
+0.5
+-0.9
+XOR / XNOR
+2.3
+0.3
+-0.7
+changes. As a result, the drop port transmission at λin changes
+to logic ’1’ level (the green dot on the Y-axis). Hence, the
+drop port transmission at λin for our MRR-PEOLG changes
+with the applied input operand bits, and follows the truth table
+of the AND logic function (see the truth table in Fig. 3(a)).
+As discussed earlier, since the through-port response provides
+a logical complement to the drop-port response, this AND
+function at the drop port of the MRR-PEOLG corresponds to
+NAND function at the through port of the MRR-PEOLG as
+illustrated in Fig. 3(d).
+Similarly, our MRR-PEOLG can be reconfigured to imple-
+ment OR (NOR) and XOR (XNOR) gate functions as well, by
+applying a suitable voltage to the programming terminals of
+our MRR-PEOLG to set the relative position of κ with respect
+to λin as shown in Figs. 3(b) and 3(c) (transmission spectra
+corresponding to NOR and XNOR are shown in figs. 3(e) and
+3(f) respectively). Table I provides the total power consumed
+in the microheaters, the programmed detuning (κ-λin), and
+the required resonance shifting (η-κ), to program our MRR-
+PEOLG for implementing various logic functions. From Table
+I, the power consumed in the microheaters is proportional to
+the required resonance shifting (η-κ).
+III. TRANSIENT ANALYSIS
+A. Method
+As illustrated in Fig. 2(d), to perform transient analysis
+of our MRR-PEOLG in the INTERCONNECT tool, we con-
+nected a pseudo random bit sequence (PRBS) generator and
+a non-return-to-zero (NRZ) pulse generator to each of the
+input terminals of the MRR-PEOLG. Each PRBS generator
+generates a random bit sequence of 10 Gb/s, which is given
+as input to the NRZ pulse generator. Each NRZ pulse generator
+then generates a sequence of electrical NRZ pulses of 1.5
+V amplitude at 10 Gb/s. The blue and red pulses shown in
+Figs. 4(a) and 4(b) respectively are the electrical NRZ pulses
+that we have provided as inputs to the two input terminals
+of our MRR-PEOLG for the transient analysis. We have also
+connected a continuous wave (CW) laser to the input port
+of the MRR-PEOLG, which generates an optical signal of
+wavelength 1545 nm (λin = 1545 nm in Fig. 3) with an optical
+power of 5 dBm. We connected optical oscilloscopes to the
+drop and through ports to record the output pulse patterns
+corresponding to different logic functions for the given input
+electrical pulse signals. The results obtained from this transient
+analysis are discussed next.
+
+Fig. 3. The transmission spectra obtained at the drop port of our MRR-PEOLG for logic-gate functions (a) AND, (b) OR, and (c) XOR, and at the through
+port of our MRR-PEOLG for complementary logic-gate functions (d) NAND, (e) NOR, and (f) XNOR.
+Fig. 4.
+(a),(b) The electrical pulse signals of 10 Gb/s bit-rate provided as
+input to the PN junctions of our MRR-PEOLG. The corresponding output
+pulse patterns obtained at the drop port of our MRR-PEOLG for logic-gate
+functions (c) AND, (e) OR, and (g) XOR , and at the through port of our
+MRR-PEOLG for complementary logic-gate functions (d) NAND, (f) NOR,
+and (h) XNOR. The optical input power is 5 dBm in all cases.
+B. Results and Discussion
+Fig. 4(c), Fig. 4(e), and Fig. 4(g) illustrate the output pulse
+signals obtained at the drop-port of the MRR-PEOLG for
+different logic functions. Similarly, Fig. 4(d), Fig. 4(f), and
+Fig. 4(h) illustrate the output pulse signals simultaneously
+obtained at the through-port of the MRR-PEOLG for different
+complementary logic functions. To obtain these pulse patterns,
+we first reconfigured the MRR-PEOLG to implement various
+logic functions by changing the temperature using the inte-
+grated microheaters. We then followed the method described
+in Section III.A. As evident from Fig. 4, the output pulse
+signals follow the pulse-wise truth-tables of the respective
+logic functions, which confirms the capability of our MRR-
+PEOLG to correctly realize different logic functions.
+From Figs. 4(c) - 4(h), the optical modulation amplitude
+(OMA), which is the difference between the minimum logic
+’1’ power level and the maximum logic ’0’ power level in
+an output pulse pattern, differs for different logic functions.
+To clearly understand this, let us consider AND, XOR, and
+OR functions. For the AND function shown in Fig. 4(c), the
+OMA is ∼-2.4dBm. This is because, as can be observed from
+Fig. 4(c), the drop port transmission at λin corresponding to
+the logic ‘1’ output level (i.e., (x,w) = (1,1)) is ∼0.82 (the
+green dot on the Y-axis), whereas the maximum drop port
+transmission at λin, corresponding to the logic ‘0’ output level
+(i.e., (x,w) = (1,0) or (0,1)), is ∼0.62 (the top red dot on
+the Y-axis). Hence, the OMA, i.e., the difference between the
+logic ‘1’ optical power level (0.82×5dBm = 2.57 mW) and
+the logic ‘0’ optical power level(0.62×5dBm = 1.995 mW) is
+∼-2.4 dBm (∼0.575 mW). Similarly, for OR (NOR) and XOR
+(XNOR) functions shown in Fig. 4, the green and red dots on
+Y-axis occur at different positions compared to AND (NAND)
+function. Therefore, our MRR-PEOLG exhibits different OMA
+for different logic functions.
+Since the OMA for the output pulse pattern basically
+defines how well the logic ’1’s are distinguishable from logic
+’0’s, having different OMA values renders different reliability
+bounds for different logic functions implemented by our MRR-
+PEOLG. In general, to achieve higher reliability without trying
+to quantify its value, it is desirable to increase the OMA of an
+output pulse pattern, which can be done in two ways. First,
+OMA can be increased by increasing the input optical power at
+λin. (We considered an input optical power of 5 dBm for our
+
+uo
+(x, w) = (0,0)
+ (x,w) = (0,0) 
+(x,w) = (1,1)=
+(x,w) = (1,1):
+Logic“1'
+s
+S
+Logic “1'
+Logic1'
+ISOMA
+↑SOMA
+↑SOMA
+Logic 0"
+Logic ‘0"
+Logic ‘0"
+ 0.6
+ 0.6
+WDT(Λin)
+× w DT(Ain)
+×w DT(Ain)
+x
+0
+(x,w)= (1,0)/(0,1)
+ 0.4
+ 0.4
+0
+01
+01
+0
+: (x,w) = (1,1)
+(x,w) = (1,0)/(0,1)
+(x,w) = (1,0)/(0,1)
+0
+10
+0
+1
+10
+00.2
+00.2
+1０
+(x, w) = (0,0)
+11
+111
+1544.515451545.51546
+1546.5
+1544.515451545.515461546.5
+15461546.5
+1543.5
+1544
+1543.5
+1543.5
+1544
+1544.5
+1545
+1545.5
+ 1544
+Wavelenqth(nm)
+Wavelength(nm)
+Wavelength(nm)
+Ain
+K
+NinK
+0
+0
+Logic 1'
+Logic
+m0.8
+= 0.8
+= 0.8
+(x,w)= (1,0)/(0,1)
+(x,w) = (1,0)/(0,1)
+(x,w):= (1,0)/(0,1)
+.20.6
+Logic‘1"
+×w TT(Ain)
+×w TT(Λin)
+×w TT(An)
+００1
+(x,w) = (1,1)
+00.4
+００
+1
+00.4
+ 0.4
+(x,w) = (0,0) 
+(x,w) = (1,1) _=
+0
+1
+P
+01
+(x,w) = (1,1)-
+０１
+(x,w) = (0,0)
+0
+00.2
+101
+00.2
+1０
+(x,w) = (0,0)
++SOMA
+0
+110
+Logic ‘o"
+Logic ‘0"
+Logic '0"
+11
+１１
+1543.5
+1545.5
+1546.5
+1544
+1544.5
+1545
+1546
+1543.5
+1546.5
+1545.5
+1546
+1543.5
+1545.5
+1546
+1546.5
+1544
+1544.5
+1545
+1544.5
+1545
+1544
+Wavelength(nm)
+Wavelength(nm)
+Wavelength(nm)1.5
+1.5
+1
+Amplitude (V)
+1
+1
+1
+0.5
+0.5
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+2
+6
+2
+4
+6
+8
+8
+0
+4
+0
+Time(s)
+Time(s)
+×10-10
+×10-10
+5
+5
+AND
+NAND
+1
+4
+Bm)
+1
+1
+OMA = -2.4 dBm
+0
+--
+0
+0
+Power (
+0
+OMA = -0.48 dBm
+-5
+0
+0
+0
+1
+0
+0
+0
+-10
+2
+2
+0
+4
+6
+0
+4
+6
+8
+8
+Time(s)
+Time(s)
+×10-10
+×10-10
+5
+5
+OR
+NOR
+-5
+OMA = -0.35 dBm
+-10
+0
+0
+0
+0
+0
+OMA = -0.89 dBm
+-15
+2
+2
+4
+6
+0
+8
+0
+2
+4
+6
+8
+Time(s)
+Time(s)
+×10-10
+×10-10
+5
+XOR
+5
+XNOR
+(w)
+Power(dBm)
+1
+1
+OMA = -2.8 dBm
+.1..
+0
+OMA = -3.14 dBm
+B
+4.5
+Power(dl
+1
+-5
+-10
+4
+P-15
+0
+.0
+0
+OT
+0
+0
+3.5
+2
+4
+6
+2
+4
+6
+0
+8
+0
+8
+Time(s)
+Time(s)
+×10-10
+×10-10results discussed in previous paragraph). Second, OMA can
+be increased by decreasing the full width at half maximum
+(FWHM) or 3-dB bandwidth of the MRR-PEOLG. A lower
+FWHM would make the roll-off edges of the MRR passbands
+corresponding to (0,0), (0,1)/(1,0) and (1,1) steeper (Fig. 3),
+which in turn would increase the distance between the green
+dot and top red dot on the Y-axis, thereby increasing the OMA.
+Note that increasing OMA is not always necessary, as a low
+OMA would cause reliability issues only if it is lower than
+the OMA sensitivity (SOMA) of the receiver circuit that is
+employed to make sense of the output pulse pattern. Therefore,
+decreasing SOMA of the receiver circuit can also increase
+the reliability of our MRR-PEOLG. Thus, the FWHM (3-dB
+bandwidth) of the MRR-PEOLG, the SOMA of the receiver
+circuit, and the input power are the three factors that influence
+the impact of OMA on the reliability of our MRR-PEOLG.
+Moreover, these three factors impact the maximum speed
+(bit-rate) at which the input pulse patterns can be driven.
+Increasing the bit-rate will reduce OMA because either the
+free-carrier concentration in the PN junctions or the optical
+energy inside the MRR does not change as fast as the
+applied input electrical pulse signals. For a given FWHM
+(3-dB bandwidth), it is possible to keep increasing the bit-
+rate until the OMA becomes less than the SOMA limit of
+the receiver circuit. Once the OMA for a given input power
+crosses the SOMA limit, the OMA can be increased to support
+a higher bit-rate by increasing the input power. Therefore, the
+maximum achievable bit-rate for our MRR-PEOLG depends
+on SOMA, FWHM, and input optical power. We have evalu-
+ated the maximum achievable bit-rate for our MRR-PEOLG,
+corresponding to various logic functions, which is discussed
+in next section.
+IV. PERFORMANCE ANALYSIS
+For this analysis, we have used the scripting capabilities
+available in the ANSYS/Lumerical tools to run a performance
+evaluation of our MRR-PEOLG. We swept the input optical
+power in the range from -5 dBm to 5 dBm. Similarly, we
+swept SOMA in the range from -5 dBm to -20 dBm. Then,
+for each combination of the input optical power and SOMA,
+we evaluated the maximum achievable bit-rate for each logic-
+gate function supported by our MRR-PEOLG. The results of
+this analysis are shown in Fig. 5 in the form of colormap plots.
+A. Results and Discussion
+The colormap plots in Figs. 5(a) to 5(f) depict the maximum
+achievable bit-rate corresponding to each logic-gate function
+for an FWHM of 1.2 nm and different combinations of input
+optical power and SOMA. From the colormap plots, the AND
+function achieves a maximum bit-rate of 42 Gb/s across all
+SOMA values if the input optical power is >2 dBm, as well as
+across all input power values if the SOMA value is <-13 dBm.
+Similarly, OR and XOR functions achieve a maximum bit-rate
+of 41 Gb/s and 40 Gb/s respectively across all input optical
+power values if SOMA is <-19 dBm. Meanwhile, the NAND
+function achieves a maximum bit-rate of 40 Gb/s across all
+Fig. 5.
+Colormap plots for logic functions (a) AND, (c) OR, (e) XOR
+(obtained at the drop port of our MRR-PEOLG), and complementary logic
+functions (b) NAND, (d) NOR, (f) XNOR (obtained at the through port of
+our MRR-PEOLG) that depict the maximum achievable bit-rate for given
+input optical power and SOMA. These color maps are evaluated for drop-
+port FWHM of 1.2 nm. We also report the maximum achievable bit-rate
+corresponding to (g) AND, OR, and XOR functions, and (h) NAND, NOR,
+and XNOR functions, evaluated for different values of FWHM, 0 dBm input
+optical power, and -5 dBm SOMA.
+SOMA values if the input optical power is >2 dBm, as well as
+across all input power values if the SOMA value is <-11 dBm.
+
+And
+NAND
+40
+40
+0
+20
+10
+-20
+-20
+-5
+.15
+10
+-5
+.15
+10
+SOMA (dBm)
+SOMA (dBm)
+OR
+NOR
+40
+40
+0
+0
+20
+20
+-20
+-20
+-5
+.15
+-10
+-5
+-15
+-10
+SOMA (dBm)
+SOMA (dBm)
+XOR
+XNOR
+40
+40
+0
+0
+20
+20
+5
+-20
+-15
+-20
+-15
+-10
+-5
+-5
+SOMA (dBm)
+SOMA (dBm)
+And
+OOR
+OXOR
+Full Width at Half Maximum (
+(FWHM) (Through Port) (nm)
+2.14
+3.8
+4.1
+4.4
+4.98
+0.2
+1.5
+4.75
+5.2
+50
+Bit Rate (Gb/s)
+40
+30
+20
+10
+0
+2.4
+2.1
+1.8
+1.5
+1.2
+0.25
+0.92
+0.675
+0.45
+Full Width at Half Maximum (FWHM) (Drop Port) (nm)
+NAND
+XNOR
+△XNOR
+Full Width at Half Maximum (FWHM) (Through Port) (nm)
+0.2
+2.14
+1.5
+3.8
+4.1
+4.4
+4.75
+4.98
+5.2
+50
+40
+Bit Rate (Gb/s)
+30
+20
+10
+0
+2.4
+2.1
+1.5
+1.2
+0.92
+0.25
+1-8
+0.675
+0.45
+Full Width at Half Maximum (FWHM) (Drop Port) (nm)Similarly, NOR and XNOR functions achieve a maximum
+bit-rate of 40 Gb/s and 41 Gb/s respectively across all input
+optical power values if SOMA is <-11 dBm. Moreover, we
+also show in Figs. 5(g) and 5(h) that increasing the drop-
+port FWHM (which can be achieved by increasing the cross-
+coupling co-efficient of the MRR-PEOLG) can increase the
+maximum achievable bit-rate for each logic function. These
+results imply that our MRR-PEOLG can be operated at up to
+40 Gb/s for each of its supported logic-gate functions.
+V. COMPARISON AND ENVISIONED USE CASES
+A. Comparison with E-O Circuits from Prior Work
+We evaluated how the use of our MRR-PEOLG impacts
+the area, latency, and energy consumption of two E-O circuits
+from prior works [3] and [5]. We replaced the E-O XNOR
+gates with our MRR-PEOLG in the E-O XNOR-POP circuits
+of the binary neural network accelerator LightBulb from [3].
+Similarly, we replaced the AND gates with our MRR-PEOLG
+in the optical bit-serial multiplier circuits of the digital CNN
+accelerator from [5]. As a result, the performance of these E-
+O circuits substantially improved as shown in Table II. The
+energy values are the energy per bit values and include the
+MRR static power as well as laser power. The area and energy
+benefits in Table II are due to the compactness and better
+operand handling of our MRR-PEOLG and also our MRR-
+PEOLG’s ability to realize different logic functions with only
+a single MRR. The latency benefits are due to the fact that
+our MRR-PEOLG can operate at up to 40 Gb/s, whereas
+the original bit-serial multiplier circuit from [5] can only
+operate at up to 10 Gb/s. The E-O XNOR-POPCOUNT units
+from [3] can operate at a higher bit-rate of 50 Gb/s, but our
+MRR-PEOLG based variants provide better area-energy-delay
+product. These results corroborate the excellent capabilities
+and efficiency benefits of our MRR-PEOLG.
+TABLE II
+PERFORMANCE COMPARISON OF E-O CIRCUITS.
+A=AREA, E=ENERGY, L=LATENCY
+Metrics
+XNOR-POPCOUNT
+Bit-serial Multiplier
+[3]
+MRR-PEOLG
+[5]
+MRR-PEOLG
+A (mm2)
+0.013
+0.011 (1.16×)
+0.023
+0.011 (2.08×)
+E (nJ)
+0.05
+0.032 (1.53×)
+0.327
+0.033 (9.89×)
+L (ns)
+0.02
+0.025 (0.8×)
+0.1
+0.025 (4×)
+A*E*L
+1.3e-5
+0.9e-5 (1.44×)
+75.2e-5
+0.91e-5 (82.6×)
+B. Envisioned Use Cases for SIMD/MIMD Architectures
+We reason that it is possible to use the dense wavelength
+division multiplexing (DWDM) technique with our MRR-
+PEOLG, where cascaded arrays of MRR-PEOLGs can couple
+with DWDM-enabled rectilinear waveguides. In these cas-
+caded arrays, each MRR-PEOLG can be individually pro-
+grammed to perform a specific logic-gate function. Moreover,
+from [16], it can be inferred that OR, XOR and AND
+logic-gate functions supported by our MRR-PEOLGs can be
+useful for realizing stochastic (unary) arithmetic functions
+such as addition, subtraction and multiplication respectively.
+This enables the application of the cascaded arrays of MRR-
+PEOLGs for realizing reconfigurable SIMD/MIMD E-O pro-
+cessing units (see Fig. 6). Such E-O SIMD/MIMD units can
+outperform the traditional GPUs [17] and Tensor Processing
+Units (TPUs) [18] due to their two-fold benefits. First, they
+can be operated at higher speeds (up to 40Gb/s) compared
+to GPUs/TPUs. Second, they can provide significantly better
+area×latency product, which we plan to evaluate in the future.
+Fig. 6. Schematics of how the cascaded arrays of our MRR-PEOLG can be
+reconfigured to implement (a) a SIMD or (b) an MIMD E-O processing unit.
+The reconfiguration between SIMD/MIMD can be achieved by programming
+the individual MRR-PEOLGs for specific logic/arithmetic functions.
+VI. CONCLUSION
+In this paper, we demonstrated a microring resonator based
+polymorphic electro-optic logic gate (MRR-PEOLG) that can
+be dynamically reconfigured to implement different logic
+functions at different times. We modeled our MRR-PEOLG
+using the photonics foundry-validated simulation tools from
+ANSYS/Lumerical. Using these tools, we also performed
+frequency-domain, time-domain transient, and performance
+analysis of our MRR-PEOLG. From our analysis, we validated
+that our MRR-PEOLG design can implement various logic
+functions while operating at speeds of up to 40 Gb/s. Our
+evaluation shows that the use of our MRR-PEOLG in two E-
+O circuits from prior works can reduce their area-energy-delay
+product by up to 82.6×. We also show how our MRR-PEOLG
+can realize reconfigurable E-O SIMD/MIMD processing units.
+ACKNOWLEDGMENT
+We thank the anonymous reviewers for their valuable feed-
+back. This research is supported by a grant from NSF (CNS-
+2139167).
+REFERENCES
+[1] A.Ganguly et al., “Interconnects for dna, quantum, in-memory, and
+optical computing: Insights from a panel discussion,” IEEE micro,
+vol. 42, no. 3, pp. 40–49, 2022.
+[2] Z. Ying et al., “Electronic-photonic arithmetic logic unit for high-speed
+computing,” Nature communications, 2020.
+[3] F. Zoakee et al., “Lightbulb: A photonic-nonvolatile-memory-based
+accelerator for binarized convolutional neural networks,” in 2020 DATE.
+IEEE, 2020, pp. 1438–1443.
+[4] K. Shiflett et al., “Pixel: Photonic neural network accelerator,” in 2020
+IEEE HPCA.
+IEEE, 2020, pp. 474–487.
+[5] K. Shiflettet al., “Bitwise neural network acceleration using silicon
+photonics,” in GLSVLSI, 2021, pp. 9–14.
+[6] C. Qiu et al., “Demonstration of reconfigurable electro-optical logic with
+silicon photonic integrated circuits,” Optics letters, vol. 37, no. 19, pp.
+3942–3944, 2012.
+
+米
+米[7] Z. Ying et al., “Integrated multi-operand electro-optic logic gates for
+optical computing,” APL, 2019.
+[8] K. Venkata Sai Praneeth et al., “Design exploration and scalability
+analysis of a cmos-integrated, polymorphic, nanophotonic arithmetic-
+logic unit,” in Proceedings of the 19th ACM CenSyS, 2021.
+[9] V. Bangari et al., “Digital electronics and analog photonics for convo-
+lutional neural networks (deap-cnns),” IEEE JSTQE, vol. 26, no. 1, pp.
+1–13, 2019.
+[10] W. Liu et al., “Holylight: A nanophotonic accelerator for deep learning
+in data centers,” in 2019 DATE.
+IEEE, pp. 1483–1488.
+[11] S. Naffziger et al., “Pioneering chiplet technology and design for the
+amd epyc™ and ryzen™ processor families: Industrial product,” in 2021
+ACM/IEEE ISCA, pp. 57–70.
+[12] L. Inc. [Online]. Available: http://www-.lumerical.com/products
+[13] W. Boagerts et al., “Silicon microring resonators,” Laser & Photonics
+Reviews, 2012.
+[14] M. Bahadori et al., “Thermal rectification of integrated microheaters for
+microring resonators in silicon photonics platform,” JLT, 2017.
+[15] J. Mulcahy et al., “Modulators in silicon photonics—heterogenous
+integration & and beyond,” in Photonics, 2022.
+[16] D. Wu et al., “Ugemm: Unary computing architecture for gemm
+applications,” in 2020 ACM/IEEE ISCA, pp. 377–390.
+[17] A.Akhil et al., “Mcm-gpu: Multi-chip-module gpus for continued per-
+formance scalability,” 2017 ACM SIGARCH, vol. 45, no. 2, pp. 320–332,
+2017.
+[18] Y. Wang et al., “Benchmarking tpu, gpu, and cpu platforms for deep
+learning,” arXiv preprint arXiv:1907.10701, 2019.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf,len=535
+page_content='A Polymorphic Electro-Optic Logic Gate for  High-Speed Reconfigurable Computing Circuits  Venkata Sai Praneeth Karempudi  Department of ECE  University of Kentucky  Lexington, Kentucky, USA  kvspraneeth@uky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='edu  Sairam Sri Vatsavai  Department of ECE  University of Kentucky  Lexington, Kentucky, USA  Sairam Srivatsavai@uky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='edu  Ishan Thakkar  Department of ECE  University of Kentucky  Lexington, Kentucky, USA  igthakkar@uky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='edu  Jeffrey Todd Hastings  Department of ECE  University of Kentucky  Lexington, Kentucky, USA  todd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='hastings@uky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='edu  Abstract—In the wake of dwindling Moore’s law, integrated  electro-optic (E-O) computing circuits have shown revolutionary  potential to provide progressively faster and more efficient  hardware for computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The E-O circuits for computing from  the literature can operate with minimal latency at high bit-  rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' However, they face shortcomings due to their operand  handling complexity, non-amortizable high area and static power  overheads, and general unsuitability for large-scale integration  on reticle-limited chips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' To alleviate these shortcomings, in this  paper, we present a microring resonator (MRR) based polymor-  phic E-O logic gate (MRR-PEOLG) that can be dynamically  programmed to implement different logic functions at different  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Our MRR-PEOLG can provide compactness and polymor-  phism to E-O circuits, to consequently improve their operand  handling and amortization of area and static power overheads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  We model our MRR-PEOLG using photonics foundry-validated  tools to perform frequency and time-domain analysis of its  polymorphic logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Our evaluation shows that the use  of our MRR-PEOLG in two E-O circuits from prior works can  reduce their area-energy-delay product by up to 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' A tutorial  on the modeling and simulation of our MRR-PEOLG, along with  related codes and files, is available on https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='com/uky-  UCAT/MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Index Terms—Polymorphic, Microring Resonator, Tempera-  ture, Bit-rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' INTRODUCTION  Moore’s law has been steering the advancement of comput-  ing hardware since its inception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' But unfortunately, in recent  years, it has faced fatal challenges as the nanofabrication  technology is experiencing physical limitations due to the  exceedingly small size of transistors [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This has forced  researchers in industry and academia to develop new more-  than-Moore technologies that can continue to provide per-  sistently faster and more efficient computing hardware [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fortunately, silicon photonics (SiP) enabled electro-optic (E-  O) circuit integration has been identified as one such promising  technology [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The SiP-based E-O circuits are generally  CMOS compatible and provide several advantages over their  purely electrical counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These advantages include sub-  picosecond speeds, low dynamic power consumption and  distance-independent bit-rate [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Due to these advantages  compared to the CMOS-based electrical circuits, the early  This research is supported by a grant from NSF (CNS-2139167)  prototypes of SiP-based E-O circuits for computing (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', [2]–  [8]) have been shown to provide up to two orders of magnitude  improvements in performance and energy efficiency [9] [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  The SiP-based E-O circuits for computing, which have been  demonstrated in prior works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', [2]–[8]) are typically used  to implement the following four types of logical and arithmetic  functions: (I) Basic logic-gate functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' For instance, a  microring resonator (MRR) integrated phase change memory  (PCM) device based XNOR gate is employed in [3] to  enable acceleration of binary neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Similarly, in  [4] and [5], an add-drop MRR based AND gate is employed  to enable partial multiplications of two binary operands, to  aid the acceleration of deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' (II) Arbitrary  combinational logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' For example, the directed  logic based MRR-enabled reconfigurable E-O circuits are  demonstrated in [6] and [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These can work as the direct  optical replacement of field programmable gate arrays (FP-  GAs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' (III) Two-operand arithmetic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' High-speed  E-O circuits for partial sum accumulation and two-operand  addition have been demonstrated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', [8], [2]) with various  designs supporting custom precision [8] and full-precision  polymorphic operation [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' (IV) Multi-operand linear arith-  metic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Several analog and digital E-O circuits based  on MRRs and/or Mach-Zehnder Interferometers (MZIs) have  been demonstrated to implement Multiply-Accumulate (MAC)  and Vector Dot Product (VDP) operations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', [3], [4],  [9], [10]) for deep learning workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These logical and  arithmetic functions implemented using E-O circuits typically  fulfill the requirements of ultra-fast, highly-parallel general  purpose computing or deep learning acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  However, we observe that these SiP-based E-O circuits from  prior works face three major shortcomings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' First, the E-O  circuits for simple logic-gate functions intake the two input  operands differently;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' one operand is typically applied optically  and the other operand is applied electrically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' For instance, in  the E-O XNOR gate from [3] and the E-O AND gate from [4],  one of the two operands has to be modulated onto the incoming  optical wavelengths, for which an additional optical modulator  device per gate function is required, assuming that the utilized  laser sources provide unmodulated optical power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Having to  provide one of the operands optically through an additional  modulator device increases the hardware area overhead and  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='13626v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='ET]  30 Jan 2023  the operand handling complexity in the E-O circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Instead,  there is a need to design a simpler hardware, which can be  achieved by promoting all electrical provisioning of both the  operands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Second, the E-O circuits for arithmetic functions  occupy very large areas compared to CMOS implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  For instance, the E-O MAC circuit used in [5] occupies up  to 100× more area compared to the all-electric MAC circuit  [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Moreover, such E-O circuits for arithmetic functions can  hardly achieve more than 60% hardware utilization [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This  is because these circuits typically belong to larger processing  units where they occupy only part of the entire end-to-end  datapath [3], [9], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Such low hardware utilization often  leads to high idle time and consequently very high, non-  amortizable area and static power overheads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This in turn  motivates the need for more flexible E-O circuits that can  adapt to different arithmetic/logic functions at different times,  to increase the amortization of their high area and static power  overheads by reducing their total idle time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Third, the high area  overhead of E-O circuits makes them less suitable for highly-  parallel Single-Instruction-Multiple-Data (SIMD), Multiple-  Instruction-Multiple-Data (MIMD), and Systolic Array (SA)  based processing architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This is because SIMD, MIMD  and SA architectures typically employ thousands of streaming  processing units, with each processing unit requiring multiple  copies of basic logical and arithmetic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Implementing  these functions using bulky E-O circuits with 100× more area  can drastically reduce the number of processing units that can  be integrated on a single chip whose area is typically limited  by the reticle size (<=900 mm2 [11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Since SIMD, MIMD,  and SA based processing units have become extremely popular  for executing modern Euclidean as well as non-Euclidean  data workloads (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', workloads with grid and graph structured  data), it becomes crucial to alleviate the unsuitability of E-O  circuits for SIMD, MIMD and SA based designs by forging  new E-O circuits with relatively low area overheads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  To address these shortcomings, in this paper, we present  a single MRR based Polymorphic E-O Logic Gate (MRR-  PEOLG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Our MRR-PEOLG can accept both input operands  electrically, and its drop-port (through-port) optical response  can be thermo-optically programmed to make it dynamically  follow the truth table of different logic functions, such as  AND, OR and XOR (NAND, NOR, and XNOR), at different  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Consequently, the E-O circuits built using our MRR-  PEOLG can address the above-described shortcomings by pro-  viding (1) the ability of all-electrical application of the input  operands, (2) compactness through a single-MRR structure of  the E-O gate, and (3) high flexibility through the introduced  polymorphism, and consequently, low idle time and improved  suitability for use with SIMD/MIMD/SA based architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  The key contributions of this paper are summarized below:  We  model  our  MRR-PEOLG  using  the  photonics  foundry-validated tools from Ansys/Lumerical [12], and  then, perform the frequency, time-domain transient, and  thermal analysis for different logic-gate functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' A  tutorial on the modeling and simulation of our MRR-  PEOLG, along with related codes and files, is available  on https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='com/uky-UCAT/MRR-PEOLG;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Based on our analysis, we evaluate the performance of  our MRR-PEOLG, from which we determine the max-  imum achievable bit-rate and thermal tuning power for  each logic-gate function supported by our MRR-PEOLG;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  We show that the use of our MRR-PEOLG in two E-  O circuits from prior works can provide improvement in  area-energy-delay product of up to 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6×;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  We also discuss how MRR-PEOLG can be used to realize  E-O reconfigurable SIMD/MIMD architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Structure and cross-section of our MRR based polymorphic E-O logic  gate (MRR-PEOLG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' MRR-BASED POLYMORPHIC ELECTRO-OPTIC LOGIC  GATE (MRR-PEOLG)  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Structure  Our MRR-PEOLG is basically an add-drop MRR [13] with  four quarter-sized phase-shifting sections embedded in it, as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Two quarter-sized sections of the MRR  are two PN junctions which are operated in the forward bias  condition, whereas the remaining two quarter-sized sections  integrate micro-heaters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The cross-section of a PN-junction  based section of our MRR-PEOLG is shown in the right hand  side of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1(a), which consists of a ridge waveguide with  an embedded lateral PN junction, fabricated on the top of a  buried oxide layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The dimensions of the P-type and N-type  regions, and their corresponding carrier concentrations are also  provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The PN junction based sections of our  MRR-PEOLG work as the input terminals where the input  logic signals/operand bits are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' On the other hand, the  microheaters integrated sections of our MRR-PEOLG work  as the programming terminals that are used to program the  MRR-PEOLG to perform specific logic-gate functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Applying a voltage to the microheaters based programming  terminals can increase the temperature of the MRR, which in  turn can shift (red shift) the resonance of the MRR towards the  longer wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This is because of the thermo-optic effect  in silicon ( [14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' To program MRR-PEOLG to implement  a specific logic-gate function, the operand-independent MRR  resonance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', the programmed MRR resonance) is adjusted  to a specific spectral position with respect to the input optical  n  p  220nm  n+ 100nml  1μm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='75μm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='75μm1μm  BOX (SiO2)wavelength, by applying a voltage to the programming termi-  nals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Then, the electrical input logic signals or input operand  bits (x and w) are applied to the PN junctions based input ter-  minals of the MRR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Upon doing so, the resonance of the MRR  shifts (blue shifts) towards the shorter wavelength depending  on the combination of the applied input operand bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This is  because of the free-carrier plasma dispersion effect in silicon  ( [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Applying the input operand bits to the input terminals  makes the through-port and drop-port optical responses of our  MRR-PEOLG follow the truth-table of the logic-gate functions  for which the MRR-PEOLG is programmed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' In this manner,  our MRR-PEOLG can perform different logic-gate functions  at different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' At any given time, the through-port optical  response of the MRR-PEOLG follows logical complement  of the drop-port optical response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Therefore, AND, OR and  XOR functions can be realized (one function at a time) at  the drop port of the MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Concurrently, the through  port of the MRR-PEOLG can provide complementary logic-  gate functions such as NAND, NOR and XNOR as discussed  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Modeling  We model our MRR-PEOLG using the photonics foundry-  validated simulation tools from Ansys/Lumerical [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We  break down our MRR-PEOLG design into a set of primitive  elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(a) shows a schematic of our MRR-PEOLG,  whose breakdown into the primitive elements is shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We use different solvers in the Ansys/Lumerical  tools [12] to model each primitive element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' From these  models, we extract various parameters for each primitive  element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Later, we combine all of the extracted parameters  in Ansys/Lumerical’s INTERCONNECT tool [12] (tool for  the modeling and simulations of photonic integrated circuits)  to create our MRR-PEOLG in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Finally, we perform  the frequency-domain and time-domain transient simulations  of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Different steps for the modeling and  simulation of our MRR-PEOLG using the ANSYS/Lumerical  tools/solvers are summarized below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Step-1 - modeling MRR-waveguide coupling sections:  First, create coupling sections in the finite difference time  domain (FDTD) solver and extract the power coupling co-  efficients as a function of wavelength for the fundamental TE  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Import these coefficients in the coupling elements C 1  and C 2 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Step-2 - modeling straight waveguide sections: First,  characterize the passive, straight, channel waveguides of the  MRR-PEOLG using the finite difference eigenmode (FDE)  solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Extract the effective index, group index, and dispersion  for the waveguides as functions of wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Load this  information into the primitive elements WGD 1, WGD 2,  WGD 7, and WGD 8 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Step-3 - modeling PN-junction based input terminals:  First, create a quarter ring with an embedded lateral PN-  junction in the CHARGE tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Perform the simulation to  extract the spatial distribution of the charge carriers as a  function of the bias voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Then, export this data into the  FDE solver and calculate the perturbations in the refractive  index of the waveguides connected to the input terminals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Then, calculate the change in the effective index and resonance  of the entire MRR-PEOLG as a function of the bias voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Import this information into the primitive elements WGD 6  (connected to OM 1) and WGD 5 (connected to OM 2) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  2(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Step-4 - modeling microheaters based programming ter-  minals: Extract the temperature profile of the MRR-PEOLG  as a function of the applied microheater voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Then, import  this data into the FDE solver to calculate the change in the  effective index of the MRR-PEOLG as a function of its tem-  perature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Import this information into the primitive elements  WGD 3 (connected to OM 4) and WGD 4 (connected to  OM 5) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Step-5 - preparing for simulations: Connect the primitive-  elements based model of the MRR-PEOLG (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(b)) with  other testing and characterization apparatus in the INTER-  CONNECT tool, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(c) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' (a) Step-1 to Step-4, and (b) Step-5 of the procedure used for modeling  our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The schematic simulation setup in ANSYS/Lumerical’s  INTERCONNECT tool for (c) frequency-domain and (d) time-domain tran-  sient analysis of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Operation  To explain the operation of our MRR-PEOLG, we per-  formed frequency-domain simulations using the INTERCON-  NECT tool [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Our simulation setup for this frequency-  domain analysis is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Accordingly, we  connected an optical network analyzer (ONA) to our MRR-  PEOLG to extract the transmission spectra at its drop and  through ports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We extracted the transmission spectra for dif-  ferent values of the detuning of the operand-independent MRR  resonance position κ with respect to the input wavelength λin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  As mentioned earlier, these detuning values correspond to dif-  ferent logic-gate functions that the MRR-PEOLG can perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  In addition, we also extracted transmission spectra for different  combinations of the input operand bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' All of these transmis-  sion spectra for different logic-gate and complementary logic-  gate functions are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a) to 3(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Transmission  WGD ‘2  WGD_1  C 1  1O  0M  0M_2  WGD 6  WGD 5  WGD_3  WGD_4  0M 5  OM  DC  WGD_ 8  WGDspectra corresponding to logic-gate functions AND, OR and  XOR are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a), 3(b), and 3(c) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  These transmission spectra are drop-port transmission spectra  (Lorentzian lineshape passbands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Similarly, the transmission  spectra corresponding to complementary logic-gate functions  NAND, NOR and XNOR are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(d), 3(e), and  3(f) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These transmission spectra are through-port  transmission spectra (inverse Lorentzian lineshape passbands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  As we can see in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3, the drop port and through port  transmission exhibits two clearly distinguishable levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The  full transmission range at the drop port and through port of  our MRR-PEOLG is divided into two areas, in which the  lower part of the full transmission range is indicated with  shaded gray whereas the upper part is indicated with shaded  blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' If the drop port (DT(λin)) and through port (TT(λin))  transmission at λin falls in the lower part of the full transmis-  sion range (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', in the gray-shaded area), then it is referred  to as logic ‘0’ transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' On the other hand, if the drop  port and through port transmission at λin falls in the upper  part of the full transmission range (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', in the blue-shaded  area), then it is referred to as logic ‘1’ transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' However,  the vertical spans of the two distinguishable transmission  levels differ between the drop port and through port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This is  because, similar to the transmission spectra (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3), the spans  of transmission levels at the drop port also complement the  spans of transmission levels at the through port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The difference  between the minimum supported logic ‘1’ transmission and the  maximum supported logic ‘0’ transmission is the sensitivity of  optical modulation amplitude (SOMA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' SOMA is a property  of the photodetector based receiver circuit, and it affects the  performance of the MRR-PEOLG (as will be discussed in  Sections III and IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  To clearly understand the operation of our MRR-PEOLG,  let us consider the example of AND function, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' To program our MRR-PEOLG to implement AND  function, a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='9 V voltage (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='52 mW power) is applied to  the programming terminals of the MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This shifts  the resonance from the initial position, η, to the programmed  position, κ, where κ has the programmed detuning of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='7 nm  with respect to λin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Then, the input operand bits x and w  are applied to the input terminals of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Doing so  induces a blueshift in the MRR resonance, the magnitude of  which depends on the specific combination of the applied input  operand bits (x and w, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' If the applied  bit-combination (x,w) is (0,0), the resonance position of the  MRR stays at κ (magenta colored passband in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a)) and  the drop port transmission at λin provides logic ’0’ level (the  bottom red dot on the Y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' If the applied bit-combination  (x,w) is (0,1) or (1,0), the position of the MRR resonance  changes (red/orange colored passband in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a)), but the  blueshift is the same for both (0,1) and (1,0) bit combinations,  and the drop port transmission at λin still remains at logic ’0’  level (the top red dot on the Y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' On the other hand, if the  applied bit-combination (x,w) is (1,1), the MRR resonance  undergoes a larger blueshift (blue colored passband in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  3(a)), and the position of the passband with respect to λin  TABLE I  POWER CONSUMED IN THE MICROHEATERS, PROGRAMMED DETUNING,  AND REQUIRED RESONANCE SHIFTING, USED TO PROGRAM OUR  MRR-PEOLG FOR IMPLEMENTING DIFFERENT LOGIC FUNCTIONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Logic-Gate  Functions  Microheater  Power (mW)  Programmed  Detuning  (κ-λin) (nm)  Required  Shifting  (η-κ) (nm)  AND / NAND  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1  OR / NOR  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='9  XOR / XNOR  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='7  changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' As a result, the drop port transmission at λin changes  to logic ’1’ level (the green dot on the Y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Hence, the  drop port transmission at λin for our MRR-PEOLG changes  with the applied input operand bits, and follows the truth table  of the AND logic function (see the truth table in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  As discussed earlier, since the through-port response provides  a logical complement to the drop-port response, this AND  function at the drop port of the MRR-PEOLG corresponds to  NAND function at the through port of the MRR-PEOLG as  illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Similarly, our MRR-PEOLG can be reconfigured to imple-  ment OR (NOR) and XOR (XNOR) gate functions as well, by  applying a suitable voltage to the programming terminals of  our MRR-PEOLG to set the relative position of κ with respect  to λin as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(b) and 3(c) (transmission spectra  corresponding to NOR and XNOR are shown in figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3(e) and  3(f) respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Table I provides the total power consumed  in the microheaters, the programmed detuning (κ-λin), and  the required resonance shifting (η-κ), to program our MRR-  PEOLG for implementing various logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' From Table  I, the power consumed in the microheaters is proportional to  the required resonance shifting (η-κ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' TRANSIENT ANALYSIS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Method  As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2(d), to perform transient analysis  of our MRR-PEOLG in the INTERCONNECT tool, we con-  nected a pseudo random bit sequence (PRBS) generator and  a non-return-to-zero (NRZ) pulse generator to each of the  input terminals of the MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Each PRBS generator  generates a random bit sequence of 10 Gb/s, which is given  as input to the NRZ pulse generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Each NRZ pulse generator  then generates a sequence of electrical NRZ pulses of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  V amplitude at 10 Gb/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The blue and red pulses shown in  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(a) and 4(b) respectively are the electrical NRZ pulses  that we have provided as inputs to the two input terminals  of our MRR-PEOLG for the transient analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We have also  connected a continuous wave (CW) laser to the input port  of the MRR-PEOLG, which generates an optical signal of  wavelength 1545 nm (λin = 1545 nm in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3) with an optical  power of 5 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We connected optical oscilloscopes to the  drop and through ports to record the output pulse patterns  corresponding to different logic functions for the given input  electrical pulse signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The results obtained from this transient  analysis are discussed next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The transmission spectra obtained at the drop port of our MRR-PEOLG for logic-gate functions (a) AND, (b) OR, and (c) XOR, and at the through  port of our MRR-PEOLG for complementary logic-gate functions (d) NAND, (e) NOR, and (f) XNOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  (a),(b) The electrical pulse signals of 10 Gb/s bit-rate provided as  input to the PN junctions of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The corresponding output  pulse patterns obtained at the drop port of our MRR-PEOLG for logic-gate  functions (c) AND, (e) OR, and (g) XOR , and at the through port of our  MRR-PEOLG for complementary logic-gate functions (d) NAND, (f) NOR,  and (h) XNOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The optical input power is 5 dBm in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Results and Discussion  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(c), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(e), and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(g) illustrate the output pulse  signals obtained at the drop-port of the MRR-PEOLG for  different logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Similarly, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(d), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(f), and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(h) illustrate the output pulse signals simultaneously  obtained at the through-port of the MRR-PEOLG for different  complementary logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' To obtain these pulse patterns,  we first reconfigured the MRR-PEOLG to implement various  logic functions by changing the temperature using the inte-  grated microheaters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We then followed the method described  in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' As evident from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4, the output pulse  signals follow the pulse-wise truth-tables of the respective  logic functions, which confirms the capability of our MRR-  PEOLG to correctly realize different logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  From Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(c) - 4(h), the optical modulation amplitude  (OMA), which is the difference between the minimum logic  ’1’ power level and the maximum logic ’0’ power level in  an output pulse pattern, differs for different logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  To clearly understand this, let us consider AND, XOR, and  OR functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' For the AND function shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(c), the  OMA is ∼-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This is because, as can be observed from  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4(c), the drop port transmission at λin corresponding to  the logic ‘1’ output level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', (x,w) = (1,1)) is ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='82 (the  green dot on the Y-axis), whereas the maximum drop port  transmission at λin, corresponding to the logic ‘0’ output level  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', (x,w) = (1,0) or (0,1)), is ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='62 (the top red dot on  the Y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Hence, the OMA, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', the difference between the  logic ‘1’ optical power level (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='82×5dBm = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='57 mW) and  the logic ‘0’ optical power level(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='62×5dBm = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='995 mW) is  ∼-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4 dBm (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='575 mW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Similarly, for OR (NOR) and XOR  (XNOR) functions shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 4, the green and red dots on  Y-axis occur at different positions compared to AND (NAND)  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Therefore, our MRR-PEOLG exhibits different OMA  for different logic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Since the OMA for the output pulse pattern basically  defines how well the logic ’1’s are distinguishable from logic  ’0’s, having different OMA values renders different reliability  bounds for different logic functions implemented by our MRR-  PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' In general, to achieve higher reliability without trying  to quantify its value, it is desirable to increase the OMA of an  output pulse pattern, which can be done in two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' First,  OMA can be increased by increasing the input optical power at  λin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' (We considered an input optical power of 5 dBm for our  uo  (x, w) = (0,0)  (x,w) = (0,0)  (x,w) = (1,1)=  (x,w) = (1,1):  Logic“1\'  s  S  Logic “1\'  Logic1\'  ISOMA  ↑SOMA  ↑SOMA  Logic 0"  Logic ‘0"  Logic ‘0"  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6  WDT(Λin)  × w DT(Ain)  ×w DT(Ain)  x  0  (x,w)= (1,0)/(0,1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  0  01  01  0  : (x,w) = (1,1)  (x,w) = (1,0)/(0,1)  (x,w) = (1,0)/(0,1)  0  10  0  1  10  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  1０  (x, w) = (0,0)  11  111  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='515451545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='51546  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='515451545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='515461546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  15461546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1544  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1544  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545  1545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content="5  1544  Wavelenqth(nm)  Wavelength(nm)  Wavelength(nm)  Ain  K  NinK  0  0  Logic 1'  Logic  m0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  (x,w)= (1,0)/(0,1)  (x,w) = (1,0)/(0,1)  (x,w):= (1,0)/(0,1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6  Logic‘1"  ×w TT(Ain)  ×w TT(Λin)  ×w TT(An)  ００1  (x,w) = (1,1)  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  ００  1  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  (x,w) = (0,0)  (x,w) = (1,1) _=  0  1  P  01  (x,w) = (1,1)-  ０１  (x,w) = (0,0)  0  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  101  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  1０  (x,w) = (0,0)  +SOMA  0  110  Logic ‘o"  Logic ‘0"  Logic \'0"  11  １１  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1544  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545  1546  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1546  1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1546  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1544  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545  1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1545  1544  Wavelength(nm)  Wavelength(nm)  Wavelength(nm)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1  Amplitude (V)  1  1  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  0  0  0  0  0  0  0  0  0  0  0  2  6  2  4  6  8  8  0  4  0  Time(s)  Time(s)  ×10-10  ×10-10  5  5  AND  NAND  1  4  Bm)  1  1  OMA = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4 dBm  0  --  0  0  Power (  0  OMA = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='48 dBm  5  0  0  0  1  0  0  0  10  2  2  0  4  6  0  4  6  8  8  Time(s)  Time(s)  ×10-10  ×10-10  5  5  OR  NOR  5  OMA = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='35 dBm  10  0  0  0  0  0  OMA = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='89 dBm  15  2  2  4  6  0  8  0  2  4  6  8  Time(s)  Time(s)  ×10-10  ×10-10  5  XOR  5  XNOR  (w)  Power(dBm)  1  1  OMA = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8 dBm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='.  0  OMA = -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='14 dBm  B  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  Power(dl  1  5  10  4  P-15  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='0  0  OT  0  0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  2  4  6  2  4  6  0  8  0  8  Time(s)  Time(s)  ×10-10  ×10-10results discussed in previous paragraph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Second, OMA can  be increased by decreasing the full width at half maximum  (FWHM) or 3-dB bandwidth of the MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' A lower  FWHM would make the roll-off edges of the MRR passbands  corresponding to (0,0), (0,1)/(1,0) and (1,1) steeper (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3),  which in turn would increase the distance between the green  dot and top red dot on the Y-axis, thereby increasing the OMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Note that increasing OMA is not always necessary, as a low  OMA would cause reliability issues only if it is lower than  the OMA sensitivity (SOMA) of the receiver circuit that is  employed to make sense of the output pulse pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Therefore,  decreasing SOMA of the receiver circuit can also increase  the reliability of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Thus, the FWHM (3-dB  bandwidth) of the MRR-PEOLG, the SOMA of the receiver  circuit, and the input power are the three factors that influence  the impact of OMA on the reliability of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Moreover, these three factors impact the maximum speed  (bit-rate) at which the input pulse patterns can be driven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Increasing the bit-rate will reduce OMA because either the  free-carrier concentration in the PN junctions or the optical  energy inside the MRR does not change as fast as the  applied input electrical pulse signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' For a given FWHM  (3-dB bandwidth), it is possible to keep increasing the bit-  rate until the OMA becomes less than the SOMA limit of  the receiver circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Once the OMA for a given input power  crosses the SOMA limit, the OMA can be increased to support  a higher bit-rate by increasing the input power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Therefore, the  maximum achievable bit-rate for our MRR-PEOLG depends  on SOMA, FWHM, and input optical power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We have evalu-  ated the maximum achievable bit-rate for our MRR-PEOLG,  corresponding to various logic functions, which is discussed  in next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' PERFORMANCE ANALYSIS  For this analysis, we have used the scripting capabilities  available in the ANSYS/Lumerical tools to run a performance  evaluation of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We swept the input optical  power in the range from -5 dBm to 5 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Similarly, we  swept SOMA in the range from -5 dBm to -20 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Then,  for each combination of the input optical power and SOMA,  we evaluated the maximum achievable bit-rate for each logic-  gate function supported by our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The results of  this analysis are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 5 in the form of colormap plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Results and Discussion  The colormap plots in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 5(a) to 5(f) depict the maximum  achievable bit-rate corresponding to each logic-gate function  for an FWHM of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2 nm and different combinations of input  optical power and SOMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' From the colormap plots, the AND  function achieves a maximum bit-rate of 42 Gb/s across all  SOMA values if the input optical power is >2 dBm, as well as  across all input power values if the SOMA value is <-13 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Similarly, OR and XOR functions achieve a maximum bit-rate  of 41 Gb/s and 40 Gb/s respectively across all input optical  power values if SOMA is <-19 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Meanwhile, the NAND  function achieves a maximum bit-rate of 40 Gb/s across all  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Colormap plots for logic functions (a) AND, (c) OR, (e) XOR  (obtained at the drop port of our MRR-PEOLG), and complementary logic  functions (b) NAND, (d) NOR, (f) XNOR (obtained at the through port of  our MRR-PEOLG) that depict the maximum achievable bit-rate for given  input optical power and SOMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These color maps are evaluated for drop-  port FWHM of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We also report the maximum achievable bit-rate  corresponding to (g) AND, OR, and XOR functions, and (h) NAND, NOR,  and XNOR functions, evaluated for different values of FWHM, 0 dBm input  optical power, and -5 dBm SOMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  SOMA values if the input optical power is >2 dBm, as well as  across all input power values if the SOMA value is <-11 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  And  NAND  40  40  0  20  10  20  20  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='15  10  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='15  10  SOMA (dBm)  SOMA (dBm)  OR  NOR  40  40  0  0  20  20  20  20  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='15  10  5  15  10  SOMA (dBm)  SOMA (dBm)  XOR  XNOR  40  40  0  0  20  20  5  20  15  20  15  10  5  5  SOMA (dBm)  SOMA (dBm)  And  OOR  OXOR  Full Width at Half Maximum (  (FWHM) (Through Port) (nm)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='14  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='75  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  50  Bit Rate (Gb/s)  40  30  20  10  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='675  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='45  Full Width at Half Maximum (FWHM) (Drop Port) (nm)  NAND  XNOR  △XNOR  Full Width at Half Maximum (FWHM) (Through Port) (nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
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+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='75  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='98  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  50  40  Bit Rate (Gb/s)  30  20  10  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='25  1-8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='675  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='45  Full Width at Half Maximum (FWHM) (Drop Port) (nm)Similarly, NOR and XNOR functions achieve a maximum  bit-rate of 40 Gb/s and 41 Gb/s respectively across all input  optical power values if SOMA is <-11 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Moreover, we  also show in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 5(g) and 5(h) that increasing the drop-  port FWHM (which can be achieved by increasing the cross-  coupling co-efficient of the MRR-PEOLG) can increase the  maximum achievable bit-rate for each logic function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These  results imply that our MRR-PEOLG can be operated at up to  40 Gb/s for each of its supported logic-gate functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' COMPARISON AND ENVISIONED USE CASES  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Comparison with E-O Circuits from Prior Work  We evaluated how the use of our MRR-PEOLG impacts  the area, latency, and energy consumption of two E-O circuits  from prior works [3] and [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We replaced the E-O XNOR  gates with our MRR-PEOLG in the E-O XNOR-POP circuits  of the binary neural network accelerator LightBulb from [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Similarly, we replaced the AND gates with our MRR-PEOLG  in the optical bit-serial multiplier circuits of the digital CNN  accelerator from [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' As a result, the performance of these E-  O circuits substantially improved as shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The  energy values are the energy per bit values and include the  MRR static power as well as laser power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The area and energy  benefits in Table II are due to the compactness and better  operand handling of our MRR-PEOLG and also our MRR-  PEOLG’s ability to realize different logic functions with only  a single MRR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The latency benefits are due to the fact that  our MRR-PEOLG can operate at up to 40 Gb/s, whereas  the original bit-serial multiplier circuit from [5] can only  operate at up to 10 Gb/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' The E-O XNOR-POPCOUNT units  from [3] can operate at a higher bit-rate of 50 Gb/s, but our  MRR-PEOLG based variants provide better area-energy-delay  product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' These results corroborate the excellent capabilities  and efficiency benefits of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  TABLE II  PERFORMANCE COMPARISON OF E-O CIRCUITS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  A=AREA, E=ENERGY, L=LATENCY  Metrics  XNOR-POPCOUNT  Bit-serial Multiplier  [3]  MRR-PEOLG  [5]  MRR-PEOLG  A (mm2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
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+page_content='025 (4×)  A*E*L  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='3e-5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='9e-5 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='44×)  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='2e-5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='91e-5 (82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6×)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Envisioned Use Cases for SIMD/MIMD Architectures  We reason that it is possible to use the dense wavelength  division multiplexing (DWDM) technique with our MRR-  PEOLG, where cascaded arrays of MRR-PEOLGs can couple  with DWDM-enabled rectilinear waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' In these cas-  caded arrays, each MRR-PEOLG can be individually pro-  grammed to perform a specific logic-gate function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Moreover,  from [16], it can be inferred that OR, XOR and AND  logic-gate functions supported by our MRR-PEOLGs can be  useful for realizing stochastic (unary) arithmetic functions  such as addition, subtraction and multiplication respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  This enables the application of the cascaded arrays of MRR-  PEOLGs for realizing reconfigurable SIMD/MIMD E-O pro-  cessing units (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Such E-O SIMD/MIMD units can  outperform the traditional GPUs [17] and Tensor Processing  Units (TPUs) [18] due to their two-fold benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' First, they  can be operated at higher speeds (up to 40Gb/s) compared  to GPUs/TPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Second, they can provide significantly better  area×latency product, which we plan to evaluate in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Schematics of how the cascaded arrays of our MRR-PEOLG can be  reconfigured to implement (a) a SIMD or (b) an MIMD E-O processing unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  The reconfiguration between SIMD/MIMD can be achieved by programming  the individual MRR-PEOLGs for specific logic/arithmetic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' CONCLUSION  In this paper, we demonstrated a microring resonator based  polymorphic electro-optic logic gate (MRR-PEOLG) that can  be dynamically reconfigured to implement different logic  functions at different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We modeled our MRR-PEOLG  using the photonics foundry-validated simulation tools from  ANSYS/Lumerical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Using these tools, we also performed  frequency-domain, time-domain transient, and performance  analysis of our MRR-PEOLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' From our analysis, we validated  that our MRR-PEOLG design can implement various logic  functions while operating at speeds of up to 40 Gb/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Our  evaluation shows that the use of our MRR-PEOLG in two E-  O circuits from prior works can reduce their area-energy-delay  product by up to 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='6×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' We also show how our MRR-PEOLG  can realize reconfigurable E-O SIMD/MIMD processing units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  ACKNOWLEDGMENT  We thank the anonymous reviewers for their valuable feed-  back.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' This research is supported by a grant from NSF (CNS-  2139167).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  REFERENCES  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='Ganguly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Interconnects for dna, quantum, in-memory, and  optical computing: Insights from a panel discussion,” IEEE micro,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 40–49, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [2] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Ying et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Electronic-photonic arithmetic logic unit for high-speed  computing,” Nature communications, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [3] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Zoakee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Lightbulb: A photonic-nonvolatile-memory-based  accelerator for binarized convolutional neural networks,” in 2020 DATE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1438–1443.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [4] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Shiflett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Pixel: Photonic neural network accelerator,” in 2020  IEEE HPCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 474–487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Shiflettet al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Bitwise neural network acceleration using silicon  photonics,” in GLSVLSI, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 9–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Qiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Demonstration of reconfigurable electro-optical logic with  silicon photonic integrated circuits,” Optics letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 19, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  3942–3944, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  米  米[7] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Ying et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Integrated multi-operand electro-optic logic gates for  optical computing,” APL, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [8] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Venkata Sai Praneeth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Design exploration and scalability  analysis of a cmos-integrated, polymorphic, nanophotonic arithmetic-  logic unit,” in Proceedings of the 19th ACM CenSyS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [9] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Bangari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Digital electronics and analog photonics for convo-  lutional neural networks (deap-cnns),” IEEE JSTQE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  1–13, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [10] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Holylight: A nanophotonic accelerator for deep learning  in data centers,” in 2019 DATE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  IEEE, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 1483–1488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Naffziger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Pioneering chiplet technology and design for the  amd epyc™ and ryzen™ processor families: Industrial product,” in 2021  ACM/IEEE ISCA, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 57–70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [12] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Available: http://www-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='lumerical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='com/products  [13] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Boagerts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Silicon microring resonators,” Laser & Photonics  Reviews, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Bahadori et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Thermal rectification of integrated microheaters for  microring resonators in silicon photonics platform,” JLT, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Mulcahy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Modulators in silicon photonics—heterogenous  integration & and beyond,” in Photonics, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Ugemm: Unary computing architecture for gemm  applications,” in 2020 ACM/IEEE ISCA, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 377–390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='Akhil et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Mcm-gpu: Multi-chip-module gpus for continued per-  formance scalability,” 2017 ACM SIGARCH, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 45, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' 320–332,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content=', “Benchmarking tpu, gpu, and cpu platforms for deep  learning,” arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
+page_content='10701, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tFRT4oBgHgl3EQftDeF/content/2301.13626v1.pdf'}
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+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Higher derivative Hamiltonians with benign ghosts
+from affine Toda lattices
+Andreas Fring and Bethan Turner
+Department of Mathematics, City, University of London, Northampton Square,
+London EC1V 0HB, UK
+a.fring@city.ac.uk, bethan.turner.2@city.ac.uk
+Abstract: We provide further evidence for Smilga’s conjecture that higher charges of in-
+tegrable systems are suitable candidates for higher derivative theories that possess benign
+ghost sectors in their parameter space. As concrete examples we study the properties of
+the classical phase spaces for a number of affine Toda lattices theories related to different
+types of Kac-Moody algebras. We identify several types of scenarios for theories with
+higher charge Hamiltonians: some that possess benign ghost sectors which are stable or
+exteremely sensitive towards the initial conditions, some that have malevolent ghost sec-
+tors that can be converted into benign sectors with an appropriate choice of variables and
+some theories with benign ghost sectors that are stable towards strong deformations.
+1. Introduction
+Higher derivative Lagrangian theories, i.e. those that include derivative terms of the coor-
+dinates of order larger than one, arise naturally in a number of different contexts. For in-
+stance, in some approaches to theories of everything (TOE) that include gravity besides all
+the other known fundamental forces consist of embedding the standard (3+1)-dimensional
+universe into a higher dimensional space. In doing so, and demanding in addition these
+theories to be renormalizable, one is automatically led to higher derivative Lagrangian the-
+ories by simple scaling arguments. Unfortunately these theories are generally plagued [1]
+by so-called ghosts states that possess negative norms, thus leading to collapse and/or a
+violation of unitarity. This is the main reason why they are usually discarded and in com-
+parison only very few explicit studies of these theories have been carried out to a full extent.
+For instance, in the field gravity and cosmology they have been proposed as a resolution of
+the cosmological singularity problem [2] and some of their black holes solutions have been
+studied [3]. Furthermore, for some cases the BRST symmetries have been identified [4] and
+also some supersymmetric versions have been studied [5].
+However, in general such types of theories remain to be regarded as undesirable for the
+above mentioned reason and it unclear which theories deserve further considerations. In a
+arXiv:2301.11317v1  [hep-th]  26 Jan 2023
+
+CITY
+UNIVERSITYOFLONDON
+EST1894Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+recent series of papers [6–9] Smilga and collaborators addressed this question and gathered
+evidence to suggest that the dismissal of higher derivative theories might be too premature.
+The central idea in these studies is to distinguish between benign and malevolent ghost
+states in the sense that the latter states are genuinely unphysical while the former are
+solutions that might not be bounded from below, but are oscillatory in character hence allow
+for a unitary evolution. The next question is then of course how to identify theories that
+have such types of features and possess sectors in their parameter space with benign ghost
+solutions that in addition might be stable against small perturbations. Very recently [6]
+Smilga proposed that higher charges of integrable systems might be suitable candidates
+for such types of higher derivative Lagrangian theories. Here our main goal is to gather
+further evidence for this conjecture by considering a particular class of integrable systems
+and interpret their charges as Hamiltonians for higher derivative theories. We will analyse
+their classical phase spaces in the hope that benign classical systems will also lead to benign
+quantum systems as conjectured in [6].
+In general, we will be considering here a prototype integrable theory that is affine Toda
+lattices with Hamiltonians of the form
+Hg =
+ℓ
+�
+i=1
+p2
+i
+2 +
+r
+�
+i=0
+nieαi·q,
+(1.1)
+where q = (q1, . . . , qℓ) are the coordinates, p = (p1, . . . , pℓ) are the momenta, g is a semi-
+simple Lie algebra, r the rank of this algebra, αi for i = 1, . . . , r are the simple roots of the
+root space ∆g represented in an ℓ-dimensional space, α0 = − �r
+i=1 niαi and ni ∈ N are
+positive integers with n0 = 1. The choice of α0 ensures that the minimum of the potential
+of the theory is at q = (q1, . . . , qℓ) = (0, . . . , 0), i.e. all first order terms in the qi vanish.
+Often α0 is taken to be the negative of the highest root, so that the integers ni are the
+Kac labels, but this need not be the case and is a mere convention. The inclusion of the
+α0-root means that the associated algebra becomes a Kac-Moody algebra rather than a
+semi-simple Lie algebra. Thus we are not considering here theories of the type Hg with the
+sum in the potential starting at i = 1, which are conformally invariant and do not possess
+minima in the potentials at finite values of the coordinates.
+It is well known [10–12] that these type of theories are integrable in the Liouville
+sense, that is they possess as many conserved charges as degrees of freedom. It is these
+charges that we will be using as potential candidates for higher order derivative theories.
+The key question we will be addressing here is whether the classical trajectories in phase
+space associated to the Hamiltonian systems of these charges will be benign or malevolent
+according to the characterisation put forward by Smilga in [6–8]. The initial assumption is
+that the benign nature on the classical level is inherited in the quantum theory. Naturally,
+this supposition needs further investigation, which we leave for future studies.
+Our manuscript is organised as follows: In section 2 we recall the constructions of the
+conserved classical charges for the An-affine Toda lattice theories, with a particular focus
+on A2 and A6 for different types, i.e. dimensions, of representations of the roots in (1.1).
+Interpreting these charges as Hamiltonians we numerically study their classical solutions in
+phase space. In section 3 and 4 we carry out similar type of studies for the B3 and G2-affine
+– 2 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Toda lattice theories, respectively. We construct relevant charges from a reduction/folding
+procedure of the corresponding root systems or by direct computation. In section 5 we
+investigate the stability of the benign solutions with regard to the sensitivity of the initial
+conditions and to strong deformations by harmonic oscillator potentials. Our conclusions
+are stated in section 6.
+2. Higher derivative Hamiltonians from An-affine Toda lattice charges
+The expressions for the higher charges are central to our investigations and therefore we
+will provide here their explicit construction. All higher charges that will be considered
+are for theories associated with Hamiltonians of the general form in equation (1.1) with g
+taken to be An. Using the standard Lax approach for classical integrable systems [13] we
+employ the Lax pair given by the two operators in form of (n + 1) × (n + 1)-matrices
+L =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+p1 W1
+0
+· · · · · ·
+0
+W0
+W1 p2 W2
+0
+0
+0
+W2 p3 ...
+...
+...
+... ... ...
+...
+...
+... ... ...
+0
+0
+0
+... pn
+Wn
+W0
+0
+· · · · · · 0 Wn pn+1
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+,
+M =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+0
+W1
+0
+· · · · · ·
+0
+−W0
+−W1
+0
+W2
+0
+0
+0
+−W2
+0
+...
+...
+...
+... ... ...
+...
+...
+... ...
+...
+0
+0
+0
+...
+0
+Wn
+W0
+0
+· · · · · · 0 −Wn
+0
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+,
+(2.1)
+where we abbreviated Wi := exp(αi ·q)/2, with αi ∈ Rn+1, i = 1, . . . , n denoting the simple
+roots of An, α0 = − �n
+i=1 αi the negative of the highest An-root, q = (q1, . . . , qn+1) the
+coordinates and p = (p1, . . . , pn+1) the momenta. The dimension of the phase space is
+therefore (n + 1) × (n + 1) at this point.
+By definition of the Lax operators, the equations of motion are then equivalent to the
+Lax pair equation
+˙L+[M, L] = 0,
+⇔
+˙pi +W 2
+i −W 2
+i−1 = 0,
+αi · ˙q = pi −pi+1,
+i = 1, . . . , n+1, (2.2)
+where we formally identified Wn+1 = W0. As usual we denote here derivatives with respect
+to time by overdots. Taking ℓ = n+1 in (1.1) these equations also correspond to Hamilton’s
+equations ˙qi = ∂H/∂pi, ˙pi = −∂H/∂qi as we will show below. By construction, it then
+follows immediately that all quantities Qk := Tr(Lk)/k are conserved in time, i.e.
+˙Q = 0.
+Given the expressions in (2.1) we easily construct all of these charges. Interpreting the
+summation indices modulo 7, e.g. W7 = W0, p8 = p1, etc, we obtain
+Q1 =
+7
+�
+i=1
+pi,
+(2.3)
+Q2 = H =
+7
+�
+i=1
+�p2
+i
+2 + W 2
+i
+�
+,
+(2.4)
+– 3 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Q3 =
+7
+�
+i=1
+�p3
+i
+3 + W 2
+i (pi + pi+1)
+�
+,
+(2.5)
+Q4 =
+7
+�
+i=1
+�p4
+i
+4 + 1
+2W 4
+i + W 2
+i (p2
+i + pipi+1 + p2
+i+1) + W 2
+i W 2
+i+1
+�
+(2.6)
+Q5 =
+7
+�
+i=1
+�p5
+i
+5 + W 4
+i (pi + pi+1) + W 2
+i (p3
+i + pip2
+i+1 + p2
+i pi+1 + p3
+i+1)
+(2.7)
++W 2
+i W 2
+i+1(pi−1 + 2pi + 2pi+1)
+�
+,
+Q6 =
+7
+�
+i=1
+�p6
+i
+6 + 1
+2W 6
+i + W 4
+i
+�3
+2p2
+i + 3
+2p2
+i+1 + 2pipi+1
+�
++ W 2
+i
+�
+p4
+i + p3
+i pi+1 + p2
+i p2
+i+1
+�
+,
+(2.8)
++W 2
+i−1
+�
+p4
+i + p3
+i pi−1
+�
++ W 2
+i W 2
+i+1
+�
+p2
+i + 2pipi−1 + 3p2
+i+1 + pipi+2 + 2pi+1pi+2 + p2
+i+2
+�
++W 4
+i
+�
+W 2
+i−1 + W 2
+i+1
+�
++ W 2
+i W 2
+i+1W 2
+i+2
+�
+Q7 =
+7
+�
+i=1
+�p7
+i
+7 + W 6
+i (pi + pi+1) + W 2
+i−1W 2
+i W 2
+i+1(pi−1 + 2pi + 2pi+1 + pi+2)
+(2.9)
++W 4
+i W 2
+i−1(pi−1 + 3pi + 2pi+1) + W 4
+i−1W 2
+i (2pi−1 + 3pi + pi+1)
++W 2
+i−1W 2
+i (p3
+i−1 + 4p3
+i + 3p2
+i pi+1 + 2pip2
+i+1 + p3
+i+1)
++W 2
+i−1W 2
+i (p3
+i−1(p2
+i−1(2pi + pi+1) + pi−1(3p2
+i + 2pipi+1 + p2
+i+1))
++W 2
+i (p5
+i + p4
+i pi+1 + p3
+i p3
+i+1 + p2
+i p3
+i+1 + pip4
+i+1 + p5
+i+1)
+�
++ 2
+7
+�
+i=1
+Wi.
+These charges and versions thereof will be our potential candidates for higher derivative
+theories when interpreted as Hamiltonians.
+2.1 Higher derivative Hamiltonians from the 3 particle A2-affine Toda lattice
+Next we evaluate the expressions of the charges for the A2-theory more explicitly. First we
+notice that the second equation in (2.2) is simply solved by taking q = (q1, q2, q3), so that
+we obtain ˙qi = pi when the roots are represented as α1 = (1, −1, 0), α2 = (0, 1, −1) and
+α0 = −α1 − α2 = (−1, 0, 1). This is the standard three dimensional representation for the
+A2-roots, see for instance [14]. The charges (2.3)-(2.6) then acquire the form
+Q1 = p1 + p2 + p3,
+(2.10)
+Q2 = H = 1
+2
+�
+p2
+1 + p2
+2 + p2
+3
+�
++ V12 + V23 + V31 =
+3
+�
+i=1
+�p2
+i
+2 + eαi·q
+�
+,
+(2.11)
+Q3 = 1
+3
+�
+p3
+1 + p3
+2 + p3
+3
+�
++ p1 (V12 + V31) + p2 (V12 + V23) + p3 (V23 + V31) + 2, (2.12)
+=
+3
+�
+i=1
+�p3
+i
+3 + pi (eαi·q + eαi−1·q)
+�
++ 2,
+(2.13)
+Q4 = Q1Q3 − 1
+2Q2
+1Q2 + 1
+24Q4
+1 + 1
+2Q2
+2,
+(2.14)
+– 4 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+where we introduced the new abbreviation Vij := exp(qi −qj). We notice that only the first
+three conserved quantities are independent, as Q4 can be constructed from combinations
+of them. In fact, this property will persist for higher charges and all Qi for i > 3 can be
+build from combinations of Q1, Q2 and Q3.
+Moreover, one may easily verify that the charges Q1, Q2 and Q3 are in involution, i.e.
+their mutual Poisson brackets vanish
+{Qi, Qj} :=
+3
+�
+k=1
+∂Qi
+∂qk
+∂Qj
+∂pk
+− ∂Qi
+∂pk
+∂Qj
+∂qk
+= 0,
+for i, j = 1, 2, 3.
+(2.15)
+As indicated in (2.11), at first we identify as usual the charge Q2 with the standard Hamil-
+tonian so that the classical equations of motion resulting from Hamilton’s equations to
+˙q1 = p1,
+˙q2 = p2,
+˙q3 = p3
+˙p1 = V31 − V12,
+˙p2 = V12 − V23,
+˙p3 = V23 − V31, (2.16)
+which are identical to the equations resulting from the Lax pair equation (2.2).
+In the first instance we solve these equations numerically.
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+x1(t)
+-1.0
+-0.5
+0.5
+1.0
+p1(t)
+(a)
+t=0
+t=0.5
+t=50
+t=100
+t=150
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+x1(t)
+-1.0
+-0.5
+0.5
+1.0
+p1(t)
+(b)
+t=200
+t=250
+t=299.5
+t=300
+t=150
+200
+400
+600
+800
+t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+x1
+200
+400
+600
+800
+t
+-1.0
+-0.5
+0.5
+1.0
+p1
+Figure 1: Phase space (x1, p1) for the A2-affine Toda lattice Hamiltonian with three particles.
+Panel (a): inward spiralling trajectories from time t = 0 to t = 150. Panel (b): outward spiralling
+trajectories from time t = 150 to t = 300. The initial conditions are taken as x1(0) = x2(0) =
+x3(0) = 0, p1(0) = 1 and p2(0) = p3(0) = −1/2. The insets in panel (b) show x1 and p1 as functions
+of time t.
+In figure 1 we depict the solutions to the three particle equations of motion (2.16)
+in phase space, observing confined orbits that periodically spiral inward and outward, a
+behaviour that continues beyond the time shown in the figure. The insets in figure 1 panel
+(b) demonstrate how the small period τ s ≈ 1.778 is modulated by a larger period τ l ≈ 300.2,
+with τ s governing the quasiperiodic elliptic motion and τ l the period of the inward/outward
+pulsation. We stress here that after each period we observe a small offset and therefore
+these solutions are not exactly periodic and only quasiperiodic, i.e. f(x + τ) = g(x, f(x))
+with g being a simpler function than f or almost periodic in the sense of [15]. Almost
+periodic is here to be understood in the sense that we have a small offset after one period,
+i.e. |f(t) − f(t + τ)| ≤ ε. We may adapt these observations more rigorously to the strict
+sense of the definition of almost periodic functions by H. Bohr [15] and adjust the values
+– 5 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+of τ H for a pre-selected ϵ. For the other directions in phase space (x2, p2) and (x3, p3) we
+obtain similar types of periodic behaviour.
+Now we come to the key point in this approach and interpret the higher charges as
+Hamiltonians following the suggestion in [7, 8]. Thus we take here the charge Q3 as the
+Hamiltonian.
+Deriving the new set of equations of motion from ˙qi = ∂Q3/∂pi, ˙pi =
+−∂Q3/∂qi we obtain
+˙q1 = p2
+1 + V12 + V31,
+˙p1 = (p1 + p3)V31 − (p1 + p2)V12,
+(2.17)
+˙q2 = p2
+2 + V12 + V23,
+˙p2 = (p1 + p2)V12 − (p2 + p3)V23,
+(2.18)
+˙q3 = p2
+3 + V23 + V31,
+˙p3 = (p2 + p3)V23 − (p1 + p3)V31,
+(2.19)
+which are identical to the equations previously considered in [7]. Once more we solve these
+equations, (2.17)-(2.19), numerically and depict the solutions in figure 2.
+5
+10
+15
+20
+25
+xi(t)
+-1.0
+-0.5
+0.5
+1.0
+pi(t)
+(a)
+t=0
+t=0
+t=5
+t=5
+t=10
+t=10
+i = 3
+i = 2
+i = 1
+2
+4
+6
+8
+10 t
+5
+10
+15
+20
+25
+xi
+(b)
+20
+40
+60
+80
+100t
+-1.0
+-0.5
+0.5
+1.0
+pi
+(c)
+Figure 2: Panel (a): Phase space (xi, pi), i = 1, 2, 3 for the A2-affine Toda lattice with unrestricted
+Q3-Hamiltonian, with initial conditions x1(0) = x2(0) = x3(0) = 0, p1(0) = 1 and p2(0) = p3(0) =
+−1/2. Panel (b) and (c): xi and pi as functions of time t, respectively.
+We observe that while the momenta are bounded as −1 ≤ pi ≤ 1, the coordinate
+components xi grow linearly in time so that the trajectories do not close in phase space.
+Thus this system appears to have malevolent ghosts. However, this is due to the fact that
+we have treated the A2-system as a three rather than a two particle system. In the next
+section we will represent the roots in a lower dimensional space and consequently re-define
+the coordinates and momenta of the model in the dual space. The effect will be that the
+trajectories become confined and quasi-oscillatory in phase space so that we can say that
+the ghosts have become benign.
+2.2 Higher derivative Hamiltonians from the 2 particle A2-affine Toda lattice
+We will now constrain the (3 × 3)-dimensional phase space to a (2 × 2)-dimensional one.
+Recalling that root systems are isomorphic to each other as long as they reproduce the
+same Cartan matrix Kij = 2αiαj/α2
+j we may achieve this by defining a new set of simple
+– 6 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+roots βi in a two-dimensional representation through an orthogonal transformation that
+preserve K of the A2 root system obtained from the roots αi in the standard representation.
+This means we have to solve
+Kij = αi · αj = Aβi · Aβj = βi · βj =
+�
+2 −1
+−1 2
+�
+ij
+,
+βi = A−1αi, A−1 = A⊺, i, j = 1, 2,
+(2.20)
+for the orthogonal matrix A and the roots βi. We find the solutions
+A =
+�
+�
+�
+�
+1
+√
+6
+1
+√
+2
+1
+√
+3
+−
+�
+2
+3
+0
+1
+√
+3
+1
+√
+6
+− 1
+√
+2
+1
+√
+3
+�
+�
+�
+� ,
+β1 =
+��
+3
+2, 1
+√
+2, 0
+�
+β2 =
+�
+−
+�
+3
+2, 1
+√
+2, 0
+�
+.
+(2.21)
+The negative of the highest root is therefore β0 = −β1 − β2 = (0, −
+√
+2, 0).
+Having reduced the dimension of the representation space for the roots from 3 to 2,
+we shift this reduction now to the dual space of the roots, i.e. the coordinates and the
+momenta. For this we define a new set of dynamical variables (ζ, η) in the dual space of
+the roots by
+αi · q = Aβi · Aζ = βi · ζ,
+for
+ζ = A−1q, i = 1, 2,
+(2.22)
+αi · p = Aβi · Aη = βi · η,
+for
+η = A−1p, i = 1, 2.
+(2.23)
+With A as identified in (2.21) we have
+q =
+�
+ζ1
+√
+6 + ζ2
+√
+2, −
+�
+2
+3ζ1, ζ1
+√
+6 − ζ2
+√
+2
+�
+= (q1, q2, q3),
+(2.24)
+p =
+�
+η1
+√
+6 + η2
+√
+2, −
+�
+2
+3η1, η1
+√
+6 − η2
+√
+2
+�
+= (p1, p2, p3),
+(2.25)
+or when inverted
+ζ =
+�q1 − 2q2 + q3
+√
+6
+, q1 − q3
+√
+2
+, q1 + q2 + q3
+√
+3
+�
+= (ζ1, ζ2, 0),
+(2.26)
+η =
+�p1 − 2p2 + p3
+√
+6
+, p1 − p3
+√
+2
+, p1 + p2 + p3
+√
+3
+�
+= (η1, η2, 0).
+(2.27)
+From the last component in (2.26) and (2.27) we observe that we can interpret the new
+(2 × 2)-dimensional phase space (ζ, η) as the old (3 × 3)-dimensional phase space (q, p) in
+the centre of mass frame with additional constraints. We stress that this property is not
+imposed, but the conditions q1 +q2 +q3 = 0 and p1 +p2 +p3 = 0 are automatically satisfied
+with the definitions of the new variables in (2.24), which in turn results from representing
+the roots in a lower dimensional space.
+The conserved quantities Q1, Q2, Q3 in (2.10)-(2.12) can now also be transformed to
+the new variables as
+Q1 = 0,
+Q2 = H(ζ, η) = 1
+2
+�
+η2
+1 + η2
+2
+�
++ e−
+√
+2ζ2 + 2e
+ζ2
+√
+2 cosh
+��
+3
+2ζ1
+�
+,
+(2.28)
+– 7 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Q3 =
+η1
+�
+6e−
+√
+2ζ2 − η2
+1 + 3η2
+2
+�
+3
+√
+6
+−
+√
+2e
+ζ2
+√
+2
+�
+η1
+√
+3 cosh
+��
+3
+2ζ1
+�
+− η2 sinh
+��
+3
+2ζ1
+��
++ 2.
+The equations of motion resulting from the standard Hamiltonian H(ζ, η) become
+˙ζ1 = η1,
+˙ζ2 = η2,
+(2.29)
+˙η1 = −
+√
+6e
+ζ2
+√
+2 sinh
+��
+3
+2ζ1
+�
+,
+˙η2 =
+√
+2e−
+√
+2ζ2
+�
+1 − e
+3ζ2
+√
+2 cosh
+��
+3
+2ζ1
+��
+,
+(2.30)
+whereas the equations resulting from taking Q3(ζ, η) interpreted as the Hamiltonian are
+˙ζ1 =
+2e−
+√
+2ζ2 − 2e
+ζ2
+√
+2 cosh
+��
+3
+2ζ1
+�
+− η2
+1 + η2
+2
+√
+6
+,
+(2.31)
+˙ζ2 =
+√
+2e
+ζ2
+√
+2 sinh
+��
+3
+2ζ1
+�
++
+�
+2
+3η1η2,
+(2.32)
+˙η1 = e
+ζ2
+√
+2
+�
+η1 sinh
+��
+3
+2ζ1
+�
+−
+√
+3η2 cosh
+��
+3
+2ζ1
+��
+,
+(2.33)
+˙η2 = 2e−
+√
+2ζ2η1
+√
+3
++ 1
+3e
+ζ2
+√
+2
+�
+√
+3η1 cosh
+��
+3
+2ζ1
+�
+− 3η2 sinh
+��
+3
+2ζ1
+��
+.
+(2.34)
+The phase space trajectories obtained from the standard equations of motion for the Hamil-
+tonian, (2.29) and (2.30), are still confined to a finite region in phase space as seen from
+the numerical solutions figure 3. We may still identify a small period τ H that governs
+-0.5
+0.5
+ζ1(t)
+-1.0
+-0.5
+0.5
+1.0
+η1(t)
+(a)
+0 < t < τH
+τH < t < 48.5
+48.5 < t < 210
+210 < t < 300
+50 100 150 200 250 300 350
+t
+-1.0
+-0.5
+0.5
+1.0
+ζ1,η1
+ζ1
+η1
+-0.5
+0.5
+ζ2(t)
+-1.0
+-0.5
+0.5
+1.0
+η2(t)
+(b)
+0 < t < τH
+τH < t < 48.5
+48.5 < t < 210
+210 < t < 300
+50 100 150 200 250 300 350
+t
+-1.0
+-0.5
+0.5
+1.0
+ζ2,η2
+ζ2
+η2
+Figure 3: Phase spaces (ζi, ηi), i = 1, 2 for the standard Hamiltonian of the reduced two particle
+A2-affine Toda lattice with initial conditions ζ1(0) = ζ2(0) = 0, η1(0) =
+√
+3/2
+√
+2 and η2(0) = 3/2
+√
+2
+(≡ p1(0) = 1, p2(0) = p3(0) = −1/2) for times t = 0 to t = 300 with “almost period” τ H ≈ 3.543.
+The insets in panels (a) and (b) show ζ1, η1 and ζ2, η2 as functions of time, respectively.
+one turn, up to a small displacement, and a larger period controlling the inward/outward
+motion.
+– 8 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+In figure 4 we depict the numerical solutions to the equations (2.31) - (2.34) obtained
+as equations of motions from the third order derivative Q3-Hamiltonian. We determine an
+almost period τ Q for the small intersecting almost closed loops. The larger period now
+governs the rotation of these loops that due to the repeated offset fill in the phase space
+regions that appear to be identical to the regions identified for the Hamiltonian H.
+-0.5
+0.5
+ζ1(t)
+-1.0
+-0.5
+0.5
+1.0
+η1(t)
+(a)
+0 < t < τQ
+τQ < t < 72
+72 < t < 144
+144 < t < 216
+50 100 150 200 250 300 350
+t
+-1.0
+-0.5
+0.5
+1.0
+ζ1,η1
+ζ1
+η1
+-0.5
+0.5
+ζ2(t)
+-1.0
+-0.5
+0.5
+1.0
+η2(t)
+(b)
+0 < t < τQ
+τQ < t < 72
+72 < t < 144
+144 < t < 216
+50 100 150 200 250 300 350
+t
+-1.0
+-0.5
+0.5
+1.0
+ζ2,η2
+ζ2
+η2
+Figure 4: Phase space (ζi, ηi), i = 1, 2 for the Q3-Hamiltonian of the reduced two particle A2-Toda
+lattice with initial conditions ζ1(0) = ζ2(0) = 0, η1(0) =
+√
+3/2
+√
+2 and η2(0) = 3/2
+√
+2 for times
+t = 0 to t = 216 with τ Q ≈ 3.347. The insets in panels (a) and (b) show ζ1, η1 and ζ2, η2 as
+functions of time, respectively.
+Thus while the trajectories resulting from the three and two particle A2-Hamiltonians
+are all confined in phase space, this behaviour is different for those derived from the higher
+Q3-charge where only the trajectories for the reduced model are confined. The divergent
+behaviour was already reported in [7], where it was also conjectured that in the centre
+of mass system convergence might be achieved. Here we have shown explicitly that this
+conjecture is partially correct, in the sense that the system can be interpreted as being in
+the centre of mass, but the more accurate statement is to view the system as the reduction
+from three to two particles along the change of the dimensions of the representation space of
+the roots. One should say that the two particle picture of the A2-theory is the more natural
+one as for instance also in the closely related affine Toda quantum field theory the number
+of particles always equals the rank of the semi-simple Lie algebra [16,17]. The mismatch
+between rank and particles simply results form the higher dimensional representation space
+of the simple roots. In [18] a similar reduction procedure was carried out by imposing
+additional constraints in order to “exorcise” Ostrogradski’s ghosts.
+One may view the
+centre-of-mass condition as such a constraint, although here we have not employed Lagrange
+multipliers is to implement them.
+2.3 Higher derivative Hamiltonians from the A6-affine Toda lattice
+Next we consider a system that possesses more than one higher charge. Specifying the
+general Lax operator in (2.1) to n = 6 and computing the traces over the products of this
+operator we calculate the seven independent charges (2.3)-(2.9). For the seven particle
+system with the roots taken in the fundamental representation we obtain the explicit ex-
+– 9 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+pressions for the charges by replacing W 2
+i → Vi,i+1. For instance, when taking all the roots
+in the standard representation the Hamiltonian acquires the form
+H = 1
+2
+7
+�
+i=1
+p2
+i +
+6
+�
+i=1
+eqi−qi+1 + eq7−q1,
+(2.35)
+with α7 taken as the negative of the highest root. We also convince ourselves that all
+mutual Poisson brackets vanish.
+We proceed now as for the A3-system by interpreting all of the charges as Hamiltonians
+and solve their respective Hamilton’s equations. For the seven particle system we find
+periodic solutions for the momenta and coordinates in the phase space of the standard
+Hamiltonian, as seen in figure 5. However, for all higher charges only the momenta remain
+periodic whereas the coordinates diverge. In figure 5 we present as sample solution for the
+phase space of the higher charges the one for the Q6-charge. In panel (d) we observe the
+divergence of all coordinates. This characteristic behaviour is shared by the solutions for
+all the other higher charge Hamiltonians which we do not represent here.
+Similarly as for the A2-case, we attempt to eliminate the divergence by reducing the
+number of particles to the rank, that is from seven to six. For this purpose we solve the
+analogue to the equation (2.20) with the A6-Cartan matrix instead. Taking the α-roots in
+the standard representation we find an orthogonal matrix as
+A =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+1
+√
+6
+1
+√
+2
+1
+2
+√
+3 −
+1
+2
+√
+5 −
+1
+√
+42 −
+1
+√
+30 − 1
+√
+7
+−
+�
+2
+3
+0
+1
+2
+√
+3 −
+1
+2
+√
+5 −
+1
+√
+42 −
+1
+√
+30 − 1
+√
+7
+1
+√
+6
+− 1
+√
+2
+1
+2
+√
+3 −
+1
+2
+√
+5 −
+1
+√
+42 −
+1
+√
+30 − 1
+√
+7
+0
+0
+−
+√
+3
+2 −
+1
+2
+√
+5 −
+1
+√
+42 −
+1
+√
+30 − 1
+√
+7
+0
+0
+0
+2
+√
+5
+−
+1
+√
+42 −
+1
+√
+30 − 1
+√
+7
+0
+0
+0
+0
+−
+1
+√
+42
+�
+5
+6
+− 1
+√
+7
+0
+0
+0
+0
+�
+6
+7
+0
+− 1
+√
+7
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+,
+(2.36)
+together with the new six dimensional roots βi = A−1αi
+β1 =
+��
+3
+2,
+1
+√
+2, 0, 0, 0, 0, 0
+�
+,
+β2 =
+�
+−
+�
+3
+2,
+1
+√
+2, 0, 0, 0, 0, 0
+�
+,
+β3 =
+�
+1
+√
+6, − 1
+√
+2,
+2
+√
+3, 0, 0, 0, 0
+�
+,
+β4 =
+�
+0, 0, −
+√
+3
+2 , −
+√
+5
+2 , 0, 0, 0
+�
+,
+β5 =
+�
+0, 0, 0,
+2
+√
+5, 0, −
+�
+6
+5, 0
+�
+,
+β6 =
+�
+0, 0, 0, 0, −
+�
+7
+6,
+�
+5
+6, 0
+�
+.
+(2.37)
+The corresponding coordinate transformations resulting from this are
+q = (q1, q2, q3, q4, q5, q6, q7)
+(2.38)
+=
+�
+ζ1
+√
+6 + ζ2
+√
+2 + ζ3
+2
+√
+3 − ζ4
+2
+√
+5 − ζ5
+√
+42 − ζ6
+√
+30, −
+�
+2
+3ζ1 + ζ3
+2
+√
+3 − ζ4
+2
+√
+5 − ζ5
+√
+42 − ζ6
+√
+30,
+ζ1
+√
+6 − ζ2
+√
+2 + ζ3
+2
+√
+3 − ζ4
+2
+√
+5 − ζ5
+√
+42 − ζ6
+√
+30, −1
+2
+√
+3ζ3 − ζ4
+2
+√
+5 − ζ5
+√
+42 − ζ6
+√
+30,
+2ζ4
+√
+5 − ζ5
+√
+42 − ζ6
+√
+30,
+�
+5
+6ζ6 − ζ5
+√
+42,
+�
+6
+7ζ5
+�
+,
+– 10 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+and
+ζ = (ζ1, ζ2, ζ3, ζ4, ζ5, ζ6, 0)
+(2.39)
+=
+�q1 − 2q2 + q3
+√
+6
+, q1 − q3
+√
+2
+, q1 + q2 + q3 − 3q4
+2
+√
+3
+, −q1 + q2 + q3 + q4 − 4q5
+2
+√
+5
+,
+−q1 + q2 + q3 + q4 + q5 + q6 − 6q7
+√
+42
+, −q1 + q2 + q3 + q4 + q5 − 5q6
+√
+30
+, −
+�7
+i=1 qi
+√
+7
+�
+.
+Since the last entry for ζ in (2.39) is zero, we note that once again the new coordinates
+transform the old ones to the centre-of-mass frame. The momenta are transformed in the
+same way, with pi → ηi. The Hamiltonian now acquires the form
+H = 1
+2
+6
+�
+i=1
+η2
+i + e
+ζ2−
+√
+3ζ1
+√
+2
++ e
+√
+3ζ1+ζ2
+√
+2
++ e
+ζ1
+√
+6 − ζ2
+√
+2 + 2ζ3
+√
+3 + e− 1
+2
+√
+3ζ3−
+√
+5ζ4
+2
+(2.40)
++e
+�
+5
+6 ζ6−
+�
+7
+6 ζ5 + e
+2ζ4−
+√
+6ζ6
+√
+5
++ e
+1
+30(−5
+√
+6ζ1−15
+√
+2ζ2−5
+√
+3ζ3+3
+√
+5ζ4+5
+√
+42ζ5+
+√
+30ζ6).
+In this reduced space all trajectories become benign as we observe in figure 6. We recognise
+once more that each of the solutions is made up of superposition of various quasi/almost
+periodic functions.
+50
+100
+150
+200t
+-0.5
+0.5
+pi
+(a)
+p1(t)
+p2(t)
+p3(t)
+p4(t)
+p5(t)
+p6(t)
+p7(t)
+50
+100
+150
+200t
+-0.4
+-0.2
+0.2
+0.4
+qi
+(b)
+q1(t)
+q2(t)
+q3(t)
+q4(t)
+q5(t)
+q6(t)
+q7(t)
+10
+20
+30
+40 t
+-0.5
+0.5
+pi
+(c)
+p1(t)
+p2(t)
+p3(t)
+p4(t)
+p5(t)
+p6(t)
+p7(t)
+10
+20
+30
+40 t
+-3
+-2
+-1
+qi
+(d)
+q1(t)
+q2(t)
+q3(t)
+q4(t)
+q5(t)
+q6(t)
+q7(t)
+Figure 5: A6-affine Toda lattice phase spaces as functions of time t of the Hamiltonian, panels (a),
+(b), and the Q6-charge Hamiltonian,panels (c), (d), with seven particles. The initial conditions are
+taken in both cases as qi = 0, i = 1, . . . , 7 and p1 = −p2 = p3 = −p4 = p5 = −2p6 = 2p7 = −1/2.
+Thus all five higher charges of the A6-affine Toda lattice theory when interpreted as
+Hamiltonians for a six particle system possess benign solutions of oscillatory type in their
+classical phase spaces.
+– 11 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+50
+100
+150
+200t
+-2
+-1
+1
+2
+ηi
+(a)
+η1(t)
+η2(t)
+η3(t)
+η4(t)
+η5(t)
+η6(t)
+50
+100
+150
+200t
+-2
+-1
+1
+2
+ζi
+(b)
+ζ1(t)
+ζ2(t)
+ζ3(t)
+ζ4(t)
+ζ5(t)
+ζ6(t)
+10
+20
+30
+40 t
+-2
+-1
+1
+2
+ηi
+(c)
+η1(t)
+η2(t)
+η3(t)
+η4(t)
+η5(t)
+η6(t)
+10
+20
+30
+40 t
+-2
+-1
+1
+2
+ζi
+(d)
+ζ1(t)
+ζ2(t)
+ζ3(t)
+ζ4(t)
+ζ5(t)
+ζ6(t)
+Figure 6: A6-affine Toda lattice phase spaces as functions of time t of the Hamiltonian, panels
+(a), (b), and the Q6-charge Hamiltonian, panels (c), (d), with six particles. The initial conditions
+are taken in both cases as ζi = 0, i = 1, . . . , 6 and η1 = η2 = η3 = −3/
+√
+6, η2 = η4 = η6 = 3/2
+√
+2.
+3. Higher derivative Hamiltonians from the B3 affine Toda lattice
+Many physical systems based on non-simply laced algebras display quite different behaviour
+from those based on simply laced ones. To find out whether this also holds for higher order
+derivative theories we will also investigate some sample representative theories based on
+non-simply laced algebras. We first recall how to obtain the latter.
+3.1 Reduction of the root spaces and charges
+It is well known that non-simply laced Lie algebras can be obtained from a folding proce-
+dure of the associated Dynkin diagrams for a simply laced Lie algebra along a non-trivial
+automorphism [19–22]. Here we use a reduction from the A6 root space ∆A6 to the B3 root
+space ˆ∆B3 with a subsequent reduction to the G2 root space ˜∆G2 previously constructed
+in [22]. Denoting the corresponding simple roots as αi ∈ ∆A6, i = 1, . . . , 6, ˆαi ∈ ˆ∆B3,
+i = 1, 2, 3 and ˜αi ∈ ˜∆G2, i = 1, 2 we define the following reduction maps and their inverses
+ω : ∆A6 → ˆ∆B3,
+αi �→ ω(αi) =
+�
+ˆαi
+for i = 1, 2, 3
+ˆα7−i
+for i = 4, 5, 6 ,
+(3.1)
+ω−1 : ˆ∆B3 → ∆A6,
+ˆαi �→ ω−1(ˆαi) = αi + α7−i
+for i = 1, 2, 3,
+(3.2)
+ˆω : ˆ∆B3 → ˜∆G2,
+ˆαi �→ ˆω(ˆαi) =
+�
+˜α1
+for i = 1, 3
+˜α2
+for i = 2
+,
+(3.3)
+– 12 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+ˆω−1 : ˜∆G2 → ˆ∆B3,
+˜αi �→ ˜ω−1(˜αi) =
+�
+ˆα1 + 2ˆα3
+for i = 1
+3ˆα1
+for i = 2 .
+(3.4)
+One may verify that the roots involved reproduce the respective Cartan matrices. The
+associated charges are then reduced by the appropriate actions of the coordinates and
+momenta according to
+QA6
+n (q, p) → ˆQB3
+n (ˆq, ˆp) = QA6
+n [ω−1(ˆq), ω−1(ˆp)] → ˜QG2
+n (˜q, ˜p) = ˆQB3
+n [˜ω−1(˜q), ˜ω−1(˜p)].
+(3.5)
+We will employ the root systems from above, but will construct the G2-charges in a different
+manner. Let us now see in detail how the consecutive steps are carried out.
+3.2 Higher derivative Hamiltonians from B3 affine Toda lattice theory
+In order to define the reduced charges according to equation (3.5) we expand the coordinates
+of the B3-system as ˆq = ˆq1ˆα1 + (ˆq1 + ˆq2)ˆα2 + (ˆq1 + ˆq2 + ˆq3)ˆα3 and compute ω−1(ˆq) using
+the defining relation for this map in (3.2). We expand the momenta in a similar fashion.
+Representing the A6-roots in the standard seven dimensional Euclidean space as specified
+in section 2.2, we obtain in this manner the reduction of the coordinates and momenta
+q → ω−1(ˆq) = (ˆq1, ˆq2, ˆq3, 0, −ˆq3, −ˆq2, −ˆq1),
+(3.6)
+p → ω−1(ˆp) = (ˆp1, ˆp2, ˆp3, 0, −ˆp3, −ˆp2, −ˆp1),
+(3.7)
+respectively.
+We notice that when employing the new phase space variables we obtain
+another solutions of the second equation in Lax pair equations (2.2) with ˆpi = (ˆxi)t for
+i = 1, 2, 3. It is easily seen from (2.3)-(2.9) that with the replacements (3.6) and (3.7) the
+charges of odd order vanish
+Q1 → ˆQ1 = 0,
+Q3 → ˆQ3 = 0,
+Q5 → ˆQ5 = 0,
+(3.8)
+and the remaining B3-charges acquire the forms
+Q2 → ˆQ2 = ˆH =
+3
+�
+i=1
+ˆp2
+i + 2eˆq1−ˆq2 + 2eˆq2−ˆq3 + 2eˆq3 + e−2ˆq1
+(3.9)
+=
+3
+�
+i=1
+ˆp2
+i +
+3
+�
+i=1
+2eˆαi·ˆq + e−(ˆγ+ˆα1)·ˆq
+(3.10)
+Q4 → ˆQ4 = ˆp4
+1
+2 + ˆp4
+2
+2 + ˆp4
+3
+2 + ˆp2
+1e−2ˆq1 + 2ˆp2
+1eˆq1−ˆq2 + 2ˆp2ˆp1eˆq1−ˆq2 + 2ˆp2
+2eˆq1−ˆq2
+(3.11)
++2ˆp2
+3eˆq2−ˆq3 + 2ˆp2
+3eˆq3 + 2ˆp2ˆp3eˆq2−ˆq3 + 1
+2e−4ˆq1 + e2ˆq1−2ˆq2 + 2e−ˆq1−ˆq2 + 2eˆq2
++e2ˆq2−2ˆq3 + 2ˆp2
+2eˆq2−ˆq3 + 2eˆq1−ˆq3 + 2e2ˆq3
+Q6 → ˆQ6 = ˆp6
+1
+3 + ˆp6
+2
+3 + ˆp6
+3
+3 + 1
+3e−6ˆq1 + 2eˆq1 + 2e−3ˆq1−ˆq2 + 2
+3e3(ˆq1−ˆq2) + 2
+3e3(ˆq2−ˆq3)
+(3.12)
++ˆp4
+1e−2ˆq1 + ˆp2
+1
+�
+e−4ˆq1 + 4e−ˆq1−ˆq2 + 3e2(ˆq1−ˆq2)�
++ ˆp2ˆp1
+�
+2e−ˆq1−ˆq2 + 4e2(ˆq1−ˆq2)�
++2ˆp4
+3eˆq3 + ˆp2
+2
+�
+2e−ˆq1−ˆq2 + 3e2(ˆq1−ˆq2) + 2eˆq2 + 3e2(ˆq2−ˆq3)�
++ ˆp2ˆp3
+�
+4eˆq2 + 4e2(ˆq2−ˆq3)�
++2
+�
+ˆp4
+1 + ˆp2ˆp3
+1 + ˆp2
+2ˆp2
+1 + ˆp3
+2ˆp1 + ˆp4
+2
+�
+eˆq1−ˆq2 + 2
+�
+ˆp4
+2 + ˆp3ˆp3
+2 + ˆp2
+3ˆp2
+2 + ˆp3
+3ˆp2 + ˆp4
+3
+�
+eˆq2−ˆq3
++2
+�
+ˆp2
+1 + (2ˆp2 + ˆp3) ˆp1 + 3ˆp2
+2 + ˆp2
+3 + 2ˆp2ˆp3
+�
+eˆq1−ˆq3 + ˆp2
+3
+�
+6eˆq2 + 3e2(ˆq2−ˆq3) + 4e2ˆq3�
+– 13 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
++3e−2ˆq2 + 2eˆq1+ˆq2−2ˆq3 + 2e−ˆq1−ˆq3 + 2e2ˆq1−ˆq2−ˆq3 + 2e2ˆq2−ˆq3 + 8
+3e3ˆq3 + 4eˆq2+ˆq3
+Here ˆγ is the highest root ˆγ = ˆα1 + 2ˆα2 + 2ˆα3 in ˆ∆B3. We notice that unlike for the An-
+case the number of particles already matches the rank of B3 in the standard representation
+ˆα1 = (1, −1, 0), ˆα2 = (0, 1, −1) and ˆα3 = (0, 0, 1).
+-0.2
+-0.1
+0.1
+0.2q
+1
+-0.3
+-0.2
+-0.1
+0.1
+0.2
+0.3
+p
+1
+(a)
+0 < t < τH
+τH < t < 5 τH
+5 τH < t < 10 τH
+10 τH < t < 15 τH
+100
+200
+300
+400 t
+-0.2
+-0.1
+0.1
+0.2
+q
+1
+(a1)
+100
+200
+300
+400 t
+-0.10
+-0.05
+0.05
+0.10
+q
+2
+(a3)
+100
+200
+300
+400 t
+-0.2
+-0.1
+0.1
+0.2
+q
+3
+(a5)
+100
+200
+300
+400 t
+-0.3
+-0.2
+-0.1
+0.1
+0.2
+0.3
+p
+1
+(a2)
+100
+200
+300
+400 t
+-0.2
+-0.1
+0.1
+0.2
+p
+2
+(a4)
+100
+200
+300
+400 t
+-0.3
+-0.2
+-0.1
+0.1
+0.2
+0.3
+p
+3
+(a6)
+-0.4
+-0.2
+0.2
+0.4
+q
+1
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+p
+1
+(b)
+0 < t < τQ4
+τQ4 < t < 5 τQ4
+5 τQ4 < t < 10 τQ4
+10 τQ4 < t < 30 τQ4
+20
+40
+60
+80
+100
+120
+140
+t
+-0.2
+0.2
+0.4
+q
+1
+(b1)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.4
+-0.2
+0.2
+0.4q
+2
+(b3)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.4
+-0.2
+0.2
+0.4
+q
+3
+(b5)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6p
+1
+(b2)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.4
+-0.2
+0.2
+0.4
+p
+2
+(b4)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+p
+3
+(b6)
+-0.5
+0.5
+1.0q
+1
+-1.0
+-0.5
+0.5
+1.0
+p
+1
+(c)
+0 < t < τQ6
+τQ6 < t < 10 τQ6
+10 τQ6 < t < 20 τQ6
+20 τQ6 < t < 30 τQ6
+10
+20
+30
+40
+50
+60 t
+-0.5
+0.5
+1.0q
+1
+(c1)
+10
+20
+30
+40
+50
+60 t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+q
+2
+(c3)
+10
+20
+30
+40
+50
+60 t
+-0.5
+0.5
+q
+3
+(c5)
+10
+20
+30
+40
+50
+60 t
+-1.0
+-0.5
+0.5
+1.0
+p
+1 (c2)
+10
+20
+30
+40
+50
+60 t
+-1.0
+-0.5
+0.5
+1.0p
+2
+(c4)
+10
+20
+30
+40
+50
+60 t
+-1.0
+-0.5
+0.5
+1.0
+p
+3
+(c6)
+Figure 7: Affine B3-Toda lattice phase space (ˆq1, ˆp1), as function of t for the standard Hamiltonian
+in panel (a), for Q4 taken as higher derivative Hamiltonian in panel (b) and for Q6 taken as higher
+derivative Hamiltonian in panel (c). The corresponding functions xi(t) and pi(t) are displayed in
+the respective panels ai, bi, ci for i = 1, . . . , 6. For the initial condition we always chose ˆq1(0) =
+ˆq2(0) = ˆq3(0) = 0 and ˆp1(0) = −0.1, ˆp2(0) = −0.2, ˆp3(0) = 0.3, in panels (a), ˆp1(0) = 0.5,
+ˆp2(0) = ˆp3(0) = −0.25, in panels (b) and ˆp1(0) = 1, ˆp2(0) = ˆp3(0) = −0.5 in panels (c). The
+quasi-periods are: panel (a): τ H ≈ 7.9824, panel (b): τ Q4 ≈ 2.7181, panel (c): τ Q6 ≈ 0.4719.
+– 14 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Again we interpret all charges as Hamiltonians and compute their corresponding phase
+spaces. As depicted in figure 7, all trajectories are benign and are confined in phase space.
+As in this case the dimension of the standard representation already equals the rank
+of the algebra there was no need for a reduction or the imposition of any constraints in
+order to obtain benign trajectories for the higher charge Hamiltonians. Nonetheless, for
+the sake of interest we consider now the reverse scenario and construct a theory in which
+the roots are represented in a larger dimensional space. When drawing on the A2-example
+one might expect malign ghost trajectories in this case, but as we will demonstrate this is
+not the case.
+Thus we solve once more equation (2.20) for the orthogonal matrix A and the four-
+dimensional roots ˆβi reproducing the B3-Cartan matrix
+K =
+�
+�
+�
+2 −1 0
+−1 2 −2
+0 −1 2
+�
+�
+� .
+(3.13)
+We find the four dimensional representation for the roots
+ˆβ1 = (1, 0, 1, 0) ˆβ2 =
+�
+−1
+2,
+√
+3
+2 , −1
+2,
+√
+3
+2
+�
+ˆβ3 =
+�
+0, −2 +
+√
+2
+2
+√
+3 , 0, −2 −
+√
+2
+2
+√
+3
+�
+,
+(3.14)
+together with the orthogonal matrix
+ˆA =
+�
+�
+�
+�
+�
+�
+�
+1
+2
+1−
+√
+2
+2
+√
+3
+1
+2
+1+
+√
+2
+2
+√
+3
+− 1
+2
+1−
+√
+2
+2
+√
+3
+− 1
+2
+1+
+√
+2
+2
+√
+3
+0
+− 2+
+√
+2
+2
+√
+3
+0
+1−
+√
+2
+√
+6
+− 1
+√
+2
+0
+1
+√
+2
+0
+�
+�
+�
+�
+�
+�
+�
+.
+(3.15)
+This in turn leads to the coordinate transformation
+ˆq = (ˆq1, ˆq2, ˆq3, 0) = A( ˆρ1, ˆρ2, ˆρ3, ˆρ4)
+(3.16)
+=
+�
+1
+2ˆρ1 + 1 −
+√
+2
+2
+√
+3 ˆρ2 + 1
+2ˆρ3 + 1 +
+√
+2
+2
+√
+3 ˆρ4, −1
+2ˆρ1 + 1 −
+√
+2
+2
+√
+3 ˆρ2 − 1
+2ˆρ3 + 1 +
+√
+2
+2
+√
+3 ˆρ4,
+−
+√
+2 + 1
+√
+6
+ˆρ2 + −
+√
+2 + 1
+√
+6
+ˆρ4, 1
+√
+2(ˆρ3 − ˆρ1)
+�
+.
+Thus instead of the centre-of-mass constraint �4
+i=1 ρi = 0 we have now the constraint
+ˆρ1 = ˆρ3 as we can read off from the last component in the four dimensional system.
+Indeed, when computing the new coordinates we find precisely this dependence in the first
+and third coordinate
+ˆρ = (ˆρ1, ˆρ2, ˆρ3, ˆρ4) = ˆA−1(ˆq1, ˆq2, ˆq3, 0)
+(3.17)
+= 1
+2
+�
+ˆq1 − ˆq2, 1 −
+√
+2
+√
+3
+(ˆq1 + ˆq2 + ˆq3) + 1
+√
+3 ˆq3, ˆq1 − ˆq2,
+√
+2 + 1
+√
+3
+(ˆq1 + ˆq2 + ˆq3) − 3
+√
+3 ˆq3
+�
+.
+– 15 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+-0.10
+-0.05
+0.05
+0.10
+ρ
+1(t)
+-0.15
+-0.10
+-0.05
+0.05
+0.10
+0.15
+ξ
+
+1(t)
+0<t<τH
+τH<t<5τH
+5τH<t<10τH
+10τH<t<15τH
+a)
+10
+20
+30
+40
+50
+60t
+-0.4
+-0.2
+0.2
+0.4
+ρ
+i(t)
+i=1,3
+i=2
+i=4
+10
+20
+30
+40
+50
+60t
+-0.4
+-0.2
+0.2
+0.4
+ξ
+i(t)
+i=1,3
+i=2
+i=4
+-0.10
+-0.05
+0.05
+0.10
+0.15ρ
+1(t)
+-0.15
+-0.10
+-0.05
+0.05
+0.10
+0.15
+ξ
+
+1(t)
+0<t<τQ4
+τQ4<t<2τQ4
+2τQ4<t<4τQ4
+4τQ4<t<6τQ4
+(b)
+2
+4
+6
+8
+10
+12
+14
+t
+-0.4
+-0.2
+0.2
+0.4
+ρ
+i(t)
+i=1,3
+i=2
+i=4
+2
+4
+6
+8
+10
+12
+14
+t
+-0.4
+-0.2
+0.2
+0.4
+ξ
+i(t)
+i=1,3
+i=2
+i=4
+-0.10
+-0.05
+0.05
+0.10
+0.15ρ
+1(t)
+-0.15
+-0.10
+-0.05
+0.05
+0.10
+0.15
+ξ
+
+1(t)
+0<t<τQ6
+τQ6<t<2τQ6
+2τQ6<t<3τQ6
+3τQ6<t<4τQ6
+(c)
+1
+2
+3
+4
+5 t
+-0.4
+-0.2
+0.2
+0.4
+ρ
+i(t)
+i=1,3
+i=2
+i=4
+1
+2
+3
+4
+5 t
+-0.4
+-0.2
+0.2
+0.4
+ξ
+i(t)
+i=1,3
+i=2
+i=4
+Figure 8: Affine B3-Toda lattice phase space (ˆξ1,ˆ(ρ)1) as fuunctions of t for the standard Hamil-
+tonian panel (a), for Q4 taken as higher derivative Hamiltonian panel (b) and for Q6 taken as
+higher derivative Hamiltonian panel (c). The initial conditions are teken in all cases as ˆρ(0) =
+(0, 0, 0, 0), ˆξ(0) =
+1
+10(1, 2, 1, −4). The quasi-periods are: τ H ≈ 28.80, τ Q4 ≈ 14.99, τ Q6 ≈ 4.103.
+When setting any other component in ˆq to zero we will obtain more complicated depen-
+dencies.
+– 16 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Transforming now also the B3 charges into the new coordinates we proceed as previ-
+ously and compute the classical trajectories numerically. Our results are shown in figure 8.
+The main observation is that all solutions found are benign. Thus unlike for the An cases
+we do not encounter divergencies in the case where the dimension of the root representation
+space does not match the rank of the algebra.
+4. Higher derivative Hamiltonians from the G2-affine Toda lattice
+In order to compare and identify universal features we investigate now also the G2-affine
+Toda lattice theory that is similar to the A2-theory, in the sense that it has a natural three
+and two particle representation, with the former being the standard one. Its Hamiltonian
+in the standard form reads
+˜H = 1
+2 ˜p2 + 3eα1·˜q + 2eα2·˜q + eα0·˜q,
+(4.1)
+where α1 and α2 are the two simple roots of G2 and α0 = −3α1 − 2α2 is the negative of
+the highest G2-root. In order to construct the higher charges we may use the reduction
+from B3 or directly construct a higher order expression from a suitable Ansatz whose
+Poisson bracket vanishes with ˜H. Here we do not use the folding procedure, as for it to
+apply in this case the Lax pair has to be slightly modified, but instead we use the latter
+approach. Taking initially the standard representation for the simple roots α1 = (1, −1, 0)
+and α2 = (−2, 1, 1), [23], we find the non-trivial independent charges
+˜Q1 = ˜p1 + ˜p2 + ˜p3
+(4.2)
+˜Q6 =
+3
+�
+i,j=1
+1
+6 ˜p6
+i + 3
+14(˜p4
+i ˜p2
+i+1 + ˜p2
+i ˜p4
+i+1) + 10
+21 ˜p3
+i ˜p3
+i+1 + 6
+7 ˜pi˜pi+1˜pi+2 + cj
+j3
+7 e3˜αj.˜q
+(4.3)
++njnj+1
+7
+e(˜αj+˜αj+1).˜q �
+c(1)
+j nje˜αj.˜q + c(2)
+j nj+1e˜αj+1.˜q + c(3)
+ij ˜pi˜pj+1 + c(4)
+ij ˜p2
+i
+�
++nj
+7 e˜j.˜q �
+c(5)
+ij ˜p4
+i + c(6)
+ij ˜p2
+i ˜p2
+i+1 + c(7)
+ij ˜p3
+i ˜pi+1 + c(8)
+ij ˜pi˜p3
+i+1 + c(9)
+ij ˜p2
+i ˜pi+1˜pi+2
+�
++
+n2
+j
+7 e2˜αj.˜q �
+c(10)
+ij
+˜p2
+i + c(11)
+ij
+˜pi˜pi+1
+�
+,
+with abbreviations c = (2, 6, 6), c(1) = (6, 18, −18), c(2) = (18, 18, 42),
+c(3) =
+�
+�
+�
+22 −2 −20
+46 −2 40
+10 34
+40
+�
+�
+�,
+c(4) =
+�
+�
+�
+26 26 32
+8 44 32
+14 26 2
+�
+�
+�, c(5) =
+�
+�
+�
+7 7 7
+7 7 7
+3 7 7
+�
+�
+�, c(6) =
+�
+�
+�
+0 2 20
+6 20 2
+6 0
+0
+�
+�
+�,
+c(7) =
+�
+�
+�
+4
+2 −4
+0 −4 8
+10 0
+0
+�
+�
+�,
+c(8) =
+�
+�
+�
+4
+8 −4
+10 −4 2
+0
+0
+0
+�
+�
+�,
+c(9) =
+�
+�
+�
+0
+2
+−16
+0
+−16 −16
+−30 −16
+2
+�
+�
+�,
+c(10) =
+�
+�
+�
+12 13 4
+12 4
+4
+21 4 13
+�
+�
+�,
+c(11) =
+�
+�
+�
+18 8 26
+0 26 8
+0
+8
+8
+�
+�
+�.
+These charge are all in involution with the Hamiltonian ˜H and with each other. We note
+– 17 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+that there is no non-trivial independent charge ˜Q4, as the only quantity that one can
+construct at that order is proportional to ˜H2.
+We solve the corresponding equations of motion for ˜H
+˙˜q1 = p1,
+˙˜q2 = p2,
+˙˜q3 = p3,
+˙˜p1 = 4e−2˜q1+˜q2+˜q3 − 3e˜q1−˜q2 − e˜q1+˜q2−2˜q3
+(4.4)
+˙˜p2 = 3e˜q1−˜q2 − e˜q1+˜q2−2˜q3 − 2e−2˜q1+˜q2+˜q3
+˙˜p3 = 2e˜q1+˜q2−2˜q3 − 2e−2˜q1+˜q2+˜q3
+and ˜Q6, which we will note report here, numerically and depict our results in figure 9.
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+q
+1(t)
+-3
+-2
+-1
+1
+2
+3
+p
+1(t)
+(a)
+0 < t < τH
+τH < t < 15 τH
+15 τH < t < 25 τH
+25 τH < t < 35 τH
+-1.5
+-1.0
+-0.5
+0.5
+q
+2(t)
+-3
+-2
+-1
+1
+2
+3
+p
+2(t)
+(b)
+0 < t < τH
+τH < t < 15 τH
+15 τH < t < 25 τH
+25 τH < t < 35 τH
+-0.5
+0.5
+1.0
+1.5 q
+3(t)
+-3
+-2
+-1
+1
+2
+3
+p
+3(t)
+(c)
+0 < t < τH
+τH < t < 15 τ
+15 τH < t < 25
+25 τH < t < 35
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+q
+1(t)
+-3
+-2
+-1
+1
+2
+3
+p
+1(t)
+(d)
+0 < t < τQ6
+τQ6 < t < 5 τQ6
+5 τQ6 < t < 10 τQ6
+-1.5
+-1.0
+-0.5
+0.5
+q
+2(t)
+-3
+-2
+-1
+1
+2
+3
+p
+2(t)
+(e)
+0 < t < τQ6
+τQ6 < t < 5 τQ6
+5 τQ6 < t < 10 τQ6
+-0.5
+0.5
+1.0
+1.5 q
+3(t)
+-3
+-2
+-1
+1
+2
+3
+p
+3(t)
+(f)
+0 < t < τQ6
+τQ6 < t < 5 τQ6
+5 τQ6 < t < 10 τQ6
+Figure 9: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜qi, ˜pi), 1, 2, 3 as functions
+of t panels (a), (b), (c) and panels (d), (e), (f), respectively. The initial condition are taken in all
+cases to ˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = −1, ˜p2(0) = −2 and ˜p3(0) = 3.
+Once again we identify almost periodic motions from the trajectories in both cases with
+periods numerically computed as τ H ≈ 7.04819143 and τ Q6 ≈ 0.10294605 for the phase
+spaces of ˜H and ˜Q6, respectively. In our concrete solutions for the equations of motion for
+˜H we find |ζ1(0) − ζ1(τ H)| ≈ 2.3 × 10−9, |ζ2(0) − ζ2(τ H)| = |ζ3(0) − ζ3(τ H)| ≈ 0.0229121,
+|η1(0)−η1(τ H)| ≈ 0.0122752, |η2(0)−η2(τ H)| ≈ 0.009117525 and |η3(0)−η3(τ H)| ≈ 0.0031.
+As previously, in our depiction we distinguish between the first almost period and some
+further periods that illustrate how the phase space is gradually filled inward and outwardly.
+Comparing the ˜H and ˜Q6 phase spaces we notice that for large time the same confined
+region in phase space will be filled out.
+Furthermore we notice that, unlike as in the A2-case, even for the case when the
+particle number does not match the rank of the algebra the motion is of a benign nature.
+Thus in principal there is no need for a dimensional reduction to the centre-of-mass
+frame from the point of view to obtain finite trajectories, but for completeness we also
+analyse that case. For this purpose we need to solve once more equation (2.20) for the
+orthogonal matrix A and the two-dimensional roots βi, but now involving the G2-Cartan
+matrix
+K =
+�
+2 −1
+−3 2
+�
+.
+(4.5)
+– 18 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+In this case we find the solutions
+A =
+�
+�
+�
+�
+1
+√
+2
+− 1
+√
+6
+1
+√
+3
+− 1
+√
+2 − 1
+√
+6
+1
+√
+3
+0
+�
+2
+3
+1
+√
+3
+�
+�
+�
+� ,
+β1 =
+�√
+2, 0, 0
+�
+,
+β2 =
+�
+− 3
+√
+2,
+�
+3
+2, 0
+�
+,
+(4.6)
+for the orthogonal matrix and the three dimensional roots.
+-0.5
+0.5
+1.0
+ζ
+1(t)
+-4
+-2
+2
+4
+η
+1(t)
+(a)
+0 < t < τH
+τH < t < 15 τH
+15 τH < t < 25 τH
+25 τH < t < 35 τH
+-1.0
+-0.5
+0.5
+1.0
+1.5
+2.0ζ
+2(t)
+-4
+-2
+2
+4
+η
+2(t)
+(b)
+0 < t < τH
+τH < t < 15 τH
+15 τH < t < 25 τH
+25 τH < t < 35 τH
+-0.5
+0.5
+1.0
+ζ
+1(t)
+-4
+-2
+2
+4
+η
+1(t)
+(c)
+0 < t < τQ6
+τQ6 < t < 5 τQ6
+5 τQ6 < t < 10 τQ6
+-1.0
+-0.5
+0.5
+1.0
+1.5
+2.0ζ
+2(t)
+-4
+-2
+2
+4
+η
+2(t)
+(d)
+0 < t < τQ6
+τQ6 < t < 5 τQ6
+5 τQ6 < t < 10 τQ6
+Figure 10: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜ζi, ˜ηi), 1, 2 as functions
+of t panels (a), (b) and panels (c), (d), respectively. The initial condition are taken in both cases
+as ˜ζ1(0) = ˜ζ2(0) = 0, ˜η1(0) = 3/2
+√
+2 and ˜η2(0) = −
+√
+3/2
+√
+2.
+Then, according to (2.22) and (2.23) the coordinates and momenta transform as
+˜q =
+� ˜ζ1
+√
+2 −
+˜ζ2
+√
+6, −
+˜ζ1
+√
+2 −
+˜ζ2
+√
+6,
+�
+2
+3
+˜ζ2
+�
+= (˜q1, ˜q2, ˜q3),
+(4.7)
+˜p =
+�
+˜η1
+√
+2 − ˜η2
+√
+6, − ˜η1
+√
+2 − ˜η2
+√
+6,
+�
+2
+3˜η2
+�
+= (˜p1, ˜p2, ˜p3),
+(4.8)
+and in reverse as
+˜ζ =
+� ˜q1 − ˜q2
+√
+2
+, − ˜q1 + ˜q2 − 2˜q3
+√
+6
+, ˜q1 + ˜q2 + ˜q3
+√
+3
+�
+= (˜ζ1, ˜ζ2, 0),
+(4.9)
+˜η =
+� ˜p1 − ˜p2
+√
+2
+, − ˜p1 + ˜p2 − 2˜p3
+√
+6
+, ˜p1 + ˜p2 + ˜p3
+√
+3
+�
+= (˜η1, ˜η2, 0).
+(4.10)
+– 19 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Transforming the charges according to (4.9) and (4.10) the equations of motion for the
+Hamiltonian ˜H(˜ζ, ˜η) become
+˙˜ζ1 = ˜η1,
+˙˜ζ2 = ˜η2,
+(4.11)
+˙˜η1 = 3
+√
+2e
+�
+3
+2 ˜ζ2− 3
+√
+2 ˜ζ1 − 3
+√
+2e
+√
+2˜ζ1,
+˙˜η2 =
+√
+6e−
+√
+6˜ζ2 −
+√
+6e
+�
+3
+2 ˜ζ2− 3
+√
+2 ˜ζ1,
+and similarly for the ˜Q6-charge Hamiltonian that we do not report. We solve these equa-
+tions numerically with the results depicted in figure 10. Once more we find almost periodic
+solutions with the same period as in the three dimensional case for all charges.
+Remarkably, for some special initial conditions we can also identify full periodic so-
+lutions. The numerical solutions for the three dimensional case with the special initial
+conditions ˜p2(0) = ˜p3(0) are depicted in figure 11 panel (a). We observe that the periodic
+solutions for i = 2 and i = 3 becoming identical. Moreover, the trajectories for the ˜H
+and ˜Q6 phase spaces coincide. However, as seen in the inlets the periods differ by orders
+of magnitude with τ H ≈ 1.4210841 and τ Q6 ≈ 0.0068228. Similar features are observed
+-0.4
+-0.2
+0.2
+0.4
+0.6q
+i(t)
+-2
+-1
+1
+2
+p
+i(t)
+(a)
+q
+1
+q
+2,3
+p
+1
+p
+2,3
+0.5
+1.0
+1.5
+2.0
+2.5
+-2
+-1
+1
+2
+q
+i,p
+i
+q
+1
+q
+2,3
+p
+1
+p
+2,3
+0.0068
+-2
+-1
+1
+2
+q
+i,p
+i
+q,p
+1
+q/p
+2,3
+-0.4
+-0.2
+0.2
+0.4
+0.6ζ
+i(t)
+-2
+-1
+1
+2
+η
+i(t)
+(b)
+ζ
+
+1
+ζ
+
+2
+η
+1
+η
+2
+0.5
+1.0
+1.5
+2.0
+2.5
+-2
+-1
+1
+2
+ζ i,η
+i
+ζ
+
+1
+ζ
+
+2
+η
+1
+η
+2
+0.0068
+-2
+-1
+1
+2
+ζ
+
+i,η
+i
+ζ
+1,η
+1
+ζ
+2,η
+2
+Figure 11: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜qi, ˜pi), 1, 2, 3 and
+(˜ζi, ˜ηi), 1, 2 as functions of t panel (a) and panel (b), respectively. The initial condition are taken
+in both cases as ˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = 2, ˜p2(0) = ˜p3(0) = −1 and ˜ζ1(0) = ˜ζ2(0) = 0,
+˜η1(0) = 3/
+√
+2 and ˜η2(0) = −
+√
+3/
+√
+2.
+for the dimensionally reduced case depicted in panel (b). The condition ˜p2(0) → ˜p3(0)
+translates into ˜η2(0) → −1/
+√
+3˜η2(0).
+5. Non-integrable perturbations
+5.1 Sensitivity of the initial conditions
+There are various possibilities to investigate the stability of the above benign ghost solu-
+tions. The most delicate way to perturb them is to just vary the initial conditions. So far
+we have always chosen them to be compatible with the centre-of-mass frame conditions
+�
+i pi = 0 and �
+i qi = 0 or other constraints that result from reducing the dimensionality
+of the representation space for the roots. It turns out that in the representations for which
+the dimensions do not match up with the rank of the algebra the trajectories are rather
+sensitive towards these impositions. In figure 12 panels (a) to (c) we see that even a very
+– 20 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+small violation of the condition �3
+i=1 pi = 0 leads to the divergence of the trajectories
+in the xi-directions in the phase spaces even for the Hamiltonians H and ˜H for A2 and
+G2-theories as well as for the ˜Q6-charge of G2. In panels (d) to (f) we observe that the
+trajectories for all independent B3-charges remain benign when �
+i pi ̸= 0. The violation
+of �
+i qi = 0 does not produce this effect.
+50
+100
+150
+200
+250t
+-1
+1
+2
+3
+4
+5
+qi(t)
+(a)
+i=1
+i=2
+i=3
+50
+100
+150
+200
+250t
+-1
+1
+2
+3
+4
+5
+q
+i(t)
+(b)
+0.05
+0.10
+0.15
+0.20
+0.25t
+2
+4
+6
+8
+10
+q
+i(t)
+(c)
+20
+40
+60
+80
+100
+120
+140
+t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+q
+i(t)
+(d)
+i=1
+i=2
+i=3
+20
+40
+60
+80
+100
+120
+140
+t
+-0.4
+-0.2
+0.2
+0.4
+q
+i(t)
+(e)
+10
+20
+30
+40 t
+-0.4
+-0.2
+0.2
+0.4
+q
+i(t)
+(f)
+Figure 12: Three dimensional phase space solutions for the coordinates as functions of t with
+initial conditions �3
+i=1 pi ̸= 0. Panels (a), (b), (c): Manevolent A2-solutions for the Hamiltonian
+H, G2-solutions for the Hamiltonian ˜H and the charge ˜Q6, respectively, all with initial conditions
+˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = −1, ˜p2(0) = −2 ˜p3(0) = 3 + 0.05. Panels (d), (e), (f): Benign
+B3-solutions for the Hamiltonian ˆH and the charge ˆQ4, ˆQ6 respectively, all initial conditions are
+taken to ˆq1(0) = ˆq2(0) = ˆq3(0) = 0, ˆp1(0) = 0.2, ˆp2(0) = −1/2 ˆp3(0) = 1/2.
+-1.0
+-0.5
+0.5
+1.0
+1.5
+2.0
+2.5ζ
+i(t)
+-4
+-2
+2
+4
+η
+i(t)
+(a)
+i=1
+i=2
+-1
+1
+2
+3
+ζ
+i(t)
+-4
+-2
+2
+4
+η
+i(t)
+(b)
+Figure 13: Two-dimensional affine G2-Toda lattice ˜H and ˜Q6 phase spaces (˜ζi, ˜ηi), 1, 2, panels
+(a) and (b) respectively, for perturbed initial conditions as functions of t. The initial conditions are
+taken in both cases as ˜ζ1(0) = ˜ζ2(0) = 0, ˜η1(0) = 1/
+√
+2 and ˜η2(0) = 3
+√
+3/
+√
+2 + 1.
+In contrast the trajectories in the two dimensional phase spaces are rather robust
+against very large perturbations of Q1(0) ̸= 0 as seen in figure 13 panels (a) and (b), where
+we present the G2-case. In this case the divergence would occur in the third component
+– 21 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+that has already been set to zero in the construction. The trajectories may be compared
+to the unperturbed case presented in figure 10.
+5.2 Breaking of the integrability
+There are of course many more options to perturb the higher derivative charge Hamiltonians
+by adding small terms to them or even by deforming with additional terms of the same or
+larger magnitude. Here we only present one example to illustrate the general feature and
+to establish the robustness of some of the higher charge Hamiltonian trajectories. We leave
+a more systematic presentation to future investigations [24]. We consider a Hamiltonian
+in form of a soft deformation of the Q3-charge in the A2-theory in the two-dimensional
+representation (2.28) by adding a two-dimensional harmonic oscillator potential
+Qp
+3 (ζ1, ζ2, η1, η2) = Q3 (ζ1, ζ2, η1, η2) + ϵ1
+2
+�
+ζ2
+1 + ζ2
+2
+�
+.
+(5.1)
+The solutions of the corresponding equations of motion ζi(t), ηi(t) with i = 1, 2 as functions
+of time are depicted in figure 14 for several typical values of ϵ. We still find the previously
+observed superposition of frequencies which vary with ϵ.
+A transition between rather
+different types of qualitative behaviours is seen at ϵc ≈ 0.8944. When approaching this
+value from below the maximal values for ζi(t) and ηi(t) increase smoothly and the functions
+become more localised, but once ϵc is passed these values drop significantly and oscillations
+re-occur. At this point we do not have proper explanation of this behaviour.
+20
+40
+60
+80
+100
+120
+140t
+-0.4
+-0.2
+0.2
+0.4
+ζi
+(a)
+ϵ = -0.3
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+ζi
+(b)
+ϵ = -0.1
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140t
+-1.0
+-0.5
+0.5
+1.0
+ζi
+(c)
+ϵ = 0
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-2
+-1
+1
+2
+ζi
+(d)
+ϵ = 0.1
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-6
+-4
+-2
+2
+4
+6
+ζi
+(e)
+ϵ = 0.3
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-5
+5
+ζi
+(f)
+ϵ = 0.5
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-5
+5
+10
+ζi
+(g)
+ϵ = 0.89
+ζ1(t) ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-1.0
+-0.5
+0.5
+1.0
+ζi
+(h)
+ϵ = 0.9
+ζ1(t)ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-0.5
+0.5
+ζi
+(i)
+ϵ = 1.0
+ζ1(t)ζ2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-0.6
+-0.4
+-0.2
+0.2
+0.4
+0.6
+ζi
+(j)
+ϵ = 1.2
+ζ1(t)ζ2(t)
+20
+40
+60
+80
+100
+120
+140t
+-1.5
+-1.0
+-0.5
+0.5
+1.0
+1.5
+ηi
+(k)
+ϵ = -0.3
+η1(t) η2(t)
+20
+40
+60
+80
+100
+120
+140t
+-1.5
+-1.0
+-0.5
+0.5
+1.0
+1.5
+ηi
+(l)
+ϵ = -0.1
+η1(t) η2(t)
+20
+40
+60
+80
+100
+120
+140t
+-1.5
+-1.0
+-0.5
+0.5
+1.0
+1.5
+ηi
+(m)
+ϵ = 0
+η1(t) η2(t)
+20
+40
+60
+80
+100
+120
+140t
+-2
+-1
+1
+2
+ηi
+(n)
+ϵ = 0.1
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-10
+-5
+5
+10
+ηi
+(o)
+ϵ = 0.3
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-20
+-10
+10
+20
+ηi
+(p)
+ϵ = 0.5
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-40
+-20
+20
+40
+ηi
+(q)
+ϵ = 0.89
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-4
+-2
+2
+4
+ηi
+(r)
+ϵ = 0.9
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-4
+-2
+2
+4
+ηi
+(s)
+ϵ = 1.0
+η1(t)η2(t)
+20
+40
+60
+80
+100
+120
+140 t
+-3
+-2
+-1
+1
+2
+3
+ηi
+(t)
+ϵ = 1.2
+η1(t)η2(t)
+Figure 14: Two-dimensional phase space components ζi and ηi with i = 1, 2 for the deformed
+affine A2-Toda lattice charge Hamiltonian ˜Q3 in (5.1) as functions of time t for different values of
+ϵ. The initial conditions are taken in all cases as ζ1 = ζ2 = 0, η1 = −3/
+√
+6 and η2 = 3/2
+√
+2.
+Naturally there are many more options to break the integrability of these systems [24].
+– 22 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+6. Conclusions
+We investigated many more examples that support the conjecture, originally put forward by
+Smilga [9], that charges of integrable systems provide very promising candidates for higher
+derivative theories that possess benign ghost sectors in part or all of their parameter space.
+For our examples of affine Toda lattice theories associated to different algebras we found
+a multitude of possible scenarios. We demonstrated that proper choice of the dimension
+of the representation space is crucial. Especially for the theories that used roots in their
+formulation represented in the same dimension as the rank of the underlying algebras we
+found benign solutions for higher charge Hamiltonians. Moreover, these solutions were quite
+robust with regard to perturbations of the choice of the initial conditions. When deviating
+from this setup and using higher dimensional representations for the roots we found the
+coordinate solutions diverge as functions of time t for all the An examples investigated.
+However, for the non-simply laced algebras G2 and B3 the trajectories for the higher charge
+Hamiltonians stayed benign even in the higher dimensional cases, with the difference that
+the former where very sensitive to changes of the initial conditions whereas the latter turned
+out to be stable. So far these features remain at the level of observations and we can not
+provide a deeper reason for these types of behaviour. Based on the data generated here so
+far it is too early to extract more generic features that might be shared by some class of
+systems, e.g. simply laced versus non-simply laced etc. We leave these aspects for future
+investigations.
+We have also investigated some more extreme deformations of the integrable systems
+by a soft harmonic oscillator potential in section 5.2. As noted previously for different
+types of perturbations [9] many of the benign trajectories found maintain this feature, but
+we also observed a critical point in the strength ϵ of these additional terms with an extreme
+sensitivity regarding the characteristic behaviour of the phase space trajectories. It seems
+worth to carry out some systematic investigations that clarify which type of perturbations,
+and even deformations, might be permitted in order to maintain the benign nature of the
+solutions [24].
+Our results are summarised in table 1.
+Q (D of rep) \ g
+A2
+G2
+B3
+A6
+A2, p1
+G2, p1
+B3, p1
+A6, p1
+A2, p2
+H (r + 1)
+b
+b
+b
+b
+m
+m
+b
+m
+H (r)
+b
+b
+b
+b
+b
+b
+b
+b
+Q3 (r + 1)
+m
+×
+×
+m
+m
+×
+×
+m
+Q3 (r)
+b
+×
+×
+b
+b
+×
+×
+b
+b
+Q4 (r + 1)
+×
+b
+m
+×
+b
+m
+Q4 (r)
+×
+b
+b
+×
+b
+b
+Q6 (r + 1)
+b
+b
+m
+m
+b
+m
+Q6 (r)
+b
+b
+b
+b
+b
+b
+Table 1:
+Summary of results. (b ≡ benign, m ≡ manevolent, × charge does not exist, r
+≡ rank of g, p1 ≡ perturbation with Q1(0) ̸= 0, p2 ≡ perturbation with harmonic oscillator
+potential)
+– 23 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+Acknowledgments: BT is supported by a City, University of London Research Fellow-
+ship. AF thanks the Instituto de Ciencias F´ısicas y Matem´aticas of the Universidad Austral
+de Chile, where part of this work was completed for kind hospitality and Francisco Correa
+for financial support.
+References
+[1] M. Raidal and H. Veerm¨ae, On the quantisation of complex higher derivative theories and
+avoiding the Ostrogradsky ghost, Nucl. Phys. B 916, 607–626 (2017).
+[2] T. Biswas, T. Koivisto, and A. Mazumdar, Towards a resolution of the cosmological
+singularity in non-local higher derivative theories of gravity, J. Cos. and Astropart. Phys.
+2010(11), 008 (2010).
+[3] S. Mignemi and D. L. Wiltshire, Black holes in higher-derivative gravity theories, Phys. Rev.
+D 46(4), 1475 (1992).
+[4] V. O. Rivelles, Triviality of higher derivative theories, Phys. Lett. B 577(3-4), 137–142
+(2003).
+[5] M. Dine and N. Seiberg, Comments on higher derivative operators in some SUSY field
+theories, Phys. Lett. B 409(1-4), 239–244 (1997).
+[6] A. Smilga, Benign vs. malicious ghosts in higher-derivative theories, Nucl. Phys. B 706(3),
+598–614 (2005).
+[7] A. Smilga, On exactly solvable ghost-ridden systems, Phys. Lett. A 389, 127104 (2021).
+[8] T. Damour and A. Smilga, Dynamical systems with benign ghosts, Phys. Rev. D 105(4),
+045018 (2022).
+[9] A. Smilga, Benign ghosts in higher-derivative systems, in J. of Phys.: Conf. Series, 2038,
+012023 (2021).
+[10] M. A. Olshanetsky and A. M. Perelomov, Classical integrable finite dimensional systems
+related to Lie algebras, Phys. Rept. 71, 313–400 (1981).
+[11] A. V. Mikhailov, M. A. Olshanetsky, and A. M. Perelomov, Two-dimensional generalized
+Toda lattice, Comm. Math. Phys. 79(4), 473–488 (1981).
+[12] M. A. Olshanetsky and A. M. Perelomov, Quantum integrable systems related to Lie
+algebras, Phys. Rept. 94, 313–404 (1983).
+[13] P. Lax, Integrals of nonlinear equations and solitary waves, Commun. Pure Appl. Math. 21,
+467–490 (1968).
+[14] N. Bourbaki, Groupes et Algebres de Lie: Elements de Mathematique, Hermann, Paris,1968 .
+[15] H. Bohr, Zur theorie der fastperiodischen Funktionen, Acta Math. 46(1), 101–214 (1925).
+[16] H. W. Braden, E. Corrigan, P. E. Dorey, and R. Sasaki, Affine Toda field theory and exact S
+matrices, Nucl. Phys. B338, 689–746 (1990).
+[17] A. Fring and D. I. Olive, The Fusing rule and the scattering matrix of affine Toda theory,
+Nucl. Phys. B379, 429–447 (1992).
+– 24 –
+
+Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
+[18] T.-J. Chen, M. Fasiello, E. A. Lim, and A. J. Tolley, Higher derivative theories with
+constraints: Exorcising Ostrogradski’s Ghost, J. Cos. and Astropart. Phys. 2013(02), 042
+(2013).
+[19] D. I. Olive and N. Turok, The symmetries of Dynkin diagrams and the reduction of Toda
+field equations, Nucl. Phys. B215, 470 (1983).
+[20] J. A. Bordner, R. Sasaki, and K. Takasaki, Calogero-Moser models. II: Symmetries and
+foldings, Prog. of Theor. Phys. 101(3), 487–518 (1999).
+[21] A. Fring and C. Korff, Affine Toda field theories related to Coxeter groups of
+noncrystallographic type, Nucl. Phys. B 729(3), 361–386 (2005).
+[22] A. Fring and N. Manojlovi´c, G2-Calogero-Moser Lax operators from reduction, J. of Nonlin.
+Math. Phys. 13(4), 467–478 (2006).
+[23] N. Bourbaki, Elements of Mathematics, Lie Groups and Lie Algebras, Chapters 4-6,
+Springer, Berlin (2002).
+[24] A. Fring and B. Turner, in preparation.
+– 25 –
+
diff --git a/ddFIT4oBgHgl3EQfoCum/content/tmp_files/load_file.txt b/ddFIT4oBgHgl3EQfoCum/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,1306 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf,len=1305
+page_content='Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Higher derivative Hamiltonians with benign ghosts  from affine Toda lattices  Andreas Fring and Bethan Turner  Department of Mathematics, City, University of London, Northampton Square,  London EC1V 0HB, UK  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='fring@city.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='uk, bethan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='turner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2@city.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='uk  Abstract: We provide further evidence for Smilga’s conjecture that higher charges of in-  tegrable systems are suitable candidates for higher derivative theories that possess benign  ghost sectors in their parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' As concrete examples we study the properties of  the classical phase spaces for a number of affine Toda lattices theories related to different  types of Kac-Moody algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We identify several types of scenarios for theories with  higher charge Hamiltonians: some that possess benign ghost sectors which are stable or  exteremely sensitive towards the initial conditions, some that have malevolent ghost sec-  tors that can be converted into benign sectors with an appropriate choice of variables and  some theories with benign ghost sectors that are stable towards strong deformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Introduction  Higher derivative Lagrangian theories, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' those that include derivative terms of the coor-  dinates of order larger than one, arise naturally in a number of different contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For in-  stance, in some approaches to theories of everything (TOE) that include gravity besides all  the other known fundamental forces consist of embedding the standard (3+1)-dimensional  universe into a higher dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In doing so, and demanding in addition these  theories to be renormalizable, one is automatically led to higher derivative Lagrangian the-  ories by simple scaling arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Unfortunately these theories are generally plagued [1]  by so-called ghosts states that possess negative norms, thus leading to collapse and/or a  violation of unitarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' This is the main reason why they are usually discarded and in com-  parison only very few explicit studies of these theories have been carried out to a full extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  For instance, in the field gravity and cosmology they have been proposed as a resolution of  the cosmological singularity problem [2] and some of their black holes solutions have been  studied [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Furthermore, for some cases the BRST symmetries have been identified [4] and  also some supersymmetric versions have been studied [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  However, in general such types of theories remain to be regarded as undesirable for the  above mentioned reason and it unclear which theories deserve further considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In a  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='11317v1  [hep-th]  26 Jan 2023  CITY  UNIVERSITYOFLONDON  EST1894Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  recent series of papers [6–9] Smilga and collaborators addressed this question and gathered  evidence to suggest that the dismissal of higher derivative theories might be too premature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The central idea in these studies is to distinguish between benign and malevolent ghost  states in the sense that the latter states are genuinely unphysical while the former are  solutions that might not be bounded from below, but are oscillatory in character hence allow  for a unitary evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The next question is then of course how to identify theories that  have such types of features and possess sectors in their parameter space with benign ghost  solutions that in addition might be stable against small perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Very recently [6]  Smilga proposed that higher charges of integrable systems might be suitable candidates  for such types of higher derivative Lagrangian theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Here our main goal is to gather  further evidence for this conjecture by considering a particular class of integrable systems  and interpret their charges as Hamiltonians for higher derivative theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We will analyse  their classical phase spaces in the hope that benign classical systems will also lead to benign  quantum systems as conjectured in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  In general, we will be considering here a prototype integrable theory that is affine Toda  lattices with Hamiltonians of the form  Hg =  ℓ  �  i=1  p2  i  2 +  r  �  i=0  nieαi·q,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1)  where q = (q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , qℓ) are the coordinates, p = (p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , pℓ) are the momenta, g is a semi-  simple Lie algebra, r the rank of this algebra, αi for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , r are the simple roots of the  root space ∆g represented in an ℓ-dimensional space, α0 = − �r  i=1 niαi and ni ∈ N are  positive integers with n0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The choice of α0 ensures that the minimum of the potential  of the theory is at q = (q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , qℓ) = (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , 0), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' all first order terms in the qi vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Often α0 is taken to be the negative of the highest root, so that the integers ni are the  Kac labels, but this need not be the case and is a mere convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The inclusion of the  α0-root means that the associated algebra becomes a Kac-Moody algebra rather than a  semi-simple Lie algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Thus we are not considering here theories of the type Hg with the  sum in the potential starting at i = 1, which are conformally invariant and do not possess  minima in the potentials at finite values of the coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  It is well known [10–12] that these type of theories are integrable in the Liouville  sense, that is they possess as many conserved charges as degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' It is these  charges that we will be using as potential candidates for higher order derivative theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The key question we will be addressing here is whether the classical trajectories in phase  space associated to the Hamiltonian systems of these charges will be benign or malevolent  according to the characterisation put forward by Smilga in [6–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial assumption is  that the benign nature on the classical level is inherited in the quantum theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Naturally,  this supposition needs further investigation, which we leave for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Our manuscript is organised as follows: In section 2 we recall the constructions of the  conserved classical charges for the An-affine Toda lattice theories, with a particular focus  on A2 and A6 for different types, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' dimensions, of representations of the roots in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Interpreting these charges as Hamiltonians we numerically study their classical solutions in  phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In section 3 and 4 we carry out similar type of studies for the B3 and G2-affine  – 2 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Toda lattice theories, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We construct relevant charges from a reduction/folding  procedure of the corresponding root systems or by direct computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In section 5 we  investigate the stability of the benign solutions with regard to the sensitivity of the initial  conditions and to strong deformations by harmonic oscillator potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Our conclusions  are stated in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Higher derivative Hamiltonians from An-affine Toda lattice charges  The expressions for the higher charges are central to our investigations and therefore we  will provide here their explicit construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' All higher charges that will be considered  are for theories associated with Hamiltonians of the general form in equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1) with g  taken to be An.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Using the standard Lax approach for classical integrable systems [13] we  employ the Lax pair given by the two operators in form of (n + 1) × (n + 1)-matrices  L =  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  p1 W1  0  · · · · ·  0  W0  W1 p2 W2  0  0  0  W2 p3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' pn  Wn  W0  0  · · · · · 0 Wn pn+1  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  ,  M =  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  0  W1  0  · · · · ·  0  −W0  −W1  0  W2  0  0  0  −W2  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0  Wn  W0  0  · · · · · 0 −Wn  0  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1)  where we abbreviated Wi := exp(αi ·q)/2, with αi ∈ Rn+1, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , n denoting the simple  roots of An, α0 = − �n  i=1 αi the negative of the highest An-root, q = (q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , qn+1) the  coordinates and p = (p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , pn+1) the momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The dimension of the phase space is  therefore (n + 1) × (n + 1) at this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  By definition of the Lax operators, the equations of motion are then equivalent to the  Lax pair equation  ˙L+[M, L] = 0,  ⇔  ˙pi +W 2  i −W 2  i−1 = 0,  αi · ˙q = pi −pi+1,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , n+1, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2)  where we formally identified Wn+1 = W0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' As usual we denote here derivatives with respect  to time by overdots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Taking ℓ = n+1 in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1) these equations also correspond to Hamilton’s  equations ˙qi = ∂H/∂pi, ˙pi = −∂H/∂qi as we will show below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' By construction, it then  follows immediately that all quantities Qk := Tr(Lk)/k are conserved in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  ˙Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Given the expressions in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1) we easily construct all of these charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Interpreting the  summation indices modulo 7, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' W7 = W0, p8 = p1, etc, we obtain  Q1 =  7  �  i=1  pi,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)  Q2 = H =  7  �  i=1  �p2  i  2 + W 2  i  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4)  – 3 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Q3 =  7  �  i=1  �p3  i  3 + W 2  i (pi + pi+1)  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5)  Q4 =  7  �  i=1  �p4  i  4 + 1  2W 4  i + W 2  i (p2  i + pipi+1 + p2  i+1) + W 2  i W 2  i+1  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6)  Q5 =  7  �  i=1  �p5  i  5 + W 4  i (pi + pi+1) + W 2  i (p3  i + pip2  i+1 + p2  i pi+1 + p3  i+1)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='7)  +W 2  i W 2  i+1(pi−1 + 2pi + 2pi+1)  �  ,  Q6 =  7  �  i=1  �p6  i  6 + 1  2W 6  i + W 4  i  �3  2p2  i + 3  2p2  i+1 + 2pipi+1  �  + W 2  i  �  p4  i + p3  i pi+1 + p2  i p2  i+1  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='8)  +W 2  i−1  �  p4  i + p3  i pi−1  �  + W 2  i W 2  i+1  �  p2  i + 2pipi−1 + 3p2  i+1 + pipi+2 + 2pi+1pi+2 + p2  i+2  �  +W 4  i  �  W 2  i−1 + W 2  i+1  �  + W 2  i W 2  i+1W 2  i+2  �  Q7 =  7  �  i=1  �p7  i  7 + W 6  i (pi + pi+1) + W 2  i−1W 2  i W 2  i+1(pi−1 + 2pi + 2pi+1 + pi+2)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9)  +W 4  i W 2  i−1(pi−1 + 3pi + 2pi+1) + W 4  i−1W 2  i (2pi−1 + 3pi + pi+1)  +W 2  i−1W 2  i (p3  i−1 + 4p3  i + 3p2  i pi+1 + 2pip2  i+1 + p3  i+1)  +W 2  i−1W 2  i (p3  i−1(p2  i−1(2pi + pi+1) + pi−1(3p2  i + 2pipi+1 + p2  i+1))  +W 2  i (p5  i + p4  i pi+1 + p3  i p3  i+1 + p2  i p3  i+1 + pip4  i+1 + p5  i+1)  �  + 2  7  �  i=1  Wi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  These charges and versions thereof will be our potential candidates for higher derivative  theories when interpreted as Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 Higher derivative Hamiltonians from the 3 particle A2-affine Toda lattice  Next we evaluate the expressions of the charges for the A2-theory more explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' First we  notice that the second equation in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2) is simply solved by taking q = (q1, q2, q3), so that  we obtain ˙qi = pi when the roots are represented as α1 = (1, −1, 0), α2 = (0, 1, −1) and  α0 = −α1 − α2 = (−1, 0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' This is the standard three dimensional representation for the  A2-roots, see for instance [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The charges (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6) then acquire the form  Q1 = p1 + p2 + p3,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10)  Q2 = H = 1  2  �  p2  1 + p2  2 + p2  3  �  + V12 + V23 + V31 =  3  �  i=1  �p2  i  2 + eαi·q  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='11)  Q3 = 1  3  �  p3  1 + p3  2 + p3  3  �  + p1 (V12 + V31) + p2 (V12 + V23) + p3 (V23 + V31) + 2, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='12)  =  3  �  i=1  �p3  i  3 + pi (eαi·q + eαi−1·q)  �  + 2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='13)  Q4 = Q1Q3 − 1  2Q2  1Q2 + 1  24Q4  1 + 1  2Q2  2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='14)  – 4 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  where we introduced the new abbreviation Vij := exp(qi −qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We notice that only the first  three conserved quantities are independent, as Q4 can be constructed from combinations  of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In fact, this property will persist for higher charges and all Qi for i > 3 can be  build from combinations of Q1, Q2 and Q3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Moreover, one may easily verify that the charges Q1, Q2 and Q3 are in involution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  their mutual Poisson brackets vanish  {Qi, Qj} :=  3  �  k=1  ∂Qi  ∂qk  ∂Qj  ∂pk  − ∂Qi  ∂pk  ∂Qj  ∂qk  = 0,  for i, j = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15)  As indicated in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='11), at first we identify as usual the charge Q2 with the standard Hamil-  tonian so that the classical equations of motion resulting from Hamilton’s equations to  ˙q1 = p1,  ˙q2 = p2,  ˙q3 = p3  ˙p1 = V31 − V12,  ˙p2 = V12 − V23,  ˙p3 = V23 − V31, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='16)  which are identical to the equations resulting from the Lax pair equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  In the first instance we solve these equations numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  x1(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  p1(t)  (a)  t=0  t=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  t=50  t=100  t=150  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  x1(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  p1(t)  (b)  t=200  t=250  t=299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  t=300  t=150  200  400  600  800  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  x1  200  400  600  800  t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  p1  Figure 1: Phase space (x1, p1) for the A2-affine Toda lattice Hamiltonian with three particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Panel (a): inward spiralling trajectories from time t = 0 to t = 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Panel (b): outward spiralling  trajectories from time t = 150 to t = 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions are taken as x1(0) = x2(0) =  x3(0) = 0, p1(0) = 1 and p2(0) = p3(0) = −1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The insets in panel (b) show x1 and p1 as functions  of time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  In figure 1 we depict the solutions to the three particle equations of motion (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='16)  in phase space, observing confined orbits that periodically spiral inward and outward, a  behaviour that continues beyond the time shown in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The insets in figure 1 panel  (b) demonstrate how the small period τ s ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='778 is modulated by a larger period τ l ≈ 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2,  with τ s governing the quasiperiodic elliptic motion and τ l the period of the inward/outward  pulsation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We stress here that after each period we observe a small offset and therefore  these solutions are not exactly periodic and only quasiperiodic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' f(x + τ) = g(x, f(x))  with g being a simpler function than f or almost periodic in the sense of [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Almost  periodic is here to be understood in the sense that we have a small offset after one period,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' |f(t) − f(t + τ)| ≤ ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We may adapt these observations more rigorously to the strict  sense of the definition of almost periodic functions by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Bohr [15] and adjust the values  – 5 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  of τ H for a pre-selected ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For the other directions in phase space (x2, p2) and (x3, p3) we  obtain similar types of periodic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Now we come to the key point in this approach and interpret the higher charges as  Hamiltonians following the suggestion in [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Thus we take here the charge Q3 as the  Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Deriving the new set of equations of motion from ˙qi = ∂Q3/∂pi, ˙pi =  −∂Q3/∂qi we obtain  ˙q1 = p2  1 + V12 + V31,  ˙p1 = (p1 + p3)V31 − (p1 + p2)V12,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='17)  ˙q2 = p2  2 + V12 + V23,  ˙p2 = (p1 + p2)V12 − (p2 + p3)V23,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='18)  ˙q3 = p2  3 + V23 + V31,  ˙p3 = (p2 + p3)V23 − (p1 + p3)V31,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='19)  which are identical to the equations previously considered in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Once more we solve these  equations, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='17)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='19), numerically and depict the solutions in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  5  10  15  20  25  xi(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  pi(t)  (a)  t=0  t=0  t=5  t=5  t=10  t=10  i = 3  i = 2  i = 1  2  4  6  8  10 t  5  10  15  20  25  xi  (b)  20  40  60  80  100t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  pi  (c)  Figure 2: Panel (a): Phase space (xi, pi), i = 1, 2, 3 for the A2-affine Toda lattice with unrestricted  Q3-Hamiltonian, with initial conditions x1(0) = x2(0) = x3(0) = 0, p1(0) = 1 and p2(0) = p3(0) =  −1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Panel (b) and (c): xi and pi as functions of time t, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  We observe that while the momenta are bounded as −1 ≤ pi ≤ 1, the coordinate  components xi grow linearly in time so that the trajectories do not close in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus this system appears to have malevolent ghosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' However, this is due to the fact that  we have treated the A2-system as a three rather than a two particle system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In the next  section we will represent the roots in a lower dimensional space and consequently re-define  the coordinates and momenta of the model in the dual space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The effect will be that the  trajectories become confined and quasi-oscillatory in phase space so that we can say that  the ghosts have become benign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 Higher derivative Hamiltonians from the 2 particle A2-affine Toda lattice  We will now constrain the (3 × 3)-dimensional phase space to a (2 × 2)-dimensional one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Recalling that root systems are isomorphic to each other as long as they reproduce the  same Cartan matrix Kij = 2αiαj/α2  j we may achieve this by defining a new set of simple  – 6 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  roots βi in a two-dimensional representation through an orthogonal transformation that  preserve K of the A2 root system obtained from the roots αi in the standard representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  This means we have to solve  Kij = αi · αj = Aβi · Aβj = βi · βj =  �  2 −1  −1 2  �  ij  ,  βi = A−1αi, A−1 = A⊺, i, j = 1, 2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='20)  for the orthogonal matrix A and the roots βi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We find the solutions  A =  �  �  �  �  1  √  6  1  √  2  1  √  3  −  �  2  3  0  1  √  3  1  √  6  − 1  √  2  1  √  3  �  �  �  � ,  β1 =  ��  3  2, 1  √  2, 0  �  β2 =  �  −  �  3  2, 1  √  2, 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='21)  The negative of the highest root is therefore β0 = −β1 − β2 = (0, −  √  2, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Having reduced the dimension of the representation space for the roots from 3 to 2,  we shift this reduction now to the dual space of the roots, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' the coordinates and the  momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For this we define a new set of dynamical variables (ζ, η) in the dual space of  the roots by  αi · q = Aβi · Aζ = βi · ζ,  for  ζ = A−1q, i = 1, 2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='22)  αi · p = Aβi · Aη = βi · η,  for  η = A−1p, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='23)  With A as identified in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='21) we have  q =  �  ζ1  √  6 + ζ2  √  2, −  �  2  3ζ1, ζ1  √  6 − ζ2  √  2  �  = (q1, q2, q3),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='24)  p =  �  η1  √  6 + η2  √  2, −  �  2  3η1, η1  √  6 − η2  √  2  �  = (p1, p2, p3),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='25)  or when inverted  ζ =  �q1 − 2q2 + q3  √  6  , q1 − q3  √  2  , q1 + q2 + q3  √  3  �  = (ζ1, ζ2, 0),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='26)  η =  �p1 − 2p2 + p3  √  6  , p1 − p3  √  2  , p1 + p2 + p3  √  3  �  = (η1, η2, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='27)  From the last component in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='26) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='27) we observe that we can interpret the new  (2 × 2)-dimensional phase space (ζ, η) as the old (3 × 3)-dimensional phase space (q, p) in  the centre of mass frame with additional constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We stress that this property is not  imposed, but the conditions q1 +q2 +q3 = 0 and p1 +p2 +p3 = 0 are automatically satisfied  with the definitions of the new variables in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='24), which in turn results from representing  the roots in a lower dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The conserved quantities Q1, Q2, Q3 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='12) can now also be transformed to  the new variables as  Q1 = 0,  Q2 = H(ζ, η) = 1  2  �  η2  1 + η2  2  �  + e−  √  2ζ2 + 2e  ζ2  √  2 cosh  ��  3  2ζ1  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='28)  – 7 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Q3 =  η1  �  6e−  √  2ζ2 − η2  1 + 3η2  2  �  3  √  6  −  √  2e  ζ2  √  2  �  η1  √  3 cosh  ��  3  2ζ1  �  − η2 sinh  ��  3  2ζ1  ��  + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The equations of motion resulting from the standard Hamiltonian H(ζ, η) become  ˙ζ1 = η1,  ˙ζ2 = η2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='29)  ˙η1 = −  √  6e  ζ2  √  2 sinh  ��  3  2ζ1  �  ,  ˙η2 =  √  2e−  √  2ζ2  �  1 − e  3ζ2  √  2 cosh  ��  3  2ζ1  ��  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='30)  whereas the equations resulting from taking Q3(ζ, η) interpreted as the Hamiltonian are  ˙ζ1 =  2e−  √  2ζ2 − 2e  ζ2  √  2 cosh  ��  3  2ζ1  �  − η2  1 + η2  2  √  6  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='31)  ˙ζ2 =  √  2e  ζ2  √  2 sinh  ��  3  2ζ1  �  +  �  2  3η1η2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='32)  ˙η1 = e  ζ2  √  2  �  η1 sinh  ��  3  2ζ1  �  −  √  3η2 cosh  ��  3  2ζ1  ��  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='33)  ˙η2 = 2e−  √  2ζ2η1  √  3  + 1  3e  ζ2  √  2  �  √  3η1 cosh  ��  3  2ζ1  �  − 3η2 sinh  ��  3  2ζ1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='34)  The phase space trajectories obtained from the standard equations of motion for the Hamil-  tonian, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='29) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='30), are still confined to a finite region in phase space as seen from  the numerical solutions figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We may still identify a small period τ H that governs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζ1(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  η1(t)  (a)  0 < t < τH  τH < t < 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5 < t < 210  210 < t < 300  50 100 150 200 250 300 350  t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ1,η1  ζ1  η1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζ2(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  η2(t)  (b)  0 < t < τH  τH < t < 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5 < t < 210  210 < t < 300  50 100 150 200 250 300 350  t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ2,η2  ζ2  η2  Figure 3: Phase spaces (ζi, ηi), i = 1, 2 for the standard Hamiltonian of the reduced two particle  A2-affine Toda lattice with initial conditions ζ1(0) = ζ2(0) = 0, η1(0) =  √  3/2  √  2 and η2(0) = 3/2  √  2  (≡ p1(0) = 1, p2(0) = p3(0) = −1/2) for times t = 0 to t = 300 with “almost period” τ H ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The insets in panels (a) and (b) show ζ1, η1 and ζ2, η2 as functions of time, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  one turn, up to a small displacement, and a larger period controlling the inward/outward  motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 8 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  In figure 4 we depict the numerical solutions to the equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='31) - (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='34) obtained  as equations of motions from the third order derivative Q3-Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We determine an  almost period τ Q for the small intersecting almost closed loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The larger period now  governs the rotation of these loops that due to the repeated offset fill in the phase space  regions that appear to be identical to the regions identified for the Hamiltonian H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζ1(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  η1(t)  (a)  0 < t < τQ  τQ < t < 72  72 < t < 144  144 < t < 216  50 100 150 200 250 300 350  t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ1,η1  ζ1  η1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζ2(t)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  η2(t)  (b)  0 < t < τQ  τQ < t < 72  72 < t < 144  144 < t < 216  50 100 150 200 250 300 350  t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ2,η2  ζ2  η2  Figure 4: Phase space (ζi, ηi), i = 1, 2 for the Q3-Hamiltonian of the reduced two particle A2-Toda  lattice with initial conditions ζ1(0) = ζ2(0) = 0, η1(0) =  √  3/2  √  2 and η2(0) = 3/2  √  2 for times  t = 0 to t = 216 with τ Q ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The insets in panels (a) and (b) show ζ1, η1 and ζ2, η2 as  functions of time, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus while the trajectories resulting from the three and two particle A2-Hamiltonians  are all confined in phase space, this behaviour is different for those derived from the higher  Q3-charge where only the trajectories for the reduced model are confined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The divergent  behaviour was already reported in [7], where it was also conjectured that in the centre  of mass system convergence might be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Here we have shown explicitly that this  conjecture is partially correct, in the sense that the system can be interpreted as being in  the centre of mass, but the more accurate statement is to view the system as the reduction  from three to two particles along the change of the dimensions of the representation space of  the roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' One should say that the two particle picture of the A2-theory is the more natural  one as for instance also in the closely related affine Toda quantum field theory the number  of particles always equals the rank of the semi-simple Lie algebra [16,17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The mismatch  between rank and particles simply results form the higher dimensional representation space  of the simple roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In [18] a similar reduction procedure was carried out by imposing  additional constraints in order to “exorcise” Ostrogradski’s ghosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  One may view the  centre-of-mass condition as such a constraint, although here we have not employed Lagrange  multipliers is to implement them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3 Higher derivative Hamiltonians from the A6-affine Toda lattice  Next we consider a system that possesses more than one higher charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Specifying the  general Lax operator in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1) to n = 6 and computing the traces over the products of this  operator we calculate the seven independent charges (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For the seven particle  system with the roots taken in the fundamental representation we obtain the explicit ex-  – 9 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  pressions for the charges by replacing W 2  i → Vi,i+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For instance, when taking all the roots  in the standard representation the Hamiltonian acquires the form  H = 1  2  7  �  i=1  p2  i +  6  �  i=1  eqi−qi+1 + eq7−q1,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='35)  with α7 taken as the negative of the highest root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We also convince ourselves that all  mutual Poisson brackets vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  We proceed now as for the A3-system by interpreting all of the charges as Hamiltonians  and solve their respective Hamilton’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For the seven particle system we find  periodic solutions for the momenta and coordinates in the phase space of the standard  Hamiltonian, as seen in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' However, for all higher charges only the momenta remain  periodic whereas the coordinates diverge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In figure 5 we present as sample solution for the  phase space of the higher charges the one for the Q6-charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In panel (d) we observe the  divergence of all coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' This characteristic behaviour is shared by the solutions for  all the other higher charge Hamiltonians which we do not represent here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Similarly as for the A2-case, we attempt to eliminate the divergence by reducing the  number of particles to the rank, that is from seven to six.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For this purpose we solve the  analogue to the equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='20) with the A6-Cartan matrix instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Taking the α-roots in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='the standard representation we find an orthogonal matrix as  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='A =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
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+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='36)  together with the new six dimensional roots βi = A−1αi  β1 =  ��  3  2,  1  √  2, 0, 0, 0, 0, 0  �  ,  β2 =  �  −  �  3  2,  1  √  2, 0, 0, 0, 0, 0  �  ,  β3 =  �  1  √  6, − 1  √  2,  2  √  3, 0, 0, 0, 0  �  ,  β4 =  �  0, 0, −  √  3  2 , −  √  5  2 , 0, 0, 0  �  ,  β5 =  �  0, 0, 0,  2  √  5, 0, −  �  6  5, 0  �  ,  β6 =  �  0, 0, 0, 0, −  �  7  6,  �  5  6, 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='37)  The corresponding coordinate transformations resulting from this are  q = (q1, q2, q3, q4, q5, q6, q7)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='38)  =  �  ζ1  √  6 + ζ2  √  2 + ζ3  2  √  3 − ζ4  2  √  5 − ζ5  √  42 − ζ6  √  30, −  �  2  3ζ1 + ζ3  2  √  3 − ζ4  2  √  5 − ζ5  √  42 − ζ6  √  30,  ζ1  √  6 − ζ2  √  2 + ζ3  2  √  3 − ζ4  2  √  5 − ζ5  √  42 − ζ6  √  30, −1  2  √  3ζ3 − ζ4  2  √  5 − ζ5  √  42 − ζ6  √  30,  2ζ4  √  5 − ζ5  √  42 − ζ6  √  30,  �  5  6ζ6 − ζ5  √  42,  �  6  7ζ5  �  ,  – 10 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  and  ζ = (ζ1, ζ2, ζ3, ζ4, ζ5, ζ6, 0)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='39)  =  �q1 − 2q2 + q3  √  6  , q1 − q3  √  2  , q1 + q2 + q3 − 3q4  2  √  3  , −q1 + q2 + q3 + q4 − 4q5  2  √  5  ,  −q1 + q2 + q3 + q4 + q5 + q6 − 6q7  √  42  , −q1 + q2 + q3 + q4 + q5 − 5q6  √  30  , −  �7  i=1 qi  √  7  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Since the last entry for ζ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='39) is zero, we note that once again the new coordinates  transform the old ones to the centre-of-mass frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The momenta are transformed in the  same way, with pi → ηi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The Hamiltonian now acquires the form  H = 1  2  6  �  i=1  η2  i + e  ζ2−  √  3ζ1  √  2  + e  √  3ζ1+ζ2  √  2  + e  ζ1  √  6 − ζ2  √  2 + 2ζ3  √  3 + e− 1  2  √  3ζ3−  √  5ζ4  2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='40)  +e  �  5  6 ζ6−  �  7  6 ζ5 + e  2ζ4−  √  6ζ6  √  5  + e  1  30(−5  √  6ζ1−15  √  2ζ2−5  √  3ζ3+3  √  5ζ4+5  √  42ζ5+  √  30ζ6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  In this reduced space all trajectories become benign as we observe in figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We recognise  once more that each of the solutions is made up of superposition of various quasi/almost  periodic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  50  100  150  200t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  pi  (a)  p1(t)  p2(t)  p3(t)  p4(t)  p5(t)  p6(t)  p7(t)  50  100  150  200t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  qi  (b)  q1(t)  q2(t)  q3(t)  q4(t)  q5(t)  q6(t)  q7(t)  10  20  30  40 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  pi  (c)  p1(t)  p2(t)  p3(t)  p4(t)  p5(t)  p6(t)  p7(t)  10  20  30  40 t  3  2  1  qi  (d)  q1(t)  q2(t)  q3(t)  q4(t)  q5(t)  q6(t)  q7(t)  Figure 5: A6-affine Toda lattice phase spaces as functions of time t of the Hamiltonian, panels (a),  (b), and the Q6-charge Hamiltonian,panels (c), (d), with seven particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions are  taken in both cases as qi = 0, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , 7 and p1 = −p2 = p3 = −p4 = p5 = −2p6 = 2p7 = −1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus all five higher charges of the A6-affine Toda lattice theory when interpreted as  Hamiltonians for a six particle system possess benign solutions of oscillatory type in their  classical phase spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 11 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  50  100  150  200t  2  1  1  2  ηi  (a)  η1(t)  η2(t)  η3(t)  η4(t)  η5(t)  η6(t)  50  100  150  200t  2  1  1  2  ζi  (b)  ζ1(t)  ζ2(t)  ζ3(t)  ζ4(t)  ζ5(t)  ζ6(t)  10  20  30  40 t  2  1  1  2  ηi  (c)  η1(t)  η2(t)  η3(t)  η4(t)  η5(t)  η6(t)  10  20  30  40 t  2  1  1  2  ζi  (d)  ζ1(t)  ζ2(t)  ζ3(t)  ζ4(t)  ζ5(t)  ζ6(t)  Figure 6: A6-affine Toda lattice phase spaces as functions of time t of the Hamiltonian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' panels  (a),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' (b),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' and the Q6-charge Hamiltonian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' panels (c),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' (d),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' with six particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions  are taken in both cases as ζi = 0, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , 6 and η1 = η2 = η3 = −3/  √  6, η2 = η4 = η6 = 3/2  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Higher derivative Hamiltonians from the B3 affine Toda lattice  Many physical systems based on non-simply laced algebras display quite different behaviour  from those based on simply laced ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' To find out whether this also holds for higher order  derivative theories we will also investigate some sample representative theories based on  non-simply laced algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We first recall how to obtain the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 Reduction of the root spaces and charges  It is well known that non-simply laced Lie algebras can be obtained from a folding proce-  dure of the associated Dynkin diagrams for a simply laced Lie algebra along a non-trivial  automorphism [19–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Here we use a reduction from the A6 root space ∆A6 to the B3 root  space ˆ∆B3 with a subsequent reduction to the G2 root space ˜∆G2 previously constructed  in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Denoting the corresponding simple roots as αi ∈ ∆A6, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , 6, ˆαi ∈ ˆ∆B3,  i = 1, 2, 3 and ˜αi ∈ ˜∆G2, i = 1, 2 we define the following reduction maps and their inverses  ω : ∆A6 → ˆ∆B3,  αi �→ ω(αi) =  �  ˆαi  for i = 1, 2, 3  ˆα7−i  for i = 4, 5, 6 ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1)  ω−1 : ˆ∆B3 → ∆A6,  ˆαi �→ ω−1(ˆαi) = αi + α7−i  for i = 1, 2, 3,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2)  ˆω : ˆ∆B3 → ˜∆G2,  ˆαi �→ ˆω(ˆαi) =  �  ˜α1  for i = 1, 3  ˜α2  for i = 2  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)  – 12 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  ˆω−1 : ˜∆G2 → ˆ∆B3,  ˜αi �→ ˜ω−1(˜αi) =  �  ˆα1 + 2ˆα3  for i = 1  3ˆα1  for i = 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4)  One may verify that the roots involved reproduce the respective Cartan matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The  associated charges are then reduced by the appropriate actions of the coordinates and  momenta according to  QA6  n (q, p) → ˆQB3  n (ˆq, ˆp) = QA6  n [ω−1(ˆq), ω−1(ˆp)] → ˜QG2  n (˜q, ˜p) = ˆQB3  n [˜ω−1(˜q), ˜ω−1(˜p)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5)  We will employ the root systems from above, but will construct the G2-charges in a different  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Let us now see in detail how the consecutive steps are carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 Higher derivative Hamiltonians from B3 affine Toda lattice theory  In order to define the reduced charges according to equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5) we expand the coordinates  of the B3-system as ˆq = ˆq1ˆα1 + (ˆq1 + ˆq2)ˆα2 + (ˆq1 + ˆq2 + ˆq3)ˆα3 and compute ω−1(ˆq) using  the defining relation for this map in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We expand the momenta in a similar fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Representing the A6-roots in the standard seven dimensional Euclidean space as specified  in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2, we obtain in this manner the reduction of the coordinates and momenta  q → ω−1(ˆq) = (ˆq1, ˆq2, ˆq3, 0, −ˆq3, −ˆq2, −ˆq1),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6)  p → ω−1(ˆp) = (ˆp1, ˆp2, ˆp3, 0, −ˆp3, −ˆp2, −ˆp1),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='7)  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  We notice that when employing the new phase space variables we obtain  another solutions of the second equation in Lax pair equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2) with ˆpi = (ˆxi)t for  i = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' It is easily seen from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9) that with the replacements (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='7) the  charges of odd order vanish  Q1 → ˆQ1 = 0,  Q3 → ˆQ3 = 0,  Q5 → ˆQ5 = 0,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='8)  and the remaining B3-charges acquire the forms  Q2 → ˆQ2 = ˆH =  3  �  i=1  ˆp2  i + 2eˆq1−ˆq2 + 2eˆq2−ˆq3 + 2eˆq3 + e−2ˆq1  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9)  =  3  �  i=1  ˆp2  i +  3  �  i=1  2eˆαi·ˆq + e−(ˆγ+ˆα1)·ˆq  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10)  Q4 → ˆQ4 = ˆp4  1  2 + ˆp4  2  2 + ˆp4  3  2 + ˆp2  1e−2ˆq1 + 2ˆp2  1eˆq1−ˆq2 + 2ˆp2ˆp1eˆq1−ˆq2 + 2ˆp2  2eˆq1−ˆq2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='11)  +2ˆp2  3eˆq2−ˆq3 + 2ˆp2  3eˆq3 + 2ˆp2ˆp3eˆq2−ˆq3 + 1  2e−4ˆq1 + e2ˆq1−2ˆq2 + 2e−ˆq1−ˆq2 + 2eˆq2  +e2ˆq2−2ˆq3 + 2ˆp2  2eˆq2−ˆq3 + 2eˆq1−ˆq3 + 2e2ˆq3  Q6 → ˆQ6 = ˆp6  1  3 + ˆp6  2  3 + ˆp6  3  3 + 1  3e−6ˆq1 + 2eˆq1 + 2e−3ˆq1−ˆq2 + 2  3e3(ˆq1−ˆq2) + 2  3e3(ˆq2−ˆq3)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='12)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1e−2ˆq1 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='e−4ˆq1 + 4e−ˆq1−ˆq2 + 3e2(ˆq1−ˆq2)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+ ˆp2ˆp1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2e−ˆq1−ˆq2 + 4e2(ˆq1−ˆq2)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+2ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3eˆq3 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2e−ˆq1−ˆq2 + 3e2(ˆq1−ˆq2) + 2eˆq2 + 3e2(ˆq2−ˆq3)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+ ˆp2ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4eˆq2 + 4e2(ˆq2−ˆq3)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 + ˆp2ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 + ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2ˆp1 + ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='eˆq1−ˆq2 + 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 + ˆp3ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 + ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3ˆp2 + ˆp4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='eˆq2−ˆq3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 + (2ˆp2 + ˆp3) ˆp1 + 3ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3 + 2ˆp2ˆp3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='eˆq1−ˆq3 + ˆp2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6eˆq2 + 3e2(ˆq2−ˆq3) + 4e2ˆq3�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='– 13 –  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='+3e−2ˆq2 + 2eˆq1+ˆq2−2ˆq3 + 2e−ˆq1−ˆq3 + 2e2ˆq1−ˆq2−ˆq3 + 2e2ˆq2−ˆq3 + 8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3e3ˆq3 + 4eˆq2+ˆq3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='Here ˆγ is the highest root ˆγ = ˆα1 + 2ˆα2 + 2ˆα3 in ˆ∆B3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We notice that unlike for the An-  case the number of particles already matches the rank of B3 in the standard representation  ˆα1 = (1, −1, 0), ˆα2 = (0, 1, −1) and ˆα3 = (0, 0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2q\uf111  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  p\uf111  1  (a)  0 < t < τH  τH < t < 5 τH  5 τH < t < 10 τH  10 τH < t < 15 τH  100  200  300  400 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  q\uf111  1  (a1)  100  200  300  400 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  q\uf111  2  (a3)  100  200  300  400 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  q\uf111  3  (a5)  100  200  300  400 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
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+page_content='0  p\uf111  3  (c6)  Figure 7: Affine B3-Toda lattice phase space (ˆq1, ˆp1), as function of t for the standard Hamiltonian  in panel (a), for Q4 taken as higher derivative Hamiltonian in panel (b) and for Q6 taken as higher  derivative Hamiltonian in panel (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The corresponding functions xi(t) and pi(t) are displayed in  the respective panels ai, bi, ci for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' , 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For the initial condition we always chose ˆq1(0) =  ˆq2(0) = ˆq3(0) = 0 and ˆp1(0) = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1, ˆp2(0) = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2, ˆp3(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3, in panels (a), ˆp1(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5,  ˆp2(0) = ˆp3(0) = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='25, in panels (b) and ˆp1(0) = 1, ˆp2(0) = ˆp3(0) = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5 in panels (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The  quasi-periods are: panel (a): τ H ≈ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9824, panel (b): τ Q4 ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='7181, panel (c): τ Q6 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 14 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Again we interpret all charges as Hamiltonians and compute their corresponding phase  spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' As depicted in figure 7, all trajectories are benign and are confined in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  As in this case the dimension of the standard representation already equals the rank  of the algebra there was no need for a reduction or the imposition of any constraints in  order to obtain benign trajectories for the higher charge Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Nonetheless, for  the sake of interest we consider now the reverse scenario and construct a theory in which  the roots are represented in a larger dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' When drawing on the A2-example  one might expect malign ghost trajectories in this case, but as we will demonstrate this is  not the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus we solve once more equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='20) for the orthogonal matrix A and the four-  dimensional roots ˆβi reproducing the B3-Cartan matrix  K =  �  �  �  2 −1 0  −1 2 −2  0 −1 2  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='13)  We find the four dimensional representation for the roots  ˆβ1 = (1, 0, 1, 0) ˆβ2 =  �  −1  2,  √  3  2 , −1  2,  √  3  2  �  ˆβ3 =  �  0, −2 +  √  2  2  √  3 , 0, −2 −  √  2  2  √  3  �  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='14)  together with the orthogonal matrix  ˆA =  �  �  �  �  �  �  �  1  2  1−  √  2  2  √  3  1  2  1+  √  2  2  √  3  − 1  2  1−  √  2  2  √  3  − 1  2  1+  √  2  2  √  3  0  − 2+  √  2  2  √  3  0  1−  √  2  √  6  − 1  √  2  0  1  √  2  0  �  �  �  �  �  �  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15)  This in turn leads to the coordinate transformation  ˆq = (ˆq1, ˆq2, ˆq3, 0) = A( ˆρ1, ˆρ2, ˆρ3, ˆρ4)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='16)  =  �  1  2ˆρ1 + 1 −  √  2  2  √  3 ˆρ2 + 1  2ˆρ3 + 1 +  √  2  2  √  3 ˆρ4, −1  2ˆρ1 + 1 −  √  2  2  √  3 ˆρ2 − 1  2ˆρ3 + 1 +  √  2  2  √  3 ˆρ4,  −  √  2 + 1  √  6  ˆρ2 + −  √  2 + 1  √  6  ˆρ4, 1  √  2(ˆρ3 − ˆρ1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus instead of the centre-of-mass constraint �4  i=1 ρi = 0 we have now the constraint  ˆρ1 = ˆρ3 as we can read off from the last component in the four dimensional system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Indeed, when computing the new coordinates we find precisely this dependence in the first  and third coordinate  ˆρ = (ˆρ1, ˆρ2, ˆρ3, ˆρ4) = ˆA−1(ˆq1, ˆq2, ˆq3, 0)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='17)  = 1  2  �  ˆq1 − ˆq2, 1 −  √  2  √  3  (ˆq1 + ˆq2 + ˆq3) + 1  √  3 ˆq3, ˆq1 − ˆq2,  √  2 + 1  √  3  (ˆq1 + ˆq2 + ˆq3) − 3  √  3 ˆq3  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 15 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  ρ\uf111  1(t)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  ξ  \uf111  1(t)  0<t<τH  τH<t<5τH  5τH<t<10τH  10τH<t<15τH  a)  10  20  30  40  50  60t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ρ\uf111  i(t)  i=1,3  i=2  i=4  10  20  30  40  50  60t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ξ\uf111  i(t)  i=1,3  i=2  i=4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15ρ\uf111  1(t)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  ξ  \uf111  1(t)  0<t<τQ4  τQ4<t<2τQ4  2τQ4<t<4τQ4  4τQ4<t<6τQ4  (b)  2  4  6  8  10  12  14  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ρ\uf111  i(t)  i=1,3  i=2  i=4  2  4  6  8  10  12  14  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ξ\uf111  i(t)  i=1,3  i=2  i=4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15ρ\uf111  1(t)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  ξ  \uf111  1(t)  0<t<τQ6  τQ6<t<2τQ6  2τQ6<t<3τQ6  3τQ6<t<4τQ6  (c)  1  2  3  4  5 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ρ\uf111  i(t)  i=1,3  i=2  i=4  1  2  3  4  5 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ξ\uf111  i(t)  i=1,3  i=2  i=4  Figure 8: Affine B3-Toda lattice phase space (ˆξ1,ˆ(ρ)1) as fuunctions of t for the standard Hamil-  tonian panel (a), for Q4 taken as higher derivative Hamiltonian panel (b) and for Q6 taken as  higher derivative Hamiltonian panel (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions are teken in all cases as ˆρ(0) =  (0, 0, 0, 0), ˆξ(0) =  1  10(1, 2, 1, −4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The quasi-periods are: τ H ≈ 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='80, τ Q4 ≈ 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='99, τ Q6 ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  When setting any other component in ˆq to zero we will obtain more complicated depen-  dencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 16 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Transforming now also the B3 charges into the new coordinates we proceed as previ-  ously and compute the classical trajectories numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Our results are shown in figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  The main observation is that all solutions found are benign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Thus unlike for the An cases  we do not encounter divergencies in the case where the dimension of the root representation  space does not match the rank of the algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Higher derivative Hamiltonians from the G2-affine Toda lattice  In order to compare and identify universal features we investigate now also the G2-affine  Toda lattice theory that is similar to the A2-theory, in the sense that it has a natural three  and two particle representation, with the former being the standard one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Its Hamiltonian  in the standard form reads  ˜H = 1  2 ˜p2 + 3eα1·˜q + 2eα2·˜q + eα0·˜q,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1)  where α1 and α2 are the two simple roots of G2 and α0 = −3α1 − 2α2 is the negative of  the highest G2-root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In order to construct the higher charges we may use the reduction  from B3 or directly construct a higher order expression from a suitable Ansatz whose  Poisson bracket vanishes with ˜H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Here we do not use the folding procedure, as for it to  apply in this case the Lax pair has to be slightly modified, but instead we use the latter  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Taking initially the standard representation for the simple roots α1 = (1, −1, 0)  and α2 = (−2, 1, 1), [23], we find the non-trivial independent charges  ˜Q1 = ˜p1 + ˜p2 + ˜p3  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2)  ˜Q6 =  3  �  i,j=1  1  6 ˜p6  i + 3  14(˜p4  i ˜p2  i+1 + ˜p2  i ˜p4  i+1) + 10  21 ˜p3  i ˜p3  i+1 + 6  7 ˜pi˜pi+1˜pi+2 + cj  j3  7 e3˜αj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3)  +njnj+1  7  e(˜αj+˜αj+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q �  c(1)  j nje˜αj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q + c(2)  j nj+1e˜αj+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q + c(3)  ij ˜pi˜pj+1 + c(4)  ij ˜p2  i  �  +nj  7 e˜j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q �  c(5)  ij ˜p4  i + c(6)  ij ˜p2  i ˜p2  i+1 + c(7)  ij ˜p3  i ˜pi+1 + c(8)  ij ˜pi˜p3  i+1 + c(9)  ij ˜p2  i ˜pi+1˜pi+2  �  +  n2  j  7 e2˜αj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='˜q �  c(10)  ij  ˜p2  i + c(11)  ij  ˜pi˜pi+1  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  with abbreviations c = (2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 6),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' c(1) = (6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' −18),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' c(2) = (18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 42),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(3) =  �  �  �  22 −2 −20  46 −2 40  10 34  40  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(4) =  �  �  �  26 26 32  8 44 32  14 26 2  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' c(5) =  �  �  �  7 7 7  7 7 7  3 7 7  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' c(6) =  �  �  �  0 2 20  6 20 2  6 0  0  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(7) =  �  �  �  4  2 −4  0 −4 8  10 0  0  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(8) =  �  �  �  4  8 −4  10 −4 2  0  0  0  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(9) =  �  �  �  0  2  −16  0  −16 −16  −30 −16  2  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(10) =  �  �  �  12 13 4  12 4  4  21 4 13  �  �  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  c(11) =  �  �  �  18 8 26  0 26 8  0  8  8  �  �  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  These charge are all in involution with the Hamiltonian ˜H and with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We note  – 17 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  that there is no non-trivial independent charge ˜Q4, as the only quantity that one can  construct at that order is proportional to ˜H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  We solve the corresponding equations of motion for ˜H  ˙˜q1 = p1,  ˙˜q2 = p2,  ˙˜q3 = p3,  ˙˜p1 = 4e−2˜q1+˜q2+˜q3 − 3e˜q1−˜q2 − e˜q1+˜q2−2˜q3  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4)  ˙˜p2 = 3e˜q1−˜q2 − e˜q1+˜q2−2˜q3 − 2e−2˜q1+˜q2+˜q3  ˙˜p3 = 2e˜q1+˜q2−2˜q3 − 2e−2˜q1+˜q2+˜q3  and ˜Q6, which we will note report here, numerically and depict our results in figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
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+page_content='6  q\uf02d  1(t)  3  2  1  1  2  3  p\uf02d  1(t)  (a)  0 < t < τH  τH < t < 15 τH  15 τH < t < 25 τH  25 τH < t < 35 τH  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
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+page_content='5  q\uf02d  2(t)  3  2  1  1  2  3  p\uf02d  2(t)  (b)  0 < t < τH  τH < t < 15 τH  15 τH < t < 25 τH  25 τH < t < 35 τH  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5 q\uf02d  3(t)  3  2  1  1  2  3  p\uf02d  3(t)  (c)  0 < t < τH  τH < t < 15 τ  15 τH < t < 25  25 τH < t < 35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  q\uf02d  1(t)  3  2  1  1  2  3  p\uf02d  1(t)  (d)  0 < t < τQ6  τQ6 < t < 5 τQ6  5 τQ6 < t < 10 τQ6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  q\uf02d  2(t)  3  2  1  1  2  3  p\uf02d  2(t)  (e)  0 < t < τQ6  τQ6 < t < 5 τQ6  5 τQ6 < t < 10 τQ6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5 q\uf02d  3(t)  3  2  1  1  2  3  p\uf02d  3(t)  (f)  0 < t < τQ6  τQ6 < t < 5 τQ6  5 τQ6 < t < 10 τQ6  Figure 9: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜qi, ˜pi), 1, 2, 3 as functions  of t panels (a), (b), (c) and panels (d), (e), (f), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial condition are taken in all  cases to ˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = −1, ˜p2(0) = −2 and ˜p3(0) = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Once again we identify almost periodic motions from the trajectories in both cases with  periods numerically computed as τ H ≈ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='04819143 and τ Q6 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10294605 for the phase  spaces of ˜H and ˜Q6, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In our concrete solutions for the equations of motion for  ˜H we find |ζ1(0) − ζ1(τ H)| ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3 × 10−9, |ζ2(0) − ζ2(τ H)| = |ζ3(0) − ζ3(τ H)| ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0229121,  |η1(0)−η1(τ H)| ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0122752, |η2(0)−η2(τ H)| ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='009117525 and |η3(0)−η3(τ H)| ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  As previously, in our depiction we distinguish between the first almost period and some  further periods that illustrate how the phase space is gradually filled inward and outwardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Comparing the ˜H and ˜Q6 phase spaces we notice that for large time the same confined  region in phase space will be filled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Furthermore we notice that, unlike as in the A2-case, even for the case when the  particle number does not match the rank of the algebra the motion is of a benign nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Thus in principal there is no need for a dimensional reduction to the centre-of-mass  frame from the point of view to obtain finite trajectories, but for completeness we also  analyse that case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' For this purpose we need to solve once more equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='20) for the  orthogonal matrix A and the two-dimensional roots βi, but now involving the G2-Cartan  matrix  K =  �  2 −1  −3 2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5)  – 18 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  In this case we find the solutions  A =  �  �  �  �  1  √  2  − 1  √  6  1  √  3  − 1  √  2 − 1  √  6  1  √  3  0  �  2  3  1  √  3  �  �  �  � ,  β1 =  �√  2, 0, 0  �  ,  β2 =  �  − 3  √  2,  �  3  2, 0  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6)  for the orthogonal matrix and the three dimensional roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ\uf02d  1(t)  4  2  2  4  η\uf02d  1(t)  (a)  0 < t < τH  τH < t < 15 τH  15 τH < t < 25 τH  25 τH < t < 35 τH  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0ζ\uf02d  2(t)  4  2  2  4  η\uf02d  2(t)  (b)  0 < t < τH  τH < t < 15 τH  15 τH < t < 25 τH  25 τH < t < 35 τH  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ\uf02d  1(t)  4  2  2  4  η\uf02d  1(t)  (c)  0 < t < τQ6  τQ6 < t < 5 τQ6  5 τQ6 < t < 10 τQ6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0ζ\uf02d  2(t)  4  2  2  4  η\uf02d  2(t)  (d)  0 < t < τQ6  τQ6 < t < 5 τQ6  5 τQ6 < t < 10 τQ6  Figure 10: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜ζi, ˜ηi), 1, 2 as functions  of t panels (a), (b) and panels (c), (d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial condition are taken in both cases  as ˜ζ1(0) = ˜ζ2(0) = 0, ˜η1(0) = 3/2  √  2 and ˜η2(0) = −  √  3/2  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Then, according to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='22) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='23) the coordinates and momenta transform as  ˜q =  � ˜ζ1  √  2 −  ˜ζ2  √  6, −  ˜ζ1  √  2 −  ˜ζ2  √  6,  �  2  3  ˜ζ2  �  = (˜q1, ˜q2, ˜q3),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='7)  ˜p =  �  ˜η1  √  2 − ˜η2  √  6, − ˜η1  √  2 − ˜η2  √  6,  �  2  3˜η2  �  = (˜p1, ˜p2, ˜p3),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='8)  and in reverse as  ˜ζ =  � ˜q1 − ˜q2  √  2  , − ˜q1 + ˜q2 − 2˜q3  √  6  , ˜q1 + ˜q2 + ˜q3  √  3  �  = (˜ζ1, ˜ζ2, 0),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9)  ˜η =  � ˜p1 − ˜p2  √  2  , − ˜p1 + ˜p2 − 2˜p3  √  6  , ˜p1 + ˜p2 + ˜p3  √  3  �  = (˜η1, ˜η2, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10)  – 19 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Transforming the charges according to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10) the equations of motion for the  Hamiltonian ˜H(˜ζ, ˜η) become  ˙˜ζ1 = ˜η1,  ˙˜ζ2 = ˜η2,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='11)  ˙˜η1 = 3  √  2e  �  3  2 ˜ζ2− 3  √  2 ˜ζ1 − 3  √  2e  √  2˜ζ1,  ˙˜η2 =  √  6e−  √  6˜ζ2 −  √  6e  �  3  2 ˜ζ2− 3  √  2 ˜ζ1,  and similarly for the ˜Q6-charge Hamiltonian that we do not report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We solve these equa-  tions numerically with the results depicted in figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Once more we find almost periodic  solutions with the same period as in the three dimensional case for all charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Remarkably, for some special initial conditions we can also identify full periodic so-  lutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The numerical solutions for the three dimensional case with the special initial  conditions ˜p2(0) = ˜p3(0) are depicted in figure 11 panel (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We observe that the periodic  solutions for i = 2 and i = 3 becoming identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Moreover, the trajectories for the ˜H  and ˜Q6 phase spaces coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' However, as seen in the inlets the periods differ by orders  of magnitude with τ H ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4210841 and τ Q6 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0068228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Similar features are observed  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6q\uf02d  i(t)  2  1  1  2  p\uf02d  i(t)  (a)  q\uf02d  1  q\uf02d  2,3  p\uf02d  1  p\uf02d  2,3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2  1  1  2  q\uf02d  i,p\uf02d  i  q\uf02d  1  q\uf02d  2,3  p\uf02d  1  p\uf02d  2,3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0068  2  1  1  2  q\uf02d  i,p\uf02d  i  q\uf02d,p\uf02d  1  q\uf02d/p\uf02d  2,3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6ζ\uf02d  i(t)  2  1  1  2  η\uf02d  i(t)  (b)  ζ  \uf02d  1  ζ  \uf02d  2  η\uf02d  1  η\uf02d  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2  1  1  2  ζ i,η\uf02d  i  ζ  \uf02d  1  ζ  \uf02d  2  η\uf02d  1  η\uf02d  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0068  2  1  1  2  ζ  \uf02d  i,η\uf02d  i  ζ\uf02d  1,η\uf02d  1  ζ\uf02d  2,η\uf02d  2  Figure 11: Affine G2-Toda lattice ˜H and ˜Q6 phase spaces for the variables (˜qi, ˜pi), 1, 2, 3 and  (˜ζi, ˜ηi), 1, 2 as functions of t panel (a) and panel (b), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial condition are taken  in both cases as ˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = 2, ˜p2(0) = ˜p3(0) = −1 and ˜ζ1(0) = ˜ζ2(0) = 0,  ˜η1(0) = 3/  √  2 and ˜η2(0) = −  √  3/  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  for the dimensionally reduced case depicted in panel (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The condition ˜p2(0) → ˜p3(0)  translates into ˜η2(0) → −1/  √  3˜η2(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Non-integrable perturbations  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1 Sensitivity of the initial conditions  There are various possibilities to investigate the stability of the above benign ghost solu-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The most delicate way to perturb them is to just vary the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' So far  we have always chosen them to be compatible with the centre-of-mass frame conditions  �  i pi = 0 and �  i qi = 0 or other constraints that result from reducing the dimensionality  of the representation space for the roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' It turns out that in the representations for which  the dimensions do not match up with the rank of the algebra the trajectories are rather  sensitive towards these impositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In figure 12 panels (a) to (c) we see that even a very  – 20 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  small violation of the condition �3  i=1 pi = 0 leads to the divergence of the trajectories  in the xi-directions in the phase spaces even for the Hamiltonians H and ˜H for A2 and  G2-theories as well as for the ˜Q6-charge of G2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In panels (d) to (f) we observe that the  trajectories for all independent B3-charges remain benign when �  i pi ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The violation  of �  i qi = 0 does not produce this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  50  100  150  200  250t  1  1  2  3  4  5  qi(t)  (a)  i=1  i=2  i=3  50  100  150  200  250t  1  1  2  3  4  5  q\uf02d  i(t)  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='25t  2  4  6  8  10  q\uf02d  i(t)  (c)  20  40  60  80  100  120  140  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  q\uf111  i(t)  (d)  i=1  i=2  i=3  20  40  60  80  100  120  140  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  q\uf111  i(t)  (e)  10  20  30  40 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  q\uf111  i(t)  (f)  Figure 12: Three dimensional phase space solutions for the coordinates as functions of t with  initial conditions �3  i=1 pi ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Panels (a), (b), (c): Manevolent A2-solutions for the Hamiltonian  H, G2-solutions for the Hamiltonian ˜H and the charge ˜Q6, respectively, all with initial conditions  ˜q1(0) = ˜q2(0) = ˜q3(0) = 0, ˜p1(0) = −1, ˜p2(0) = −2 ˜p3(0) = 3 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Panels (d), (e), (f): Benign  B3-solutions for the Hamiltonian ˆH and the charge ˆQ4, ˆQ6 respectively, all initial conditions are  taken to ˆq1(0) = ˆq2(0) = ˆq3(0) = 0, ˆp1(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2, ˆp2(0) = −1/2 ˆp3(0) = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5ζ\uf02d  i(t)  4  2  2  4  η\uf02d  i(t)  (a)  i=1  i=2  1  1  2  3  ζ\uf02d  i(t)  4  2  2  4  η\uf02d  i(t)  (b)  Figure 13: Two-dimensional affine G2-Toda lattice ˜H and ˜Q6 phase spaces (˜ζi, ˜ηi), 1, 2, panels  (a) and (b) respectively, for perturbed initial conditions as functions of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions are  taken in both cases as ˜ζ1(0) = ˜ζ2(0) = 0, ˜η1(0) = 1/  √  2 and ˜η2(0) = 3  √  3/  √  2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  In contrast the trajectories in the two dimensional phase spaces are rather robust  against very large perturbations of Q1(0) ̸= 0 as seen in figure 13 panels (a) and (b), where  we present the G2-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' In this case the divergence would occur in the third component  – 21 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  that has already been set to zero in the construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The trajectories may be compared  to the unperturbed case presented in figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2 Breaking of the integrability  There are of course many more options to perturb the higher derivative charge Hamiltonians  by adding small terms to them or even by deforming with additional terms of the same or  larger magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Here we only present one example to illustrate the general feature and  to establish the robustness of some of the higher charge Hamiltonian trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We leave  a more systematic presentation to future investigations [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We consider a Hamiltonian  in form of a soft deformation of the Q3-charge in the A2-theory in the two-dimensional  representation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='28) by adding a two-dimensional harmonic oscillator potential  Qp  3 (ζ1, ζ2, η1, η2) = Q3 (ζ1, ζ2, η1, η2) + ϵ1  2  �  ζ2  1 + ζ2  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1)  The solutions of the corresponding equations of motion ζi(t), ηi(t) with i = 1, 2 as functions  of time are depicted in figure 14 for several typical values of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We still find the previously  observed superposition of frequencies which vary with ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  A transition between rather  different types of qualitative behaviours is seen at ϵc ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='8944.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' When approaching this  value from below the maximal values for ζi(t) and ηi(t) increase smoothly and the functions  become more localised, but once ϵc is passed these values drop significantly and oscillations  re-occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' At this point we do not have proper explanation of this behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  20  40  60  80  100  120  140t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  ζi  (a)  ϵ = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  ζ1(t) ζ2(t)  20  40  60  80  100  120  140t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  ζi  (b)  ϵ = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  ζ1(t) ζ2(t)  20  40  60  80  100  120  140t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζi  (c)  ϵ = 0  ζ1(t) ζ2(t)  20  40  60  80  100  120  140 t  2  1  1  2  ζi  (d)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  ζ1(t) ζ2(t)  20  40  60  80  100  120  140 t  6  4  2  2  4  6  ζi  (e)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  ζ1(t) ζ2(t)  20  40  60  80  100  120  140 t  5  5  ζi  (f)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζ1(t) ζ2(t)  20  40  60  80  100  120  140 t  5  5  10  ζi  (g)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='89  ζ1(t) ζ2(t)  20  40  60  80  100  120  140 t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζi  (h)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9  ζ1(t)ζ2(t)  20  40  60  80  100  120  140 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ζi  (i)  ϵ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  ζ1(t)ζ2(t)  20  40  60  80  100  120  140 t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='6  ζi  (j)  ϵ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  ζ1(t)ζ2(t)  20  40  60  80  100  120  140t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ηi  (k)  ϵ = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  η1(t) η2(t)  20  40  60  80  100  120  140t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ηi  (l)  ϵ = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  η1(t) η2(t)  20  40  60  80  100  120  140t  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  ηi  (m)  ϵ = 0  η1(t) η2(t)  20  40  60  80  100  120  140t  2  1  1  2  ηi  (n)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1  η1(t)η2(t)  20  40  60  80  100  120  140 t  10  5  5  10  ηi  (o)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='3  η1(t)η2(t)  20  40  60  80  100  120  140 t  20  10  10  20  ηi  (p)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='5  η1(t)η2(t)  20  40  60  80  100  120  140 t  40  20  20  40  ηi  (q)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='89  η1(t)η2(t)  20  40  60  80  100  120  140 t  4  2  2  4  ηi  (r)  ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='9  η1(t)η2(t)  20  40  60  80  100  120  140 t  4  2  2  4  ηi  (s)  ϵ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='0  η1(t)η2(t)  20  40  60  80  100  120  140 t  3  2  1  1  2  3  ηi  (t)  ϵ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2  η1(t)η2(t)  Figure 14: Two-dimensional phase space components ζi and ηi with i = 1, 2 for the deformed  affine A2-Toda lattice charge Hamiltonian ˜Q3 in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='1) as functions of time t for different values of  ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' The initial conditions are taken in all cases as ζ1 = ζ2 = 0, η1 = −3/  √  6 and η2 = 3/2  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Naturally there are many more options to break the integrability of these systems [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 22 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Conclusions  We investigated many more examples that support the conjecture, originally put forward by  Smilga [9], that charges of integrable systems provide very promising candidates for higher  derivative theories that possess benign ghost sectors in part or all of their parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  For our examples of affine Toda lattice theories associated to different algebras we found  a multitude of possible scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We demonstrated that proper choice of the dimension  of the representation space is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Especially for the theories that used roots in their  formulation represented in the same dimension as the rank of the underlying algebras we  found benign solutions for higher charge Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Moreover, these solutions were quite  robust with regard to perturbations of the choice of the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' When deviating  from this setup and using higher dimensional representations for the roots we found the  coordinate solutions diverge as functions of time t for all the An examples investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  However, for the non-simply laced algebras G2 and B3 the trajectories for the higher charge  Hamiltonians stayed benign even in the higher dimensional cases, with the difference that  the former where very sensitive to changes of the initial conditions whereas the latter turned  out to be stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' So far these features remain at the level of observations and we can not  provide a deeper reason for these types of behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Based on the data generated here so  far it is too early to extract more generic features that might be shared by some class of  systems, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' simply laced versus non-simply laced etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' We leave these aspects for future  investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  We have also investigated some more extreme deformations of the integrable systems  by a soft harmonic oscillator potential in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' As noted previously for different  types of perturbations [9] many of the benign trajectories found maintain this feature, but  we also observed a critical point in the strength ϵ of these additional terms with an extreme  sensitivity regarding the characteristic behaviour of the phase space trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' It seems  worth to carry out some systematic investigations that clarify which type of perturbations,  and even deformations, might be permitted in order to maintain the benign nature of the  solutions [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Our results are summarised in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Q (D of rep) \\ g  A2  G2  B3  A6  A2, p1  G2, p1  B3, p1  A6, p1  A2, p2  H (r + 1)  b  b  b  b  m  m  b  m  H (r)  b  b  b  b  b  b  b  b  Q3 (r + 1)  m  ×  ×  m  m  ×  ×  m  Q3 (r)  b  ×  ×  b  b  ×  ×  b  b  Q4 (r + 1)  ×  b  m  ×  b  m  Q4 (r)  ×  b  b  ×  b  b  Q6 (r + 1)  b  b  m  m  b  m  Q6 (r)  b  b  b  b  b  b  Table 1:  Summary of results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' (b ≡ benign, m ≡ manevolent, × charge does not exist, r  ≡ rank of g, p1 ≡ perturbation with Q1(0) ̸= 0, p2 ≡ perturbation with harmonic oscillator  potential)  – 23 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  Acknowledgments: BT is supported by a City, University of London Research Fellow-  ship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' AF thanks the Instituto de Ciencias F´ısicas y Matem´aticas of the Universidad Austral  de Chile, where part of this work was completed for kind hospitality and Francisco Correa  for financial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  References  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Raidal and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Veerm¨ae, On the quantisation of complex higher derivative theories and  avoiding the Ostrogradsky ghost, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B 916, 607–626 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [2] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Biswas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Koivisto, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Mazumdar, Towards a resolution of the cosmological  singularity in non-local higher derivative theories of gravity, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Cos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' and Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  2010(11), 008 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Mignemi and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Wiltshire, Black holes in higher-derivative gravity theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  D 46(4), 1475 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Rivelles, Triviality of higher derivative theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B 577(3-4), 137–142  (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Dine and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Seiberg, Comments on higher derivative operators in some SUSY field  theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B 409(1-4), 239–244 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Smilga, Benign vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' malicious ghosts in higher-derivative theories, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B 706(3),  598–614 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Smilga, On exactly solvable ghost-ridden systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A 389, 127104 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Damour and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Smilga, Dynamical systems with benign ghosts, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' D 105(4),  045018 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Smilga, Benign ghosts in higher-derivative systems, in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' of Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Series, 2038,  012023 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Olshanetsky and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Perelomov, Classical integrable finite dimensional systems  related to Lie algebras, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 71, 313–400 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Mikhailov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Olshanetsky, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Perelomov, Two-dimensional generalized  Toda lattice, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 79(4), 473–488 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Olshanetsky and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Perelomov, Quantum integrable systems related to Lie  algebras, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 94, 313–404 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [13] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Lax, Integrals of nonlinear equations and solitary waves, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 21,  467–490 (1968).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [14] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Bourbaki, Groupes et Algebres de Lie: Elements de Mathematique, Hermann, Paris,1968 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Bohr, Zur theorie der fastperiodischen Funktionen, Acta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 46(1), 101–214 (1925).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Braden, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Corrigan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Dorey, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Sasaki, Affine Toda field theory and exact S  matrices, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B338, 689–746 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Fring and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Olive, The Fusing rule and the scattering matrix of affine Toda theory,  Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B379, 429–447 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 24 –  Higher derivative Hamiltonians with benign ghosts from affine Toda lattices  [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Fasiello, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Lim, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Tolley, Higher derivative theories with  constraints: Exorcising Ostrogradski’s Ghost, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Cos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' and Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 2013(02), 042  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Olive and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Turok, The symmetries of Dynkin diagrams and the reduction of Toda  field equations, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B215, 470 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Bordner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Sasaki, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Takasaki, Calogero-Moser models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' II: Symmetries and  foldings, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' of Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 101(3), 487–518 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Fring and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Korff, Affine Toda field theories related to Coxeter groups of  noncrystallographic type, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' B 729(3), 361–386 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Fring and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Manojlovi´c, G2-Calogero-Moser Lax operators from reduction, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' of Nonlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' 13(4), 467–478 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [23] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Bourbaki, Elements of Mathematics, Lie Groups and Lie Algebras, Chapters 4-6,  Springer, Berlin (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Fring and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content=' Turner, in preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
+page_content='  – 25 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddFIT4oBgHgl3EQfoCum/content/2301.11317v1.pdf'}
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+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+Tao Yang 1 Yuwang Wang 2 Yan Lv 3 Nanning Zheng 1
+Abstract
+In this paper, targeting to understand the underly-
+ing explainable factors behind observations and
+modeling the conditional generation process on
+these factors, we propose a new task, disentangle-
+ment of diffusion probabilistic models (DPMs), to
+take advantage of the remarkable modeling ability
+of DPMs. To tackle this task, we further devise
+an unsupervised approach named DisDiff. For the
+first time, we achieve disentangled representation
+learning in the framework of diffusion probabilis-
+tic models. Given a pre-trained DPM, DisDiff
+can automatically discover the inherent factors be-
+hind the image data and disentangle the gradient
+fields of DPM into sub-gradient fields, each con-
+ditioned on the representation of each discovered
+factor. We propose a novel Disentangling Loss
+for DisDiff to facilitate the disentanglement of the
+representation and sub-gradients. The extensive
+experiments on synthetic and real-world datasets
+demonstrate the effectiveness of DisDiff.
+1. Introduction
+As one of the most successful generative models, diffusion
+probabilistic models (DPMs) achieves remarkable perfor-
+mance in image synthesis. They use a series of probabilistic
+distributions to corrupt images in the forward process and
+train a sequence of probabilistic models converging to im-
+age distribution to reverse the forward process. Despite the
+remarkable success of DPM in tasks such as image gener-
+ation (Song et al., 2020b), text to images (Saharia et al.,
+2022), image editing (Meng et al., 2021), little attention
+has been paid on the representation learning (Zhang et al.,
+2022) based on DPM. Diff-AE (Preechakul et al., 2022) and
+PADE (Zhang et al., 2022) are the two methods proposed
+recently for representation learning by reconstructing the
+images in the DPM framework. However, the learned la-
+1Xi’an
+Jiaotong
+University
+2Tsinghua
+University
+3Microsoft
+Research
+Asia.
+Contact
+Tao
+Yang
+by
+<yt14212@stu.xjtu.edu.cn>.
+Correspondence to:
+Yuwang
+Wang <wang-yuwang@@mail.tsinghua.edu.cn>.
+tent representation can only be interpreted relying on an
+extra pre-trained with predefined semantics linear classifier.
+Although there are some degrees of freedom during imple-
+mentation, in this paper, we will refer DPMs exclusively to
+the Denoising Diffusion Probabilistic Models (DDPMs) (Ho
+et al., 2020).
+On the other hand, disentangled representation learn-
+ing (Higgins et al., 2018) aims to learn the representation
+of the underlying explainable factors behind the observed
+data and is thought to be one of the possible ways for AI to
+understand the world fundamentally. Different factors cor-
+respond to different kinds of image variations, respectively,
+and independently. Most of the methods learn the disen-
+tangled representation based on generative models, such as
+VAE (Higgins et al., 2017; Chen et al., 2018; Kim & Mnih,
+2018) and GAN (Lin et al., 2020). The VAE-based meth-
+ods have an inherent trade-off between the disentangling
+ability and generating quality (Higgins et al., 2017; Chen
+et al., 2018; Kim & Mnih, 2018). The GAN-based methods
+suffer from the problem of reconstruction due to the diffi-
+culty of gan-inversion (Wang et al., 2022). To the best of
+our knowledge, there is no method of learning disentangled
+representation using DPM.
+In this paper, we connect DPM to disentangled represen-
+tation learning, for the first time, and propose a new task:
+the disentanglement of DPM. Given a pre-trained DPM
+model, the goal of disentanglement of DPM is to learn dis-
+entangled representations for the underlying factors in an
+unsupervised manner, and learn the corresponding disentan-
+gled conditional sub-gradient fields, with each conditioned
+on the representation of each discovered factor.
+The benefits of the disentanglement of DPM are two-folds:
+(i) It enables totally unsupervised controlling of images
+by automatically discovering the inherent semantic factors
+behind the image data. These factors helps to extends the
+DPM conditions information from human defined ones such
+as annotations (Zhang et al., 2022)/image-text pairs (Kawar
+et al., 2022), or supervised pre-trained models (Kim et al.,
+2022) such as CLIP (Radford et al., 2021). One can also
+flexibly sample partial conditions on the part of the infor-
+mation introduced by the superposition of the sub-gradient
+field, which is novel in existing DPM works. (ii) DPM
+has remarkable performance on image generation quality,
+arXiv:2301.13721v1  [cs.CV]  31 Jan 2023
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+and is naturally friendly for the inverse problem, e.g., the
+inversion of DDIM (Song et al., 2020a), PADE. Compared
+to VAE (trade-off between the disentangling ability and gen-
+erating quality) or GAN (problem of gan-inversion), DPM
+is a better framework for disentangled representation learn-
+ing. Besides, as Locatello et al. (2019) points out, other
+inductive biases should be proposed except for total correla-
+tion. DPM makes it possible to adopt constraints from all
+different timesteps as a new type of inductive bias. Further,
+as Srivastava et al. (2020) points out, the information of
+data includes: factorized and non-factorized. DPM has the
+ability to sample non-factorized (non-conditioned) informa-
+tion (Ho & Salimans, 2022), which is naturally fitting for
+disentanglement.
+To address the task of disentangling the DPM, we further
+propose a unsupervised solution for the disentanglement of
+a pretrained DPM, named as DisDiff. DisDiff adopts an
+encoder to learn the disentangled presentation for each fac-
+tor, and a decoder to learn the corresponding disentangled
+conditional sub-gradient fields. We further propose a novel
+Disentangling Loss to make the encoded representation sat-
+isfy the disentanglement requirement, and reconstruct the
+input image as well.
+Our main contributions can be summarized as follows:
+• We present a new task: disentanglement of DPM, disen-
+tangling a DPM into several disentangled sub-gradient
+fields, which can improve the interpretability of DPM.
+• We build an unsupervised framework for disentangle-
+ment of DPM, DisDiff, which not only learns a disen-
+tangled representation but also disentangled gradient
+field for each factor.
+• We propose a Disentangling Loss for DPM to facilitate
+the disentanglement of different factor conditions and
+the sub-gradient fields.
+2. Related Works
+Diffusion Probabilistic Models DPMs have achieved
+comparable or superior image generation quality (Sohl-
+Dickstein et al., 2015; Song & Ermon, 2019; Ho et al.,
+2020; Song et al., 2020b; Jolicoeur-Martineau et al., 2020)
+than GAN (Goodfellow et al., 2020). Diffusion-based image
+editing has drawn much attention, and there are mainly two
+categories of works. Firstly, image-guided works edit an
+image by mixing the latent variables of DPM and the input
+image (Choi et al., 2021; Lugmayr et al., 2022; Meng et al.,
+2021). However, using images to specify the attributes for
+editing may cause ambiguity, as pointed out by Kwon et al.
+(2022). Secondly, the classifier-guided works (Dhariwal
+& Nichol, 2021; Avrahami et al., 2022; Liu et al., 2023)
+edit image by utilizing the gradient of an extra classifier.
+These methods require calculating the gradient, which is
+costly. Meanwhile, these methods require annotations or
+models pre-trained with labeled data. In this paper, we
+propose DisDiff to edit the image in an unsupervised way.
+On the other hand, little attention has been paid to repre-
+sentation learning in the literature on the diffusion model.
+Two related works are Diff-ae (Preechakul et al., 2022) and
+PADE (Zhang et al., 2022). Diff-ae (Preechakul et al., 2022)
+proposes a diffusion-based auto-encoder for image recon-
+struction. PADE (Zhang et al., 2022) uses a pre-trained
+DPM to build an auto-encoder for image reconstruction.
+However, the latent representation learned by these two
+works does not explicitly respond to the underlying factors
+of the dataset. To the best of our knowledge, our DisD-
+iff is the first diffusion-based framework for disentangled
+representation learning.
+Disentangled Representation Learning Bengio et al.
+(2013) introduced disentangled representation learning. The
+target of disentangled representation learning is to discover
+the underline explanatory factors of the observed data. The
+disentangled representation is defined as each dimension
+of the disentangled representation corresponding to an in-
+dependent factor. Based on such a definition, some VAE-
+based works achieve disentanglement (Chen et al., 2018;
+Kim & Mnih, 2018; Higgins et al., 2017; Burgess et al.,
+2018) only by the constraints on probabilistic distributions
+of representations. Locatello et al. (2019) points out the
+identifiable problem by proving that only these constraints
+are not enough for disentanglement, and extra inductive bias
+is required. For example, Yang et al. (2021) proposes to use
+symmetry properties modeled by group theory as inductive
+bias. Most of the methods of disentanglement are based on
+VAE. There are also some works based on GAN, including
+leveraging pretrained generative model (Ren et al., 2021).
+Our DisDiff introduces the constraint of all time steps during
+the diffusion process as a new type of inductive bias. Fur-
+thermore, DPM is capable of sampling non-factorized (non-
+conditioned) information (Ho & Salimans, 2022), which is
+naturally fitting for disentanglement. In this way, we shed
+light on disentanglement based on a new framework of the
+DPM.
+3. Background
+3.1. Diffusion Probabilistic Models (DPM)
+We take DDPM (Ho et al., 2020) as an example. DDPM
+adopts a sequence of fixed variance distributions q(xt|xt−1)
+as the forward process to collapse the image distribution
+p(x0) to N(0, I). These distributions are
+q(xt|xt−1) = N(xt;
+�
+1 − βtxt−1, βtI).
+(1)
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+Then we can sample xt by the following formula xt ∼
+N(xt; √¯αtx0, (1 − ¯αt)), where αt = 1 − βt and ¯αt =
+Πt
+t=1αt, i.e., xt = √¯αtx0+√1 − ¯αtϵ. The reverse process
+is fitting by other distributions parameterized by θ:
+pθ(xt−1|xt) = N(xt; µθ(xt, t), σtI).
+(2)
+where µθ(xt, t) is parameterize by a Unet ϵθ(xt, t). The
+training of it is to minimize the variational upper bound of
+negative log-likelihood:
+Lθ =
+E
+x0,t,ϵ ∥ϵ − ϵθ(xt, t)∥.
+(3)
+3.2. Representation learning from DPMs
+The classifier-guided method (Dhariwal & Nichol, 2021)
+uses the gradient of pre-trained classifier ∇xt log p(y|xt)
+to
+impose
+a
+condition
+on
+pre-trained
+DPM
+and
+obtain
+a
+new
+conditional
+DPM:
+N(xt; µθ(xt, t) +
+σt∇xt log p(y|xt), σt). Based on the classifier-guided sam-
+pling method, PADE (Zhang et al., 2022) proposes a method
+to learn auto-encoder for pre-trained DPM. Specifically,
+given a pre-trained DPM, PADE introduces an encoder Eφ,
+and the representation can be derived by z = Eφ(x0). They
+use a gradient estimator Gψ(xt, z, t) to simulate gradient
+∇xt log p(z|xt) for reconstruction.
+By this means, they use it to assemble the unconditional
+DPM as a new conditional DPM as the decoder. Similar
+to regular DPM N(xt; µθ(xt, t) + σtGψ(xt, z, t), σt), we
+can use the following objective to train encoder Eφ and the
+network Gψ:
+Lψ =
+E
+x0,t,ϵ ∥ϵ − ϵθ(xt, t) +
+√αt
+√1 − ¯αt
+βt
+σtGψ(xt, z, t)∥.
+(4)
+4. Method
+In this section, we first introduce the formulation of the
+proposed task in Section 4.1. Then we present the overview
+of DisDiff in Section 4.2. After that, we present the detailed
+implementation of the proposed Disentangling Loss in Sec-
+tion 4.3 and how to balance it with reconstruction loss in
+Section 4.4. Finally, in Section 4.5, we discuss the relation
+between Disentangling Loss and the total correlation, which
+is a necessary condition for disentanglement.
+4.1. Disentanglement of DPM
+We assume that dataset D is generated by N underlying
+ground truth factors N factors C = {1, 2, . . . , N}. For ex-
+ample, for Shapes3D, the underlying concept factors include
+background color, floor color, object color, object shape, ob-
+ject scale, and pose. Therefore, there is a one-one mapping
+(a) Image Space
+①
+𝐺!(𝑥", 𝑡, 𝑧!)
+𝐺#(𝑥", 𝑡, 𝑧#)
+𝐺$(𝑥", 𝑡, 𝑧$)
+②
+⑤
+⑥
+⑦
+①
+③
+④
+Background
+Color is Blue
+Object Color is Red
+Floor Color
+is Green
+②
+③
+④
+⑤
+⑥
+⑦
+(c) Sampled Images
+(b) Ground Truth Factor Space
+①
+②
+③
+④
+⑤
+⑥
+⑦
+Figure 1. Illustration of disentanglement of DPMs. (a) is the di-
+agram of image space. (b) is the diagram of factor space. (c)
+is the demonstration of sampled images. Surface indicates the
+conditional distribution of a single factor p(x|zc). Different col-
+ors correspond to different factors. Here we show three factors:
+object color, background color, and floor color. Arrows are gradi-
+ent fields ∇xt log p(zc|xt) parameterized by Gc
+φ(xt, t, zc). The
+learned Gc
+φ(xt, t, zc) converges the noise data to the conditional
+distribution. The black points are the sampled images, which are
+shown in (c).
+between each sample and each tuple of factor representa-
+tions, h : x0 �→ (f 1, . . . , f N), ∀x0 ∈ D. The data distri-
+bution p(x) can be disentangled into N independent distri-
+butions {p(x|f k)|k = 1, . . . , N}, and each conditioned on
+only one factor, which is shown as the curved surface of
+image space in Figure 1(a). The DPM learns a sequence
+of distributions {pt(x)|t = T, T − 1, . . . , 0} converging to
+p(x). Such convergence is achieved by optimizing the corre-
+sponding gradient fields {∇x log pt(x)|t = T, T−1, . . . , 0}
+(learned by ϵθ with parameters θ). The disentangled DPM
+contains N sequences of distributions, converging to N dis-
+tributions {p(x|f c)|c = 1, . . . , N} respectively. The target
+of disentanglement of a DPM is, for each factor c, to learn
+Gc
+ψ to estimate ∇x log pt(x|f c), which corresponds to the
+arrows pointing to the curve surface in Figure 1(a). One
+may note that in the data sample space, such as image space,
+the curved surfaces indicate that the data sample space is not
+well-organized, and the variations of the factors are entan-
+gled. Compared to the image space, the ground truth factor
+space is well-organized, and the subspaces of factors are
+orthogonal between each other, as shown in Figure 1(b). Dis-
+entangled representation learning aims to model the ground
+truth factor space using an encoder Eφ, which encodes the
+raw data into disentangled representations. The disentan-
+gled representation is ideal for representing the conditions
+for the conditional distributions {p(x|f c)|c = 1, . . . , N}
+of the disentangled DPM. Conditioned on the disentangled
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+𝑥!
+𝑥"
+𝜖#(𝑥", 𝑡)
+𝐺$(𝑥", 𝑡, 𝑧$)
+𝐺%(𝑥", 𝑡, 𝑧%)
+𝐺&(𝑥", 𝑡, 𝑧&)
+Pre-trained DPM
+Encoder 𝐸'
+Decoder 𝐺#
+(
+Disentangled 
+Representations
+𝑧$
+𝑧%
+𝑧&
+Disentangled
+Gradient Fields
+Figure 2. Illustration of DisDiff. Gray networks indicate the pre-
+trained Unet of DPM ϵθ(xt, t). Image x0 is first to be encoded
+to representations {z1, z2, . . . zN} of different factors by encoder
+Eφ (N = 3 in the figure). We thus decode the representations by
+decoder Gc
+θ. By this means, we can obtain the gradient field of
+the corresponding factor. With the obtained gradient field, we can
+sample the image under the corresponding condition.
+representation, the disentangled DPM can flexibly generate
+the data samples. In this paper, we propose a method named
+DisDiff, as a solution for the disentanglement of a DPM.
+4.2. Overview of DisDiff
+The overview framework of DisDiff is shown in Figure
+2. Given a pre-trained unconditional DPM on dataset D
+with N factors C = {1, 2, . . . , N}, e.g., a DDPM model
+with parameters θ, pθ(xt−1|xt) = N(xt−1; µθ(xt, t), σt),
+our target is to disentangle the DPM in an unsupervised
+manner. Specifically, given x0 ∈ D, for each factor c ∈ C,
+the goal is to learn the disentangled representation zc via
+an encoder Eφ (with learnable parameters φ) as Eφ(x0) =
+{E1
+φ(x0), E2
+φ(x0), . . . , EN
+φ (x0)} = {z1, z2, . . . , zN}, and
+the disentangled gradient field ∇xt log p(zc|xt). Therefore,
+the conditional reverse process (condition on factors S ⊆ C,
+and zS = {zc|c ∈ S}) can be formulated by a Gaussian
+distribution pθ(xt−1|xt, zS) with a shifted mean:
+N(xt−1; µθ(xt, t) + Σt
+�
+c∈S
+∇xt log p(zc|xt), σt).
+(5)
+Since p(zc|xt) is intractable, we use Gc
+ψ(xt, zc, t), c ∈ C,
+with learnable parameters ψ, to estimate the gradient fields
+∇xt log p(zc|xt), c ∈ C.
+With different options of S, one can flexibly devise the ap-
+proximator following score-based conditioning trick (Song
+et al., 2020b; Song & Ermon, 2019) as follows:
+ϵψ(xt, zS, t) = ϵθ(xt, t)−
+�
+c∈S
+√
+1 − ¯αtGc
+ψ(xt, zc, t). (6)
+Then one can derive the corresponding data sample using
+Tweedie’s Formula as:
+ˆxS
+0 = xt − √1 − ¯αtϵψ(xt, zS, t)
+√¯αt
+.
+(7)
+𝜖!(𝑥", 𝑡)
+Disentangling 
+Loss
+𝑧#
+𝑧$
+𝑧%
+𝐺#(𝑥", 𝑡, 𝑧#)
+𝐺$(𝑥", 𝑡, 𝑧$)
+𝐺%(𝑥", 𝑡, 𝑧%)
+Encoder 𝐸&
+Encoder 𝐸&
+Decoder 𝐺!
+'
+Figure 3. The demonstration of disentangling loss. We first sample
+a factor c and then decode the representation zc to obtain the
+gradient field of the corresponding factor. With this gradient field,
+we can obtain the predicted x0 of the corresponding factor. On the
+other hand, we can obtain predicted ˆx0 of the original pre-trained
+DPM. We then encode the images into two different representations
+and calculate the disentangling loss.
+For example, one can choose only one disentangled factor,
+i.e., setting S = c, and use the gradient ∇xt log p(zc|xt)
+(only conditioned on zc) to guide the sampling of the pre-
+trained DPM, resulting in the predicted sample ˆxc
+0. We leave
+ˆx0 to denote the predicted data sample using the pretrained
+unconditioned DPM ϵθ(xt, t).
+According to the completeness requirement of disentan-
+glement, the disentangled representation Eφ(x0) should
+contain the full information of sample x0, i.e., one can re-
+construct x0 by using all the disentangled representations
+Eφ(x0) as a condition. Following Equation 7, we set S = C
+to include all the disentangled representation, resulting in
+the derived data sample ˆxC
+0. One may note that this is ex-
+actly the reconstruction case in PDAE. Here, we adopt the
+same reconstruction loss, denoted as
+Lr =
+E
+x0,t,ϵ ∥ϵ − ϵθ(xt, t)
++
+√αt
+√1−¯αt
+βt
+σt
+�
+c∈C Gc
+ψ(xt, zc, t)∥.
+(8)
+Besides the above completeness requirement, each disen-
+tangled representation should only reflect one correspond-
+ing factor independently, i.e., the disentanglement require-
+ment. We devise a novel loss, named Disentangling Loss,
+to achieve the disentanglement of the pre-trained DPM. In
+the following, we will present the Disentangling Loss and
+the total loss.
+4.3. Disentangling Loss
+In this section, we provide the detailed implementation of
+Disentangling Loss. As discussed above, given sample x0
+and its disentangled representation E(x0), we randomly
+sample c ∈ C and use S = c to get the conditioned sam-
+ple ˆxc
+0 (only conditioned on representation zc). Accord-
+ing to the disentanglement requirement, compared to the
+unconditioned predicted image ˆx0 (sampling with the pre-
+trained unconditioned DPM ϵθ(xt, t)), ˆxc
+0 should satisfy the
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+following two conditions: (i) invariant condition, for the
+k-th (k ̸= c, k ∈ C) disentangled representation, Ek
+φ(ˆx0)
+should be the same with Ek
+φ(ˆx0), (ii) variant condition, for
+the c-th disentangled representation, the conditioned one
+Ec
+φ(ˆx0) should be closer to Ec
+φ(x0) than the unconditioned
+one Ec
+φ(ˆx0). In the following, we provide the detailed im-
+plementation of the above two conditions. According to
+the above (i) invariant condition, the k-th (k ̸= c, k ∈ C)
+representation should be kept the same. We encode the two
+samples using Eφ and derive the distance scalar between
+the k-th representation as:
+dk = ∥Ek
+φ(ˆxc
+0) − Ek
+φ(ˆx0)∥.
+(9)
+Then the distance vector can be represented as d
+=
+[d1, d2, . . . , dC] Finally, we use the cross-entropy loss to
+identify the index c and restrain others unchanged:
+Lin =
+E
+x0,t,ϵ,c[CrossEntropy(d, c)].
+(10)
+We denote it as invariant loss Lin.
+For the (ii) variant condition, we first calculate the distance
+scalar of the k-th representation between ˆx0 (unconditioned)
+and x0, ˆxc
+0 (conditioned) and x0 as following respectively:
+dn
+k
+= ∥Ek
+φ(ˆx0) − Ek
+φ(x0)∥
+dp
+k
+= ∥Ek
+φ(ˆxc
+0) − Ek
+φ(x0)∥
+(11)
+According to the above condition (ii), for the conditioned
+factor c, dn
+c − dp
+c should be maximized, while others, i.e.
+dn
+k −dp
+k (k ̸= c, k ∈ C), should be minimized to 0. Similarly
+we adopt an entropy loss to achieve the subjective as:
+Lva =
+E
+x0,t,ϵ,c[CrossEntropy(dn − dp, c)],
+(12)
+where dn = [dn
+1, dn
+2, . . . , dn
+C] and dp = [dp
+1, dn
+2, . . . , dp
+C].
+We denote it as variant loss Lva. So far, we introduce the
+Disentangling Loss, Lin and Lva.
+4.4. Total Loss
+As we need to satisfy both the completeness and disentangle-
+ment requirements, the total loss includes the above recon-
+struction loss (Lr) and Disentangling Loss (Lin and Lva).
+However, the weight to balance the two-part loss should be
+carefully set. The reason is the following. Note that the
+above Disentangling Loss Lin and Lva is conditioned on
+the sampled time step of the diffusion process. However, the
+condition of the diffusion model varies among different time
+steps. For example, if t is close to T, Gc
+ψ(xt, zc, t) mainly
+condition on zc. And if t is close to 0, the output mainly con-
+ditions on xt. Therefore, for different time steps, different
+weights should be used for Disentangling Loss. Considering
+that the difference between the inputs of encoder reflexes
+such change on condition. Specifically, if t is close to T,
+the difference between ˆxt and ˆxc
+t is small. In addition, if
+t is close to 0, such a difference is significant. Based on
+the above discussion, the more the output condition on zc,
+the higher the weight should be. We thus propose to use
+the MSE distance between the inputs of the Encoder as the
+weight coefficient:
+γd = λ∥ˆx0 − ˆxc
+0∥2,
+(13)
+where λ is a hyper-parameter. We stop the gradient of ˆx0
+and ˆxc
+0 for calculating the weight coefficient γd.
+The total loss can be calculated as:
+La = Lr + γd(Lin + Lva).
+(14)
+4.5. Relation to Total Correlation
+In this section, we demonstrate that Total Correlation is a
+necessary condition for our disentangling loss. Total Corre-
+lation is once regarded as an important constraint for repre-
+sentation disentanglement. However, Locatello et al. (2019)
+point out that besides total Correlation, other inductive bi-
+ases should also be considered. In this paper, we introduce
+Disentangling Loss for DPM as an additional inductive bias.
+We prove that Total Correlation is a necessary condition.
+Specifically, if the reconstruction loss is minimized, we have
+∇xt log p(z1, . . . , zN|xt) =
+�
+c∈C
+Gc
+ψ(xt, zc, t)
+(15)
+On the other hand, if the disentangling loss is mini-
+mized, we have Gc
+ψ(xt, zc, t) = ∇xt log p(zc|xt). Since
+�
+c∈C ∇xt log p(zc|xt) = ∇xt log Πc∈Cp(zc|xt) always
+hold, bring these two equations into Eq. 15, we have
+∇xt log p(z1, . . . , zN|xt) = ∇xt log Πc∈Cp(zc|xt) (16)
+The equation above results in the fisher divergence between
+the joint distribution p(z1, . . . , zN|xt) and the product of
+marginal distribution Πc∈Cp(zc|xt) is 0. Therefore the Total
+Correlation holds for all xt:
+p(z1, . . . , zN|xt) = Πc∈Cp(zc|xt)
+(17)
+5. Experiments
+In this section, we conduct experiments to demonstrate the
+effectiveness of DisDiff on both synthetic and real-world
+datasets.
+5.1. Experimental Setup
+Implementation Details. x0 can be an image space or
+a latent space of images. For image diffusion, we take
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+Table 1. Comparisons of disentanglement on the FactorVAE score and DCI disentanglement metrics (mean ± std, higher is better).
+DisDiff achieves state-of-the-art performance with a large margin in almost all the cases compared to all baselines. Especially on the
+MPI3D dataset.
+Method
+Cars3D
+Shapes3D
+MPI3D
+FactorVAE score
+DCI
+FactorVAE score
+DCI
+FactorVAE score
+DCI
+VAE-based:
+FactorVAE
+0.906 ± 0.052
+0.161 ± 0.019
+0.840 ± 0.066
+0.611 ± 0.082
+0.152 ± 0.025
+0.240 ± 0.051
+β-TCVAE
+0.855 ± 0.082
+0.140 ± 0.019
+0.873 ± 0.074
+0.613 ± 0.114
+0.179 ± 0.017
+0.237 ± 0.056
+GAN-based:
+InfoGAN-CR
+0.411 ± 0.013
+0.020 ± 0.011
+0.587 ± 0.058
+0.478 ± 0.055
+0.439 ± 0.061
+0.241 ± 0.075
+Pre-trained GAN-based:
+LD
+0.852 ± 0.039
+0.216 ± 0.072
+0.805 ± 0.064
+0.380 ± 0.062
+0.391 ± 0.039
+0.196 ± 0.038
+GS
+0.932 ± 0.018
+0.209 ± 0.031
+0.788 ± 0.091
+0.284 ± 0.034
+0.465 ± 0.036
+0.229 ± 0.042
+DisCo
+0.855 ± 0.074
+0.271 ± 0.037
+0.877 ± 0.031
+0.708 ± 0.048
+0.371 ± 0.030
+0.292 ± 0.024
+Diffusion-based:
+DisDiff-VQ (Ours)
+0.976 ± 0.018
+0.232 ± 0.019
+0.902 ± 0.043
+0.723 ± 0.013
+0.617 ± 0.070
+0.337 ± 0.057
+Table 2. Ablation study of DisDiff on image tokenizer, compo-
+nents, batchsize and token numbers.
+Method
+FactorVAE score
+DCI
+DisDiff-IM
+0.783
+0.655
+DisDiff-KL
+0.837
+0.660
+DisDiff-VQ
+0.902
+0.723
+DisDiff-VQ wo Lin
+0.782
+0.538
+DisDiff-VQ wo Lva
+0.810
+0.620
+DisDiff-VQ wo Ldis
+0.653
+0.414
+wo detach
+0.324
+0.026
+constant weighting
+0.679
+0.426
+loss weighting
+0.678
+0.465
+attention condition
+0.824
+0.591
+wo pos embedding
+0.854
+0.678
+wo orth embedding
+0.807
+0.610
+latent number N= 6
+0.865
+0.654
+latent number N= 10
+0.902
+0.723
+pre-trained DDIM as the DPM (DisDiff-IM). For latent
+diffusion, we can take the pre-traind KL-version latent dif-
+fusion model (LDM) or vq-version LDM as DPM (DisDiff-
+KL and DisDiff-VQ). For detail of network Gθ, we fol-
+low Zhang et al. (2022) to use the extended Group Normal-
+ization (Dhariwal & Nichol, 2021) by applying scaling &
+shifting twice. The difference is we use learn-able position
+embedding to indicate c:
+AdaGN(h, t, zc) = zc
+s(tc
+sGN(h) + tc
+b) + zc
+b
+(18)
+where GN denotes group normalization, and [tc
+s, tc
+b], [zc
+s, zc
+b]
+are obtained from a linear projection:
+zc
+s, zc
+b
+=
+linearProj(zc), tc
+s, tc
+b = linearProj([t, pc]). In addition,
+pc is the leanable positional embedding. h is the feature
+map of Unet.
+Datasets For evaluation of disentanglement, we fol-
+low Ren et al. (2021) to use the popular public datasets:
+Shapes3D (Kim & Mnih, 2018), a dataset of 3D shapes.
+MPI3D (Gondal et al., 2019), a 3D dataset recorded in a
+controlled environment, and Cars3D (Reed et al., 2015),
+a dataset of CAD models generated by color renderings.
+All experiments are conducted on 64x64 image resolution,
+which is the same as the literature. For real-world datasets,
+we conduct our experiments on CelebA (Liu et al., 2015).
+Baselines & Metrics Since DisDiff is the first diffusion-
+based disentanglement model.
+Therefore, we compare
+the performance with VAE-based and GAN-based base-
+lines. Specifically, the VAE-based models include: Fac-
+torVAE (Kim & Mnih, 2018), and β-TCVAE (Chen et al.,
+2018). The GAN-based baselines include InfoGAN-CR
+(Lin et al., 2020), GANspace (GS) (H¨ark¨onen et al., 2020),
+LatentDiscovery (LD) (Voynov & Babenko, 2020) and
+DisCo (Ren et al., 2021). Considering the influence of
+performance on the random seed. We have 10 runs for
+each method. We use four representative metrics: Factor-
+VAE score (Kim & Mnih, 2018), and the DCI (Eastwood
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+source
+target
+factor 1
+factor 2
+factor 3
+factor 4
+factor 5
+Figure 4. The qualitative results on Shapes3D. The source images
+provide the representations of the generated image. The target
+image provides the representations for swapping. Other rows
+of images are generated by swapping the representation of the
+corresponding factor on Shapes3D. DisDiff learns pure factors by
+each representation. The learned factors are azimuth, background
+color, floor color, object color, and object shape, respectively.
+& Williams, 2018). However, since {zc} are vector-wise
+represenatation, we follow Du et al. (2021) to perform PCA
+as post-processing on the representation before evaluation.
+5.2. Main Results
+We conduct the following experiments to verify the disentan-
+glement ability of proposed DisDiff model. We regard the
+learned representation {zc} as the disentangled one and use
+the popular metrics in disentangled representation literature
+for evaluation.
+The quantitative comparison results of disentanglement un-
+der different metrics are shown in Table 1. As shown in the
+table, DisDiff outperforms the baselines, demonstrating the
+model’s superior disentanglement ability. Compared with
+the VAE-based methods, since these methods suffer from the
+trade-off between generation and disentanglement (Lezama,
+2018) but DisDiff does not. As for the GAN-based methods,
+the disentanglement is learned by exploring the latent space
+of GAN. Therefore, the performance is limited by the latent
+space of GAN. DisDiff leverages the gradient field of data
+space to learn disentanglement and does not have such limi-
+tations. In addition, DisDiff resolves the disentanglement
+problem into 1000 sub-problems under different time steps,
+which reduces the difficulty.
+source
+target
+factor 1
+factor 2
+factor 3
+factor 4
+Figure 5. The qualitative results on CelebA. Each row of images is
+generated by swapping the representation of the corresponding fac-
+tor on CelebA. DisDiff learns pure factors by each representation.
+The learned factors are bangs, skin color, expression, and hair.
+5.3. Qualitative Results
+In order to analyze the disentanglement of DisDiff qualita-
+tively. We swap the representation {zc} of two images one
+by one and sample the image conditioned on the swapped
+representation. We follow LDM-VQ to sample images in
+200 steps. For the popular dataset of disentanglement litera-
+ture, we take shapes3d as an example. As shown in Figure
+4, DisDiff successfully learned pure factors. Compared with
+the VAE-based methods, DisDiff has better image quality.
+For the real-world dataset, since there are no ground truth
+factors, we demonstrate the qualitative results in Figure. We
+take CelebA as an example, as demonstrated in Figure 5,
+DisDiff also achieves good disentanglement on real-world
+datasets. Please note that compare with Disco (Ren et al.,
+2021). DisDiff has the ability of reconstruction, which is
+not available for DisCo.
+5.4. Ablation Study
+In order to analyze the effectiveness of the proposed parts
+of DisDiff, we design an ablation study from the following
+five aspects: DPM type, Disentangling Loss, loss weighting,
+condition type, and latent number. We take shapes3d as the
+dataset to conduct these ablation studies.
+DPM type The disentanglement of DisDiff is derived by the
+decomposition of the gradient field of the diffusion model.
+Therefore, the diffusion space influence the performance of
+DisDiff. We take Shapes3D as an example, it is hard for the
+model to learn shape and scale in image space, but much
+easier in the latent space of auto-encoder. Therefore, we
+compare the performance of DisDiff with different diffusion
+types: image diffusion model, e.g., DDIM (DisDiff-IM),
+KL-version latent diffusion model (DisDiff-KL) and VQ-
+version latent diffusion model, e.g., VQ-LDM (DisDiff-VQ).
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+target
+factor 1
+factor 2
+factor 3
+factor 4
+factor 5
+Figure 6. The partially condition sampling on Shapes3D. The tar-
+get image provides the representation of partially sampling image.
+Each row of images are generated by imposing a single gradient
+field of the corresponding factor on the pre-tained DPM. DisDiff
+samples image condition on only a single factor. The sampled
+image has a fixed factor, e.g., the images of factor 1 have same
+background color with target one. The conditioned factors are:
+azimuth, background color, floor color, object color and object
+shape, respectively.
+As shown in Table 2, the LDM-version DisDiff outperforms
+image-version DisDiff as expected. In addition, KL-LDM
+has more complex latent space than VQ-LDM. DisDiff-VQ
+outperforms DisDiff-KL.
+Disentangling Loss Disentangling loss is composed of two
+parts: Invariant loss Lin and Variant loss Lva. In order to
+verify the effectiveness of each part, we train DisDiff-VQ
+without it. Lin encourages in-variance of representation not
+being sampled, which means that the sampled factor will
+not affect the representation of other factors (zk, k ̸= l of
+generated ˆxl
+0). On the other hand, Lva encourages the rep-
+resentation of sampled factor (zl of generated ˆxl
+0) should be
+close to the corresponding one of x0. As shown in Table 2,
+mainly Lin encourage the disentanglement, and Lva further
+constrain the model and improve the performance. Note that
+the disentangling loss is optimized w.r.t. Gθ but not Ec
+θ. If
+the loss is optimized on both modules, as shown in Table 2,
+DisDiff fails to achieve disentanglement. The reason is that
+the disentangling loss influenced the encoder, so DisDiff
+failed to reconstruct the input image.
+Loss weighting As introduced, considering that the condi-
+tion varies among time steps, we adopt the difference of
+the encoder as the weight coefficient. In this section, we
+explore other options to verify its effectiveness. We offer
+two different weighting types: constant weighting and loss
+weighting. The first type is the transitional way of weight-
+ing. The second one is to balance the scale of Distangling
+Loss and diffusion loss. From Table 2, these two types of
+weighting hurt the performance to a different extent.
+target
+factor 1
+factor 2
+factor 3
+factor 4
+Figure 7. The partially condition sampling on CelebA. The target
+image provides the representations of the sampling image. Images
+of each row are conditioned on a single factor. DisDiff samples
+image condition on only a single factor. Therefore, the sampled
+image in the same row has a fixed factor, e.g., the images of factor
+1 have the same bangs as the target one. The conditioned factors
+are bangs, skin color, expression, and hair, respectively.
+Condition type DisDiff follows PADE (Zhang et al., 2022)
+and (Dhariwal & Nichol, 2021) to adopt AdaGN for in-
+jecting the condition. However, there is another option in
+the literature: cross-attention. As shown in Table 2, cross-
+attention hurt the performance but not much. We infer that
+the reason may be that the condition is only a single token,
+which limits the ability of attention. We use learnable or-
+thogonal positional embedding to indicate different factors.
+As shown in Table 2, no matter whether no positional embed-
+ding (wo pos embedding) or traditional learnable positional
+embedding (wo orth embedding) hurt the performance. The
+reason is that the orthogonal embedding is always different
+from each other in all training steps.
+Latent number The number of latent is a important hyper-
+parameter set in-advance. We conduct ablation study on this
+hyper-parameter. As shown in Table 2, the latent number
+only has limited influence on the performance.
+5.5. Partially Condition Sampling
+As discussed in Section 4.2, DisDiff can partially sample
+conditions on the part of the factors. Specifically, we can
+use Equation 6 to sample image condition on factors set S.
+We take Shapes3D, as an example, when DisDiff sampling
+image condition on background color is red. We obtain a
+set of images of the background color red and other factors
+randomly sampled. From Figure 6, we see that DisDiff has
+the ability to condition individual factors on Shapes3D. In
+addition, DisDiff also has such ability on the real-world
+dataset (CelebA) in Figure 7. DisDiff has the ability to
+sample information exclusively to conditions.
+6. Conclusion
+In this paper, we demonstrate a new task: disentanglement
+of DPM, by disentangling a DPM into several disentangled
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+gradient fields, we can improve the interpreter-ability of
+DPM. To solve the task, we build an unsupervised diffusion-
+based disentanglement framework named DisDiff. DisDiff
+learns a disentangled representation of the input image in
+the diffusion process. In addition, for each factor, DisDiff
+learns a disentangled gradient field, which brings the follow-
+ing new properties for disentanglement literature. DisDiff
+adopted disentangling constraints on all different timesteps,
+which is a new inductive bias. Except for image editing,
+with the disentangled DPM, we also can sample partially
+conditions on the part of the information by superposition of
+the sub-gradient field. For future work, Applying DisDiff to
+more general conditioned DPM is a direction worth explor-
+ing. Besides, utilizing the proposed disentangling method
+to pre-trained conditional DPM makes it more flexible.
+References
+Avrahami, O., Lischinski, D., and Fried, O. Blended diffu-
+sion for text-driven editing of natural images. In Proceed-
+ings of the IEEE/CVF Conference on Computer Vision
+and Pattern Recognition, pp. 18208–18218, 2022.
+Bengio, Y., Courville, A. C., and Vincent, P. Representation
+learning: A review and new perspectives. PAMI, 2013.
+Burgess, C. P., Higgins, I., Pal, A., Matthey, L., Watters, N.,
+Desjardins, G., and Lerchner, A. Understanding disentan-
+gling in beta-vae. arXiv:1804.03599, 2018.
+Chen, R. T., Li, X., Grosse, R. B., and Duvenaud, D. K.
+Isolating sources of disentanglement in variational au-
+toencoders. In NeurPIS, 2018.
+Choi, J., Kim, S., Jeong, Y., Gwon, Y., and Yoon, S. Ilvr:
+Conditioning method for denoising diffusion probabilistic
+models. arXiv preprint arXiv:2108.02938, 2021.
+Dhariwal, P. and Nichol, A. Diffusion models beat gans
+on image synthesis. Advances in Neural Information
+Processing Systems, 34:8780–8794, 2021.
+Du, Y., Li, S., Sharma, Y., Tenenbaum, J., and Mordatch, I.
+Unsupervised learning of compositional energy concepts.
+Advances in Neural Information Processing Systems, 34,
+2021.
+Eastwood, C. and Williams, C. K. I. A framework for the
+quantitative evaluation of disentangled representations.
+In ICLR, 2018.
+Gondal, M. W., Wuthrich, M., Miladinovic, D., Locatello,
+F., Breidt, M., Volchkov, V., Akpo, J., Bachem, O.,
+Sch¨olkopf, B., and Bauer, S. On the transfer of inductive
+bias from simulation to the real world: a new disentangle-
+ment dataset. In NeurIPS, 2019.
+Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B.,
+Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y.
+Generative adversarial networks. Communications of the
+ACM, 63(11):139–144, 2020.
+H¨ark¨onen, E., Hertzmann, A., Lehtinen, J., and Paris, S.
+Ganspace: Discovering interpretable GAN controls. In
+NeurIPS, 2020.
+Higgins, I., Matthey, L., Pal, A., Burgess, C., Glorot, X.,
+Botvinick, M., Mohamed, S., and Lerchner, A. beta-
+vae: Learning basic visual concepts with a constrained
+variational framework. In ICLR, 2017.
+Higgins, I., Amos, D., Pfau, D., Racaniere, S., Matthey,
+L., Rezende, D., and Lerchner, A.
+Towards a defi-
+nition of disentangled representations. arXiv preprint
+arXiv:1812.02230, 2018.
+Ho, J. and Salimans, T. Classifier-free diffusion guidance.
+arXiv preprint arXiv:2207.12598, 2022.
+Ho, J., Jain, A., and Abbeel, P. Denoising diffusion proba-
+bilistic models. Advances in Neural Information Process-
+ing Systems, 33:6840–6851, 2020.
+Jolicoeur-Martineau, A., Pich´e-Taillefer, R., Combes, R.
+T. d., and Mitliagkas, I. Adversarial score matching and
+improved sampling for image generation. arXiv preprint
+arXiv:2009.05475, 2020.
+Kawar, B., Zada, S., Lang, O., Tov, O., Chang, H., Dekel,
+T., Mosseri, I., and Irani, M. Imagic: Text-based real
+image editing with diffusion models.
+arXiv preprint
+arXiv:2210.09276, 2022.
+Kim, G., Kwon, T., and Ye, J. C.
+Diffusionclip: Text-
+guided diffusion models for robust image manipulation.
+In Proceedings of the IEEE/CVF Conference on Com-
+puter Vision and Pattern Recognition, pp. 2426–2435,
+2022.
+Kim, H. and Mnih, A. Disentangling by factorising. In
+ICML, 2018.
+Kwon, M., Jeong, J., and Uh, Y.
+Diffusion models al-
+ready have a semantic latent space.
+arXiv preprint
+arXiv:2210.10960, 2022.
+Lezama, J. Overcoming the disentanglement vs reconstruc-
+tion trade-off via jacobian supervision. In International
+Conference on Learning Representations, 2018.
+Lin, Z., Thekumparampil, K., Fanti, G., and Oh, S. Infogan-
+cr and modelcentrality: Self-supervised model training
+and selection for disentangling gans. In ICML, 2020.
+
+DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models
+Liu, X., Park, D. H., Azadi, S., Zhang, G., Chopikyan, A.,
+Hu, Y., Shi, H., Rohrbach, A., and Darrell, T. More con-
+trol for free! image synthesis with semantic diffusion
+guidance. In Proceedings of the IEEE/CVF Winter Con-
+ference on Applications of Computer Vision, pp. 289–299,
+2023.
+Liu, Z., Luo, P., Wang, X., and Tang, X. Deep learning face
+attributes in the wild. In Proceedings of International
+Conference on Computer Vision (ICCV), December 2015.
+Locatello, F., Bauer, S., Lucic, M., Raetsch, G., Gelly, S.,
+Sch¨olkopf, B., and Bachem, O. Challenging common
+assumptions in the unsupervised learning of disentangled
+representations. In international conference on machine
+learning, pp. 4114–4124. PMLR, 2019.
+Lugmayr, A., Danelljan, M., Romero, A., Yu, F., Timofte,
+R., and Van Gool, L. Repaint: Inpainting using denoising
+diffusion probabilistic models. In Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pp. 11461–11471, 2022.
+Meng, C., He, Y., Song, Y., Song, J., Wu, J., Zhu, J.-Y., and
+Ermon, S. Sdedit: Guided image synthesis and editing
+with stochastic differential equations. In International
+Conference on Learning Representations, 2021.
+Preechakul, K., Chatthee, N., Wizadwongsa, S., and Suwa-
+janakorn, S. Diffusion autoencoders: Toward a meaning-
+ful and decodable representation. In IEEE Conference on
+Computer Vision and Pattern Recognition (CVPR), 2022.
+Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G.,
+Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J.,
+et al. Learning transferable visual models from natural
+language supervision. In International Conference on
+Machine Learning, pp. 8748–8763. PMLR, 2021.
+Reed, S. E., Zhang, Y., Zhang, Y., and Lee, H. Deep visual
+analogy-making. In NeurIPS, 2015.
+Ren, X., Yang, T., Wang, Y., and Zeng, W. Learning disen-
+tangled representation by exploiting pretrained generative
+models: A contrastive learning view. In International
+Conference on Learning Representations, 2021.
+Saharia, C., Chan, W., Saxena, S., Li, L., Whang, J., Denton,
+E., Ghasemipour, S. K. S., Ayan, B. K., Mahdavi, S. S.,
+Lopes, R. G., et al. Photorealistic text-to-image diffusion
+models with deep language understanding. arXiv preprint
+arXiv:2205.11487, 2022.
+Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and
+Ganguli, S. Deep unsupervised learning using nonequi-
+librium thermodynamics. In International Conference on
+Machine Learning, pp. 2256–2265. PMLR, 2015.
+Song, J., Meng, C., and Ermon, S. Denoising diffusion im-
+plicit models. arXiv preprint arXiv:2010.02502, 2020a.
+Song, Y. and Ermon, S. Generative modeling by estimating
+gradients of the data distribution. Advances in Neural
+Information Processing Systems, 32, 2019.
+Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Er-
+mon, S., and Poole, B. Score-based generative modeling
+through stochastic differential equations. ICLR, 2020b.
+Srivastava, A., Bansal, Y., Ding, Y., Hurwitz, C. L., Xu, K.,
+Egger, B., Sattigeri, P., Tenenbaum, J., Cox, D. D., and
+Gutfreund, D. Improving the reconstruction of disentan-
+gled representation learners via multi-stage modelling.
+CoRR, abs/2010.13187, 2020.
+Voynov, A. and Babenko, A. Unsupervised discovery of
+interpretable directions in the GAN latent space. In ICML,
+2020.
+Wang, T., Zhang, Y., Fan, Y., Wang, J., and Chen, Q. High-
+fidelity gan inversion for image attribute editing. In Pro-
+ceedings of the IEEE/CVF Conference on Computer Vi-
+sion and Pattern Recognition, pp. 11379–11388, 2022.
+Yang, T., Ren, X., Wang, Y., Zeng, W., and Zheng, N.
+Towards building a group-based unsupervised representa-
+tion disentanglement framework. In International Con-
+ference on Learning Representations, 2021.
+Zhang, Z., Zhao, Z., and Lin, Z. Unsupervised represen-
+tation learning from pre-trained diffusion probabilistic
+models. NeurIPS, 2022.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf,len=952
+page_content='DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  Tao Yang 1 Yuwang Wang 2 Yan Lv 3 Nanning Zheng 1  Abstract  In this paper, targeting to understand the underly-  ing explainable factors behind observations and  modeling the conditional generation process on  these factors, we propose a new task, disentangle-  ment of diffusion probabilistic models (DPMs), to  take advantage of the remarkable modeling ability  of DPMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' To tackle this task, we further devise  an unsupervised approach named DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For the  first time, we achieve disentangled representation  learning in the framework of diffusion probabilis-  tic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Given a pre-trained DPM, DisDiff  can automatically discover the inherent factors be-  hind the image data and disentangle the gradient  fields of DPM into sub-gradient fields, each con-  ditioned on the representation of each discovered  factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We propose a novel Disentangling Loss  for DisDiff to facilitate the disentanglement of the  representation and sub-gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The extensive  experiments on synthetic and real-world datasets  demonstrate the effectiveness of DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Introduction  As one of the most successful generative models, diffusion  probabilistic models (DPMs) achieves remarkable perfor-  mance in image synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' They use a series of probabilistic  distributions to corrupt images in the forward process and  train a sequence of probabilistic models converging to im-  age distribution to reverse the forward process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Despite the  remarkable success of DPM in tasks such as image gener-  ation (Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020b), text to images (Saharia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2022), image editing (Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2021), little attention  has been paid on the representation learning (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2022) based on DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diff-AE (Preechakul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022) and  PADE (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022) are the two methods proposed  recently for representation learning by reconstructing the  images in the DPM framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, the learned la-  1Xi’an  Jiaotong  University  2Tsinghua  University  3Microsoft  Research  Asia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Contact  Tao  Yang  by  <yt14212@stu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='xjtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='cn>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Correspondence to:  Yuwang  Wang <wang-yuwang@@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='cn>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  tent representation can only be interpreted relying on an  extra pre-trained with predefined semantics linear classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Although there are some degrees of freedom during imple-  mentation, in this paper, we will refer DPMs exclusively to  the Denoising Diffusion Probabilistic Models (DDPMs) (Ho  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  On the other hand, disentangled representation learn-  ing (Higgins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2018) aims to learn the representation  of the underlying explainable factors behind the observed  data and is thought to be one of the possible ways for AI to  understand the world fundamentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Different factors cor-  respond to different kinds of image variations, respectively,  and independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Most of the methods learn the disen-  tangled representation based on generative models, such as  VAE (Higgins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Kim & Mnih,  2018) and GAN (Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The VAE-based meth-  ods have an inherent trade-off between the disentangling  ability and generating quality (Higgins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Chen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Kim & Mnih, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The GAN-based methods  suffer from the problem of reconstruction due to the diffi-  culty of gan-inversion (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' To the best of  our knowledge, there is no method of learning disentangled  representation using DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  In this paper, we connect DPM to disentangled represen-  tation learning, for the first time, and propose a new task:  the disentanglement of DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Given a pre-trained DPM  model, the goal of disentanglement of DPM is to learn dis-  entangled representations for the underlying factors in an  unsupervised manner, and learn the corresponding disentan-  gled conditional sub-gradient fields, with each conditioned  on the representation of each discovered factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  The benefits of the disentanglement of DPM are two-folds:  (i) It enables totally unsupervised controlling of images  by automatically discovering the inherent semantic factors  behind the image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' These factors helps to extends the  DPM conditions information from human defined ones such  as annotations (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022)/image-text pairs (Kawar  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022), or supervised pre-trained models (Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2022) such as CLIP (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' One can also  flexibly sample partial conditions on the part of the infor-  mation introduced by the superposition of the sub-gradient  field, which is novel in existing DPM works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (ii) DPM  has remarkable performance on image generation quality,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='13721v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='CV]  31 Jan 2023  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  and is naturally friendly for the inverse problem, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', the  inversion of DDIM (Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020a), PADE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Compared  to VAE (trade-off between the disentangling ability and gen-  erating quality) or GAN (problem of gan-inversion), DPM  is a better framework for disentangled representation learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Besides, as Locatello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2019) points out, other  inductive biases should be proposed except for total correla-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DPM makes it possible to adopt constraints from all  different timesteps as a new type of inductive bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Further,  as Srivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2020) points out, the information of  data includes: factorized and non-factorized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DPM has the  ability to sample non-factorized (non-conditioned) informa-  tion (Ho & Salimans, 2022), which is naturally fitting for  disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  To address the task of disentangling the DPM, we further  propose a unsupervised solution for the disentanglement of  a pretrained DPM, named as DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff adopts an  encoder to learn the disentangled presentation for each fac-  tor, and a decoder to learn the corresponding disentangled  conditional sub-gradient fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We further propose a novel  Disentangling Loss to make the encoded representation sat-  isfy the disentanglement requirement, and reconstruct the  input image as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Our main contributions can be summarized as follows:  We present a new task: disentanglement of DPM, disen-  tangling a DPM into several disentangled sub-gradient  fields, which can improve the interpretability of DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  We build an unsupervised framework for disentangle-  ment of DPM, DisDiff, which not only learns a disen-  tangled representation but also disentangled gradient  field for each factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  We propose a Disentangling Loss for DPM to facilitate  the disentanglement of different factor conditions and  the sub-gradient fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Related Works  Diffusion Probabilistic Models DPMs have achieved  comparable or superior image generation quality (Sohl-  Dickstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Song & Ermon, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Ho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Jolicoeur-Martineau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020)  than GAN (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diffusion-based image  editing has drawn much attention, and there are mainly two  categories of works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Firstly, image-guided works edit an  image by mixing the latent variables of DPM and the input  image (Choi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Lugmayr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, using images to specify the attributes for  editing may cause ambiguity, as pointed out by Kwon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Secondly, the classifier-guided works (Dhariwal  & Nichol, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Avrahami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2023)  edit image by utilizing the gradient of an extra classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  These methods require calculating the gradient, which is  costly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Meanwhile, these methods require annotations or  models pre-trained with labeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In this paper, we  propose DisDiff to edit the image in an unsupervised way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  On the other hand, little attention has been paid to repre-  sentation learning in the literature on the diffusion model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Two related works are Diff-ae (Preechakul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022) and  PADE (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diff-ae (Preechakul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022)  proposes a diffusion-based auto-encoder for image recon-  struction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' PADE (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022) uses a pre-trained  DPM to build an auto-encoder for image reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  However, the latent representation learned by these two  works does not explicitly respond to the underlying factors  of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' To the best of our knowledge, our DisD-  iff is the first diffusion-based framework for disentangled  representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Disentangled Representation Learning Bengio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (2013) introduced disentangled representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The  target of disentangled representation learning is to discover  the underline explanatory factors of the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The  disentangled representation is defined as each dimension  of the disentangled representation corresponding to an in-  dependent factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Based on such a definition, some VAE-  based works achieve disentanglement (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Kim & Mnih, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Higgins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Burgess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2018) only by the constraints on probabilistic distributions  of representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Locatello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2019) points out the  identifiable problem by proving that only these constraints  are not enough for disentanglement, and extra inductive bias  is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For example, Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2021) proposes to use  symmetry properties modeled by group theory as inductive  bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Most of the methods of disentanglement are based on  VAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' There are also some works based on GAN, including  leveraging pretrained generative model (Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Our DisDiff introduces the constraint of all time steps during  the diffusion process as a new type of inductive bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Fur-  thermore, DPM is capable of sampling non-factorized (non-  conditioned) information (Ho & Salimans, 2022), which is  naturally fitting for disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In this way, we shed  light on disentanglement based on a new framework of the  DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Background  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diffusion Probabilistic Models (DPM)  We take DDPM (Ho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020) as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DDPM  adopts a sequence of fixed variance distributions q(xt|xt−1)  as the forward process to collapse the image distribution  p(x0) to N(0, I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' These distributions are  q(xt|xt−1) = N(xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  �  1 − βtxt−1, βtI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (1)  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  Then we can sample xt by the following formula xt ∼  N(xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' √¯αtx0, (1 − ¯αt)), where αt = 1 − βt and ¯αt =  Πt  t=1αt, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', xt = √¯αtx0+√1 − ¯αtϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The reverse process  is fitting by other distributions parameterized by θ:  pθ(xt−1|xt) = N(xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' µθ(xt, t), σtI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (2)  where µθ(xt, t) is parameterize by a Unet ϵθ(xt, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The  training of it is to minimize the variational upper bound of  negative log-likelihood:  Lθ =  E  x0,t,ϵ ∥ϵ − ϵθ(xt, t)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (3)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Representation learning from DPMs  The classifier-guided method (Dhariwal & Nichol, 2021)  uses the gradient of pre-trained classifier ∇xt log p(y|xt)  to  impose  a  condition  on  pre-trained  DPM  and  obtain  a  new  conditional  DPM:  N(xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' µθ(xt, t) +  σt∇xt log p(y|xt), σt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Based on the classifier-guided sam-  pling method, PADE (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022) proposes a method  to learn auto-encoder for pre-trained DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Specifically,  given a pre-trained DPM, PADE introduces an encoder Eφ,  and the representation can be derived by z = Eφ(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' They  use a gradient estimator Gψ(xt, z, t) to simulate gradient  ∇xt log p(z|xt) for reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  By this means, they use it to assemble the unconditional  DPM as a new conditional DPM as the decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Similar  to regular DPM N(xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' µθ(xt, t) + σtGψ(xt, z, t), σt), we  can use the following objective to train encoder Eφ and the  network Gψ:  Lψ =  E  x0,t,ϵ ∥ϵ − ϵθ(xt, t) +  √αt  √1 − ¯αt  βt  σtGψ(xt, z, t)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (4)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Method  In this section, we first introduce the formulation of the  proposed task in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Then we present the overview  of DisDiff in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' After that, we present the detailed  implementation of the proposed Disentangling Loss in Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='3 and how to balance it with reconstruction loss in  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Finally, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='5, we discuss the relation  between Disentangling Loss and the total correlation, which  is a necessary condition for disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Disentanglement of DPM  We assume that dataset D is generated by N underlying  ground truth factors N factors C = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For ex-  ample, for Shapes3D, the underlying concept factors include  background color, floor color, object color, object shape, ob-  ject scale, and pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore, there is a one-one mapping  (a) Image Space  ①  𝐺!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (𝑥", 𝑡, 𝑧!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=')  𝐺#(𝑥", 𝑡, 𝑧#)  𝐺$(𝑥", 𝑡, 𝑧$)  ②  ⑤  ⑥  ⑦  ①  ③  ④  Background  Color is Blue  Object Color is Red  Floor Color  is Green  ②  ③  ④  ⑤  ⑥  ⑦  (c) Sampled Images  (b) Ground Truth Factor Space  ①  ②  ③  ④  ⑤  ⑥  ⑦  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Illustration of disentanglement of DPMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (a) is the di-  agram of image space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (b) is the diagram of factor space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (c)  is the demonstration of sampled images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Surface indicates the  conditional distribution of a single factor p(x|zc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Different col-  ors correspond to different factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Here we show three factors:  object color, background color, and floor color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Arrows are gradi-  ent fields ∇xt log p(zc|xt) parameterized by Gc  φ(xt, t, zc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The  learned Gc  φ(xt, t, zc) converges the noise data to the conditional  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The black points are the sampled images, which are  shown in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  between each sample and each tuple of factor representa-  tions, h : x0 �→ (f 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , f N), ∀x0 ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The data distri-  bution p(x) can be disentangled into N independent distri-  butions {p(x|f k)|k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , N}, and each conditioned on  only one factor, which is shown as the curved surface of  image space in Figure 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The DPM learns a sequence  of distributions {pt(x)|t = T, T − 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , 0} converging to  p(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Such convergence is achieved by optimizing the corre-  sponding gradient fields {∇x log pt(x)|t = T, T−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , 0}  (learned by ϵθ with parameters θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The disentangled DPM  contains N sequences of distributions, converging to N dis-  tributions {p(x|f c)|c = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , N} respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The target  of disentanglement of a DPM is, for each factor c, to learn  Gc  ψ to estimate ∇x log pt(x|f c), which corresponds to the  arrows pointing to the curve surface in Figure 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' One  may note that in the data sample space, such as image space,  the curved surfaces indicate that the data sample space is not  well-organized, and the variations of the factors are entan-  gled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Compared to the image space, the ground truth factor  space is well-organized, and the subspaces of factors are  orthogonal between each other, as shown in Figure 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Dis-  entangled representation learning aims to model the ground  truth factor space using an encoder Eφ, which encodes the  raw data into disentangled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The disentan-  gled representation is ideal for representing the conditions  for the conditional distributions {p(x|f c)|c = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , N}  of the disentangled DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Conditioned on the disentangled  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  𝑥!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  𝑥"  𝜖#(𝑥", 𝑡)  𝐺$(𝑥", 𝑡, 𝑧$)  𝐺%(𝑥", 𝑡, 𝑧%)  𝐺&(𝑥", 𝑡, 𝑧&)  Pre-trained DPM  Encoder 𝐸\'  Decoder 𝐺#  (  Disentangled  Representations  𝑧$  𝑧%  𝑧&  Disentangled  Gradient Fields  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Illustration of DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Gray networks indicate the pre-  trained Unet of DPM ϵθ(xt, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Image x0 is first to be encoded  to representations {z1, z2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' zN} of different factors by encoder  Eφ (N = 3 in the figure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We thus decode the representations by  decoder Gc  θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' By this means, we can obtain the gradient field of  the corresponding factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' With the obtained gradient field, we can  sample the image under the corresponding condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  representation, the disentangled DPM can flexibly generate  the data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In this paper, we propose a method named  DisDiff, as a solution for the disentanglement of a DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Overview of DisDiff  The overview framework of DisDiff is shown in Figure  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Given a pre-trained unconditional DPM on dataset D  with N factors C = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , N}, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', a DDPM model  with parameters θ, pθ(xt−1|xt) = N(xt−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' µθ(xt, t), σt),  our target is to disentangle the DPM in an unsupervised  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Specifically, given x0 ∈ D, for each factor c ∈ C,  the goal is to learn the disentangled representation zc via  an encoder Eφ (with learnable parameters φ) as Eφ(x0) =  {E1  φ(x0), E2  φ(x0), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , EN  φ (x0)} = {z1, z2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , zN}, and  the disentangled gradient field ∇xt log p(zc|xt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore,  the conditional reverse process (condition on factors S ⊆ C,  and zS = {zc|c ∈ S}) can be formulated by a Gaussian  distribution pθ(xt−1|xt, zS) with a shifted mean:  N(xt−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' µθ(xt, t) + Σt  �  c∈S  ∇xt log p(zc|xt), σt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (5)  Since p(zc|xt) is intractable, we use Gc  ψ(xt, zc, t), c ∈ C,  with learnable parameters ψ, to estimate the gradient fields  ∇xt log p(zc|xt), c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  With different options of S, one can flexibly devise the ap-  proximator following score-based conditioning trick (Song  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Song & Ermon, 2019) as follows:  ϵψ(xt, zS, t) = ϵθ(xt, t)−  �  c∈S  √  1 − ¯αtGc  ψ(xt, zc, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (6)  Then one can derive the corresponding data sample using  Tweedie’s Formula as:  ˆxS  0 = xt − √1 − ¯αtϵψ(xt, zS, t)  √¯αt  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (7)  𝜖!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (𝑥", 𝑡)  Disentangling  Loss  𝑧#  𝑧$  𝑧%  𝐺#(𝑥", 𝑡, 𝑧#)  𝐺$(𝑥", 𝑡, 𝑧$)  𝐺%(𝑥", 𝑡, 𝑧%)  Encoder 𝐸&  Encoder 𝐸&  Decoder 𝐺!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content="  '  Figure 3." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The demonstration of disentangling loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We first sample  a factor c and then decode the representation zc to obtain the  gradient field of the corresponding factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' With this gradient field,  we can obtain the predicted x0 of the corresponding factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' On the  other hand, we can obtain predicted ˆx0 of the original pre-trained  DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We then encode the images into two different representations  and calculate the disentangling loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  For example, one can choose only one disentangled factor,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', setting S = c, and use the gradient ∇xt log p(zc|xt)  (only conditioned on zc) to guide the sampling of the pre-  trained DPM, resulting in the predicted sample ˆxc  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We leave  ˆx0 to denote the predicted data sample using the pretrained  unconditioned DPM ϵθ(xt, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  According to the completeness requirement of disentan-  glement, the disentangled representation Eφ(x0) should  contain the full information of sample x0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', one can re-  construct x0 by using all the disentangled representations  Eφ(x0) as a condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Following Equation 7, we set S = C  to include all the disentangled representation, resulting in  the derived data sample ˆxC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' One may note that this is ex-  actly the reconstruction case in PDAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Here, we adopt the  same reconstruction loss, denoted as  Lr =  E  x0,t,ϵ ∥ϵ − ϵθ(xt, t)  +  √αt  √1−¯αt  βt  σt  �  c∈C Gc  ψ(xt, zc, t)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (8)  Besides the above completeness requirement, each disen-  tangled representation should only reflect one correspond-  ing factor independently, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', the disentanglement require-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We devise a novel loss, named Disentangling Loss,  to achieve the disentanglement of the pre-trained DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In  the following, we will present the Disentangling Loss and  the total loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Disentangling Loss  In this section, we provide the detailed implementation of  Disentangling Loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As discussed above, given sample x0  and its disentangled representation E(x0), we randomly  sample c ∈ C and use S = c to get the conditioned sam-  ple ˆxc  0 (only conditioned on representation zc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Accord-  ing to the disentanglement requirement,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' compared to the  unconditioned predicted image ˆx0 (sampling with the pre-  trained unconditioned DPM ϵθ(xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' t)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' ˆxc  0 should satisfy the  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  following two conditions: (i) invariant condition,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' for the  k-th (k ̸= c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' k ∈ C) disentangled representation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Ek  φ(ˆx0)  should be the same with Ek  φ(ˆx0),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (ii) variant condition,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' for  the c-th disentangled representation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' the conditioned one  Ec  φ(ˆx0) should be closer to Ec  φ(x0) than the unconditioned  one Ec  φ(ˆx0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In the following, we provide the detailed im-  plementation of the above two conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' According to  the above (i) invariant condition, the k-th (k ̸= c, k ∈ C)  representation should be kept the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We encode the two  samples using Eφ and derive the distance scalar between  the k-th representation as:  dk = ∥Ek  φ(ˆxc  0) − Ek  φ(ˆx0)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (9)  Then the distance vector can be represented as d  =  [d1, d2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , dC] Finally, we use the cross-entropy loss to  identify the index c and restrain others unchanged:  Lin =  E  x0,t,ϵ,c[CrossEntropy(d, c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (10)  We denote it as invariant loss Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  For the (ii) variant condition, we first calculate the distance  scalar of the k-th representation between ˆx0 (unconditioned)  and x0, ˆxc  0 (conditioned) and x0 as following respectively:  dn  k  = ∥Ek  φ(ˆx0) − Ek  φ(x0)∥  dp  k  = ∥Ek  φ(ˆxc  0) − Ek  φ(x0)∥  (11)  According to the above condition (ii), for the conditioned  factor c, dn  c − dp  c should be maximized, while others, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  dn  k −dp  k (k ̸= c, k ∈ C), should be minimized to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Similarly  we adopt an entropy loss to achieve the subjective as:  Lva =  E  x0,t,ϵ,c[CrossEntropy(dn − dp, c)],  (12)  where dn = [dn  1, dn  2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , dn  C] and dp = [dp  1, dn  2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , dp  C].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  We denote it as variant loss Lva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' So far, we introduce the  Disentangling Loss, Lin and Lva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Total Loss  As we need to satisfy both the completeness and disentangle-  ment requirements, the total loss includes the above recon-  struction loss (Lr) and Disentangling Loss (Lin and Lva).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  However, the weight to balance the two-part loss should be  carefully set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The reason is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Note that the  above Disentangling Loss Lin and Lva is conditioned on  the sampled time step of the diffusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, the  condition of the diffusion model varies among different time  steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For example, if t is close to T, Gc  ψ(xt, zc, t) mainly  condition on zc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' And if t is close to 0, the output mainly con-  ditions on xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore, for different time steps, different  weights should be used for Disentangling Loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Considering  that the difference between the inputs of encoder reflexes  such change on condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Specifically, if t is close to T,  the difference between ˆxt and ˆxc  t is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In addition, if  t is close to 0, such a difference is significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Based on  the above discussion, the more the output condition on zc,  the higher the weight should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We thus propose to use  the MSE distance between the inputs of the Encoder as the  weight coefficient:  γd = λ∥ˆx0 − ˆxc  0∥2,  (13)  where λ is a hyper-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We stop the gradient of ˆx0  and ˆxc  0 for calculating the weight coefficient γd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  The total loss can be calculated as:  La = Lr + γd(Lin + Lva).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  (14)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Relation to Total Correlation  In this section, we demonstrate that Total Correlation is a  necessary condition for our disentangling loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Total Corre-  lation is once regarded as an important constraint for repre-  sentation disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, Locatello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2019)  point out that besides total Correlation, other inductive bi-  ases should also be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In this paper, we introduce  Disentangling Loss for DPM as an additional inductive bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  We prove that Total Correlation is a necessary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Specifically, if the reconstruction loss is minimized, we have  ∇xt log p(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , zN|xt) =  �  c∈C  Gc  ψ(xt, zc, t)  (15)  On the other hand, if the disentangling loss is mini-  mized, we have Gc  ψ(xt, zc, t) = ∇xt log p(zc|xt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Since  �  c∈C ∇xt log p(zc|xt) = ∇xt log Πc∈Cp(zc|xt) always  hold, bring these two equations into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 15, we have  ∇xt log p(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , zN|xt) = ∇xt log Πc∈Cp(zc|xt) (16)  The equation above results in the fisher divergence between  the joint distribution p(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , zN|xt) and the product of  marginal distribution Πc∈Cp(zc|xt) is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore the Total  Correlation holds for all xt:  p(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' , zN|xt) = Πc∈Cp(zc|xt)  (17)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Experiments  In this section, we conduct experiments to demonstrate the  effectiveness of DisDiff on both synthetic and real-world  datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Experimental Setup  Implementation Details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' x0 can be an image space or  a latent space of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For image diffusion, we take  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Comparisons of disentanglement on the FactorVAE score and DCI disentanglement metrics (mean ± std, higher is better).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  DisDiff achieves state-of-the-art performance with a large margin in almost all the cases compared to all baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Especially on the  MPI3D dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Method  Cars3D  Shapes3D  MPI3D  FactorVAE score  DCI  FactorVAE score  DCI  FactorVAE score  DCI  VAE-based:  FactorVAE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='906 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='052  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='161 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='019  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='840 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='066  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='611 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='082  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='152 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='240 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='051  β-TCVAE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='855 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='082  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='140 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='019  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='873 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='074  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='613 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='114  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='179 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='237 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='056  GAN-based:  InfoGAN-CR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='411 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='020 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='587 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='058  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='478 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='439 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='061  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='241 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='075  Pre-trained GAN-based:  LD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='852 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
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+page_content='284 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
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+page_content='042  DisCo  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='855 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
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+page_content='877 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='031  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='708 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='371 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='292 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='024  Diffusion-based:  DisDiff-VQ (Ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='976 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='232 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='019  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='902 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='043  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='723 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='617 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='070  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='337 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='057  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Ablation study of DisDiff on image tokenizer, compo-  nents, batchsize and token numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Method  FactorVAE score  DCI  DisDiff-IM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='783  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='655  DisDiff-KL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='837  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='660  DisDiff-VQ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='902  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='723  DisDiff-VQ wo Lin  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='782  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='538  DisDiff-VQ wo Lva  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='810  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='620  DisDiff-VQ wo Ldis  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='653  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='414  wo detach  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='324  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='026  constant weighting  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='679  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='426  loss weighting  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='678  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='465  attention condition  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='824  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='591  wo pos embedding  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='854  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='678  wo orth embedding  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='807  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='610  latent number N= 6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='865  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='654  latent number N= 10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='902  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='723  pre-trained DDIM as the DPM (DisDiff-IM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For latent  diffusion, we can take the pre-traind KL-version latent dif-  fusion model (LDM) or vq-version LDM as DPM (DisDiff-  KL and DisDiff-VQ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For detail of network Gθ, we fol-  low Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2022) to use the extended Group Normal-  ization (Dhariwal & Nichol, 2021) by applying scaling &  shifting twice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The difference is we use learn-able position  embedding to indicate c:  AdaGN(h, t, zc) = zc  s(tc  sGN(h) + tc  b) + zc  b  (18)  where GN denotes group normalization, and [tc  s, tc  b], [zc  s, zc  b]  are obtained from a linear projection:  zc  s, zc  b  =  linearProj(zc), tc  s, tc  b = linearProj([t, pc]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In addition,  pc is the leanable positional embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' h is the feature  map of Unet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Datasets For evaluation of disentanglement, we fol-  low Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2021) to use the popular public datasets:  Shapes3D (Kim & Mnih, 2018), a dataset of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  MPI3D (Gondal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2019), a 3D dataset recorded in a  controlled environment, and Cars3D (Reed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2015),  a dataset of CAD models generated by color renderings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  All experiments are conducted on 64x64 image resolution,  which is the same as the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For real-world datasets,  we conduct our experiments on CelebA (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Baselines & Metrics Since DisDiff is the first diffusion-  based disentanglement model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Therefore, we compare  the performance with VAE-based and GAN-based base-  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Specifically, the VAE-based models include: Fac-  torVAE (Kim & Mnih, 2018), and β-TCVAE (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The GAN-based baselines include InfoGAN-CR  (Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020), GANspace (GS) (H¨ark¨onen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2020),  LatentDiscovery (LD) (Voynov & Babenko, 2020) and  DisCo (Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Considering the influence of  performance on the random seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We have 10 runs for  each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We use four representative metrics: Factor-  VAE score (Kim & Mnih, 2018), and the DCI (Eastwood  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  source  target  factor 1  factor 2  factor 3  factor 4  factor 5  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The qualitative results on Shapes3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The source images  provide the representations of the generated image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The target  image provides the representations for swapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Other rows  of images are generated by swapping the representation of the  corresponding factor on Shapes3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff learns pure factors by  each representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The learned factors are azimuth, background  color, floor color, object color, and object shape, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  & Williams, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, since {zc} are vector-wise  represenatation, we follow Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' (2021) to perform PCA  as post-processing on the representation before evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Main Results  We conduct the following experiments to verify the disentan-  glement ability of proposed DisDiff model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We regard the  learned representation {zc} as the disentangled one and use  the popular metrics in disentangled representation literature  for evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  The quantitative comparison results of disentanglement un-  der different metrics are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As shown in the  table, DisDiff outperforms the baselines, demonstrating the  model’s superior disentanglement ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Compared with  the VAE-based methods, since these methods suffer from the  trade-off between generation and disentanglement (Lezama,  2018) but DisDiff does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As for the GAN-based methods,  the disentanglement is learned by exploring the latent space  of GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore, the performance is limited by the latent  space of GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff leverages the gradient field of data  space to learn disentanglement and does not have such limi-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In addition, DisDiff resolves the disentanglement  problem into 1000 sub-problems under different time steps,  which reduces the difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  source  target  factor 1  factor 2  factor 3  factor 4  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The qualitative results on CelebA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Each row of images is  generated by swapping the representation of the corresponding fac-  tor on CelebA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff learns pure factors by each representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  The learned factors are bangs, skin color, expression, and hair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Qualitative Results  In order to analyze the disentanglement of DisDiff qualita-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We swap the representation {zc} of two images one  by one and sample the image conditioned on the swapped  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We follow LDM-VQ to sample images in  200 steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For the popular dataset of disentanglement litera-  ture, we take shapes3d as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As shown in Figure  4, DisDiff successfully learned pure factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Compared with  the VAE-based methods, DisDiff has better image quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  For the real-world dataset, since there are no ground truth  factors, we demonstrate the qualitative results in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We  take CelebA as an example, as demonstrated in Figure 5,  DisDiff also achieves good disentanglement on real-world  datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Please note that compare with Disco (Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff has the ability of reconstruction, which is  not available for DisCo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Ablation Study  In order to analyze the effectiveness of the proposed parts  of DisDiff, we design an ablation study from the following  five aspects: DPM type, Disentangling Loss, loss weighting,  condition type, and latent number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We take shapes3d as the  dataset to conduct these ablation studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  DPM type The disentanglement of DisDiff is derived by the  decomposition of the gradient field of the diffusion model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Therefore, the diffusion space influence the performance of  DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We take Shapes3D as an example, it is hard for the  model to learn shape and scale in image space, but much  easier in the latent space of auto-encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore, we  compare the performance of DisDiff with different diffusion  types: image diffusion model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', DDIM (DisDiff-IM),  KL-version latent diffusion model (DisDiff-KL) and VQ-  version latent diffusion model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', VQ-LDM (DisDiff-VQ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  target  factor 1  factor 2  factor 3  factor 4  factor 5  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The partially condition sampling on Shapes3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The tar-  get image provides the representation of partially sampling image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Each row of images are generated by imposing a single gradient  field of the corresponding factor on the pre-tained DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff  samples image condition on only a single factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The sampled  image has a fixed factor, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', the images of factor 1 have same  background color with target one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The conditioned factors are:  azimuth, background color, floor color, object color and object  shape, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  As shown in Table 2, the LDM-version DisDiff outperforms  image-version DisDiff as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In addition, KL-LDM  has more complex latent space than VQ-LDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff-VQ  outperforms DisDiff-KL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Disentangling Loss Disentangling loss is composed of two  parts: Invariant loss Lin and Variant loss Lva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In order to  verify the effectiveness of each part, we train DisDiff-VQ  without it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Lin encourages in-variance of representation not  being sampled, which means that the sampled factor will  not affect the representation of other factors (zk, k ̸= l of  generated ˆxl  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' On the other hand, Lva encourages the rep-  resentation of sampled factor (zl of generated ˆxl  0) should be  close to the corresponding one of x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As shown in Table 2,  mainly Lin encourage the disentanglement, and Lva further  constrain the model and improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Note that  the disentangling loss is optimized w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Gθ but not Ec  θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' If  the loss is optimized on both modules, as shown in Table 2,  DisDiff fails to achieve disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The reason is that  the disentangling loss influenced the encoder, so DisDiff  failed to reconstruct the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Loss weighting As introduced, considering that the condi-  tion varies among time steps, we adopt the difference of  the encoder as the weight coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In this section, we  explore other options to verify its effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We offer  two different weighting types: constant weighting and loss  weighting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The first type is the transitional way of weight-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The second one is to balance the scale of Distangling  Loss and diffusion loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' From Table 2, these two types of  weighting hurt the performance to a different extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  target  factor 1  factor 2  factor 3  factor 4  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The partially condition sampling on CelebA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The target  image provides the representations of the sampling image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Images  of each row are conditioned on a single factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff samples  image condition on only a single factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Therefore, the sampled  image in the same row has a fixed factor, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', the images of factor  1 have the same bangs as the target one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The conditioned factors  are bangs, skin color, expression, and hair, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Condition type DisDiff follows PADE (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', 2022)  and (Dhariwal & Nichol, 2021) to adopt AdaGN for in-  jecting the condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' However, there is another option in  the literature: cross-attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As shown in Table 2, cross-  attention hurt the performance but not much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We infer that  the reason may be that the condition is only a single token,  which limits the ability of attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We use learnable or-  thogonal positional embedding to indicate different factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  As shown in Table 2, no matter whether no positional embed-  ding (wo pos embedding) or traditional learnable positional  embedding (wo orth embedding) hurt the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' The  reason is that the orthogonal embedding is always different  from each other in all training steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Latent number The number of latent is a important hyper-  parameter set in-advance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We conduct ablation study on this  hyper-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' As shown in Table 2, the latent number  only has limited influence on the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Partially Condition Sampling  As discussed in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='2, DisDiff can partially sample  conditions on the part of the factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Specifically, we can  use Equation 6 to sample image condition on factors set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  We take Shapes3D, as an example, when DisDiff sampling  image condition on background color is red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' We obtain a  set of images of the background color red and other factors  randomly sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' From Figure 6, we see that DisDiff has  the ability to condition individual factors on Shapes3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In  addition, DisDiff also has such ability on the real-world  dataset (CelebA) in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff has the ability to  sample information exclusively to conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Conclusion  In this paper, we demonstrate a new task: disentanglement  of DPM, by disentangling a DPM into several disentangled  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  gradient fields, we can improve the interpreter-ability of  DPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' To solve the task, we build an unsupervised diffusion-  based disentanglement framework named DisDiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff  learns a disentangled representation of the input image in  the diffusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In addition, for each factor, DisDiff  learns a disentangled gradient field, which brings the follow-  ing new properties for disentanglement literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' DisDiff  adopted disentangling constraints on all different timesteps,  which is a new inductive bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Except for image editing,  with the disentangled DPM, we also can sample partially  conditions on the part of the information by superposition of  the sub-gradient field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' For future work, Applying DisDiff to  more general conditioned DPM is a direction worth explor-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Besides, utilizing the proposed disentangling method  to pre-trained conditional DPM makes it more flexible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  References  Avrahami, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Lischinski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Fried, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Blended diffu-  sion for text-driven editing of natural images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In Proceed-  ings of the IEEE/CVF Conference on Computer Vision  and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 18208–18218, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Bengio, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Courville, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Vincent, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Representation  learning: A review and new perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' PAMI, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Burgess, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Higgins, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Pal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Matthey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Watters, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Desjardins, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Lerchner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Understanding disentan-  gling in beta-vae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='03599, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Grosse, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Duvenaud, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Isolating sources of disentanglement in variational au-  toencoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In NeurPIS, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Jeong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Gwon, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Yoon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Ilvr:  Conditioning method for denoising diffusion probabilistic  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='02938, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Dhariwal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Nichol, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diffusion models beat gans  on image synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems, 34:8780–8794, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Du, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Sharma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Tenenbaum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Mordatch, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Unsupervised learning of compositional energy concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Advances in Neural Information Processing Systems, 34,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Eastwood, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Williams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' A framework for the  quantitative evaluation of disentangled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  In ICLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Gondal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wuthrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Miladinovic, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Locatello,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Breidt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Volchkov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Akpo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Bachem, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Sch¨olkopf, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Bauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' On the transfer of inductive  bias from simulation to the real world: a new disentangle-  ment dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In NeurIPS, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Goodfellow, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Pouget-Abadie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Mirza, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Warde-Farley, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ozair, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Courville, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Bengio, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Generative adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Communications of the  ACM, 63(11):139–144, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  H¨ark¨onen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Hertzmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Lehtinen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Paris, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Ganspace: Discovering interpretable GAN controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In  NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Higgins, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Matthey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Pal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Burgess, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Glorot, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Botvinick, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Mohamed, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Lerchner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' beta-  vae: Learning basic visual concepts with a constrained  variational framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Higgins, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Amos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Pfau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Racaniere, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Matthey,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Rezende, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Lerchner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Towards a defi-  nition of disentangled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv preprint  arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='02230, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Ho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Salimans, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Classifier-free diffusion guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  arXiv preprint arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='12598, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Ho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Jain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Abbeel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Denoising diffusion proba-  bilistic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Advances in Neural Information Process-  ing Systems, 33:6840–6851, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Jolicoeur-Martineau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Pich´e-Taillefer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Combes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Mitliagkas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Adversarial score matching and  improved sampling for image generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv preprint  arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='05475, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Kawar, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Lang, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Tov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Chang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Dekel,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Mosseri, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Irani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Imagic: Text-based real  image editing with diffusion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  arXiv preprint  arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='09276, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Kim, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Kwon, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Ye, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Diffusionclip: Text-  guided diffusion models for robust image manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF Conference on Com-  puter Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 2426–2435,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Mnih, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Disentangling by factorising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In  ICML, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Kwon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Jeong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Uh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Diffusion models al-  ready have a semantic latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  arXiv preprint  arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='10960, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Lezama, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Overcoming the disentanglement vs reconstruc-  tion trade-off via jacobian supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International  Conference on Learning Representations, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Thekumparampil, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Fanti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Oh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Infogan-  cr and modelcentrality: Self-supervised model training  and selection for disentangling gans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In ICML, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models  Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Park, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Azadi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Chopikyan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Shi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Rohrbach, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Darrell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' More con-  trol for free!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' image synthesis with semantic diffusion  guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Winter Con-  ference on Applications of Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 289–299,  2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Luo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Deep learning face  attributes in the wild.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In Proceedings of International  Conference on Computer Vision (ICCV), December 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Locatello, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Bauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Lucic, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Raetsch, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Gelly, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Sch¨olkopf, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Bachem, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Challenging common  assumptions in the unsupervised learning of disentangled  representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In international conference on machine  learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 4114–4124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Lugmayr, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Danelljan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Romero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Yu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Timofte,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Van Gool, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Repaint: Inpainting using denoising  diffusion probabilistic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In Proceedings of the  IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 11461–11471, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Meng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Song, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and  Ermon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Sdedit: Guided image synthesis and editing  with stochastic differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International  Conference on Learning Representations, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Preechakul, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Chatthee, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wizadwongsa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Suwa-  janakorn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Diffusion autoencoders: Toward a meaning-  ful and decodable representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In IEEE Conference on  Computer Vision and Pattern Recognition (CVPR), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Radford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Hallacy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ramesh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Goh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Agarwal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Sastry, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Askell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Mishkin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Clark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Learning transferable visual models from natural  language supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International Conference on  Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 8748–8763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Reed, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Deep visual  analogy-making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In NeurIPS, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Ren, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Yang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Zeng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Learning disen-  tangled representation by exploiting pretrained generative  models: A contrastive learning view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International  Conference on Learning Representations, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Saharia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Chan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Saxena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Whang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Denton,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ghasemipour, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ayan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Mahdavi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Lopes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Photorealistic text-to-image diffusion  models with deep language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv preprint  arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='11487, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Sohl-Dickstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Weiss, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Maheswaranathan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and  Ganguli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Deep unsupervised learning using nonequi-  librium thermodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International Conference on  Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 2256–2265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' PMLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Song, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Meng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Ermon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Denoising diffusion im-  plicit models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='02502, 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Ermon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Generative modeling by estimating  gradients of the data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Sohl-Dickstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Er-  mon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Poole, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Score-based generative modeling  through stochastic differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' ICLR, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Srivastava, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Bansal, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ding, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Hurwitz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Xu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=',  Egger, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Sattigeri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Tenenbaum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Cox, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and  Gutfreund, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Improving the reconstruction of disentan-  gled representation learners via multi-stage modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  CoRR, abs/2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='13187, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Voynov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' and Babenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Unsupervised discovery of  interpretable directions in the GAN latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In ICML,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Fan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Chen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' High-  fidelity gan inversion for image attribute editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE/CVF Conference on Computer Vi-  sion and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' 11379–11388, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Yang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Ren, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zeng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Zheng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Towards building a group-based unsupervised representa-  tion disentanglement framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' In International Con-  ference on Learning Representations, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content='  Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=', and Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' Unsupervised represen-  tation learning from pre-trained diffusion probabilistic  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
+page_content=' NeurIPS, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/e9FST4oBgHgl3EQfGTh-/content/2301.13721v1.pdf'}
diff --git a/eNFAT4oBgHgl3EQfZR37/content/tmp_files/2301.08545v1.pdf.txt b/eNFAT4oBgHgl3EQfZR37/content/tmp_files/2301.08545v1.pdf.txt
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+Nonlinear MPC for full-pose manipulation of a cable-suspended load using
+multiple UAVs
+Sihao Sun, Antonio Franchi
+Abstract— Using multiple UAVs to manipulate the full pos-
+ture of an object is a promising capability in many industrial
+applications, such as autonomous building construction and
+heavy-load transportation. Among various methods, manipu-
+lation via cables excels in mechanical simplicity and ease of
+use, but is challenging from a control perspective. Existing
+centralized control methods either neglect the dynamic coupling
+between UAVs and the load or resort to a cascade structure,
+which limits the operational speed and cannot guarantee safety.
+In this work, we propose a centralized control method that uses
+nonlinear model predictive control. This control method takes
+into account the full nonlinear model of the load-UAV system,
+as well as the constraints of UAV thrust, collision avoidance,
+and ensuring all cables are taut. By taking into account the
+above factors, the proposed control algorithm can fully exploit
+the performance of UAVs and facilitate the speed of operation.
+We demonstrate our algorithm through 6-DoF simulations to
+achieve fast and safe manipulation of the pose of a rigid-body
+payload using multiple UAVs.
+I. INTRODUCTION
+A. Background and motivation
+• Collaborative manipulation is a promising capability
+in many industrial applications, given the fact that the
+payload capacity of a single UAV is limited.
+B. Related works
+• Works for single UAV and a point-mass sling load
+(e.g.,[1], [2]).
+• Works for multi-UAVs with a point-mass sling load
+(e.g., [3], [4], [5]).
+• Works for multi-UAVs with a rigid-body sling load
+(e.g.,[6], [7], [8], [9]).
+• Existing works for multi-UAVs manipulating the full
+pose of a rigid-body load with suspended cables can-
+not simultaneously consider the full-nonlinear dynamic
+model of the load-UAVs system, and the thrust limita-
+tion of each UAV, as well as other constraints such as
+taut cable, and collision avoidance.
+C. Contribution of this work
+• A centralized control algorithm that can automatically
+exploit the redundancy of the load-UAVs system.
+• Fully explore the load-UAVs system’s nonlinear dynam-
+ics, and consider system constraints.
+• Formulate the system model to allow real-time opti-
+mization.
+Fig. 1.
+Coordinate systems definition.
+II. PRELIMINARY
+A. Problem Formulation
+The system comprises n UAVs and a single rigid-body
+load. There is a coordinate system L = {OL, xL, yL, zL}
+attached to the load with the origin located at the centre
+of mass. For each UAV, there is a body-fixed frame Bi =
+{OBi, xBi, yBi, zBi} attached where OBi is at the center of
+mass of the ith UAV and zBi points at the thrust direction.
+The position of the load with respect to the inertial frame
+I is denoted by p, and the orientation is denoted by R ∈
+SO(3). Similarly, the position and orientation of the ith UAV
+is denoted by pi and Ri ∈ SO(3) respectively. The angular
+rate and
+Each UAV is connected to the load through a cable with
+a length of li, where subscription i ∈ N+ ≤ n is the UAV
+index. Both sides of the cable are hinge connections, with one
+side connected to the centre of mass of the UAV and another
+side connected to an arbitrary point of the load, displacing
+from its centre of mass by ρi. The cable tension is denoted
+by ti ≤ 0.
+The UAV considered in this work are uni-directional
+Thrust platforms, whose collective thrust can only vary along
+one direction (i.e., zBi). Examples are helicopters and multi-
+rotor drones whose rotors are coplanar. These platforms
+can generate moments to change their thrust direction, and
+consequently, change their position in the inertial frame.
+The objective of the controller designed in this paper is to
+generate the collective thrust fi and moment τi of all the
+UAVs, such that the position and attitude (full pose) of the
+load can follow a given value.
+arXiv:2301.08545v1  [cs.RO]  20 Jan 2023
+
+UAV #2
+UAV #1
+ZBi
+XBI
+ZL
+UAV #i
+Bi
+SiB. Modeling
+1) Load-cable model: We model the load using a 6 DoF
+rigid-body dynamic model:
+˙p = v
+(1)
+˙v = −
+n
+�
+i=1
+tisi/m + g
+(2)
+˙R = RωL
+×
+(3)
+˙ωL = I−1
+L
+�
+−ωL × ILωL +
+n
+�
+i=1
+�
+RT si × ρL
+i
+��
+(4)
+The mass-less cable is modelled with only kinematics con-
+sidered, up to angular accelerations. For the i-th cable, we
+have
+˙si = ri × si
+(5)
+¨ri = ci
+(6)
+2) UAV model: The UAV considered in this paper are
+uni-directional UAVs, meaning that only thrusts along a
+single direction (defined as zi of the vehicle) are generated,
+examples are helicopters and quadrotors. In this work, we use
+a rigid-body model to represent the kinematics and dynamics
+of the UAV. Specifically, the model of the i-th UAV is:
+˙pi = vi
+(7)
+˙vi = (fizi + tisi)/mi + g
+(8)
+˙Ri = RiωBi
+i,×
+(9)
+˙ωBi
+i
+= I−1
+i
+�
+−ωBi
+i
+× IiωBi
+i
++ τ i
+�
+(10)
+C. Kinematic Constraints
+Since each UAV is constrained at the end of the corre-
+sponding cable, for the i-th UAV, we have the following
+kinematic constraint:
+pi = p + RρL
+i − lisi
+(11)
+These constraints render the UAV states dependent on the
+load-cable model. This is also known as the differential
+flatness of the (multi-)UAV-load-cable system [10]. The UAV
+states can be derived as algebraic functions of the load pose
+and cables’ orientations. For the optimization problem in the
+next section, we need to set constraints on the collective
+thrust of each UAV to fulfil its physical limitation. Therefore
+we derive the thrust of each UAV using the kinematic
+constraints.
+By taking the second-order derivative of both sides of (11)
+and substituting (3)-(6) to it, we have
+˙vi = ˙v + R
+� ˙ωBi × ρL
+i + ωL × (ωL × ρL
+i )
+�
+− li ˙ri × si − lir × (r × si)
+= (fizi + tisi)/mi + g
+(12)
+Through simple algebra, we have
+fizi = f i = mi[ ˙v + R( ˙ωL × ρL
+i + ωL × (ωL × ρL
+i ))
+− li ˙ri × si − lir × (r × si))]
+− tisi − g
+(13)
+fi = ∥f i∥
+(14)
+zi = f i/fi
+(15)
+Collisions between UAVs and cables need to be avoided
+for safety reasons, here we express the distance between i-th
+UAV and the j-th cable as
+dij =
+�
+pi − pj
+�
+× si
+= R
+�
+ρL
+i − ρj
+�
++ (ljsj − lisi) × si
+(16)
+III. METHODOLOGY
+The control algorithm designed in this section aims at
+controlling the full pose of the load to a reference, by
+generating thrust and torque commands for all the UAVs.
+In the meantime, we guarantee safety by incorporating the
+thrust constraints and the collision constraints. This will help
+to fully exploit the capability of each UAV. The control
+diagram is illustrated in Fig. 1.
+A. Nonlinear model predictive control
+The nonlinear model predictive controller utilizes the load-
+cable model. The states and inputs of this model are defined
+as:
+x =
+�
+p,
+v,
+R,
+ωB,
+s1,
+r1,
+˙r1, ...,
+sn,
+rn,
+˙rn
+�
+(17)
+u = [c1,
+t1, ..., cn,
+tn]
+(18)
+Then the following optimal control problem (OCP) is solved
+in each control step of nonlinear MPC:
+min J =
+� τf
+τ=0
+1
+2||yref − y||2
+W + ||σ||2
+W σ
+s.t. Initial condition:
+x0 = x
+Dynamics:
+(1) − (4)
+(5)(6) for i = 1...n
+Taut cable constraint:
+0 ≤ tmin ≤ ti ≤ tmax
+Thrust constraint:
+fmin ≤ fi ≤ fmax for i = 1...n
+Collision avoidance constraint:
+dmin ≤ dij for i = 1...n
+where yref are the pose reference of the load, namely
+yref = [pref, qref]
+(19)
+Note that the above OCP includes a taut cable constraint
+to prevent cable slack in the predicted trajectory. The thrust
+constraint and the collision avoidance constraint are also
+included, where fi and dij have been derived respectively
+in (14) and (16).
+By solving the above OCP we can obtain the optimal
+states and control along the discrete nodes. We use ¯x and
+
+¯u to express the corresponding array of optimal states and
+inputs, and x|k (k ∈ [0, N]) to indicates the variables in
+the prediction horizon at node k. Given ¯x and ¯u, we can
+obtain the thrust and its direction of all the UAVs along the
+trajectory using (13)-(15). At the k-th node, they are denoted
+respectively by fi|k and zi|k.
+The inputs of the NMPC are not fed into the controller.
+Instead, we use fi|k and zi|k generated by the NMPC as the
+reference of the UAV controllers. According to (13), fi|k and
+zi|k have algebraic relationship with states of the NMPC.
+Therefore, their values on the first node on the predicted
+trajectory are equal to the current thrust and its direction. In
+practice, we use their values on the most recent node on the
+predicted trajectory for simplicity. Then for the i-th UAV, we
+have
+fi,ref = fi|1
+(20)
+zi,ref = zi|1
+(21)
+Then the angular rate of the i-th UAV along the trajectory
+can be calculated through finite differentiation, yielding
+ωi|k = (zi|k + zi|k+1) × (zi|k+1 − zi|k) /2∆T
+(22)
+Note that it is also possible to obtain ωi|k through algebraic
+derivations by taking the derivative of both sides of (13),
+but this operation requires the knowledge of ˙ti as well as ˙fi
+which still need to be acquired through finite differentiation
+along the predicted trajectories. Hence we chose to calculate
+ωi|k directly via (22).
+Specifically, for the i-th UAV, we have
+ωi,ref = ωi|0
+(23)
+which will be used by the inner-loop attitude controller of
+each UAV.
+Note that the yawing motion of each UAV is not included
+in the optimal trajectory (Here we define yaw as the angle
+that each UAV rotates about its thrust direction from a pre-
+defined reference direction, such as toward the east). This is
+because the yaw angle does not affect the thrust generated
+by each UAV and consequently brings no effect to the forces
+on the load.
+In practice, the reference heading can be set for other
+purposes such as better perception accuracy [11]. Denote the
+yaw angle of the i-th UAV as θi,ref, then from the definition
+of quaternion, we have the reference attitude of the i-th UAV
+in the quaternion form
+qi,ref =
+�
+���
+cos(θi,ref)/2
+zi,ref,x sin θ/2
+zi,ref,y sin θ/2
+zi,ref,z sin θ/2
+�
+���
+(24)
+B. Inner-loop controller of each UAV
+The inner-loop controller computes the thrust that needs
+to be generated from the rotors of each UAV, given reference
+thrust, attitude, and body rates. The choice of this inner-loop
+controller is not unique, examples are geometric attitude con-
+troller [12], or quaternion-based controller [13]. In this work,
+we choose a quaternion-based controller that separates the
+thrust direction tilt and the yaw [14]. Here we briefly write
+down the key equations of this controller for readability. We
+refer readers to [14], [15] for more details. Note that the
+subscript i is omitted in variables for simplicity.
+The attitude error is:
+[qe,w, qe,x, qe,y, qe,z]T = qref ⊗ q−1,
+(25)
+˜qe,xy =
+1
+�
+q2e,w + q2e,z
+�
+�
+qe,wqe,x − qe,yqe,z
+qe,wqe,y + qe,xqe,z
+0
+�
+� ,
+(26)
+˜qe,z =
+1
+�
+q2e,w + q2e,z
+[0
+0
+qe,z]T .
+(27)
+The following tilt-prioritized attitude law is applied to cal-
+culate the angular acceleration command of each UAV:
+˙ωB
+d = kq,xy˜qe,xy + kq,zsgn(qe,w)˜qe,z
++Krate(ωB
+ref − ωB)
+(28)
+By substituting ˙ωB
+d for ˙ωBi
+i
+in (10), we can obtain the desired
+torque command τ d. As for collective thrust, we set desired
+force
+fd = fref
+(29)
+Given the control-effective matrix of each UAV, knowing τ d
+and fd can further generate actuator commands. Details are
+omitted here.
+IV. VALIDATION
+A. Implementation details
+• Programming environment: ROS2, Python
+• NMPC solver: ACADOS, HPIPM, real-time RTK.
+B. Simulation results
+Without generality, we demonstrate a case where four
+UAVs are manipulating a rigid-body load. The load mass
+is 4kg, and each UAV weighs 1kg. The cables connecting
+each UAV and the load are 4m. The simulation results are
+presented in Fig. 2 - Fig. 5.
+V. CONCLUSION
+This draft introduces a centralized nonlinear model pre-
+dictive control method for full-pose manipulation of a cable-
+suspended load using multiple UAVs. We have validated
+the control algorithm through numerical validations. Future
+works will include analysis of parameter uncertainties and
+real-world experimental validations.
+
+Fig. 2.
+Time history of the position, orientation, velocity, and angular rate
+of the load being manipulated by 4 UAVs. The target load position p =
+[10.0, 3.0, 5.0]m and the target load orientation is [roll, pitch, yaw] =
+[30, 60, 90]deg (euler angles). Dash lines in these figures represent the
+reference.
+Fig. 3.
+Time history of the cable tension and the collective thrust of all
+UAVs. Red-dash lines represent the constraints. All cable and thrust-related
+constraints are satisfied.
+REFERENCES
+[1] S. Dai, T. Lee, and D. S. Bernstein, “Adaptive control of a quadrotor
+uav transporting a cable-suspended load with unknown mass,” in 53rd
+IEEE Conference on Decision and Control, pp. 6149–6154, IEEE,
+2014.
+[2] P. Foehn, D. Falanga, N. Kuppuswamy, R. Tedrake, and D. Scara-
+muzza, “Fast trajectory optimization for agile quadrotor maneuvers
+with a cable-suspended payload,” 2017.
+[3] G. Tartaglione, E. D’Amato, M. Ariola, P. S. Rossi, and T. A. Jo-
+hansen, “Model predictive control for a multi-body slung-load system,”
+Robotics and Autonomous Systems, vol. 92, pp. 1–11, 2017.
+[4] I. Moreno Caireta, “Planning and control of a multiple-quadcopter
+system cooperatively carrying a slung payload in dynamical environ-
+ments. a centralized model predictive control solution,” B.S. thesis,
+Universitat Polit`ecnica de Catalunya, 2018.
+[5] M. Romano, A. Ye, J. Pye, and E. Atkins, “Cooperative multilift slung
+load transportation using haptic admittance control guidance,” Journal
+of Guidance, Control, and Dynamics, vol. 45, no. 10, pp. 1899–1912,
+2022.
+Fig. 4.
+Time history of the acceleration of all UAVs. Red-dash lines
+represent the constraints. All acceleration constraints are satisfied.
+Fig. 5.
+Time history of the relative distances between UAVs. Red-dash
+lines represent the minimum distance (1.2m) set in the controller.
+[6] T. Lee, “Geometric control of quadrotor uavs transporting a cable-
+suspended rigid body,” IEEE Transactions on Control Systems Tech-
+nology, vol. 26, no. 1, pp. 255–264, 2017.
+[7] G. Li, X. Liu, and G. Loianno, “Rotortm: A flexible simulator for aerial
+transportation and manipulation,” arXiv preprint arXiv:2205.05140,
+2022.
+[8] D. Sanalitro, H. J. Savino, M. Tognon, J. Cort´es, and A. Franchi, “Full-
+pose manipulation control of a cable-suspended load with multiple
+uavs under uncertainties,” IEEE Robotics and Automation Letters,
+vol. 5, no. 2, pp. 2185–2191, 2020.
+[9] N. Michael, J. Fink, and V. Kumar, “Cooperative manipulation and
+transportation with aerial robots,” Autonomous Robots, vol. 30, no. 1,
+pp. 73–86, 2011.
+[10] K. Sreenath, N. Michael, and V. Kumar, “Trajectory generation and
+control of a quadrotor with a cable-suspended load-a differentially-flat
+hybrid system,” in 2013 IEEE international conference on robotics and
+automation, pp. 4888–4895, IEEE, 2013.
+[11] D. Falanga, P. Foehn, P. Lu, and D. Scaramuzza, “Pampc: Perception-
+aware model predictive control for quadrotors,” in 2018 IEEE/RSJ
+International Conference on Intelligent Robots and Systems (IROS),
+pp. 1–8, IEEE, 2018.
+[12] T. Lee, M. Leok, and N. H. McClamroch, “Geometric tracking control
+of a quadrotor uav on se (3),” in 49th IEEE conference on decision
+
+10
+0.75
+px
+8
+Ppy
+0.50
+zd
+6
+4
+qx
+0.00
+2
+qy
+-0.25
+zb
+0
+0.0
+2.5
+5.0
+7.5
+10.0
+0.0
+2.5
+5.0
+7.5
+10.0
+4
+1.5
+Vx
+Wx
+1.0
+Wy
+3
+0.5
+Wz
+2
+0.0
+1
+-0.5
+-1.0
+0.0
+2.5
+5.0
+7.5
+10.0
+0.0
+2.5
+5.0
+7.5
+10.015
+cable tension (N)
+UAV #1
+10
+UAV #2
+UAV #3
+5
+UAV #4
+0
+2
+4
+6
+8
+10
+30
+thrust (N)
+20
+10
+0
+0
+2
+4
+6
+8
+10
+time (s)10
+(zs/u)
+UAV #1
+UAV #2
+0
+UAV #3
+UAV #4
+-10
+0
+4
+6
+8
+10
+10
+(zs/u)
+accy
+-10
+0
+4
+6
+8
+10
+10
+(zs/u) z
+acCz
+0
+0
+2
+4
+6
+8
+10
+time (s)5.0
+4.5
+4.0
+d12
+3.5
+distance (m)
+d13
+d14
+3.0
+d23
+d24
+2.5
+d34
+2.0
+1.5
+0
+Z
+4
+6
+8
+10
+time (s)and control (CDC), pp. 5420–5425, IEEE, 2010.
+[13] E. Fresk and G. Nikolakopoulos, “Full quaternion based attitude
+control for a quadrotor,” in 2013 European control conference (ECC),
+pp. 3864–3869, IEEE, 2013.
+[14] D. Brescianini and R. D’Andrea, “Tilt-prioritized quadrocopter attitude
+control,” IEEE Transactions on Control Systems Technology, vol. 28,
+no. 2, pp. 376–387, 2018.
+[15] S. Sun, A. Romero, P. Foehn, E. Kaufmann, and D. Scaramuzza,
+“A comparative study of nonlinear mpc and differential-flatness-based
+control for quadrotor agile flight,” IEEE Transactions on Robotics,
+vol. 38, no. 6, pp. 3357–3373, 2022.
+
diff --git a/eNFAT4oBgHgl3EQfZR37/content/tmp_files/load_file.txt b/eNFAT4oBgHgl3EQfZR37/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b9803464b393a7ad57eceab9d304eb4f52b9c9e
--- /dev/null
+++ b/eNFAT4oBgHgl3EQfZR37/content/tmp_files/load_file.txt
@@ -0,0 +1,286 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf,len=285
+page_content='Nonlinear MPC for full-pose manipulation of a cable-suspended load using  multiple UAVs  Sihao Sun, Antonio Franchi  Abstract— Using multiple UAVs to manipulate the full pos-  ture of an object is a promising capability in many industrial  applications, such as autonomous building construction and  heavy-load transportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Among various methods, manipu-  lation via cables excels in mechanical simplicity and ease of  use, but is challenging from a control perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Existing  centralized control methods either neglect the dynamic coupling  between UAVs and the load or resort to a cascade structure,  which limits the operational speed and cannot guarantee safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  In this work, we propose a centralized control method that uses  nonlinear model predictive control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' This control method takes  into account the full nonlinear model of the load-UAV system,  as well as the constraints of UAV thrust, collision avoidance,  and ensuring all cables are taut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' By taking into account the  above factors, the proposed control algorithm can fully exploit  the performance of UAVs and facilitate the speed of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  We demonstrate our algorithm through 6-DoF simulations to  achieve fast and safe manipulation of the pose of a rigid-body  payload using multiple UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' INTRODUCTION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Background and motivation  Collaborative manipulation is a promising capability  in many industrial applications, given the fact that the  payload capacity of a single UAV is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Related works  Works for single UAV and a point-mass sling load  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=',[1], [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Works for multi-UAVs with a point-mass sling load  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=', [3], [4], [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Works for multi-UAVs with a rigid-body sling load  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=',[6], [7], [8], [9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Existing works for multi-UAVs manipulating the full  pose of a rigid-body load with suspended cables can-  not simultaneously consider the full-nonlinear dynamic  model of the load-UAVs system, and the thrust limita-  tion of each UAV, as well as other constraints such as  taut cable, and collision avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Contribution of this work  A centralized control algorithm that can automatically  exploit the redundancy of the load-UAVs system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fully explore the load-UAVs system’s nonlinear dynam-  ics, and consider system constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Formulate the system model to allow real-time opti-  mization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Coordinate systems definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' PRELIMINARY  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Problem Formulation  The system comprises n UAVs and a single rigid-body  load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' There is a coordinate system L = {OL, xL, yL, zL}  attached to the load with the origin located at the centre  of mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' For each UAV, there is a body-fixed frame Bi =  {OBi, xBi, yBi, zBi} attached where OBi is at the center of  mass of the ith UAV and zBi points at the thrust direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  The position of the load with respect to the inertial frame  I is denoted by p, and the orientation is denoted by R ∈  SO(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Similarly, the position and orientation of the ith UAV  is denoted by pi and Ri ∈ SO(3) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The angular  rate and  Each UAV is connected to the load through a cable with  a length of li, where subscription i ∈ N+ ≤ n is the UAV  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Both sides of the cable are hinge connections, with one  side connected to the centre of mass of the UAV and another  side connected to an arbitrary point of the load, displacing  from its centre of mass by ρi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The cable tension is denoted  by ti ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  The UAV considered in this work are uni-directional  Thrust platforms, whose collective thrust can only vary along  one direction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=', zBi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Examples are helicopters and multi-  rotor drones whose rotors are coplanar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' These platforms  can generate moments to change their thrust direction, and  consequently, change their position in the inertial frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  The objective of the controller designed in this paper is to  generate the collective thrust fi and moment τi of all the  UAVs, such that the position and attitude (full pose) of the  load can follow a given value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='08545v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='RO]  20 Jan 2023  UAV #2  UAV #1  ZBi  XBI  ZL  UAV #i  Bi  SiB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Modeling  1) Load-cable model: We model the load using a 6 DoF  rigid-body dynamic model:  ˙p = v  (1)  ˙v = −  n  �  i=1  tisi/m + g  (2)  ˙R = RωL  ×  (3)  ˙ωL = I−1  L  �  −ωL × ILωL +  n  �  i=1  �  RT si × ρL  i  ��  (4)  The mass-less cable is modelled with only kinematics con-  sidered, up to angular accelerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' For the i-th cable, we  have  ˙si = ri × si  (5)  ¨ri = ci  (6)  2) UAV model: The UAV considered in this paper are  uni-directional UAVs, meaning that only thrusts along a  single direction (defined as zi of the vehicle) are generated,  examples are helicopters and quadrotors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' In this work, we use  a rigid-body model to represent the kinematics and dynamics  of the UAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Specifically, the model of the i-th UAV is:  ˙pi = vi  (7)  ˙vi = (fizi + tisi)/mi + g  (8)  ˙Ri = RiωBi  i,×  (9)  ˙ωBi  i  = I−1  i  �  −ωBi  i  × IiωBi  i  + τ i  �  (10)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Kinematic Constraints  Since each UAV is constrained at the end of the corre-  sponding cable, for the i-th UAV, we have the following  kinematic constraint:  pi = p + RρL  i − lisi  (11)  These constraints render the UAV states dependent on the  load-cable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' This is also known as the differential  flatness of the (multi-)UAV-load-cable system [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The UAV  states can be derived as algebraic functions of the load pose  and cables’ orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' For the optimization problem in the  next section, we need to set constraints on the collective  thrust of each UAV to fulfil its physical limitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Therefore  we derive the thrust of each UAV using the kinematic  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  By taking the second-order derivative of both sides of (11)  and substituting (3)-(6) to it,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' we have  ˙vi = ˙v + R  � ˙ωBi × ρL  i + ωL × (ωL × ρL  i )  �  − li ˙ri × si − lir × (r × si)  = (fizi + tisi)/mi + g  (12)  Through simple algebra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' we have  fizi = f i = mi[ ˙v + R( ˙ωL × ρL  i + ωL × (ωL × ρL  i ))  − li ˙ri × si − lir × (r × si))]  − tisi − g  (13)  fi = ∥f i∥  (14)  zi = f i/fi  (15)  Collisions between UAVs and cables need to be avoided  for safety reasons,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' here we express the distance between i-th  UAV and the j-th cable as  dij =  �  pi − pj  �  × si  = R  �  ρL  i − ρj  �  + (ljsj − lisi) × si  (16)  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' METHODOLOGY  The control algorithm designed in this section aims at  controlling the full pose of the load to a reference, by  generating thrust and torque commands for all the UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  In the meantime, we guarantee safety by incorporating the  thrust constraints and the collision constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' This will help  to fully exploit the capability of each UAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The control  diagram is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Nonlinear model predictive control  The nonlinear model predictive controller utilizes the load-  cable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The states and inputs of this model are defined  as:  x =  �  p,  v,  R,  ωB,  s1,  r1,  ˙r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=',  sn,  rn,  ˙rn  �  (17)  u = [c1,  t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=', cn,  tn]  (18)  Then the following optimal control problem (OCP) is solved  in each control step of nonlinear MPC:  min J =  � τf  τ=0  1  2||yref − y||2  W + ||σ||2  W σ  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Initial condition:  x0 = x  Dynamics:  (1) − (4)  (5)(6) for i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='n  Taut cable constraint:  0 ≤ tmin ≤ ti ≤ tmax  Thrust constraint:  fmin ≤ fi ≤ fmax for i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='n  Collision avoidance constraint:  dmin ≤ dij for i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='n  where yref are the pose reference of the load, namely  yref = [pref, qref]  (19)  Note that the above OCP includes a taut cable constraint  to prevent cable slack in the predicted trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The thrust  constraint and the collision avoidance constraint are also  included, where fi and dij have been derived respectively  in (14) and (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  By solving the above OCP we can obtain the optimal  states and control along the discrete nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' We use ¯x and  ¯u to express the corresponding array of optimal states and  inputs, and x|k (k ∈ [0, N]) to indicates the variables in  the prediction horizon at node k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Given ¯x and ¯u, we can  obtain the thrust and its direction of all the UAVs along the  trajectory using (13)-(15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' At the k-th node, they are denoted  respectively by fi|k and zi|k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  The inputs of the NMPC are not fed into the controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Instead, we use fi|k and zi|k generated by the NMPC as the  reference of the UAV controllers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' According to (13), fi|k and  zi|k have algebraic relationship with states of the NMPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Therefore, their values on the first node on the predicted  trajectory are equal to the current thrust and its direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' In  practice, we use their values on the most recent node on the  predicted trajectory for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Then for the i-th UAV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' we  have  fi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='ref = fi|1  (20)  zi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='ref = zi|1  (21)  Then the angular rate of the i-th UAV along the trajectory  can be calculated through finite differentiation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' yielding  ωi|k = (zi|k + zi|k+1) × (zi|k+1 − zi|k) /2∆T  (22)  Note that it is also possible to obtain ωi|k through algebraic  derivations by taking the derivative of both sides of (13),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  but this operation requires the knowledge of ˙ti as well as ˙fi  which still need to be acquired through finite differentiation  along the predicted trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Hence we chose to calculate  ωi|k directly via (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Specifically, for the i-th UAV, we have  ωi,ref = ωi|0  (23)  which will be used by the inner-loop attitude controller of  each UAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Note that the yawing motion of each UAV is not included  in the optimal trajectory (Here we define yaw as the angle  that each UAV rotates about its thrust direction from a pre-  defined reference direction, such as toward the east).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' This is  because the yaw angle does not affect the thrust generated  by each UAV and consequently brings no effect to the forces  on the load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  In practice, the reference heading can be set for other  purposes such as better perception accuracy [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Denote the  yaw angle of the i-th UAV as θi,ref, then from the definition  of quaternion, we have the reference attitude of the i-th UAV  in the quaternion form  qi,ref =  �  ���  cos(θi,ref)/2  zi,ref,x sin θ/2  zi,ref,y sin θ/2  zi,ref,z sin θ/2  �  ���  (24)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Inner-loop controller of each UAV  The inner-loop controller computes the thrust that needs  to be generated from the rotors of each UAV, given reference  thrust, attitude, and body rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The choice of this inner-loop  controller is not unique, examples are geometric attitude con-  troller [12], or quaternion-based controller [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' In this work,  we choose a quaternion-based controller that separates the  thrust direction tilt and the yaw [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Here we briefly write  down the key equations of this controller for readability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' We  refer readers to [14], [15] for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Note that the  subscript i is omitted in variables for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  The attitude error is:  [qe,w, qe,x, qe,y, qe,z]T = qref ⊗ q−1,  (25)  ˜qe,xy =  1  �  q2e,w + q2e,z  �  �  qe,wqe,x − qe,yqe,z  qe,wqe,y + qe,xqe,z  0  �  � ,  (26)  ˜qe,z =  1  �  q2e,w + q2e,z  [0  0  qe,z]T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  (27)  The following tilt-prioritized attitude law is applied to cal-  culate the angular acceleration command of each UAV:  ˙ωB  d = kq,xy˜qe,xy + kq,zsgn(qe,w)˜qe,z  +Krate(ωB  ref − ωB)  (28)  By substituting ˙ωB  d for ˙ωBi  i  in (10), we can obtain the desired  torque command τ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' As for collective thrust, we set desired  force  fd = fref  (29)  Given the control-effective matrix of each UAV, knowing τ d  and fd can further generate actuator commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Details are  omitted here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' VALIDATION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Implementation details  Programming environment: ROS2, Python  NMPC solver: ACADOS, HPIPM, real-time RTK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Simulation results  Without generality, we demonstrate a case where four  UAVs are manipulating a rigid-body load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The load mass  is 4kg, and each UAV weighs 1kg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The cables connecting  each UAV and the load are 4m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The simulation results are  presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 2 - Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' CONCLUSION  This draft introduces a centralized nonlinear model pre-  dictive control method for full-pose manipulation of a cable-  suspended load using multiple UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' We have validated  the control algorithm through numerical validations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Future  works will include analysis of parameter uncertainties and  real-world experimental validations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Time history of the position, orientation, velocity, and angular rate  of the load being manipulated by 4 UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' The target load position p =  [10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='0, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='0, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='0]m and the target load orientation is [roll, pitch, yaw] =  [30, 60, 90]deg (euler angles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Dash lines in these figures represent the  reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Time history of the cable tension and the collective thrust of all  UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Red-dash lines represent the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' All cable and thrust-related  constraints are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  REFERENCES  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Dai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Lee, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Bernstein, “Adaptive control of a quadrotor  uav transporting a cable-suspended load with unknown mass,” in 53rd  IEEE Conference on Decision and Control, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 6149–6154, IEEE,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Foehn, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Falanga, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Kuppuswamy, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Tedrake, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Scara-  muzza, “Fast trajectory optimization for agile quadrotor maneuvers  with a cable-suspended payload,” 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Tartaglione, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' D’Amato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Ariola, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Rossi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Jo-  hansen, “Model predictive control for a multi-body slung-load system,”  Robotics and Autonomous Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 92, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1–11, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [4] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Moreno Caireta, “Planning and control of a multiple-quadcopter  system cooperatively carrying a slung payload in dynamical environ-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' a centralized model predictive control solution,” B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' thesis,  Universitat Polit`ecnica de Catalunya, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Romano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Ye, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Pye, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Atkins, “Cooperative multilift slung  load transportation using haptic admittance control guidance,” Journal  of Guidance, Control, and Dynamics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 45, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1899–1912,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Time history of the acceleration of all UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Red-dash lines  represent the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' All acceleration constraints are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  Time history of the relative distances between UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Red-dash  lines represent the minimum distance (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='2m) set in the controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Lee, “Geometric control of quadrotor uavs transporting a cable-  suspended rigid body,” IEEE Transactions on Control Systems Tech-  nology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 255–264, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Liu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Loianno, “Rotortm: A flexible simulator for aerial  transportation and manipulation,” arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='05140,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Sanalitro, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Savino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Tognon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Cort´es, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Franchi, “Full-  pose manipulation control of a cable-suspended load with multiple  uavs under uncertainties,” IEEE Robotics and Automation Letters,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 2185–2191, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [9] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Michael, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Fink, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Kumar, “Cooperative manipulation and  transportation with aerial robots,” Autonomous Robots, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 30, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 73–86, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [10] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Sreenath, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Michael, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Kumar, “Trajectory generation and  control of a quadrotor with a cable-suspended load-a differentially-flat  hybrid system,” in 2013 IEEE international conference on robotics and  automation, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 4888–4895, IEEE, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Falanga, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Foehn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Lu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Scaramuzza, “Pampc: Perception-  aware model predictive control for quadrotors,” in 2018 IEEE/RSJ  International Conference on Intelligent Robots and Systems (IROS),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 1–8, IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Leok, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' McClamroch, “Geometric tracking control  of a quadrotor uav on se (3),” in 49th IEEE conference on decision  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='75  px  8  Ppy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='50  zd  6  4  qx  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='00  2  qy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
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+page_content='015  cable tension (N)  UAV #1  10  UAV #2  UAV #3  5  UAV #4  0  2  4  6  8  10  30  thrust (N)  20  10  0  0  2  4  6  8  10  time (s)10  (zs/u)  UAV #1  UAV #2  0  UAV #3  UAV #4  10  0  4  6  8  10  10  (zs/u)  accy  10  0  4  6  8  10  10  (zs/u) z  acCz  0  0  2  4  6  8  10  time (s)5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
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+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='5  0  Z  4  6  8  10  time (s)and control (CDC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 5420–5425, IEEE, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [13] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Fresk and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Nikolakopoulos, “Full quaternion based attitude  control for a quadrotor,” in 2013 European control conference (ECC),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 3864–3869, IEEE, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Brescianini and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' D’Andrea, “Tilt-prioritized quadrocopter attitude  control,” IEEE Transactions on Control Systems Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 28,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 376–387, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content='  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Romero, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Foehn, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Kaufmann, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' Scaramuzza,  “A comparative study of nonlinear mpc and differential-flatness-based  control for quadrotor agile flight,” IEEE Transactions on Robotics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
+page_content=' 3357–3373, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNFAT4oBgHgl3EQfZR37/content/2301.08545v1.pdf'}
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+Quantum Representations of Sound: from
+mechanical waves to quantum circuits
+Paulo V. Itabora´ı1 and Eduardo R. Miranda1
+1Interdisciplinary Centre for Computer Music Research (ICCMR),
+University of Plymouth, Plymouth, UK
+{paulo.itaborai,eduardo.miranda}@plymouth.ac.uk
+Abstract
+By the time of writing, quantum audio still is a very young area of study, even within
+the quantum signal processing community. This chapter introduces the state of the art
+in quantum audio and discusses methods for the quantum representation of audio sig-
+nals. Currently, no quantum representation strategy claims to be the best one for audio
+applications. Each one presents advantages and disadvantages. It can be argued that
+future quantum audio representation schemes will make use of multiple strategies aimed
+at specific applications. The authors also discuss ... .
+NOTE: This is an unedited abridged version of the pre-submission draft of a chapter,
+with the same title, published in the book Quantum Computer Music: Foundations, Meth-
+ods and Advanced Concepts, by E. R. Miranda (pp. 223 - 274). Please refer to the
+version in this book for application examples and a discussion on sound synthesis meth-
+ods based on quantum audio representation and their potential for developing new types
+of musical instruments.
+https://link.springer.com/book/10.1007/978-3-031-13909-3
+1
+Introduction
+Sounds and images share common grounds. From the point of view of information pro-
+cessing, both are just signals. But obviously, we perceive them differently.
+Most signal processing methods used for sounds are applicable to images and vice-
+versa. Their main difference is with respect to dimensionality. For instance, whereas
+sound is a one-dimensional (1D) signal in the time domain, image is a two-dimensional
+(2D) one. From a mathematical perspective, the higher the dimension of a signal, the
+more complex to represent and process it. Therefore, it is logical first to learn how 1D
+signal representation and processing methods work and then extrapolate to 2D (images),
+3D (videos), and beyond. By and large, this is how textbooks on audio and visual signal
+processing introduce the subject; e.g., [1] [2].
+Thus, from a historical perspective, it would seem reasonable to expect that quantum
+representations and potential algorithms for sound would have appeared in research av-
+enues before the appearance of those for images and video. Surprisingly, this is not the
+case. An avid interest in developing quantum algorithms for image processing (primar-
+ily for facial recognition and similar applications) produced methods for quantum image
+representations and processing rapidly, leaving the case of 1D sound behind by almost
+1
+arXiv:2301.01595v1  [quant-ph]  1 Jan 2023
+
+a decade. This gap is unexpected, given the importance of speech technology to the
+electronics industry. Even more, if bearing in mind the relatively long-standing desire to
+develop quantum computing for natural language processing [4].
+The first papers describing how to represent an image on a quantum processor the-
+oretically were published in 2003 [17] and 2005 [16]. In comparison, the first papers
+proposing quantum representation methods for sound are from 2015 [6] and 2018 [7];
+they are based on a method for images proposed in 2011 [5]. Indeed, most quantum
+signal processing algorithms designed to date are for image applications. The quantum
+sound community needs to catch up. Hence the motivation for this chapter.
+The chapter is structured as follows: firstly, section 3 contains a short introduction
+that delineates essential aspects and concepts of sound, analogue and digital audio rep-
+resentations that will be used later. It generally explains how the original sound content
+is transformed from one media to another. The concepts shown in this section will propel
+us toward the quantum territory with better intuition. This introductory section concludes
+by giving an initial idea of how quantum information logic will be applied to audio signals.
+The introduction is followed by a short section (3) that explains how time information is
+generally encoded in a quantum state. The following note (3.2) identifies some confusion
+problems present in the nomenclatures used by the literature for quantum audio. It pro-
+poses a new naming system to unify and clarify the different strategies used to encode
+audio information.
+Then, the two subsequent sessions dive into various definitions and schemes pro-
+posed for representing audio in quantum machines using the previously proposed nam-
+ing system. For instance, section 4 explores Coefficient-Based representations, whereas
+section 5 focuses on State-Based ones.
+Section 6 summarizes the representations shown in the previous sections. It dis-
+cusses some obstacles that should be accounted for when considering building and run-
+ning quantum audio circuits for state-of-the-art quantum hardware.
+Section ?? details some basic quantum signal processing operations and circuit de-
+sign, such as quantum audio addition and concatenation, as well as sample-by-sample
+comparison.
+The last section (??) punctuates some potential artistic applications in the short and
+near term. Specifically, there is a case study exploring wavetable synthesis and simple
+effects that make use of configurable parameters of coefficient-based representations.
+2
+From Mechanical to Quantum
+The main objective of this section is to review how sound is represented in digital com-
+puters and electronic devices in general. It will provide the foundations to understand
+how sound can be represented for quantum computation.
+In order to store a given sound in a quantum computer (i.e., by the time of writing),
+one would need to record the sound as analogue audio and make an analogue-to-digital
+conversion. Then, the digital audio needs to be translated into a quantum audio rep-
+resentation of some kind (Figure 1). Let us go through each of these stages in more
+detail.
+2
+
+Figure 1: The signal path from mechanical sound to quantum sound.
+2.1
+From Mechanical to Analog
+In the most general sense, waves are physical entities that carry information about dis-
+turbances in a particular medium. For instance, electromagnetic waves carry information
+about disturbances in an electromagnetic field. Sound, however, is a mechanical wave. It
+can be generated by providing energy to a set of coupled vibrating systems in an acoustic
+medium, such as air.
+Upon reaching a microphone, vibrating air pressure - that is, sound - becomes electric
+voltage. This is analog audio. There are many ways to do this mechanic-to-electric
+conversion. One of the first techniques ever developed to do this can still be found in
+dynamic microphones today.
+A dynamic microphone has three main elements: a thin diaphragm, a cylindrical mag-
+net and a wire coil. The coil is wrapped around the magnet, but it does not touch it. It
+can move freely on the cylinder’s axis. The diaphragm is coupled to one end of the coil.
+So, the vibrating sound will move the diaphragm back and forth. As a consequence, the
+coil will oscillate through the magnet - or, from the perspective of the coil, the magnet
+will oscillate through it. In an oversimplified way, Faraday’s Law teaches us that when a
+magnet is moving through a conductive coil, it will induce an electric current. This move-
+ment will result in a measurable voltage. So, an oscillating coil will induce an oscillating
+voltage at its terminals. Thus, the mechanical sound has been converted into a varying
+electric voltage signal which is, by definition, analogue audio.
+2.1.1
+Audio Encoding
+Analog audio creates a direct connection between mechanical and electrical media. We
+could say that it represents sound.
+Analog audio imposes itself as a new technique for propagating and manipulating
+sound, which was not possible before its invention. For instance, a singer could try to
+sing louder or even scream, attempting to reach listeners located far away and still not
+be heard. Alternatively, this singer could convert her voice into audio and then transmit
+the signal through conductive wires or electromagnetic waves until it reaches the listener.
+The audio would then be converted back into sound through loudspeakers. The caveat
+is that transmission, reception and conversion are prone to noise and errors.
+Attempts to reduce noise and errors during long transmissions (for example, radio
+transmissions) are what motivated the first audio encoding schemes as effective ways of
+representing electric audio information. The three most widely used analogue audio en-
+coding schemes are Amplitude Modulation (AM), Frequency Modulation (FM) and Phase
+Modulation (PM) [3]. In these cases, the raw analogue signal is encoded by means of
+3
+
+QUANTUM
+MECHANICAL
+DIGITAL
+ANALOG
+ADCa measurable variation of a signal parameter, such as the frequency, amplitude (i.e.,
+power), or phase.
+2.2
+From Analog to Digital
+A digital computer is unable to process a continuous stream of audio, which contains
+voltage information at all possible points in time. There are infinitely many of them inside
+an audio signal. Thus, analog information needs to be digitized. This is done by means
+of an ADC (Analog-to-Digital Converter) device, which converts an analog signal into a
+digital signal. How is this done? How to turn continuous time and amplitude information
+into discrete binary codes?
+This section introduces the notions of sampling and quantization, which are dis-
+cretizations of time and amplitude, respectively.
+Audio sampling is the action of taking snapshots of a continuous signal and storing
+them (i.e., the values captured by the snapshots) as time-indexed samples (Figure 2).
+Figure 2: A sampled sine wave.
+As shown in Figure 2, the snapshots of a signal are conventionally taken in equally
+spaced time lapses. The speed of lapses is referred to as the sampling rate or sampling
+frequency. In other words, the sampling rate establishes how many samples are taken
+per unit of time. Good quality audio systems use a sampling rate of 44,100 Hz (or 44,100
+snapshots per second).
+The sampling rate has the role of translating an index k =
+0, 1, 2, ... into a respective instant in time tk. That is, the sampling rate SR is the constant
+responsible for carrying the conversion between the moment of the snapshot (in time
+units) and an index of time (dimensionless) (Eq. 1). The index k can be represented in
+binary form and thus stored in a classical computer.
+tk = k
+SR
+(1)
+Now, let us look at the quantization step. Bear in mind that the notion of quantization
+here is nothing to do with quantum mechanics. Here, quantizing means to restrict a
+continuous range to a prescribed set of values.
+Let us examine how the amplitude of an analogue signal, usually represented in the
+−1 to 1 range, can be quantized into binary numbers (Figure 3).
+4
+
+Sample
+7 38 39 40 41 42 43 44 45 46 47 48 49
+1.00
+Analog Audio
+Samples
+0.75
+0.50
+Audio Amplitude
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time [s]Figure 3: An analog wave and its respective quantization.
+Quantization is, in some ways, similar to sampling, but it operates alongside the ver-
+tical axis. The main difference is that the values can be negative. Nevertheless, we can
+rescale and shift the whole signal to make it fall entirely in the positive domain without
+any loss of generality. This is a resourceful operation in audio signal processing.
+The way to shift a signal along a determined axis is by adding or subtracting a defined
+quantity on all signal values. In our case, we would like to shift the entire signal up by
+1, so we add 1 to every amplitude value. After doing this, the amplitudes range from 0
+to 2 instead of −1 and 1. The range is already positive, but we can further improve this
+by rescaling the signal to the 0 to 1 range; this will be relevant to our quantum audio
+discussion later. The rescaling is done by multiplication and division, and of course,
+for our case, we divide the amplitudes by 2. With this unitary range, we can do the
+quantization scheme more easily. If we have n-bit words to store each amplitude, we
+will perform 2n subdivisions in our range. Then, the voltage values are rounded to fit the
+closest binary value afforded by the subdivision scheme.
+Hence, we have successfully digitized our audio by putting them on a grid, as shown
+in Figure 3.
+2.2.1
+Two’s Complement Scheme
+The quantization scheme presented above is perfectly valid and general for any type
+of signal in a positive range. However, we have seen that audio signals have negative
+values as well.
+Of course, this is not a problem in itself. We showed above how to shift audio to
+a positive domain. However, this shifting procedure can often render the audio unsuit-
+able for specific manipulations. A concerning example would be amplitude multiplication.
+Shifting a value to the strictly positive domain could drastically alter the result of a simple
+multiplication (as indicated in Eq. 2).
+(a1 + shift)(a2 + shift) ̸= a1a2 + shift
+(2)
+This absence of negative numbers may also prove to be at least inconvenient. Con-
+sider, for instance, the task of adding two audio signals. The way to add digitized audio
+waves is by summing their amplitudes, term-by-term. Specifically, imagine an oversim-
+plified digital noise cancellation algorithm. It relies on negative numbers. First, some
+unwanted noise in an audio signal is received. Then, it generates a copy of the noise
+with inverted polarity (In other words, all amplitudes are multiplied by −1). Finally, the
+5
+
+Sample
+0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 4344 45 46 47 48 49
+1.000
+AnalogAudio
+1101011
+DigitalAudio
+ignedj
+0.675
+[Unsigned
+AudioAmplitude
+0.325
+100|001
+0.000
+0111000
+ns
+Representatior
+-0.325
+010111
+0.675
+0011110
+Binary
+1.000
+000/101
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time [s]inverted signal is added to the original. Each amplitude is added to a negated version of
+itself, meaning they cancel each other, and the noise disappears. This phenomenon is
+nominally called destructive interference1. Even though there might be an elaborate way
+of achieving the desired result with only positive numbers, a less laborious alternative is
+desirable.
+A viable solution - which is the one that is generally used for representing audio
+signals - is to use another interpretation of the binary integers. One that could enable us
+to represent negative numbers and facilitate binary addition arithmetic. This solution is
+referred to as the Two’s Complement scheme.
+It is important to understand the underlying logic of representing negative numbers in
+binary, as this will also be useful for quantum audio representations.
+The main idea of the Two’s Complement encoding scheme is to divide the binary
+words into two sets. Half of them would represent negative numbers and the other half
+positive ones. This can be made by using the Most Significant Bit (i.e., the leftmost bit),
+or MSB, as a signing bit. If the MSB is 0, then the number is positive. Otherwise, it is
+negative (Eq. 3).
+0010... −→
+(+ or−)
+0
+(number)
+010...
+(3)
+However, just the signing bit by itself is not enough for having a ’good’ negative num-
+ber. For it to be useful, it needs to comply with binary addition properties.
+Let us consider a computer with a 4-bit architecture and then use the MSB to indicate
+the signal of the following 3 bits without applying any other logic. Now, let us try to add 2
+and −2 using this new interpretation. Consider the simplified binary addition rules in Eq.
+4, and see what happens when we add the numbers (Eq. 5).
+0 + 0 = 0
+0 + 1 = 1 + 0 = 1
+1 + 1 = 10
+{The bit to the left is added by 1}
+(4)
+2 → 0 010 ;
+−2 → 1 010 ∴ 0 010 + 1 010 = 1 100 → −4 (?)
+(5)
+What is shown in Eq. 5 clearly does not work. But this can be solved. We can
+apply another condition to our encoding scheme. That is: x + (−x) = 0. This condition
+would interestingly and conveniently change the representation of the negative numbers
+completely, as shown in Eq. 6. Now we can verify in Eq. 7 that the addition works
+perfectly.
+Regular Integer
+�
+���
+15
+14
+...
+8
+�
+���
+�
+���
+7
+...
+1
+0
+�
+���
+=
+�
+���
+1 111
+1 110
+...
+1 000
+�
+���
+�
+���
+0 111
+...
+0 001
+0 000
+�
+���
+↘
+Two′s Complement Integer
+�
+���
+0 111
+...
+0 001
+0 000
+�
+���
+�
+���
+1 111
+1 110
+...
+1 000
+�
+���
+=
+�
+���
+7
+...
+1
+0
+�
+���
+�
+���
+−1
+−2
+...
+−8
+�
+���
+(6)
+2 → 0 010 ;
+−2 → 1 110 ∴ 0 010 + 1 110 = 0 000 → 0
+(7)
+1This also appears in the context of the quantum theory, since quantum systems also show wave-like
+behaviour and thus have wave-like properties such as superposition and interference, among others. But do
+not be misled. A classical wave and a quantum particle-wave still are fundamentally different, even if they have
+similar mathematical properties
+6
+
+2.2.2
+Digital Audio as an Array
+After being digitized, the audio’s binary information is stored in a data structure. The
+most common structure for digital audio is an array vector, visualized in Figure 4. The
+time information becomes an index to a specific position of an array, and the respective
+amplitude becomes the variable stored in that position. In this way, one can retrieve the
+amplitudes by having the time index.
+a0
+a1
+a2
+a3
+a4
+a5
+a6
+a7
+t0
+t1
+t2
+t3
+t4
+t5
+t6
+t7
+Figure 4: Audio array visualization.
+In order to efficiently represent, store and transmit binary data structure as a stream
+of audio information, a digital audio encoding scheme is typically used. Similar to the
+analog case shown above, the digital domain provides some parameters that can be
+controlled (or modulated) to represent information. For example, we could represent a
+stream of digital information using pulses that are precisely controlled by piezoelectric
+crystals. The representation that has dominated the music industry is the PCM audio or
+Pulse Code Modulation. PCM has become a standard in digital audio due to its reliable
+lossless storage and transmission capacities. Furthermore, it is less prone to noise and
+errors compared to other pulse representations such as Pulse Amplitude Modulation
+(PAM), Pulse Position Modulation (PPM), and Pulse Width Modulation (PWM [3].
+We should note at this stage that the two’s complement digital audio is used in a wide
+variety of applications. However, modern 32-bit and 64-bit operating systems, as well as
+high-level programming languages like Python, further improve the representation of the
+quantized audio amplitudes by using floating-point numbers. A good approximation of
+Real (∈ R) numbers can be stored with floating-point numbers, with high precision and
+significant decimal figures. Thus, instead of storing an integer representing the middle
+number of a quantization range, we could add a new pre-processing layer and store a
+good approximation of the number itself, using the flexibility of floating-point numbers to
+process the signal in the digital medium. However, this requires a considerable amount
+of space and computing power. As we will see in the remainder of this chapter, we are
+still far from similar schemes for quantum computer audio. But imaginable nevertheless.
+2.3
+From Digital to Quantum
+Gaining an intuitive understanding of quantum audio representation is straightforward,
+in the sense that Dirac’s notation can clearly show how the audio information (time and
+amplitude) can be translated into quantum states (Figure 5). Of course, the underlying
+quantum computing paradigm can be counter-intuitive. However, this intuitive bird’s-eye
+view understanding of the organizational structure of quantum audio gives us an end goal
+and provides a guiding thread for us to cross the uncertain quantum algorithmic roads.
+On this path, we shall explore how these representations of quantum audio are prepared
+and measured, as well as potential near-term and long-term applications.
+It is important to state that quantum audio is still a very young area of study, even
+under the quantum signal processing umbrella. Therefore many fundamental questions
+remain open for discussion. There is no audio representation strategy that we could
+argue to be the best one for audio applications. Each of them presents particular advan-
+tages and disadvantages. It can be argued that quantum audio will make use of multiple
+representations targeting specific applications.
+7
+
+a0
+a1
+a2
+a3
+a4
+a5
+a6
+a7
+t0
+t1
+t2
+t3
+t4
+t5
+t6
+t7
+↓
+|t0⟩ + |t1⟩ + |t2⟩ + |t3⟩ + |t4⟩ + |t5⟩ + |t6⟩ + |t7⟩
+a0
+a1
+a2
+a3
+a4
+a5
+a6
+a7
+Figure 5: Digital to Quantum
+3
+Preparation and Retrieval of Quantum Audio
+The near-term prospects of quantum technology indicate that quantum computers will
+not replace classical computers in many ways. Rather, they will co-exist, creating hy-
+brid classical-quantum processing environments. This already occurs in current working
+quantum systems, many of which are accessible via cloud services and interact with
+classical machines. It is not going to be different for near-term quantum audio appli-
+cations. These applications rely strongly on classical computers, not only to provide a
+digital audio file to be prepared but also to post-process quantum circuit measurement
+results. There are well-known classical programming languages for this part; e.g. Python
+and MatLab. In the following sections, we will look in detail at quantum audio representa-
+tions that have been proposed to date. We will examine how quantum audio is prepared,
+measured, and envisage possible applications. Let us start by introducing the connection
+between time indexes and quantum superpositions.
+3.1
+Encoding Time Information
+As mentioned previously, a qubit is a 2-state quantum system that can be measured to
+value either 0 or 1. It can also be put in a superposition of states, written as shown in Eq.
+8, where |α|2 and |β|2 are the probabilities that a measurement of this state results in 0
+or 1, respectively. Since the sum of the probabilities of all possible outcomes needs to be
+1, it means that |α|2 + |β|2 = 1.
+|Ψ⟩ = α |0⟩ + β |1⟩
+(8)
+For 2-qubit states, a similar equation can be written, considering all possible out-
+comes, as shown in Eq. 9.
+|Ψ⟩ = a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩ ;
+|a|2 + |b|2 + |c|2 + |d|2 = 1
+(9)
+Since we have few letters in the alphabet to represent many of these probability am-
+plitudes, it might be better to change the notation slightly and use the same letter with a
+subscript. For instance, a 3-qubit state written this way is shown in Eq. 10.
+|Ψ⟩ = a(000) |000⟩ + a(001) |001⟩ + a(010) |010⟩ + a(011) |011⟩
++ a(100) |100⟩ + a(101) |101⟩ + a(110) |110⟩ + a(111) |111⟩
+(10)
+At this point, we ought to make another helpful change to the notation for improving
+our intuitiveness. Sometimes, it is convenient (and conventional) to interpret the numbers
+inside the ‘kets’ not as a sequence of states of individual qubits in a register - but as a
+classical binary bit string associated with an integer number.
+Before we do so, it is imperative to remind us that these zeros and ones inside the
+’kets’ are not numbers. Kets are a simplified notation for writing vectors. Therefore,
+whatever is written inside the ket, is just a conventionalized label that refers to a vector:
+8
+
+|label⟩. We use numbers as labels to reduce the level of abstraction of those mathemat-
+ical entities and provide some insight into their use inside a system. In other words, the
+interpretation above is not changing the state in mathematical terms. Instead, it is just
+a change of notation. It is essential to have this clear and fresh in our minds to avoid
+confusion as we introduce the representations next.
+Thus, by interpreting the qubit states as binary numbers, we can write the same 3-
+qubit state in Eq. 10 as shown in Eq. 11.
+|Ψ⟩3−qubit =
+1
+√
+8
+�
+|0⟩ + |1⟩ + |2⟩ + |3⟩ + |4⟩ + |5⟩ + |6⟩ + |7⟩
+�
+(11)
+All of the quantum audio representations presented in this text share the same encod-
+ing strategy for time information. They use a quantum register to create a superposition
+of all the possible time indexes associated with each audio sample. This is called a time
+register. Each state will be an index, indicating a position in time, similar to a classical
+array.
+Any information related to this state will encode the respective sample using differ-
+ent strategies (Eq. 12). For instance, it could use the probability amplitude or another
+coupled quantum register.
+(Amplitude) |tk⟩
+(12)
+Note the necessity of a 2n-sized signal for all of the representations. We can use zero
+padding for using audio with different sizes. We will explore in more detail below how
+amplitude information is represented in the different schemes.
+3.2
+Note on Nomenclature
+Before we proceed, let us clarify the nomenclature used to refer to the various Quantum
+Audio Representation (QAR) methods that will be reviewed below. For the sake of clarity
+and systematization, we propose slight adaptations to the names given in the research
+papers where these methods were originally introduced.
+The representation methods can be grouped into two categories related to how they
+encode the audio amplitude information and retrieve it back to the classical realm through
+measurements. The first group contains what is referred to as ’Probabilistic’ or ’Coefficient-
+Based’ representations - due to its probabilistic nature when retrieving information clas-
+sically. The second group include ’Deterministic’ or ’State-Based’ methods.
+As mentioned earlier, quantum audio representation methods are derived from meth-
+ods developed for representing images rather than sound. The research literature in-
+troduced methods such as Quantum Representation of Digital Audio (QRDA), Flexible
+Representation of Quantum Audio (FRQA), and Quantum Representation of Multichan-
+nel Audio (QRMA), which are all State-Based. However, there also are some Coefficient-
+Based methods for images that can (and will in this chapter) be easily adapted for audio
+representation.
+Also, this chapter intends to reach the signal processing community, and in this en-
+deavour, we will be proposing a new nomenclature system for the already proposed
+representations. The intention is to correlate, integrate or unify these representations
+with classic representations in the future. For that, we will use the term ‘Modulation’ as
+a central spine. This means that we will propose to rename, for example, the Flexible
+Representation of Quantum Audio (which by itself already has some confusion problems
+9
+
+in relation to quantum images2) into Quantum State Modulation (QSM), based on the
+fact that amplitude information is stored in a multi-qubit state. This naming system also
+paves the way for other coefficient-based audio representations, such as the Quantum
+Probability Amplitude Modulation (QPAM).
+4
+Coefficient-Based Representations
+Suppose that we have some digital audio A, with N = 2n, n ∈ Z∗ samples, with each
+sample quantized to [−2q−1, −2q−1 + 1, ..., 2q−1 − 1]. That is, 2q possible values.
+We can induce that the easiest way to represent those samples in a quantum state
+|A⟩ would be to create a superposition of all of its possible states t (encoding time),
+weighted by their respective probability amplitudes (encoding the sample value), in a
+way that resembles an array, but in a quantum superposition (Eq. 13 and Eq. 14).
+We can induce that the easiest way to represent those samples in a quantum state |A⟩
+would be first to create a superposition of all of its possible states t (encoding time). Then,
+each time state would be weighted by their respective probability amplitude (encoding the
+sample value).
+an
+tn −→ αi |ti⟩
+(13)
+|A⟩(3−qubitArray) = α0 |0⟩ + α1 |1⟩ + α2 |2⟩ + α3 |3⟩ + α4 |4⟩ + α5 |5⟩ + α6 |6⟩ + α7 |7⟩ (14)
+4.1
+Quantum Probability Amplitude Modulation: QPAM
+More generally, we could write an arbitrary quantum audio of size N, with n (or
+�
+log N
+�
+)
+qubits and build an encoding scheme where each possible amplitude value of the audio
+is mapped onto a probability amplitude(Eq. 15).
+|AQPAM⟩ =
+N−1
+�
+i=0
+αi |i⟩
+(15)
+Quantum computing theory usually presents the upper bound of the sum showing
+the number of qubits explicitly, like (2n − 1). Instead, we chose to use N = 2n as our
+primary notation, as this will make more sense to the reader with an audio digital signal
+processing background.
+With Eq. 15, we achieved a simple but still very useful QAR. We refer to this method
+as Quantum Probability Amplitude Modulation representation of audio, or QPAM. It is a
+convenient name, as the amplitude information is encoded as probability amplitudes of
+each quantum state.
+2It would feel logical to induce that the Flexible Representation of Quantum Audio (FRQA) was derived from
+the Flexible Representation of Quantum Images (FRQI). Unfortunately, this is not the case, since the FRQI is a
+Probability-Oriented Representation, and the FQRA is a State-Oriented one, derived from the Novel Enhanced
+Quantum Representation for digital images (NEQR). The choice to name the FQRA as such is unclear and
+might have been made for historical reasons. The FRQI was one of the pioneering representations for images
+(like FRQA) and probably the first to be widely studied in the literature with a variety of applications.
+10
+
+4.1.1
+Mapping the Digital Amplitudes to QPAM
+Now, let us examine how to convert a digital signal representation to QPAM representa-
+tion and vice-versa.
+The audio amplitudes an are not equal to the probability amplitudes αi of measuring
+each sample state. Instead, there is a specific mapping between them, which makes this
+encoding scheme possible. Let us see how this works using the hypothetic snippet of
+audio depicted in Figure 6.
+In Quantum Mechanics, we can affirm that given an arbitrary qubit |φ⟩ = α |0⟩ + β |1⟩
+the probability of measuring the state |0⟩ is |α|2, with the proviso that:
+• Probabilities are numbers ranging between 0 and 1
+• The sum of probabilities of all possible states should be equal to 1
+Digital audio amplitudes in Figure 6, however, are numbers ranging between −1 and
+1. Their sum does not necessarily add to 1 at all. So, in order to go from digital to
+quantum, we need to take the following steps to normalize the amplitudes:
+• Step 1: add 1 to all amplitudes an
+• Step 2: divide the amplitudes by 2
+• Step 3: divide again, by the sum of all of the amplitudes
+• Step 4: take the square root of the result
+Figure 6: Hypothetic audio.
+Consider the amplitudes of our example listed before the down arrow in Figure 7.
+The normalized values are shown after the down arrow. Firstly, we shifted the amplitude
+values to the positive domain by adding 1 to every value. At this point, the amplitudes
+range between 0 and 2. Next, we scaled them to fit the range between 0 and 1. Then, we
+summed all their values and divided every value by the result of the sum. At this point,
+the sum of all amplitudes should be equal to 1.
+The last step is to turn these amplitudes into probability values by taking their square
+root (Eq. 16).
+αi =
+1
+√g
+�
+(ai + 1)
+2
+;
+g =
+�
+k
+(ak + 1)
+2
+(16)
+11
+
+Original Audio
+1.0
+0.5
+litude
+Ampli
+0.0
+0.5
+1.0
+0
+2
+4
+5
+6
+Sample0.0
+−0.3
+0.7
+1.0
+−0.7
+−1
+0.3
+0.0
+↓
+0.3
+0.2
+0.5
+0.6
+0.1
+0.0
+0.4
+0.3
+Figure 7: Normalization process.
+4.1.2
+QPAM Preparation
+The QPAM representation is the most straightforward to prepare. As the information is
+stored in the probability amplitudes, we just need to initialize the quantum audio at the
+desired quantum superposition. This can be done by using the probability amplitudes to
+calculate a unitary gate. Alternatively, one could create a quantum circuit that maps a
+set of qubits initialized in the |0000...⟩ state into the arbitrary state. Fortunately, we do not
+need to worry about calculating these matrices and circuits in a more practical sense.
+Most quantum computing programming tools available nowadays provide commands to
+initialize qubit states. So, it suffices to assume that any arbitrary superposition of states
+can be initialized by providing a set of probability amplitudes to the respective command
+(Figure 8). Consequently, for preparing a QPAM quantum audio, we would only need to
+convert the digital samples into probability amplitudes.
+t0 :
+initialize([α0, α1, α2, α3, α4, α5, α6, α7])
+t1 :
+t2 :
+Figure 8: Initializing qubit states for QPAM.
+Thus, preparing an arbitrary n-qubit state usually requires O(n) simple operations,
+which implies that QPAM preparation needs O(⌈log N⌉) operations.
+4.1.3
+QPAM Retrieval
+Retrieving information from the quantum domain means taking measurements from our
+quantum system. Measuring a quantum system means that only one of the possible
+state outcomes of that system will be ’materialized’ in our measurement apparatus. In
+other words, once we measure our time registers, the superpositions will be ’destroyed’,
+and only one of the possible time states will be returned.
+Figure 9 portrays a hypothetical QPAM representation (i.e., histogram of amplitudes)
+of the audio shown in Fig 6. Furthermore, Figure 10 shows the respective audio recon-
+structed by retrieving measurements with an allegedly perfect quantum machine. Let us
+look into this in more detail.
+The Probabilistic representations have this name precisely because of their retrieval
+strategy. Retrieving audio requires that we prepare many identical quantum versions of
+the said audio and make a statistical analysis of the result of all measurements. The
+analysis will return a histogram of the measurements (e.g., Fig. 9), from which we can
+assess the approximate probability of measuring each state. When considering how the
+system was prepared in the first place, it indicates that the histogram itself is already a
+scaled and shifted version of a digital audio. We just need to scale the audio back to its
+original range, using an inverted version of Eq. 16 for ai, shown in Eq. 17.
+ai = 2g|αi|2 − 1
+(17)
+12
+
+Figure 9: A hypothetical QPAM representation.
+Figure 10: Reconstructed audio from QPAM in Figure 9.
+There are two critical aspects of Eq. 17 to be noticed. First, the sum inside the
+sum is a defined constant value, which is referred to as g. Second, the addition of a
+”||” on αi. We need to be careful with αi because it is, rigorously, a complex number
+(α2
+i ̸= |αi|2). Nevertheless, the valuable information lies in its absolute value squared,
+which corresponds to the probability pi = |αi|2 of |i⟩ being measured. After completing
+the measurements, a histogram bin will not return pi, but rather an approximation ˜pi.
+By replacing equation 17 with ˜pi, the final post-processing step for retrieving a digital
+audio is achieved, as shown in Eq. 18.
+ai = 2g˜pi − 1
+(18)
+4.1.4
+A caveat
+The constant g in Eq. 16 presents an important caveat. The equation contains terms
+related to digital amplitudes ak. What is the caveat?
+Let us consider the preparation stage. The constant g is the denominator, meaning
+that the sum over the terms (ai+1)
+2
+cannot be equal to 0. This condition occurs if all values
+of ai were equal to −1, which is a perfectly valid audio signal.
+From a retrieval perspective, there is another consideration. The presence of g makes
+the normalization of the original input necessary for retrieving a QPAM representation.
+13
+
+QuantumProbabilityAmplitudeModulationRetrievalHistogram
+0.4
+0.369
+0.3
+Probabilities
+0.250
+0.2
+0.156
+0.1
+_0.0.88
+.0.089
+0.039
+0.009
+0.0
+0
+0
+3Reconstructed QPAM
+1.00
+Original
+Reconstructed
+0.75
+0.50
+0.25
+Amplitude
+0.00
+0.25
+0.50
+0.75
+1.00
+0
+1
+2
+4
+5
+6
+SampleHowever, in more general terms, one could consider g to be any arbitrary constant, which
+would define the overall amplitude range of the signal.
+This arbitrariness of choice for g can be a problem if not properly assessed. It un-
+desirably changes the amplitude range for the retrieved audio. Let us imagine a thought
+experiment to illustrate this.
+Consider a QPAM audio signal with 8 samples. All sample values are equal to 0.
+Equation 16, confirms that g = 4.
+Then, suppose that a certain quantum algorithm
+transforms this signal into the measured waveform shown in Fig. 9. The signal will be
+reconstructed using Equation 17. Particularly, consider the peak value of the histogram.
+Applying Eq. 17 will result in 2g|0.369|2 − 1 = 0.089288. Moreover, when a low prob-
+ability sample is picked: 2g|0.09|2 − 1 = −0.999352. Therefore, the amplitude range is
+compressed.
+A possible approach to this reconstruction problem may be to use the normalization
+of the output to calculate a new g, as shown in Eq. 19.
+g =
+�
+k
+˜pk
+(19)
+4.2
+Single Qubit Probability Amplitude Modulations: SQPAM
+Another coefficient-based quantum audio representation instance can be derived from an
+image representation scheme known as Flexible Representation of Quantum Images or
+FRQI [9]. We propose calling this method Single Qubit Probability Amplitude Modulation,
+or SQPAM.
+SQPAM works similarly to QPAM. However, instead of using the raw probability am-
+plitudes, it uses ⌈log N⌉ + 1 qubits. It improves the logic to encode the samples in the
+probability amplitudes of one extra, dedicated qubit, added as a new register, |γi⟩, using
+trigonometric functions. It is a more reliable and editable encoding scheme than QPAM
+(Eq. 22).
+an −→ |γi⟩ = cos θi |0⟩ + sin θi |1⟩
+(20)
+|A⟩3−qubit =
+1
+√
+8
+�
+(cos θ0 |0⟩ + sin θ0 |1⟩) ⊗ |0⟩ + (cos θ1 |0⟩ + sin θ1 |1⟩) ⊗ |1⟩ +
+(cos θ2 |0⟩ + sin θ2 |1⟩) ⊗ |2⟩ + (cos θ3 |0⟩ + sin θ3 |1⟩) ⊗ |3⟩ +
+(cos θ4 |0⟩ + sin θ4 |1⟩) ⊗ |4⟩ + (cos θ5 |0⟩ + sin θ5 |1⟩) ⊗ |5⟩ +
+(cos θ6 |0⟩ + sin θ6 |1⟩) ⊗ |6⟩ + (cos θ7 |0⟩ + sin θ7 |1⟩) ⊗ |7⟩
+�
+(21)
+Generalizing for a N-sized audio, he have:
+|ASQPAM⟩ =
+1
+√
+N
+N−1
+�
+i=0
+(cos θi |0⟩ + sin θi |1⟩) ⊗ |i⟩
+(22)
+4.2.1
+Mapping the SQPAM Audio Amplitudes
+Similarly to the previous representation, there are some pre-processing steps for map-
+ping the amplitudes to a normalized scope. Trigonometric functions are often used to
+represent probability amplitudes since their absolute value ranges from 0 to 1, and the
+relation between the cosine and sine functions satisfies the normalization requirement
+perfectly3.
+3
+cos (θ)2 + sin(θ)2 = 1
+14
+
+Essentially, this describes a simple change of variables, where αi = cos θi and βi =
+sin θi. Notice how only real numbers are being considered, analogous to QPAM.
+The introduction of an extra qubit |γi⟩ significantly improves the representation in
+terms of both encoding and retrieval of the audio.
+The first improvement is that the
+encoding scheme does not rely on the entirety of the audio size content (the total number
+of states on the superposition and their relative amplitudes) anymore.
+It is encoded
+locally in the new qubit and therefore could be independently manipulated, using rotation
+matrices as gates. This opens a new range of possibilities.
+The function that maps the audio amplitudes ai into angles θi is displayed in eq. 23.
+This mapping can also be conceived as the following set of instructions:
+• Step 1: Add 1 to all amplitudes an.
+• Step 2: Divide the amplitudes by 2.
+• Step 3: Take the square root.
+• Step 4: Evaluate the Inverse Sine of the result (The Inverse Cosine is also applica-
+ble, as long as the same convention is followed throughout the implementation).
+θi = sin−1
+��
+ai + 1
+2
+�
+(23)
+The mapped array of angles will enable the preparation of the SQPAM quantum audio
+state.
+4.2.2
+Preparation
+The SQPAM state preparation requires n qubits for encoding time (like QPAM) and 1
+qubit for the amplitude (γi). They can all be initialized in the |0⟩ state, as denoted in Eq.
+24.
+|000...⟩ ≡ |0⟩ ⊗ |0⟩ ⊗ |0⟩ ⊗ ... ≡ |0⟩⊗n+1 ≡ |0⟩
+(γi)
+⊗ |0⟩⊗n
+(24)
+The qubits of the time register are put in a balanced superposition by applying Hadamard
+gates in each one of them (Figure 11). The resulting quantum state is written in Eq. 25.
+γ :
+t0 :
+H
+t1 :
+H
+t2 :
+H
+Figure 11: Circuit segment with Hadamard gates applied to a 3-qubit time register.
+|Ψ⟩ =
+1
+√
+N
+�
+|0⟩ ⊗ |0⟩ + |0⟩ ⊗ |1⟩ + |0⟩ ⊗ |2⟩ + ... + |0⟩ ⊗ |N − 1⟩
+�
+(25)
+At this stage, we should discuss the particular strategy for transforming the amplitude
+qubit into the desired form (|0⟩ → |γi⟩). There is a perfect quantum gate for the task,
+called Ry. It applies rotations in the y axis of a Bloch Sphere (Eq. 264).
+Ry(2θ) =
+�cos θ
+− sin θ
+sin θ
+cos θ
+�
+(26)
+4Ry(2θ) has the same form of a 2D rotation matrix, found in many Linear Algebra textbooks. The main
+difference is that the angle theta rotates twice as fast in a Bloch Sphere compared to a regular Euclidean
+space.
+15
+
+Let us take a look at what happens when we apply Ry(2θ) to the state |0⟩. Reminding
+that quantum states represent vectors, this will resolve in a matrix-vector multiplication
+(Eq. 27).
+Ry(2θi) |0⟩ =
+�cos θi
+− sin θi
+sin θi
+cos θi
+� �1
+0
+�
+=
+�cos θi
+sin θi
+�
+= cos θi |0⟩ + sin θi |1⟩ = |γi⟩
+(27)
+Lastly, there should be a way to, somehow, loop through the different indexes of the
+time register for applying a particular Ry(2θi) to them. As a result, the angles |γi⟩ would
+be entangled to their respective states |i⟩. How to access and correlate specific states if
+they are in a superposition?
+The desired correlations can be achieved by controlling our value setting gate Ry
+using a multi-controlled version of Ry. Let us explore the effect of controlled gates on a
+quantum state.
+Imagine a 1-qubit length audio example. Assume that a superposition was created
+in the time register by following the first preparation step. The quantum state would be
+described by Eq. 28.
+|φ0⟩ =
+1
+√
+2
+�
+|0⟩ |0⟩ + |0⟩ |1⟩
+�
+(28)
+Then, a controlled Ry(2θ) gate is applied. By analyzing the circuit in Fig. 12, we could
+conclude that the Ry gate will only be applied if the time qubit is 1. Eq. 29 shows the
+resulting state.
+γ0 :
+Ry(2θ)
+t0 :
+H
+•
+Figure 12: Application of a controlled Ry(2θ)
+|φ1⟩ = cRy[t0] |φ0⟩ =
+1
+√
+2
+�
+|0⟩ |0⟩ + Ry(2θ) |0⟩ |1⟩
+�
+(29)
+Now, let us place an X gate before and after Ry (Fig. 13). What is the effect? If the
+time qubit happens to be in the |0⟩ state, it will be flipped to |1⟩. Consequently, it triggers
+the control condition, which leads to Eq. 30. Then, it is flipped back to |0⟩. Notice that it
+would not trigger the controlled gate otherwise.
+γ0 :
+Ry(2θ)
+t0 :
+H
+X
+•
+X
+≡
+γ0 :
+Ry(2θ)
+t0 :
+H
+Figure 13: Inverting the control condition using two X gates
+| ˜φ!⟩ = (I ⊗ X)cRy[t0](I ⊗ X) |φ0⟩ =
+1
+√
+2
+�
+Ry(2θ) |0⟩ |0⟩ + |0⟩ |1⟩
+�
+(30)
+The X gates create a strategy for effectively switching the control condition, triggering
+when the qubit is in the |0⟩ state instead of |1⟩. This is denoted by a white circle at the
+control position, as shown on the right side of Fig. 13.
+For two-qubit systems, the same strategy can be used to access particular indexes.
+In this case, there are two control conditions to verify simultaneously. For instance, the
+16
+
+address for the third sample - θ2 - is |10⟩. Hence, the control condition on t0 (the rightmost
+bit) is ”|0⟩”, whereas t1 is ”|1⟩”. Equation 31 demonstrates that Ry(2θ2) is only being
+applied to the third position.
+By using four 2-controlled Ry(2θi) gates, each amplitude can be addressed and
+stored accordingly (Fig. 14).
+|φ0⟩ = 1
+2
+�
+|0⟩ |00⟩ + |0⟩ |01⟩ + |0⟩ |10⟩ + |0⟩ |11⟩
+�
+∴
+|φθ2⟩ = (I ⊗ X ⊗ I)(ccRy[t0t1](θ2))(I ⊗ X ⊗ I) |φ0⟩
+= 1
+2
+�
+|0⟩ |00⟩ + |0⟩ |01⟩ + Ry(θ2) |0⟩ |10⟩ + |0⟩ |11⟩
+�
+(31)
+By generalizing this strategy, we arrive at an algorithm for the second preparation
+step of the SQPAM audio. For each time state,
+• Have a binary version of the state’s label stored in a classical variable.
+• If a bit in a given position of the string is zero, apply an X gate at the respective
+qubit.
+• Apply the Ry(2θ) gate.
+• Apply another X gate, following the second instruction.
+γ0 :
+Ry(2θ0)
+Ry(2θ1)
+Ry(2θ2)
+Ry(2θ3)
+t0 :
+H
+•
+•
+t1 :
+H
+•
+•
+Figure 14: Preparation of a SQPAM representation using Value-Setting operations with Ry gates
+Notice how this strategy depends on classical numbers. Depending on the program-
+ming language of the framework, this can be easily done while constructing the circuit,
+using a classical ’for loop’.
+This preparation strategy (using multi-controlled gates) can be called Value-Setting
+Operation. This operation will be applicable to other representations as well.
+This preparation process applies ⌈logN⌉ Hadamard gates, and N N-controlled Ry(2θ)
+gates. Since the N-controlled Ry(2θ) have O(N) of basic operations, this means that
+O
+�
+N2�
+operations are needed for preparing a SQPAM audio.
+4.2.3
+Retrieval
+Figure 15 shows what to expect of a SQPAM retrieval histogram. Each sample is en-
+coded in complementary sine and cosine pairs embedded in |γi⟩ probabilities (Eq. 32).
+Hence, 16 bins instead of 8.
+In Equation 23, there is a arcsin function. Therefore, the audio’s profile appears if the
+sine components (pγi(|1⟩)) are picked.
+Then, it suffices to use Eq. 33 to reconstruct the signal5. Figure 16 shows a signal
+reconstruction using the histogram in Fig 15 and Equation 33.
+pγi(|0⟩) = (cos(θi))2
+;
+pγi(|1⟩) = (sin(θi))2
+(32)
+5Consider using the cosine term (pγi(|0⟩)) in the nominator of Eq. 33. What would happen? The comple-
+mentarity of the trigonometric functions would result in a reconstructed audio with inverted polarity.
+17
+
+Figure 15: Hypothetical SQPAM representation
+Figure 16: Reconstructed audio from SQPAM in Figure 15
+ai =
+2pγi(|1⟩)
+pγi(|0⟩) + pγi(|1⟩) − 1
+(33)
+5
+State-Oriented Representations
+In the previous section, the quantum audio representation schemes stored the time do-
+main into a superposition of multi-qubit states and the amplitudes into probability ampli-
+tudes. In this section, the main difference is that the audio amplitudes will also be stored
+in a multi-qubit state. This new quantum register will produce a set of time-amplitude
+pairs of entangled information when put together with the time register. Put another way,
+if a given time sample ti is measured, there will be a correlated state that will provide the
+respective amplitude once measured.
+It can be seen as an evolutionary branch of the previous representations (regarding
+the quantum image representation timeline). For instance, they can potentially be ma-
+nipulated in more detail and used in a wider range of applications. Of course, this needs
+to be discussed on a case-by-case basis. There is no way to know which representation
+type is more adequate for different audio and musical applications yet. This will be further
+discussed in the next section.
+The consequence of these ”finer” capabilities is that they might increase the amount
+of space required to represent and manipulate the audio. In other words, there is a trade-
+off between the number of qubits required to store the quantum audio and the amount of
+known potential applications.
+18
+
+Single-Qubit Probability AmplitudeModulation Retrieval Histogram
+0.128
+0.120
+0.12
+-0.111
+0.103
+lities
+0.087
+0.082
+Probabili
+0.08
+0.0620.059
+0.0620.060
+0.042
+0.041
+0.04
+0.021
+0.021
+0.00
+0
+010
+010
+011
+011
+100
+7Y
+101
+110
+111
+000
+TO0
+100
+101
+110
+111Reconstructed SQ-PAM
+1.00
+Original
+Reconstructed
+0.75
+0.50
+0.25
+Amplitude
+0.00
+0.25
+0.50
+0.75
+1.00
+0
+1
+2
+4
+5
+6
+7
+SampleIn addition, another historical motivation to develop the following representation strate-
+gies is related to their preparation complexity (e.g. the number of instructions needed for
+encoding). Furthermore, the logic of storing the audio amplitudes as binary quantum
+states align with the quantized digital amplitudes of section 2.2.
+5.1
+QSM and uQSM
+The two following quantum audio representations were derived from the Novel Enhanced
+Quantum Representation of Images, or NEQR [5]. They were the first proposed quan-
+tum representations of audio, namely, QRDA (Quantum Representation for Digital Audio)
+and FRQA (Flexible Representation of Quantum Audio). Both are identical from a no-
+tation standpoint, but there is a slight difference in the interpretation of the qubit states.
+Respectively, they are read as either unsigned or signed integers.
+The QRDA [6] was the first quantum audio representation proposed in the literature.
+It was responsible for indicating the path towards its preparation and retrieval techniques,
+bringing many of the primary foundations of a State-Oriented Representation. In section
+2.2, we discussed how the analogue amplitudes were converted into digital. The samples
+were approximated to the closest binary integer of the quantization scheme. The same
+quantized amplitudes will be used in this section to prepare multi-qubit states.
+The QRDA has a dedicated quantum register that encodes the sample using strictly
+positive integers (directly inherited from the NEQR Image that encoded Gray colour infor-
+mation ranging from 0 to 1). The FRQA, or Flexible Representation of Quantum Audio, on
+the other hand, uses the Two’s Complement scheme to interpret the amplitudes (Section
+2.2.1).
+The signed integer makes audio mixing extremely convenient since only a regular
+bit-wise adder algorithm is needed. This indicates that the FRQA’s interpretation of the
+states is more suitable for quantum audio than QRDA.
+Apart from the variable class interpretation, the logics of preparation and retrieval
+are identical. These similarities suggest merging their names onto our proposed naming
+system: Quantum State Modulation, or QSM. Whenever a specific application requires
+unsigned integers explicitly (QRDA), we could indicate that with a lower case ‘u’ before
+the acronym (uQSM). This terminology can be extended to fit other variable types in the
+future, like fixed-point (Sec. 5.3) or floating-point numbers.
+5.2
+QSM
+Consider a digital audio file with 8 samples and amplitude values quantized in a 3-bit
+depth two’s complement scheme. Let us assume that the seventh sample of the signal
+was represented by the following integer bit string: ”001”. In possession of this string,
+we somehow prepare an analogous 3-qubit string on a dedicated amplitude register by
+initializing it in the ground state and then flipping the rightmost qubit. This amplitude
+state can be later entangled with a respective state of the time register, in this case, t7,
+as described in Eq. 34.
+(a7, t7) ≡ (001, 110) −→ |001⟩ |110⟩ ≡ |a7⟩ ⊗ |t7⟩
+(34)
+Applying this structure for all of the samples would result in the superposition shown
+in equations 35 and 36. More generally, the QSM could be written as in Eq. 37.
+19
+
+binary notation
+|AQSM⟩
+=
+1
+√
+8
+�
+|000⟩ ⊗ |000⟩ + |111⟩ ⊗ |001⟩ + |010⟩ ⊗ |010⟩ +
+|011⟩ ⊗ |011⟩ + |110⟩ ⊗ |100⟩ + |101⟩ ⊗ |101⟩ +
+|001⟩ ⊗ |110⟩ + |000⟩ ⊗ |111⟩
+�
+(35)
+decimal notation
+|AQRDA⟩
+=
+1
+√
+8
+�
+|0⟩ ⊗ |0⟩ + |−1⟩ ⊗ |1⟩ + |2⟩ ⊗ |2⟩ + |3⟩ ⊗ |3⟩ +
+|−2⟩ ⊗ |4⟩ + |−3⟩ ⊗ |5⟩ + |1⟩ ⊗ |6⟩ + |0⟩ ⊗ |7⟩
+�
+(36)
+|A⟩ =
+1
+√
+N
+N−1
+�
+i=0
+|Si⟩ ⊗ |i⟩
+(37)
+The time register uses n qubits (audio length), and the amplitude register needs q
+qubits (qubit-depth).
+As previously mentioned, this strategy has some foreseeable advantages. The multi-
+qubit register for amplitude directly relates to the digital audio. This similarity suggests
+that some quantum algorithms could be developed to apply the same operations as
+known digital signal processing. From there, developers could explore if the quantum
+media would improve, extend or optimize some of them. This ”intuition” layer contributes
+to the instant popularity of the State-Based representations compared to the less ex-
+plored Coefficient-Based ones.
+5.2.1
+Preparation
+The same strategy mentioned in the SQPAM case will be used here: a Value-Setting
+Operation. In this case, instead of using Ry(2θi), the operation will use multi-controlled
+CNOT gates for flipping the qubit states of the amplitude register. As a result, the algo-
+rithm will access and entangle specific amplitude states with their respective time states.
+Value-Setting Operation: For each time state,
+• Step 1: Have a binary form of the time state’s label stored in a classical variable.
+• Step 2: Have the binary form of the quantized audio sample at the same index
+• Step 3: If a bit in a given position of the time variable is zero, apply an X gate at the
+respective qubit. Verify all bits.
+• Step 4: If a bit in a given position of the audio sample is 1, apply a multi-controlled
+CNOT gate. Verify all bits.
+• Step 5: Repeat the third instruction to reset the control condition.
+Figures 17 and 18 exemplify a preparation circuit for an audio with 8 samples and
+3-bit depth
+Compared with SQPAM (Ry(2θi)), the preparing circuit for the audio in fig. 17 will
+apply N value-setting operations, demanding O(q + log N) basic instructions. In conclu-
+sion, the preparation circuit for the QSM is exponentially faster, requiring O(qN log N)
+simple operations.
+20
+
+Figure 17: Example audio used to prepare the QSM circuit
+a0 :
+a1 :
+a2 :
+t0 :
+H
+•
+•
+•
+•
+•
+•
+•
+t1 :
+H
+•
+•
+•
+•
+t2 :
+H
+•
+•
+•
+•
+•
+Figure 18: Preparation of a QSM representation using Value-Setting operations
+5.2.2
+Retrieval
+The interesting part of retrieving a state-based quantum audio is that it can be seen as
+deterministic. It guarantees a perfect reconstruction of the digital audio. This is assured
+since the sample is represented as a binary state.
+In the coefficient-based version, the samples were statistical quantities that needed to
+be approximated through many measurements and statistical analysis. There will always
+be an intrinsic statistical error whenever the amount of measurements is finite. It is a
+trade-off between lying an error inside some tolerance range (depending on musical,
+psychoacoustic, perceptual factors) and time consumption (mainly the number of times
+a circuit will be prepared and measured) 6.
+In the case of state retrieval, we would only need to measure all valid time-amplitude
+pairs to retrieve the audio. Each time state is entangled to an amplitude state. So this
+theoretically assures that a given time state would certainly measure its correlated am-
+plitude; there is no other combined state possible.
+That being the case, we could in principle measure each time state just once, en-
+abling the retrieval of all respective amplitudes. Unfortunately, it is potentially impossible
+to devise a method that could guarantee only one measurement per sample based on
+a quantum time state in a superposition. In other words, controlled measurements (only
+measuring a quantum state based on another quantum state) are non-unitary instruc-
+tions and cannot be written as a set of quantum gates. 7.
+6In his paper about generative quantum images using a coefficient based image representation, James
+Wootton [15] states that he measured the n-qubit image state 4n times before considering it was a good
+approximation for his application. This number can be much higher for reliable retrieval, and it scales exponen-
+tially.
+7We can build circuits that use the result of measurements for controlling quantum gates (due to the de-
+ferred measurement principle). But only unitary instructions.
+21
+
+Original Audio
+1.0
+0.5
+litude
+Ampli
+0.0
+0.5
+1.0
+0
+2
+4
+5
+6
+SampleFigure 19: Hypothetical QSM histogram
+Figure 20: Reconstructed audio from QSM in Figure 19
+With that said, the strategy for retrieving the QSM will be similar in many ways to the
+previous ones: preparing several copies, making measurements, and analyzing a his-
+togram. Enough measurements are needed to assure a sufficient probability of having
+all possible states measured. Then, the histogram is analyzed and the valid measured
+states are parsed into digital amplitudes and time indexes. This analysis is also a good
+strategy for dealing with quantum error in real-life quantum processors. Making enough
+measurements to separate noise from a signal. In an ideal situation, a state-modulated
+representation will have a balanced superposition of the possible states (states contain-
+ing the audio amplitudes and their time index), meaning they should be equally likely to
+be measured (Fig. 19). Moreover, the measured states of the amplitude register are
+decoded into the correspondent digital amplitudes using the Two’s Complement scheme
+(Fig. 20).
+The QSM framework is powerful due to its relatability with digital representations. It
+looks like PCM audio in a superposition. It promptly awakes the idea of comparing the
+computational efficiency of known classical DSP algorithms (of course, even if quantum
+parallelism helps with computational complexity, we need to consider the preparation and
+retrieval time consumption as well).
+22
+
+QuantumState ModulationRetrievalHistogram
+0.126
+0.128
+0.1300.130
+0.1210.122
+0.1200.122
+0.12
+abilities
+0.08
+Probal
+0.04
+0.00
+000
+111
+OTO
+011
+110
+101
+100
+000
+000
+010
+011
+0
+110ReconstructedQSM
+011
+Original
+Reconstructed
+010-
+001
+000-
+111
+110
+101
+0
+1
+2
+3
+4
+65.3
+Fixed Point QSM
+Preparation complexity and quantum states interpreted as integers made QSM (FRQA)
+well known. Nevertheless, it raises the question: why stop at integers? We could easily
+interpret the qubit registers as fixed (or floating) point numbers and use the same state
+structure of the QSM. A fixed point, QSM-based representation was formalized by Li et
+al. [19] and was named QRDS (Quantum Representation of Digital Signals). For the
+terminology purposes of this text, this representation could be named fixed-point QSM
+or fpQSM.
+It essentially divides the q qubits used to represent integers into three parts: one sign
+bit, m integer bits and q − m − 1 fractional bits8, as shown in Eq. 38.
+|A⟩ =
+1
+√
+N
+N−1
+�
+i=0
+|fixedi⟩ ⊗ |i⟩ =
+1
+√
+N
+N−1
+�
+i=0
+|xm
+i , xm−1
+i
+· · · x0
+i . x−1
+i
+· · · xq−m−1
+i
+⟩ ⊗ |i⟩
+(38)
+5.4
+Multichannel Audio
+The QRMA (Quantum Representation of Multi-Channel Audio), proposed by [21] extends
+the logic of a state-oriented representation for quantum audio. In our naming system, it is
+called Multichannel Quantum State Modulation (MQSM). It furthers the QSM implemen-
+tation logic by introducing a new quantum register in the circuit: the channel register (Eq.
+39). With this new register, we can address, for example, left (|0⟩) and right (|1⟩) channels
+of a stereo audio (Eq. 40). Also, it enables efficient storage of multichannel audio in the
+same quantum state (or a soundbank multiple mono tracks with the same length).
+(an,m, tn,m, cm) −→ |cj⟩ ⊗ |ai,j⟩ ⊗ |ti,j⟩
+(39)
+|AStereo⟩ =
+1
+√
+2N
+�
+|L⟩ ⊗
+�
+|0⟩ |0⟩ + |0⟩ |1⟩ + |0⟩ |2⟩ + |0⟩ |3⟩ + ...
+�
+|R⟩ ⊗
+�
+|0⟩ |0⟩ + |0⟩ |1⟩ + |0⟩ |2⟩ + |0⟩ |3⟩ + ...
+�
+�
+(40)
+|AMQSM⟩ =
+1
+√
+NC
+N−1
+�
+i=0
+C−1
+�
+j=0
+|cj⟩ ⊗ |ai,j⟩ ⊗ |ti,j⟩
+(41)
+The general equation of the MQSM is shown in Equation 41, where C = 2c is the
+number of channels used. Similar to N, if the number of channels is not a power of two,
+the remaining possible channels would be zero-padded before preparing the state.
+Correspondingly, a channel register could be added to Coefficient-Based represen-
+tations. As exemplified in the next section, it can become a valuable tool for feature
+extraction algorithms. For instance, A Multichannel version of the SQPAM could be de-
+rived as shown in Equation 42.
+|AMSQPAM⟩ =
+1
+√
+NC
+N−1
+�
+i=0
+C−1
+�
+j=0
+|cj⟩ ⊗ (cos θi |0⟩ + sin θi |1⟩) ⊗ |i⟩
+(42)
+8the q − m − 1 was adapted to our notation. In the original notation, the text uses n + 1 qubits instead of q
+23
+
+6
+Summary
+Different strategies for encoding audio in quantum systems were developed from quan-
+tum image representations. A change in the quantum audio representation terminology
+was also proposed (which could be extended to images and other signals in the future).
+The key pieces of information and features discussed are compared in Table 1.
+When progressing down the table, the representations require more and more qubit
+space to store all of the information. As a result, the probabilistic representations are ca-
+pable of storing larger samples in the same hardware. This is also true for bit depth: since
+the probability amplitudes are continuous variables, they can store as much amplitude
+resolution as classical computers can provide after the retrieval process. In comparison,
+the state-based representations use qubit binary words, which require significantly more
+quantum space to achieve a comparable resolution. Also, the bit depth q has a role in
+the preparation complexity of the state modulation.
+On the other hand, the amount of instructions necessary to prepare the SQPAM state
+considering only the audio size N is significantly worse than the deterministic represen-
+tations for larger audio samples.
+Representation
+Original
+Acronym
+Basic Structure
+Amplitude
+Map-
+ping
+Space Required
+Preparation
+Complexity
+Retrieval
+QPAM
+——
+αn |tn⟩
+Normalized,
+strictly
+positive vector
+�
+log N
+�
+O(N)
+Probabilistic
+SQPAM
+——
+(cos θn |0⟩
++
+sin θn |1⟩) |tn⟩
+Angle Vector
+�
+log N
+�
++ 1
+O
+�
+N2�
+Probabilistic
+uQSM
+QRDA
+|Un⟩ |tn⟩
+Unsigned
+Integer
+Vector
+�
+log N
+�
++ q
+O
+�
+qN
+�
+log N
+��
+Deterministic
+QSM
+FRQA
+|Sn⟩ |tn⟩
+Signed Integer Vec-
+tor
+�
+log N
+�
++ q
+O
+�
+qN
+�
+log N
+��
+Deterministic
+fpQSM
+QRDS
+|Fpn⟩ |tn⟩
+Fixed Point Integer
+Vector
+�
+log N
+�
++ q
+O
+�
+qN
+�
+log N
+��
+Deterministic
+MQSM
+QRMA
+|ci⟩ |Sn⟩ |tn⟩
+Multiple Signed Inte-
+ger Vectors
+�
+log N
+�
++
+q
++
+�
+log C
+�
+O
+�
+CqN
+�
+log N
+��
+Deterministic
+Table 1: Comparison between quantum representations of audio
+These comparisons are essential for imagining near-term applications of music-quality
+audio on quantum hardware. Imagine that a composer wants to process two different
+audio samples in a quantum machine for some hypothetical artistic reason. The first
+sample may be coming from a real-time audio signal processing language, with a block
+of 64 samples that needs to run on a brand-new quantum audio effect. The second
+one is stored on a computer and has approximately 1.5 seconds of audio, containing
+216 = 65536 samples that will be fed to a large quantum sound database. Both samples
+have CD quality: A sample rate of 44,100Hz and a 16-bit resolution. We will compare
+three representations: QPAM, SQPAM and QSM.
+According to Table 1, QPAM will require 6 qubits and ∼ 64 instructions for storing the
+first sample; 7 qubits and ∼ 4096 instructions for SQPAM. QSM will need to allocate 16
+more qubits for achieving the necessary amplitude resolution, with a total of 22 qubits
+and ∼ 6144 instructions.
+For the second audio, things scale up in the time register. QPAM will use 16 qubits
+and ∼ 65 thousand instructions; SQPAM, 17 qubits and a surprising amount of ∼ 4.3
+billion instructions. Finally, QSM will need 32 qubits and ∼ 16 million instructions.
+24
+
+A noticeable result of this comparison is that SQPAM might be better suited for pro-
+cessing small signal samples or segmented blocks of audio, useful for algorithms for
+information retrieval). QSM, on the other hand, would handle large sounds effectively.
+Also, QPAM needs the lowest amount of resources for preparation, which is very useful
+for near-term applications.
+6.1
+Running on Real Hardware
+This chapter focuses on surveying and consolidating a smooth and didactic theoretical
+transition path between digital audio and the new field of quantum audio, underlying po-
+tential problems of the computational level, proposing a more unified terminology, and fi-
+nally glimpsing at potential artistic applications. This approach is why the chapter focuses
+on a high-level discussion, assuming that the qubits are perfect and perfectly manipula-
+ble, referred to as a logical qubit. Even so, it is worth saying something about running
+these algorithms on real hardware. The state-of-the-art computers that are publicly avail-
+able at the time of writing have a range of three to sixteen rather noisy physical qubits. It
+is possible to correct potential errors for a better approximation of a logical qubit. For that
+purpose, multiple physical qubits can be combined into a fault-tolerant qubit. This field is
+known as Quantum Error Correction [22]. The state-of-the-art machines and their qubits
+are not fault-tolerant.
+A real-world qubit is prone to a myriad of errors and noises. For example, its state can
+be flipped spontaneously due to external electromagnetic interference. It also tends to
+lose energy and go to a lower energy level state. Furthermore, a quantum system might
+lose coherence as time evolves. Also, each gate or instruction applied to a qubit has a
+chance of failing or being inaccurate, introducing more noise and potentially leading to
+incorrigible errors. Additionally, qubits might interfere with each other in different ways,
+depending on their displacement on the actual quantum chip.
+Unfortunately, the depth of the circuits necessary to prepare quantum audio represen-
+tations might be too high for near-term, fault intolerant machines (as previously shown
+in the last section). The more instructions present in a fault-intolerant machine (and the
+more physical qubits you have), the less reliable the result will be9. This technologi-
+cal barrier has propelled the quantum audio community towards theory and simulations
+rather than real-hardware experiments on state-of-the-art technology.
+As a reference for future analysis and comparison, this text underlines how some
+of the presented encoding schemes (QPAM, SQPAM, QSM) perform in state-of-the-art
+hardware. An experiment was made using IBM Q hardware [23]. Specifically, a 7-qubit
+(32 Quantum Volume) chip called ibmq casablanca. These experiments (along with re-
+sults and simulations in the following sections) were run by using quantum audio mod-
+ules implemented in Python and Qiskit, within the scope of the QuTune Project [25]. The
+QuTune module was used to map and generate the quantum audio circuits from a signal
+(shown in Fig. 21). Then, the circuit was fed to the IBMQ system. Finally, the resulting
+histograms - ehxhibited in Figures 22, 24, 26 - were retrieved and post-processed. The
+reconstructed audio signals are shown in Figures 23, 25 and 27.
+QPAM (Figs. 23, 22)) had the lowest preparation complexity (approximately 8 instruc-
+tions and 3 qubits). It seems to retain most of the original information.
+The SQPAM (24, 25), on the other hand, introduced value-setting operations, which
+are more expensive. The retrieved audio lost most of its amplitude range (notice the
+values in the y axis) but retained some of the original profile.
+9While this limitation may be true, it can be seen as an advantage inside a sensible noise/degraded aes-
+thetic for artistic purposes.
+25
+
+Figure 21: Test audio with 8 samples.
+Figure 22: Retrieved QPAM histogram.
+In contrast, QSM (Fig. 26) produced an result. Surprisingly, its resemblance with
+the original file was gone. This was probably caused by the amount of multi-controlled
+instructions for preparation and the time required for the operations. Moreover, some
+qubits might have flipped to a lower energy state. Even though it has a guarantee of
+exact retrieval, the reconstruction process relies on the states that are most likely to be
+measured. At this stage of loss of information, the QSM audio was irrecoverable (27)10.
+7
+Final Remarks
+This chapter discussed various different approaches for quantum representation of audio
+that have been proposed to date. Quantum audio is still a very young field of study.
+Naturally, the different approaches presented here have advantages and disadvantages.
+At this stage, we are not in a position to foresee which of the method(s) discussed here, if
+any, might end up being adopted by the industry simply because the hardware to realize
+them is not available.
+Nevertheless, as shown above, we can already start developing approaches and
+dream of interesting applications (e.g., a quantum electric guitar effects pedal) based
+on simulations and educated guesses about how quantum processors will evolve. An
+important caveat of quantum computing that needs to be addressed is the problem of
+memory. Essentially, quantum information cannot be stored and retrieved in the same
+way that digital information can with classical processors. The development of quantum
+random access memory (qRAM) technology would make a significant impact on quan-
+tum audio. A number of propositions for developing qRAM have been put forward (e.g.,
+[26, 27]), but a practical device for more general use is still not in sight yet.
+10Still, in the QSM histogram (26), there is a slight emergence of periodicity on the qubit sequencing. Can it
+be used artistically?
+26
+
+Original Audio
+1.00
+0.75
+0.50
+0.25
+Amplitude
+0.00
+0.25
+0.50
+0.75
+1.00
+1
+2
+4
+5
+6
+7
+SampleReal Hardware QPAM Retrieval Histogram
+0.32
+0.2740.278
+0.24
+Probabilities
+0.16
+0.128
+0.104
+0.089
+0.084
+0.08
+0.033
+0.011
+0.00Figure 23: Reconstructed audio from Fig. 22.
+Figure 24: Retrieved SQPAM histogram.
+quantumaudio: A Python package for quantum representations of audio in Qiskit is
+available:
+https://pypi.org/project/quantumaudio/
+quantumaudio is developed and maintained by the quantum computer music team
+at the Interdisciplinary Centre for Computer Music Research (ICCMR), University of Ply-
+mouth, UK.
+8
+Acknowledgements
+The authors acknowledge the support of the University of Plymouth and the QuTune
+Project, funded by the UK Quantum Technology Hub in Computing and Simulation.
+References
+[1] Rabiner, Lawrence R., and Bernard Gold. Theory and application of digital signal
+processing. Englewood Cliffs: Prentice-Hall, 1975.
+[2] Broughton. S. Allen & Bryan, Kurt. Discrete Fourier Analysis and Wavelets: Appli-
+cations to Signal and Image Processing. John Wiley & Sons, Ltd, 2008.
+[3] Ziemer, Rodger E., and William H. Tranter. Principles of communications, chapters
+3-4. John Wiley & Sons, 2014.
+[4] K Meichanetzidis, S Gogioso, G De Felice, N Chiappori, A Toumi and B Co-
+ecke. Quantum Natural Language Processing on Near-Term Quantum Computers,
+2021. arXiv:2005.04147 [cs.CL]
+27
+
+Real Hardware Reconstructed QPAM
+0.6-
+0.4-
+0.2
+Amplitude
+0.0
+0.2
+-0.4
+-0.6
+0
+1
+2
+3
+4
+5
+6
+7
+SampleReal Hardware SQ-PAM Retrieval Histogram
+0.100
+0.090
+0.081
+0.080
+0.080
+0.075
+0.071
+0.072
+abilities
+0.060
+0.061
+0.058
+0.053
+0.052
+0.056
+Probab
+0.047
+0.049
+0.050
+0.044
+0.045
+0.025
+0.000
+TO0
+010
+010
+011
+100
+101
+110
+3
+YFigure 25: Reconstructed audio from Fig. 24.
+Figure 26: Retrieved QSM histogram.
+[5] Yi Zhang, Kai Lu, Yinghui Gao, and Mo Wang. NEQR: A Novel Enhanced
+Quantum Representation of digital images. Quantum Information Processing,
+12(8):2833–2860, 2013.
+[6] Wang, Jian. QRDA: Quantum Representation of Digital Audio. International Jour-
+nal of Theoretical Physics, 55(3):1622–1641, 2016.
+[7] Fei Yan, Abdullah M Iliyasu, Yiming Guo, and Huamin Yang. Flexible Representa-
+tion and Manipulation of Audio Signals on Quantum Computers. Theoretical Com-
+puter Science,752:71–85, 2018.
+[8] Vlatko Vedral, Adriano Barenco, and Artur Ekert. Quantum Networks for Elemen-
+tary Arithmetic operations. Physical Review A, 54(1):147, 1996.
+[9] Fei Yan, Abdullah M Iliyasu, and Salvador E Venegas-Andraca. A Survey of Quan-
+tum Image Representations. Quantum Information Processing, 15(1):1–35, 2016.
+[10] D Wang, Z-H Liu, W-N Zhu, and SZ Li. Design of Quantum Comparator Based
+on Extended General Toffoli Gates with Multiple Targets. Computer Science,
+39(9):302–306,2012.
+[11] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao. Exploring the Imple-
+mentation of Steganography Protocols on Quantum Audio Signals. International
+Journal of Theoretical Physics, 57(2):476–494, 2018.
+[12] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao. A Quantum Audio
+Watermarking Scheme. In 2018 37th Chinese Control Conference (CCC), pages
+3180–3185.IEEE, 2018.
+[13] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao. Dual Quantum Audio
+Watermarking Schemes Based on Quantum Discrete Cosine Transform. Interna-
+tional Journal of Theoretical Physics, 58(2):502–521, 2019.
+28
+
+Real Hardware Reconstructed SQ-PAM
+-0.075
+-0.100
+0.125
+Amplitude
+0.150
+-0.175
+-0.200
+0.225
+0
+1
+2
+3
+4
+5
+6
+7
+SampleTypical State-Based Quantum Audio Retrieval Histogram
+0.04
+0.034
+0.034
+0.031
+0.030
+0.030
+0.03
+0.027
+0.027
+0.026
+0.025
+0.024
+0.025
+Probabilities
+023
+.023
+0.024
+0.022
+0.023
+0.022
+0.022
+.021
+.019
+.020
+.020
+0.02
+.018
+.017
+.019
+0.01
+016
+.017
+.016
+.014
+.015
+.013
+.011
+010
+.010
+010
+011
+.010
+.01
+0.01
+:00
+0:00
+.00
+.980
+.009
+.00090
+.009
+.90
+.0080
+.00
+00
+00
+.99807
+.00
+.00
+.0.0
+.00
+0.00Figure 27: Reconstruction attempt from Fig. 26.
+[14] Michael A Nielsen and Isaac Chuang. Quantum Computation and Quantum Infor-
+mation, pages 216–221. American Association of Physics Teachers, 2002.
+[15] James R Wootton. Procedural Generation Using Quantum Computation. In Inter-
+national Conference on the Foundations of Digital Games, pages 1–8, 2020.
+[16] Salvador El´ıas Venegas-Andraca. Discrete Quantum Walks and Quantum Image
+Processing. 2005.
+[17] Salvador E Venegas-Andraca and Sougato Bose. Storing, Processing, and Re-
+trieving an Image Using Quantum Mechanics. In Quantum Information and Com-
+putation, volume 5105, pages 137–147. International Society for Optics and Pho-
+tonics, 2003.
+[18] S¸ ahin, Engin. Quantum arithmetic operations based on quantum fourier transform
+on signed integers. International Journal of Quantum Information 18(06):2050035,
+2020.
+[19] Li, P., Wang, B., Xiao, H. et al. Quantum Representation and Basic Operations of
+Digital Signals. International Journal of Theoretical Physics, 57:3242–3270, 2018.
+[20] Yan, Fei & Iliyasu, Abdullah & Le, Phuc & Sun, Bo & Dong, Fangyan & Hirota,
+Kaoru. A Parallel Comparison of Multiple Pairs of Images on Quantum Computers.
+International Journal of Innovative Computing and Applications. 5. 199-212, 2013.
+[21] S¸ ahin, Engin, and ˙Ihsan Yilmaz. QRMA: quantum representation of multichannel
+audio. Quantum Information Processing 18.7: 1-30, 2019.
+[22] Lidar, Daniel A., and Todd A. Brun, eds. Quantum error correction. Cambridge
+University Press, 2013.
+[23] IBM Quantum. https://quantum-computing.ibm.com/ , Last Accessed 01
+Feb 2022.
+[24] Miranda, E. R. Computer Sound Design: Synthesis techniques and programming.
+Focal Press; 2nd edition, 2002.
+[25] QuTune Project - Quantum Computer Music Resources. https://iccmr-
+quantum.github.io/, Last Accessed 01 Feb 2022.
+[26] Chen, K. C., Dai, W., Errando-Herranz, C., Lloyd, S. and Englund, D. Scalable and
+High-Fidelity Quantum Random Access Memory in Spin-Photon Networks. PRX
+Quantum, 2, 030319, 2021.
+[27] Asaka, R., Sakai, K. and Yahagi, R. Quantum random access memory via quantum
+walk. Quantum Science and Technology, 6(3): 035004, 2021.
+29
+
+RealHardwareReconstructed OPAM
+010
+001-
+000-
+Amplitude
+111 -
+110-
+101-
+100
+0
+1
+2
+3
+4
+5
+6
+7
+Sample
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+page_content='Quantum Representations of Sound: from  mechanical waves to quantum circuits  Paulo V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Itabora´ı1 and Eduardo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Miranda1  1Interdisciplinary Centre for Computer Music Research (ICCMR),  University of Plymouth, Plymouth, UK  {paulo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='itaborai,eduardo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='miranda}@plymouth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='uk  Abstract  By the time of writing, quantum audio still is a very young area of study, even within  the quantum signal processing community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This chapter introduces the state of the art  in quantum audio and discusses methods for the quantum representation of audio sig-  nals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Currently, no quantum representation strategy claims to be the best one for audio  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each one presents advantages and disadvantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It can be argued that  future quantum audio representation schemes will make use of multiple strategies aimed  at specific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The authors also discuss .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  NOTE: This is an unedited abridged version of the pre-submission draft of a chapter,  with the same title, published in the book Quantum Computer Music: Foundations, Meth-  ods and Advanced Concepts, by E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Miranda (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 223 - 274).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Please refer to the  version in this book for application examples and a discussion on sound synthesis meth-  ods based on quantum audio representation and their potential for developing new types  of musical instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='com/book/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1007/978-3-031-13909-3  1  Introduction  Sounds and images share common grounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' From the point of view of information pro-  cessing, both are just signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' But obviously, we perceive them differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Most signal processing methods used for sounds are applicable to images and vice-  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Their main difference is with respect to dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, whereas  sound is a one-dimensional (1D) signal in the time domain, image is a two-dimensional  (2D) one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' From a mathematical perspective, the higher the dimension of a signal, the  more complex to represent and process it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Therefore, it is logical first to learn how 1D  signal representation and processing methods work and then extrapolate to 2D (images),  3D (videos), and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' By and large, this is how textbooks on audio and visual signal  processing introduce the subject;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', [1] [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Thus, from a historical perspective, it would seem reasonable to expect that quantum  representations and potential algorithms for sound would have appeared in research av-  enues before the appearance of those for images and video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Surprisingly, this is not the  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' An avid interest in developing quantum algorithms for image processing (primar-  ily for facial recognition and similar applications) produced methods for quantum image  representations and processing rapidly, leaving the case of 1D sound behind by almost  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='01595v1  [quant-ph]  1 Jan 2023  a decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This gap is unexpected, given the importance of speech technology to the  electronics industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Even more, if bearing in mind the relatively long-standing desire to  develop quantum computing for natural language processing [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The first papers describing how to represent an image on a quantum processor the-  oretically were published in 2003 [17] and 2005 [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In comparison, the first papers  proposing quantum representation methods for sound are from 2015 [6] and 2018 [7];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  they are based on a method for images proposed in 2011 [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Indeed, most quantum  signal processing algorithms designed to date are for image applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The quantum  sound community needs to catch up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Hence the motivation for this chapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The chapter is structured as follows: firstly, section 3 contains a short introduction  that delineates essential aspects and concepts of sound, analogue and digital audio rep-  resentations that will be used later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It generally explains how the original sound content  is transformed from one media to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The concepts shown in this section will propel  us toward the quantum territory with better intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This introductory section concludes  by giving an initial idea of how quantum information logic will be applied to audio signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The introduction is followed by a short section (3) that explains how time information is  generally encoded in a quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The following note (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2) identifies some confusion  problems present in the nomenclatures used by the literature for quantum audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It pro-  poses a new naming system to unify and clarify the different strategies used to encode  audio information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Then, the two subsequent sessions dive into various definitions and schemes pro-  posed for representing audio in quantum machines using the previously proposed nam-  ing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, section 4 explores Coefficient-Based representations, whereas  section 5 focuses on State-Based ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Section 6 summarizes the representations shown in the previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It dis-  cusses some obstacles that should be accounted for when considering building and run-  ning quantum audio circuits for state-of-the-art quantum hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Section ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' details some basic quantum signal processing operations and circuit de-  sign, such as quantum audio addition and concatenation, as well as sample-by-sample  comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The last section (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=') punctuates some potential artistic applications in the short and  near term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Specifically, there is a case study exploring wavetable synthesis and simple  effects that make use of configurable parameters of coefficient-based representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2  From Mechanical to Quantum  The main objective of this section is to review how sound is represented in digital com-  puters and electronic devices in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It will provide the foundations to understand  how sound can be represented for quantum computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In order to store a given sound in a quantum computer (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', by the time of writing),  one would need to record the sound as analogue audio and make an analogue-to-digital  conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, the digital audio needs to be translated into a quantum audio rep-  resentation of some kind (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us go through each of these stages in more  detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2  Figure 1: The signal path from mechanical sound to quantum sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  From Mechanical to Analog  In the most general sense, waves are physical entities that carry information about dis-  turbances in a particular medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, electromagnetic waves carry information  about disturbances in an electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Sound, however, is a mechanical wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It  can be generated by providing energy to a set of coupled vibrating systems in an acoustic  medium, such as air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Upon reaching a microphone, vibrating air pressure - that is, sound - becomes electric  voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is analog audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There are many ways to do this mechanic-to-electric  conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' One of the first techniques ever developed to do this can still be found in  dynamic microphones today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  A dynamic microphone has three main elements: a thin diaphragm, a cylindrical mag-  net and a wire coil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The coil is wrapped around the magnet, but it does not touch it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It  can move freely on the cylinder’s axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The diaphragm is coupled to one end of the coil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  So, the vibrating sound will move the diaphragm back and forth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As a consequence, the  coil will oscillate through the magnet - or, from the perspective of the coil, the magnet  will oscillate through it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In an oversimplified way, Faraday’s Law teaches us that when a  magnet is moving through a conductive coil, it will induce an electric current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This move-  ment will result in a measurable voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' So, an oscillating coil will induce an oscillating  voltage at its terminals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Thus, the mechanical sound has been converted into a varying  electric voltage signal which is, by definition, analogue audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Audio Encoding  Analog audio creates a direct connection between mechanical and electrical media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We  could say that it represents sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Analog audio imposes itself as a new technique for propagating and manipulating  sound, which was not possible before its invention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, a singer could try to  sing louder or even scream, attempting to reach listeners located far away and still not  be heard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Alternatively, this singer could convert her voice into audio and then transmit  the signal through conductive wires or electromagnetic waves until it reaches the listener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The audio would then be converted back into sound through loudspeakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The caveat  is that transmission, reception and conversion are prone to noise and errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Attempts to reduce noise and errors during long transmissions (for example, radio  transmissions) are what motivated the first audio encoding schemes as effective ways of  representing electric audio information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The three most widely used analogue audio en-  coding schemes are Amplitude Modulation (AM), Frequency Modulation (FM) and Phase  Modulation (PM) [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In these cases, the raw analogue signal is encoded by means of  3  QUANTUM  MECHANICAL  DIGITAL  ANALOG  ADCa measurable variation of a signal parameter, such as the frequency, amplitude (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=',  power), or phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  From Analog to Digital  A digital computer is unable to process a continuous stream of audio, which contains  voltage information at all possible points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There are infinitely many of them inside  an audio signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Thus, analog information needs to be digitized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is done by means  of an ADC (Analog-to-Digital Converter) device, which converts an analog signal into a  digital signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' How is this done?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' How to turn continuous time and amplitude information  into discrete binary codes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  This section introduces the notions of sampling and quantization, which are dis-  cretizations of time and amplitude, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Audio sampling is the action of taking snapshots of a continuous signal and storing  them (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', the values captured by the snapshots) as time-indexed samples (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figure 2: A sampled sine wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  As shown in Figure 2, the snapshots of a signal are conventionally taken in equally  spaced time lapses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The speed of lapses is referred to as the sampling rate or sampling  frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In other words, the sampling rate establishes how many samples are taken  per unit of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Good quality audio systems use a sampling rate of 44,100 Hz (or 44,100  snapshots per second).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The sampling rate has the role of translating an index k =  0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' into a respective instant in time tk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' That is, the sampling rate SR is the constant  responsible for carrying the conversion between the moment of the snapshot (in time  units) and an index of time (dimensionless) (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The index k can be represented in  binary form and thus stored in a classical computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  tk = k  SR  (1)  Now, let us look at the quantization step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Bear in mind that the notion of quantization  here is nothing to do with quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Here, quantizing means to restrict a  continuous range to a prescribed set of values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Let us examine how the amplitude of an analogue signal, usually represented in the  −1 to 1 range, can be quantized into binary numbers (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4  Sample  7 38 39 40 41 42 43 44 45 46 47 48 49  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  Analog Audio  Samples  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  Audio Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  Time [s]Figure 3: An analog wave and its respective quantization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Quantization is, in some ways, similar to sampling, but it operates alongside the ver-  tical axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The main difference is that the values can be negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Nevertheless, we can  rescale and shift the whole signal to make it fall entirely in the positive domain without  any loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is a resourceful operation in audio signal processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The way to shift a signal along a determined axis is by adding or subtracting a defined  quantity on all signal values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In our case, we would like to shift the entire signal up by  1, so we add 1 to every amplitude value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' After doing this, the amplitudes range from 0  to 2 instead of −1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The range is already positive, but we can further improve this  by rescaling the signal to the 0 to 1 range;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' this will be relevant to our quantum audio  discussion later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The rescaling is done by multiplication and division, and of course,  for our case, we divide the amplitudes by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' With this unitary range, we can do the  quantization scheme more easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' If we have n-bit words to store each amplitude, we  will perform 2n subdivisions in our range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, the voltage values are rounded to fit the  closest binary value afforded by the subdivision scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Hence, we have successfully digitized our audio by putting them on a grid, as shown  in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Two’s Complement Scheme  The quantization scheme presented above is perfectly valid and general for any type  of signal in a positive range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, we have seen that audio signals have negative  values as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Of course, this is not a problem in itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We showed above how to shift audio to  a positive domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, this shifting procedure can often render the audio unsuit-  able for specific manipulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A concerning example would be amplitude multiplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Shifting a value to the strictly positive domain could drastically alter the result of a simple  multiplication (as indicated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  (a1 + shift)(a2 + shift) ̸= a1a2 + shift  (2)  This absence of negative numbers may also prove to be at least inconvenient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Con-  sider, for instance, the task of adding two audio signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The way to add digitized audio  waves is by summing their amplitudes, term-by-term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Specifically, imagine an oversim-  plified digital noise cancellation algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It relies on negative numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' First, some  unwanted noise in an audio signal is received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, it generates a copy of the noise  with inverted polarity (In other words, all amplitudes are multiplied by −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Finally, the  5  Sample  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 4344 45 46 47 48 49  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='000  AnalogAudio  1101011  DigitalAudio  ignedj  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='675  [Unsigned  AudioAmplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='325  100|001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='000  0111000  ns  Representatior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='325  010111  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='675  0011110  Binary  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='000  000/101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  Time [s]inverted signal is added to the original.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each amplitude is added to a negated version of  itself, meaning they cancel each other, and the noise disappears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This phenomenon is  nominally called destructive interference1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Even though there might be an elaborate way  of achieving the desired result with only positive numbers, a less laborious alternative is  desirable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  A viable solution - which is the one that is generally used for representing audio  signals - is to use another interpretation of the binary integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' One that could enable us  to represent negative numbers and facilitate binary addition arithmetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This solution is  referred to as the Two’s Complement scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It is important to understand the underlying logic of representing negative numbers in  binary, as this will also be useful for quantum audio representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The main idea of the Two’s Complement encoding scheme is to divide the binary  words into two sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Half of them would represent negative numbers and the other half  positive ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This can be made by using the Most Significant Bit (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', the leftmost bit),  or MSB, as a signing bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' If the MSB is 0, then the number is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Otherwise, it is  negative (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  0010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' −→  (+ or−)  0  (number)  010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  (3)  However, just the signing bit by itself is not enough for having a ’good’ negative num-  ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For it to be useful, it needs to comply with binary addition properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Let us consider a computer with a 4-bit architecture and then use the MSB to indicate  the signal of the following 3 bits without applying any other logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Now, let us try to add 2  and −2 using this new interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Consider the simplified binary addition rules in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4, and see what happens when we add the numbers (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  0 + 0 = 0  0 + 1 = 1 + 0 = 1  1 + 1 = 10  {The bit to the left is added by 1}  (4)  2 → 0 010 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  −2 → 1 010 ∴ 0 010 + 1 010 = 1 100 → −4 (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=')  (5)  What is shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 5 clearly does not work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' But this can be solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We can  apply another condition to our encoding scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' That is: x + (−x) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This condition  would interestingly and conveniently change the representation of the negative numbers  completely, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Now we can verify in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 7 that the addition works  perfectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Regular Integer  �  ���  15  14  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  8  �  ���  �  ���  7  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  1  0  �  ���  =  �  ���  1 111  1 110  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  1 000  �  ���  �  ���  0 111  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  0 001  0 000  �  ���  ↘  Two′s Complement Integer  �  ���  0 111  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  0 001  0 000  �  ���  �  ���  1 111  1 110  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  1 000  �  ���  =  �  ���  7  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  1  0  �  ���  �  ���  −1  −2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  −8  �  ���  (6)  2 → 0 010 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  −2 → 1 110 ∴ 0 010 + 1 110 = 0 000 → 0  (7)  1This also appears in the context of the quantum theory, since quantum systems also show wave-like  behaviour and thus have wave-like properties such as superposition and interference, among others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' But do  not be misled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A classical wave and a quantum particle-wave still are fundamentally different, even if they have  similar mathematical properties  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  Digital Audio as an Array  After being digitized, the audio’s binary information is stored in a data structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The  most common structure for digital audio is an array vector, visualized in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The  time information becomes an index to a specific position of an array, and the respective  amplitude becomes the variable stored in that position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In this way, one can retrieve the  amplitudes by having the time index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  a0  a1  a2  a3  a4  a5  a6  a7  t0  t1  t2  t3  t4  t5  t6  t7  Figure 4: Audio array visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In order to efficiently represent, store and transmit binary data structure as a stream  of audio information, a digital audio encoding scheme is typically used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Similar to the  analog case shown above, the digital domain provides some parameters that can be  controlled (or modulated) to represent information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For example, we could represent a  stream of digital information using pulses that are precisely controlled by piezoelectric  crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The representation that has dominated the music industry is the PCM audio or  Pulse Code Modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' PCM has become a standard in digital audio due to its reliable  lossless storage and transmission capacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Furthermore, it is less prone to noise and  errors compared to other pulse representations such as Pulse Amplitude Modulation  (PAM), Pulse Position Modulation (PPM), and Pulse Width Modulation (PWM [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  We should note at this stage that the two’s complement digital audio is used in a wide  variety of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, modern 32-bit and 64-bit operating systems, as well as  high-level programming languages like Python, further improve the representation of the  quantized audio amplitudes by using floating-point numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A good approximation of  Real (∈ R) numbers can be stored with floating-point numbers, with high precision and  significant decimal figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Thus, instead of storing an integer representing the middle  number of a quantization range, we could add a new pre-processing layer and store a  good approximation of the number itself, using the flexibility of floating-point numbers to  process the signal in the digital medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, this requires a considerable amount  of space and computing power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As we will see in the remainder of this chapter, we are  still far from similar schemes for quantum computer audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' But imaginable nevertheless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  From Digital to Quantum  Gaining an intuitive understanding of quantum audio representation is straightforward,  in the sense that Dirac’s notation can clearly show how the audio information (time and  amplitude) can be translated into quantum states (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Of course, the underlying  quantum computing paradigm can be counter-intuitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, this intuitive bird’s-eye  view understanding of the organizational structure of quantum audio gives us an end goal  and provides a guiding thread for us to cross the uncertain quantum algorithmic roads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  On this path, we shall explore how these representations of quantum audio are prepared  and measured, as well as potential near-term and long-term applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It is important to state that quantum audio is still a very young area of study, even  under the quantum signal processing umbrella.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Therefore many fundamental questions  remain open for discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There is no audio representation strategy that we could  argue to be the best one for audio applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each of them presents particular advan-  tages and disadvantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It can be argued that quantum audio will make use of multiple  representations targeting specific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  7  a0  a1  a2  a3  a4  a5  a6  a7  t0  t1  t2  t3  t4  t5  t6  t7  ↓  |t0⟩ + |t1⟩ + |t2⟩ + |t3⟩ + |t4⟩ + |t5⟩ + |t6⟩ + |t7⟩  a0  a1  a2  a3  a4  a5  a6  a7  Figure 5: Digital to Quantum  3  Preparation and Retrieval of Quantum Audio  The near-term prospects of quantum technology indicate that quantum computers will  not replace classical computers in many ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Rather, they will co-exist, creating hy-  brid classical-quantum processing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This already occurs in current working  quantum systems, many of which are accessible via cloud services and interact with  classical machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It is not going to be different for near-term quantum audio appli-  cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' These applications rely strongly on classical computers, not only to provide a  digital audio file to be prepared but also to post-process quantum circuit measurement  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There are well-known classical programming languages for this part;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Python  and MatLab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In the following sections, we will look in detail at quantum audio representa-  tions that have been proposed to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We will examine how quantum audio is prepared,  measured, and envisage possible applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us start by introducing the connection  between time indexes and quantum superpositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Encoding Time Information  As mentioned previously, a qubit is a 2-state quantum system that can be measured to  value either 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It can also be put in a superposition of states, written as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  8, where |α|2 and |β|2 are the probabilities that a measurement of this state results in 0  or 1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Since the sum of the probabilities of all possible outcomes needs to be  1, it means that |α|2 + |β|2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |Ψ⟩ = α |0⟩ + β |1⟩  (8)  For 2-qubit states, a similar equation can be written, considering all possible out-  comes, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |Ψ⟩ = a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |a|2 + |b|2 + |c|2 + |d|2 = 1  (9)  Since we have few letters in the alphabet to represent many of these probability am-  plitudes, it might be better to change the notation slightly and use the same letter with a  subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, a 3-qubit state written this way is shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |Ψ⟩ = a(000) |000⟩ + a(001) |001⟩ + a(010) |010⟩ + a(011) |011⟩  + a(100) |100⟩ + a(101) |101⟩ + a(110) |110⟩ + a(111) |111⟩  (10)  At this point, we ought to make another helpful change to the notation for improving  our intuitiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Sometimes, it is convenient (and conventional) to interpret the numbers  inside the ‘kets’ not as a sequence of states of individual qubits in a register - but as a  classical binary bit string associated with an integer number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Before we do so, it is imperative to remind us that these zeros and ones inside the  ’kets’ are not numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Kets are a simplified notation for writing vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Therefore,  whatever is written inside the ket, is just a conventionalized label that refers to a vector:  8  |label⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We use numbers as labels to reduce the level of abstraction of those mathemat-  ical entities and provide some insight into their use inside a system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In other words, the  interpretation above is not changing the state in mathematical terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Instead, it is just  a change of notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It is essential to have this clear and fresh in our minds to avoid  confusion as we introduce the representations next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Thus, by interpreting the qubit states as binary numbers, we can write the same 3-  qubit state in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 10 as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |Ψ⟩3−qubit =  1  √  8  �  |0⟩ + |1⟩ + |2⟩ + |3⟩ + |4⟩ + |5⟩ + |6⟩ + |7⟩  �  (11)  All of the quantum audio representations presented in this text share the same encod-  ing strategy for time information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' They use a quantum register to create a superposition  of all the possible time indexes associated with each audio sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is called a time  register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each state will be an index, indicating a position in time, similar to a classical  array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Any information related to this state will encode the respective sample using differ-  ent strategies (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, it could use the probability amplitude or another  coupled quantum register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  (Amplitude) |tk⟩  (12)  Note the necessity of a 2n-sized signal for all of the representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We can use zero  padding for using audio with different sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We will explore in more detail below how  amplitude information is represented in the different schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  Note on Nomenclature  Before we proceed, let us clarify the nomenclature used to refer to the various Quantum  Audio Representation (QAR) methods that will be reviewed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For the sake of clarity  and systematization, we propose slight adaptations to the names given in the research  papers where these methods were originally introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The representation methods can be grouped into two categories related to how they  encode the audio amplitude information and retrieve it back to the classical realm through  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The first group contains what is referred to as ’Probabilistic’ or ’Coefficient-  Based’ representations - due to its probabilistic nature when retrieving information clas-  sically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The second group include ’Deterministic’ or ’State-Based’ methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  As mentioned earlier, quantum audio representation methods are derived from meth-  ods developed for representing images rather than sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The research literature in-  troduced methods such as Quantum Representation of Digital Audio (QRDA), Flexible  Representation of Quantum Audio (FRQA), and Quantum Representation of Multichan-  nel Audio (QRMA), which are all State-Based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, there also are some Coefficient-  Based methods for images that can (and will in this chapter) be easily adapted for audio  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Also, this chapter intends to reach the signal processing community, and in this en-  deavour, we will be proposing a new nomenclature system for the already proposed  representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The intention is to correlate, integrate or unify these representations  with classic representations in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For that, we will use the term ‘Modulation’ as  a central spine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This means that we will propose to rename, for example, the Flexible  Representation of Quantum Audio (which by itself already has some confusion problems  9  in relation to quantum images2) into Quantum State Modulation (QSM), based on the  fact that amplitude information is stored in a multi-qubit state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This naming system also  paves the way for other coefficient-based audio representations, such as the Quantum  Probability Amplitude Modulation (QPAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4  Coefficient-Based Representations  Suppose that we have some digital audio A, with N = 2n, n ∈ Z∗ samples, with each  sample quantized to [−2q−1, −2q−1 + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', 2q−1 − 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' That is, 2q possible values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  We can induce that the easiest way to represent those samples in a quantum state  |A⟩ would be to create a superposition of all of its possible states t (encoding time),  weighted by their respective probability amplitudes (encoding the sample value), in a  way that resembles an array, but in a quantum superposition (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 13 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  We can induce that the easiest way to represent those samples in a quantum state |A⟩  would be first to create a superposition of all of its possible states t (encoding time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then,  each time state would be weighted by their respective probability amplitude (encoding the  sample value).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  an  tn −→ αi |ti⟩  (13)  |A⟩(3−qubitArray) = α0 |0⟩ + α1 |1⟩ + α2 |2⟩ + α3 |3⟩ + α4 |4⟩ + α5 |5⟩ + α6 |6⟩ + α7 |7⟩ (14)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Quantum Probability Amplitude Modulation: QPAM  More generally, we could write an arbitrary quantum audio of size N, with n (or  �  log N  �  )  qubits and build an encoding scheme where each possible amplitude value of the audio  is mapped onto a probability amplitude(Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |AQPAM⟩ =  N−1  �  i=0  αi |i⟩  (15)  Quantum computing theory usually presents the upper bound of the sum showing  the number of qubits explicitly, like (2n − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Instead, we chose to use N = 2n as our  primary notation, as this will make more sense to the reader with an audio digital signal  processing background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  With Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 15, we achieved a simple but still very useful QAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We refer to this method  as Quantum Probability Amplitude Modulation representation of audio, or QPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It is a  convenient name, as the amplitude information is encoded as probability amplitudes of  each quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  2It would feel logical to induce that the Flexible Representation of Quantum Audio (FRQA) was derived from  the Flexible Representation of Quantum Images (FRQI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Unfortunately, this is not the case, since the FRQI is a  Probability-Oriented Representation, and the FQRA is a State-Oriented one, derived from the Novel Enhanced  Quantum Representation for digital images (NEQR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The choice to name the FQRA as such is unclear and  might have been made for historical reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The FRQI was one of the pioneering representations for images  (like FRQA) and probably the first to be widely studied in the literature with a variety of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  10  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Mapping the Digital Amplitudes to QPAM  Now, let us examine how to convert a digital signal representation to QPAM representa-  tion and vice-versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The audio amplitudes an are not equal to the probability amplitudes αi of measuring  each sample state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Instead, there is a specific mapping between them, which makes this  encoding scheme possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us see how this works using the hypothetic snippet of  audio depicted in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In Quantum Mechanics, we can affirm that given an arbitrary qubit |φ⟩ = α |0⟩ + β |1⟩  the probability of measuring the state |0⟩ is |α|2, with the proviso that:  Probabilities are numbers ranging between 0 and 1  The sum of probabilities of all possible states should be equal to 1  Digital audio amplitudes in Figure 6, however, are numbers ranging between −1 and  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Their sum does not necessarily add to 1 at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' So, in order to go from digital to  quantum, we need to take the following steps to normalize the amplitudes:  Step 1: add 1 to all amplitudes an  Step 2: divide the amplitudes by 2  Step 3: divide again, by the sum of all of the amplitudes  Step 4: take the square root of the result  Figure 6: Hypothetic audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Consider the amplitudes of our example listed before the down arrow in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The normalized values are shown after the down arrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Firstly, we shifted the amplitude  values to the positive domain by adding 1 to every value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' At this point, the amplitudes  range between 0 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Next, we scaled them to fit the range between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, we  summed all their values and divided every value by the result of the sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' At this point,  the sum of all amplitudes should be equal to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The last step is to turn these amplitudes into probability values by taking their square  root (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  αi =  1  √g  �  (ai + 1)  2  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  g =  �  k  (ak + 1)  2  (16)  11  Original Audio  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5  litude  Ampli  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0  2  4  5  6  Sample0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='7  −1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  ↓  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  Figure 7: Normalization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  QPAM Preparation  The QPAM representation is the most straightforward to prepare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As the information is  stored in the probability amplitudes, we just need to initialize the quantum audio at the  desired quantum superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This can be done by using the probability amplitudes to  calculate a unitary gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Alternatively, one could create a quantum circuit that maps a  set of qubits initialized in the |0000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='⟩ state into the arbitrary state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Fortunately, we do not  need to worry about calculating these matrices and circuits in a more practical sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Most quantum computing programming tools available nowadays provide commands to  initialize qubit states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' So, it suffices to assume that any arbitrary superposition of states  can be initialized by providing a set of probability amplitudes to the respective command  (Figure 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Consequently, for preparing a QPAM quantum audio, we would only need to  convert the digital samples into probability amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  t0 :  initialize([α0, α1, α2, α3, α4, α5, α6, α7])  t1 :  t2 :  Figure 8: Initializing qubit states for QPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Thus, preparing an arbitrary n-qubit state usually requires O(n) simple operations,  which implies that QPAM preparation needs O(⌈log N⌉) operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  QPAM Retrieval  Retrieving information from the quantum domain means taking measurements from our  quantum system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Measuring a quantum system means that only one of the possible  state outcomes of that system will be ’materialized’ in our measurement apparatus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In  other words, once we measure our time registers, the superpositions will be ’destroyed’,  and only one of the possible time states will be returned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figure 9 portrays a hypothetical QPAM representation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', histogram of amplitudes)  of the audio shown in Fig 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Furthermore, Figure 10 shows the respective audio recon-  structed by retrieving measurements with an allegedly perfect quantum machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us  look into this in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The Probabilistic representations have this name precisely because of their retrieval  strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Retrieving audio requires that we prepare many identical quantum versions of  the said audio and make a statistical analysis of the result of all measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The  analysis will return a histogram of the measurements (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 9), from which we can  assess the approximate probability of measuring each state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' When considering how the  system was prepared in the first place, it indicates that the histogram itself is already a  scaled and shifted version of a digital audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We just need to scale the audio back to its  original range, using an inverted version of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 16 for ai, shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  ai = 2g|αi|2 − 1  (17)  12  Figure 9: A hypothetical QPAM representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figure 10: Reconstructed audio from QPAM in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  There are two critical aspects of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 17 to be noticed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' First, the sum inside the  sum is a defined constant value, which is referred to as g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Second, the addition of a  ”||” on αi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We need to be careful with αi because it is, rigorously, a complex number  (α2  i ̸= |αi|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Nevertheless, the valuable information lies in its absolute value squared,  which corresponds to the probability pi = |αi|2 of |i⟩ being measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' After completing  the measurements, a histogram bin will not return pi, but rather an approximation ˜pi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  By replacing equation 17 with ˜pi, the final post-processing step for retrieving a digital  audio is achieved, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  ai = 2g˜pi − 1  (18)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  A caveat  The constant g in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 16 presents an important caveat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The equation contains terms  related to digital amplitudes ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' What is the caveat?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Let us consider the preparation stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The constant g is the denominator, meaning  that the sum over the terms (ai+1)  2  cannot be equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This condition occurs if all values  of ai were equal to −1, which is a perfectly valid audio signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  From a retrieval perspective, there is another consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The presence of g makes  the normalization of the original input necessary for retrieving a QPAM representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  13  QuantumProbabilityAmplitudeModulationRetrievalHistogram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='369  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  Probabilities  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='156  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  _0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='88  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='089  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='039  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0  0  3Reconstructed QPAM  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  Original  Reconstructed  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0  1  2  4  5  6  SampleHowever, in more general terms, one could consider g to be any arbitrary constant, which  would define the overall amplitude range of the signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  This arbitrariness of choice for g can be a problem if not properly assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It un-  desirably changes the amplitude range for the retrieved audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us imagine a thought  experiment to illustrate this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Consider a QPAM audio signal with 8 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' All sample values are equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Equation 16, confirms that g = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Then, suppose that a certain quantum algorithm  transforms this signal into the measured waveform shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The signal will be  reconstructed using Equation 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Particularly, consider the peak value of the histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Applying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 17 will result in 2g|0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='369|2 − 1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='089288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Moreover, when a low prob-  ability sample is picked: 2g|0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='09|2 − 1 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='999352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Therefore, the amplitude range is  compressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  A possible approach to this reconstruction problem may be to use the normalization  of the output to calculate a new g, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  g =  �  k  ˜pk  (19)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  Single Qubit Probability Amplitude Modulations: SQPAM  Another coefficient-based quantum audio representation instance can be derived from an  image representation scheme known as Flexible Representation of Quantum Images or  FRQI [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We propose calling this method Single Qubit Probability Amplitude Modulation,  or SQPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  SQPAM works similarly to QPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' However, instead of using the raw probability am-  plitudes, it uses ⌈log N⌉ + 1 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It improves the logic to encode the samples in the  probability amplitudes of one extra, dedicated qubit, added as a new register, |γi⟩, using  trigonometric functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It is a more reliable and editable encoding scheme than QPAM  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  an −→ |γi⟩ = cos θi |0⟩ + sin θi |1⟩  (20)  |A⟩3−qubit =  1  √  8  �  (cos θ0 |0⟩ + sin θ0 |1⟩) ⊗ |0⟩ + (cos θ1 |0⟩ + sin θ1 |1⟩) ⊗ |1⟩ +  (cos θ2 |0⟩ + sin θ2 |1⟩) ⊗ |2⟩ + (cos θ3 |0⟩ + sin θ3 |1⟩) ⊗ |3⟩ +  (cos θ4 |0⟩ + sin θ4 |1⟩) ⊗ |4⟩ + (cos θ5 |0⟩ + sin θ5 |1⟩) ⊗ |5⟩ +  (cos θ6 |0⟩ + sin θ6 |1⟩) ⊗ |6⟩ + (cos θ7 |0⟩ + sin θ7 |1⟩) ⊗ |7⟩  �  (21)  Generalizing for a N-sized audio, he have:  |ASQPAM⟩ =  1  √  N  N−1  �  i=0  (cos θi |0⟩ + sin θi |1⟩) ⊗ |i⟩  (22)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Mapping the SQPAM Audio Amplitudes  Similarly to the previous representation, there are some pre-processing steps for map-  ping the amplitudes to a normalized scope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Trigonometric functions are often used to  represent probability amplitudes since their absolute value ranges from 0 to 1, and the  relation between the cosine and sine functions satisfies the normalization requirement  perfectly3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  3  cos (θ)2 + sin(θ)2 = 1  14  Essentially, this describes a simple change of variables, where αi = cos θi and βi =  sin θi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Notice how only real numbers are being considered, analogous to QPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The introduction of an extra qubit |γi⟩ significantly improves the representation in  terms of both encoding and retrieval of the audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The first improvement is that the  encoding scheme does not rely on the entirety of the audio size content (the total number  of states on the superposition and their relative amplitudes) anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It is encoded  locally in the new qubit and therefore could be independently manipulated, using rotation  matrices as gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This opens a new range of possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The function that maps the audio amplitudes ai into angles θi is displayed in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  This mapping can also be conceived as the following set of instructions:  Step 1: Add 1 to all amplitudes an.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 2: Divide the amplitudes by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 3: Take the square root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 4: Evaluate the Inverse Sine of the result (The Inverse Cosine is also applica-  ble, as long as the same convention is followed throughout the implementation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  θi = sin−1  ��  ai + 1  2  �  (23)  The mapped array of angles will enable the preparation of the SQPAM quantum audio  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  Preparation  The SQPAM state preparation requires n qubits for encoding time (like QPAM) and 1  qubit for the amplitude (γi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' They can all be initialized in the |0⟩ state, as denoted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='⟩ ≡ |0⟩ ⊗ |0⟩ ⊗ |0⟩ ⊗ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' ≡ |0⟩⊗n+1 ≡ |0⟩  (γi)  ⊗ |0⟩⊗n  (24)  The qubits of the time register are put in a balanced superposition by applying Hadamard  gates in each one of them (Figure 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The resulting quantum state is written in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  γ :  t0 :  H  t1 :  H  t2 :  H  Figure 11: Circuit segment with Hadamard gates applied to a 3-qubit time register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |Ψ⟩ =  1  √  N  �  |0⟩ ⊗ |0⟩ + |0⟩ ⊗ |1⟩ + |0⟩ ⊗ |2⟩ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' + |0⟩ ⊗ |N − 1⟩  �  (25)  At this stage, we should discuss the particular strategy for transforming the amplitude  qubit into the desired form (|0⟩ → |γi⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There is a perfect quantum gate for the task,  called Ry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It applies rotations in the y axis of a Bloch Sphere (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 264).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Ry(2θ) =  �cos θ  − sin θ  sin θ  cos θ  �  (26)  4Ry(2θ) has the same form of a 2D rotation matrix, found in many Linear Algebra textbooks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The main  difference is that the angle theta rotates twice as fast in a Bloch Sphere compared to a regular Euclidean  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  15  Let us take a look at what happens when we apply Ry(2θ) to the state |0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Reminding  that quantum states represent vectors, this will resolve in a matrix-vector multiplication  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Ry(2θi) |0⟩ =  �cos θi  − sin θi  sin θi  cos θi  � �1  0  �  =  �cos θi  sin θi  �  = cos θi |0⟩ + sin θi |1⟩ = |γi⟩  (27)  Lastly, there should be a way to, somehow, loop through the different indexes of the  time register for applying a particular Ry(2θi) to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As a result, the angles |γi⟩ would  be entangled to their respective states |i⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' How to access and correlate specific states if  they are in a superposition?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The desired correlations can be achieved by controlling our value setting gate Ry  using a multi-controlled version of Ry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us explore the effect of controlled gates on a  quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Imagine a 1-qubit length audio example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Assume that a superposition was created  in the time register by following the first preparation step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The quantum state would be  described by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |φ0⟩ =  1  √  2  �  |0⟩ |0⟩ + |0⟩ |1⟩  �  (28)  Then, a controlled Ry(2θ) gate is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' By analyzing the circuit in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 12, we could  conclude that the Ry gate will only be applied if the time qubit is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 29 shows the  resulting state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  γ0 :  Ry(2θ)  t0 :  H Figure 12: Application of a controlled Ry(2θ)  |φ1⟩ = cRy[t0] |φ0⟩ =  1  √  2  �  |0⟩ |0⟩ + Ry(2θ) |0⟩ |1⟩  �  (29)  Now, let us place an X gate before and after Ry (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' What is the effect?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' If the  time qubit happens to be in the |0⟩ state, it will be flipped to |1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Consequently, it triggers  the control condition, which leads to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, it is flipped back to |0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Notice that it  would not trigger the controlled gate otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  γ0 :  Ry(2θ)  t0 :  H  X X  ≡  γ0 :  Ry(2θ)  t0 :  H  Figure 13: Inverting the control condition using two X gates  | ˜φ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='⟩ = (I ⊗ X)cRy[t0](I ⊗ X) |φ0⟩ =  1  √  2  �  Ry(2θ) |0⟩ |0⟩ + |0⟩ |1⟩  �  (30)  The X gates create a strategy for effectively switching the control condition, triggering  when the qubit is in the |0⟩ state instead of |1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is denoted by a white circle at the  control position, as shown on the right side of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  For two-qubit systems, the same strategy can be used to access particular indexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In this case, there are two control conditions to verify simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, the  16  address for the third sample - θ2 - is |10⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Hence, the control condition on t0 (the rightmost  bit) is ”|0⟩”, whereas t1 is ”|1⟩”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Equation 31 demonstrates that Ry(2θ2) is only being  applied to the third position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  By using four 2-controlled Ry(2θi) gates, each amplitude can be addressed and  stored accordingly (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |φ0⟩ = 1  2  �  |0⟩ |00⟩ + |0⟩ |01⟩ + |0⟩ |10⟩ + |0⟩ |11⟩  �  ∴  |φθ2⟩ = (I ⊗ X ⊗ I)(ccRy[t0t1](θ2))(I ⊗ X ⊗ I) |φ0⟩  = 1  2  �  |0⟩ |00⟩ + |0⟩ |01⟩ + Ry(θ2) |0⟩ |10⟩ + |0⟩ |11⟩  �  (31)  By generalizing this strategy, we arrive at an algorithm for the second preparation  step of the SQPAM audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For each time state,  Have a binary version of the state’s label stored in a classical variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  If a bit in a given position of the string is zero, apply an X gate at the respective  qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Apply the Ry(2θ) gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Apply another X gate, following the second instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  γ0 :  Ry(2θ0)  Ry(2θ1)  Ry(2θ2)  Ry(2θ3)  t0 :  H t1 :  H Figure 14: Preparation of a SQPAM representation using Value-Setting operations with Ry gates  Notice how this strategy depends on classical numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Depending on the program-  ming language of the framework, this can be easily done while constructing the circuit,  using a classical ’for loop’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  This preparation strategy (using multi-controlled gates) can be called Value-Setting  Operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This operation will be applicable to other representations as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  This preparation process applies ⌈logN⌉ Hadamard gates, and N N-controlled Ry(2θ)  gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Since the N-controlled Ry(2θ) have O(N) of basic operations, this means that  O  �  N2�  operations are needed for preparing a SQPAM audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  Retrieval  Figure 15 shows what to expect of a SQPAM retrieval histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each sample is en-  coded in complementary sine and cosine pairs embedded in |γi⟩ probabilities (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Hence, 16 bins instead of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In Equation 23, there is a arcsin function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Therefore, the audio’s profile appears if the  sine components (pγi(|1⟩)) are picked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Then, it suffices to use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 33 to reconstruct the signal5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Figure 16 shows a signal  reconstruction using the histogram in Fig 15 and Equation 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  pγi(|0⟩) = (cos(θi))2  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  pγi(|1⟩) = (sin(θi))2  (32)  5Consider using the cosine term (pγi(|0⟩)) in the nominator of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' What would happen?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The comple-  mentarity of the trigonometric functions would result in a reconstructed audio with inverted polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  17  Figure 15: Hypothetical SQPAM representation  Figure 16: Reconstructed audio from SQPAM in Figure 15  ai =  2pγi(|1⟩)  pγi(|0⟩) + pγi(|1⟩) − 1  (33)  5  State-Oriented Representations  In the previous section, the quantum audio representation schemes stored the time do-  main into a superposition of multi-qubit states and the amplitudes into probability ampli-  tudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In this section, the main difference is that the audio amplitudes will also be stored  in a multi-qubit state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This new quantum register will produce a set of time-amplitude  pairs of entangled information when put together with the time register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Put another way,  if a given time sample ti is measured, there will be a correlated state that will provide the  respective amplitude once measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It can be seen as an evolutionary branch of the previous representations (regarding  the quantum image representation timeline).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, they can potentially be ma-  nipulated in more detail and used in a wider range of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Of course, this needs  to be discussed on a case-by-case basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There is no way to know which representation  type is more adequate for different audio and musical applications yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This will be further  discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The consequence of these ”finer” capabilities is that they might increase the amount  of space required to represent and manipulate the audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In other words, there is a trade-  off between the number of qubits required to store the quantum audio and the amount of  known potential applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  18  Single-Qubit Probability AmplitudeModulation Retrieval Histogram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='128  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='120  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='111  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='103  lities  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='087  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='082  Probabili  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='059  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='060  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='042  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='041  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='021  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='021  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0  010  010  011  011  100  7Y  101  110  111  000  TO0  100  101  110  111Reconstructed SQ-PAM  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  Original  Reconstructed  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  0  1  2  4  5  6  7  SampleIn addition, another historical motivation to develop the following representation strate-  gies is related to their preparation complexity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' the number of instructions needed for  encoding).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Furthermore, the logic of storing the audio amplitudes as binary quantum  states align with the quantized digital amplitudes of section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  QSM and uQSM  The two following quantum audio representations were derived from the Novel Enhanced  Quantum Representation of Images, or NEQR [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' They were the first proposed quan-  tum representations of audio, namely, QRDA (Quantum Representation for Digital Audio)  and FRQA (Flexible Representation of Quantum Audio).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Both are identical from a no-  tation standpoint, but there is a slight difference in the interpretation of the qubit states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Respectively, they are read as either unsigned or signed integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The QRDA [6] was the first quantum audio representation proposed in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It was responsible for indicating the path towards its preparation and retrieval techniques,  bringing many of the primary foundations of a State-Oriented Representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2, we discussed how the analogue amplitudes were converted into digital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The samples  were approximated to the closest binary integer of the quantization scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The same  quantized amplitudes will be used in this section to prepare multi-qubit states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The QRDA has a dedicated quantum register that encodes the sample using strictly  positive integers (directly inherited from the NEQR Image that encoded Gray colour infor-  mation ranging from 0 to 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The FRQA, or Flexible Representation of Quantum Audio, on  the other hand, uses the Two’s Complement scheme to interpret the amplitudes (Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The signed integer makes audio mixing extremely convenient since only a regular  bit-wise adder algorithm is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This indicates that the FRQA’s interpretation of the  states is more suitable for quantum audio than QRDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Apart from the variable class interpretation, the logics of preparation and retrieval  are identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' These similarities suggest merging their names onto our proposed naming  system: Quantum State Modulation, or QSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Whenever a specific application requires  unsigned integers explicitly (QRDA), we could indicate that with a lower case ‘u’ before  the acronym (uQSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This terminology can be extended to fit other variable types in the  future, like fixed-point (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3) or floating-point numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  QSM  Consider a digital audio file with 8 samples and amplitude values quantized in a 3-bit  depth two’s complement scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Let us assume that the seventh sample of the signal  was represented by the following integer bit string: ”001”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In possession of this string,  we somehow prepare an analogous 3-qubit string on a dedicated amplitude register by  initializing it in the ground state and then flipping the rightmost qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This amplitude  state can be later entangled with a respective state of the time register, in this case, t7,  as described in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  (a7, t7) ≡ (001, 110) −→ |001⟩ |110⟩ ≡ |a7⟩ ⊗ |t7⟩  (34)  Applying this structure for all of the samples would result in the superposition shown  in equations 35 and 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' More generally, the QSM could be written as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  19  binary notation  |AQSM⟩  =  1  √  8  �  |000⟩ ⊗ |000⟩ + |111⟩ ⊗ |001⟩ + |010⟩ ⊗ |010⟩ +  |011⟩ ⊗ |011⟩ + |110⟩ ⊗ |100⟩ + |101⟩ ⊗ |101⟩ +  |001⟩ ⊗ |110⟩ + |000⟩ ⊗ |111⟩  �  (35)  decimal notation  |AQRDA⟩  =  1  √  8  �  |0⟩ ⊗ |0⟩ + |−1⟩ ⊗ |1⟩ + |2⟩ ⊗ |2⟩ + |3⟩ ⊗ |3⟩ +  |−2⟩ ⊗ |4⟩ + |−3⟩ ⊗ |5⟩ + |1⟩ ⊗ |6⟩ + |0⟩ ⊗ |7⟩  �  (36)  |A⟩ =  1  √  N  N−1  �  i=0  |Si⟩ ⊗ |i⟩  (37)  The time register uses n qubits (audio length), and the amplitude register needs q  qubits (qubit-depth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  As previously mentioned, this strategy has some foreseeable advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The multi-  qubit register for amplitude directly relates to the digital audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This similarity suggests  that some quantum algorithms could be developed to apply the same operations as  known digital signal processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' From there, developers could explore if the quantum  media would improve, extend or optimize some of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This ”intuition” layer contributes  to the instant popularity of the State-Based representations compared to the less ex-  plored Coefficient-Based ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Preparation  The same strategy mentioned in the SQPAM case will be used here: a Value-Setting  Operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In this case, instead of using Ry(2θi), the operation will use multi-controlled  CNOT gates for flipping the qubit states of the amplitude register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As a result, the algo-  rithm will access and entangle specific amplitude states with their respective time states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Value-Setting Operation: For each time state,  Step 1: Have a binary form of the time state’s label stored in a classical variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 2: Have the binary form of the quantized audio sample at the same index  Step 3: If a bit in a given position of the time variable is zero, apply an X gate at the  respective qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Verify all bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 4: If a bit in a given position of the audio sample is 1, apply a multi-controlled  CNOT gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Verify all bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Step 5: Repeat the third instruction to reset the control condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figures 17 and 18 exemplify a preparation circuit for an audio with 8 samples and  3-bit depth  Compared with SQPAM (Ry(2θi)), the preparing circuit for the audio in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 17 will  apply N value-setting operations, demanding O(q + log N) basic instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In conclu-  sion, the preparation circuit for the QSM is exponentially faster, requiring O(qN log N)  simple operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  20  Figure 17: Example audio used to prepare the QSM circuit  a0 :  a1 :  a2 :  t0 :  H t1 :  H t2 :  H Figure 18: Preparation of a QSM representation using Value-Setting operations  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='2  Retrieval  The interesting part of retrieving a state-based quantum audio is that it can be seen as  deterministic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It guarantees a perfect reconstruction of the digital audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is assured  since the sample is represented as a binary state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In the coefficient-based version, the samples were statistical quantities that needed to  be approximated through many measurements and statistical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' There will always  be an intrinsic statistical error whenever the amount of measurements is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It is a  trade-off between lying an error inside some tolerance range (depending on musical,  psychoacoustic, perceptual factors) and time consumption (mainly the number of times  a circuit will be prepared and measured) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In the case of state retrieval, we would only need to measure all valid time-amplitude  pairs to retrieve the audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Each time state is entangled to an amplitude state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' So this  theoretically assures that a given time state would certainly measure its correlated am-  plitude;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' there is no other combined state possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  That being the case, we could in principle measure each time state just once, en-  abling the retrieval of all respective amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Unfortunately, it is potentially impossible  to devise a method that could guarantee only one measurement per sample based on  a quantum time state in a superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In other words, controlled measurements (only  measuring a quantum state based on another quantum state) are non-unitary instruc-  tions and cannot be written as a set of quantum gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  6In his paper about generative quantum images using a coefficient based image representation, James  Wootton [15] states that he measured the n-qubit image state 4n times before considering it was a good  approximation for his application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This number can be much higher for reliable retrieval, and it scales exponen-  tially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  7We can build circuits that use the result of measurements for controlling quantum gates (due to the de-  ferred measurement principle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' But only unitary instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  21  Original Audio  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5  litude  Ampli  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='0  0  2  4  5  6  SampleFigure 19: Hypothetical QSM histogram  Figure 20: Reconstructed audio from QSM in Figure 19  With that said, the strategy for retrieving the QSM will be similar in many ways to the  previous ones: preparing several copies, making measurements, and analyzing a his-  togram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Enough measurements are needed to assure a sufficient probability of having  all possible states measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, the histogram is analyzed and the valid measured  states are parsed into digital amplitudes and time indexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This analysis is also a good  strategy for dealing with quantum error in real-life quantum processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Making enough  measurements to separate noise from a signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In an ideal situation, a state-modulated  representation will have a balanced superposition of the possible states (states contain-  ing the audio amplitudes and their time index), meaning they should be equally likely to  be measured (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Moreover, the measured states of the amplitude register are  decoded into the correspondent digital amplitudes using the Two’s Complement scheme  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The QSM framework is powerful due to its relatability with digital representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It  looks like PCM audio in a superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It promptly awakes the idea of comparing the  computational efficiency of known classical DSP algorithms (of course, even if quantum  parallelism helps with computational complexity, we need to consider the preparation and  retrieval time consumption as well).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  22  QuantumState ModulationRetrievalHistogram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='126  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='128  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='130  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='122  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='122  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='12  abilities  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='08  Probal  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='00  000  111  OTO  011  110  101  100  000  000  010  011  0  110ReconstructedQSM  011  Original  Reconstructed  010-  001  000-  111  110  101  0  1  2  3  4  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  Fixed Point QSM  Preparation complexity and quantum states interpreted as integers made QSM (FRQA)  well known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Nevertheless, it raises the question: why stop at integers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We could easily  interpret the qubit registers as fixed (or floating) point numbers and use the same state  structure of the QSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A fixed point, QSM-based representation was formalized by Li et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' [19] and was named QRDS (Quantum Representation of Digital Signals).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For the  terminology purposes of this text, this representation could be named fixed-point QSM  or fpQSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  It essentially divides the q qubits used to represent integers into three parts: one sign  bit, m integer bits and q − m − 1 fractional bits8, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |A⟩ =  1  √  N  N−1  �  i=0  |fixedi⟩ ⊗ |i⟩ =  1  √  N  N−1  �  i=0  |xm  i , xm−1  i  · · x0  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' x−1  i  · · xq−m−1  i  ⟩ ⊗ |i⟩  (38)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='4  Multichannel Audio  The QRMA (Quantum Representation of Multi-Channel Audio), proposed by [21] extends  the logic of a state-oriented representation for quantum audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In our naming system, it is  called Multichannel Quantum State Modulation (MQSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It furthers the QSM implemen-  tation logic by introducing a new quantum register in the circuit: the channel register (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' With this new register, we can address, for example, left (|0⟩) and right (|1⟩) channels  of a stereo audio (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Also, it enables efficient storage of multichannel audio in the  same quantum state (or a soundbank multiple mono tracks with the same length).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  (an,m, tn,m, cm) −→ |cj⟩ ⊗ |ai,j⟩ ⊗ |ti,j⟩  (39)  |AStereo⟩ =  1  √  2N  �  |L⟩ ⊗  �  |0⟩ |0⟩ + |0⟩ |1⟩ + |0⟩ |2⟩ + |0⟩ |3⟩ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  �  |R⟩ ⊗  �  |0⟩ |0⟩ + |0⟩ |1⟩ + |0⟩ |2⟩ + |0⟩ |3⟩ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  �  �  (40)  |AMQSM⟩ =  1  √  NC  N−1  �  i=0  C−1  �  j=0  |cj⟩ ⊗ |ai,j⟩ ⊗ |ti,j⟩  (41)  The general equation of the MQSM is shown in Equation 41, where C = 2c is the  number of channels used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Similar to N, if the number of channels is not a power of two,  the remaining possible channels would be zero-padded before preparing the state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Correspondingly, a channel register could be added to Coefficient-Based represen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As exemplified in the next section, it can become a valuable tool for feature  extraction algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For instance, A Multichannel version of the SQPAM could be de-  rived as shown in Equation 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  |AMSQPAM⟩ =  1  √  NC  N−1  �  i=0  C−1  �  j=0  |cj⟩ ⊗ (cos θi |0⟩ + sin θi |1⟩) ⊗ |i⟩  (42)  8the q − m − 1 was adapted to our notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In the original notation, the text uses n + 1 qubits instead of q  23  6  Summary  Different strategies for encoding audio in quantum systems were developed from quan-  tum image representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A change in the quantum audio representation terminology  was also proposed (which could be extended to images and other signals in the future).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The key pieces of information and features discussed are compared in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  When progressing down the table, the representations require more and more qubit  space to store all of the information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' As a result, the probabilistic representations are ca-  pable of storing larger samples in the same hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This is also true for bit depth: since  the probability amplitudes are continuous variables, they can store as much amplitude  resolution as classical computers can provide after the retrieval process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In comparison,  the state-based representations use qubit binary words, which require significantly more  quantum space to achieve a comparable resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Also, the bit depth q has a role in  the preparation complexity of the state modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  On the other hand, the amount of instructions necessary to prepare the SQPAM state  considering only the audio size N is significantly worse than the deterministic represen-  tations for larger audio samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Representation  Original  Acronym  Basic Structure  Amplitude  Map-  ping  Space Required  Preparation  Complexity  Retrieval  QPAM  ——  αn |tn⟩  Normalized,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='strictly  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='positive vector  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='O(N)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Probabilistic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='SQPAM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='——  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='(cos θn |0⟩  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='sin θn |1⟩) |tn⟩  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Angle Vector  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='+ 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='O  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='N2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Probabilistic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='uQSM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='QRDA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='|Un⟩ |tn⟩  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Unsigned  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Integer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Vector  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='+ q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='O  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='qN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Deterministic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='QSM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='FRQA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='|Sn⟩ |tn⟩  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Signed Integer Vec-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='tor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='+ q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='O  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='qN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Deterministic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='Fixed Point Integer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Vector  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='O  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='MQSM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='QRMA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='|ci⟩ |Sn⟩ |tn⟩  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Multiple Signed Inte-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='ger Vectors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='CqN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='log N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Deterministic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='Table 1: Comparison between quantum representations of audio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='These comparisons are essential for imagining near-term applications of music-quality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='audio on quantum hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Imagine that a composer wants to process two different  audio samples in a quantum machine for some hypothetical artistic reason.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The first  sample may be coming from a real-time audio signal processing language, with a block  of 64 samples that needs to run on a brand-new quantum audio effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The second  one is stored on a computer and has approximately 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='5 seconds of audio, containing  216 = 65536 samples that will be fed to a large quantum sound database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Both samples  have CD quality: A sample rate of 44,100Hz and a 16-bit resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' We will compare  three representations: QPAM, SQPAM and QSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  According to Table 1, QPAM will require 6 qubits and ∼ 64 instructions for storing the  first sample;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 7 qubits and ∼ 4096 instructions for SQPAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' QSM will need to allocate 16  more qubits for achieving the necessary amplitude resolution, with a total of 22 qubits  and ∼ 6144 instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  For the second audio, things scale up in the time register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' QPAM will use 16 qubits  and ∼ 65 thousand instructions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' SQPAM, 17 qubits and a surprising amount of ∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='3  billion instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Finally, QSM will need 32 qubits and ∼ 16 million instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  24  A noticeable result of this comparison is that SQPAM might be better suited for pro-  cessing small signal samples or segmented blocks of audio, useful for algorithms for  information retrieval).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' QSM, on the other hand, would handle large sounds effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Also, QPAM needs the lowest amount of resources for preparation, which is very useful  for near-term applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='1  Running on Real Hardware  This chapter focuses on surveying and consolidating a smooth and didactic theoretical  transition path between digital audio and the new field of quantum audio, underlying po-  tential problems of the computational level, proposing a more unified terminology, and fi-  nally glimpsing at potential artistic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This approach is why the chapter focuses  on a high-level discussion, assuming that the qubits are perfect and perfectly manipula-  ble, referred to as a logical qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Even so, it is worth saying something about running  these algorithms on real hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The state-of-the-art computers that are publicly avail-  able at the time of writing have a range of three to sixteen rather noisy physical qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It  is possible to correct potential errors for a better approximation of a logical qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For that  purpose, multiple physical qubits can be combined into a fault-tolerant qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This field is  known as Quantum Error Correction [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The state-of-the-art machines and their qubits  are not fault-tolerant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  A real-world qubit is prone to a myriad of errors and noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' For example, its state can  be flipped spontaneously due to external electromagnetic interference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It also tends to  lose energy and go to a lower energy level state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Furthermore, a quantum system might  lose coherence as time evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Also, each gate or instruction applied to a qubit has a  chance of failing or being inaccurate, introducing more noise and potentially leading to  incorrigible errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Additionally, qubits might interfere with each other in different ways,  depending on their displacement on the actual quantum chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Unfortunately, the depth of the circuits necessary to prepare quantum audio represen-  tations might be too high for near-term, fault intolerant machines (as previously shown  in the last section).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The more instructions present in a fault-intolerant machine (and the  more physical qubits you have), the less reliable the result will be9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This technologi-  cal barrier has propelled the quantum audio community towards theory and simulations  rather than real-hardware experiments on state-of-the-art technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  As a reference for future analysis and comparison, this text underlines how some  of the presented encoding schemes (QPAM, SQPAM, QSM) perform in state-of-the-art  hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' An experiment was made using IBM Q hardware [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Specifically, a 7-qubit  (32 Quantum Volume) chip called ibmq casablanca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' These experiments (along with re-  sults and simulations in the following sections) were run by using quantum audio mod-  ules implemented in Python and Qiskit, within the scope of the QuTune Project [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The  QuTune module was used to map and generate the quantum audio circuits from a signal  (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Then, the circuit was fed to the IBMQ system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Finally, the resulting  histograms - ehxhibited in Figures 22, 24, 26 - were retrieved and post-processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The  reconstructed audio signals are shown in Figures 23, 25 and 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  QPAM (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 23, 22)) had the lowest preparation complexity (approximately 8 instruc-  tions and 3 qubits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' It seems to retain most of the original information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  The SQPAM (24, 25), on the other hand, introduced value-setting operations, which  are more expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' The retrieved audio lost most of its amplitude range (notice the  values in the y axis) but retained some of the original profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  9While this limitation may be true, it can be seen as an advantage inside a sensible noise/degraded aes-  thetic for artistic purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  25  Figure 21: Test audio with 8 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figure 22: Retrieved QPAM histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  In contrast, QSM (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 26) produced an result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Surprisingly, its resemblance with  the original file was gone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' This was probably caused by the amount of multi-controlled  instructions for preparation and the time required for the operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Moreover, some  qubits might have flipped to a lower energy state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Even though it has a guarantee of  exact retrieval, the reconstruction process relies on the states that are most likely to be  measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' At this stage of loss of information, the QSM audio was irrecoverable (27)10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  7  Final Remarks  This chapter discussed various different approaches for quantum representation of audio  that have been proposed to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum audio is still a very young field of study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Naturally, the different approaches presented here have advantages and disadvantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  At this stage, we are not in a position to foresee which of the method(s) discussed here, if  any, might end up being adopted by the industry simply because the hardware to realize  them is not available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Nevertheless, as shown above, we can already start developing approaches and  dream of interesting applications (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', a quantum electric guitar effects pedal) based  on simulations and educated guesses about how quantum processors will evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' An  important caveat of quantum computing that needs to be addressed is the problem of  memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' The development of quantum  random access memory (qRAM) technology would make a significant impact on quan-  tum audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Figure 24: Retrieved SQPAM histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  quantumaudio: A Python package for quantum representations of audio in Qiskit is  available:  https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='org/project/quantumaudio/  quantumaudio is developed and maintained by the quantum computer music team  at the Interdisciplinary Centre for Computer Music Research (ICCMR), University of Ply-  mouth, UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  8  Acknowledgements  The authors acknowledge the support of the University of Plymouth and the QuTune  Project, funded by the UK Quantum Technology Hub in Computing and Simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  References  [1] Rabiner, Lawrence R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', and Bernard Gold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Theory and application of digital signal  processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Englewood Cliffs: Prentice-Hall, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [2] Broughton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Allen & Bryan, Kurt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Discrete Fourier Analysis and Wavelets: Appli-  cations to Signal and Image Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' John Wiley & Sons, Ltd, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [3] Ziemer, Rodger E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', and William H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Tranter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Principles of communications, chapters  3-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' John Wiley & Sons, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [4] K Meichanetzidis, S Gogioso, G De Felice, N Chiappori, A Toumi and B Co-  ecke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='  [5] Yi Zhang, Kai Lu, Yinghui Gao, and Mo Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' Quantum Information Processing,  12(8):2833–2860, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [6] Wang, Jian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' QRDA: Quantum Representation of Digital Audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' International Jour-  nal of Theoretical Physics, 55(3):1622–1641, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [7] Fei Yan, Abdullah M Iliyasu, Yiming Guo, and Huamin Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Flexible Representa-  tion and Manipulation of Audio Signals on Quantum Computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Theoretical Com-  puter Science,752:71–85, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [8] Vlatko Vedral, Adriano Barenco, and Artur Ekert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum Networks for Elemen-  tary Arithmetic operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Physical Review A, 54(1):147, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [9] Fei Yan, Abdullah M Iliyasu, and Salvador E Venegas-Andraca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A Survey of Quan-  tum Image Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum Information Processing, 15(1):1–35, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [10] D Wang, Z-H Liu, W-N Zhu, and SZ Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Design of Quantum Comparator Based  on Extended General Toffoli Gates with Multiple Targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Computer Science,  39(9):302–306,2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [11] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Exploring the Imple-  mentation of Steganography Protocols on Quantum Audio Signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' International  Journal of Theoretical Physics, 57(2):476–494, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [12] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A Quantum Audio  Watermarking Scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' In 2018 37th Chinese Control Conference (CCC), pages  3180–3185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [13] Kehan Chen, Fei Yan, Abdullah M Iliyasu, and Jianping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='  [14] Michael A Nielsen and Isaac Chuang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [17] Salvador E Venegas-Andraca and Sougato Bose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' In Quantum Information and Com-  putation, volume 5105, pages 137–147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' International Society for Optics and Pho-  tonics, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [18] S¸ ahin, Engin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum arithmetic operations based on quantum fourier transform  on signed integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' International Journal of Quantum Information 18(06):2050035,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [19] Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Xiao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum Representation and Basic Operations of  Digital Signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' International Journal of Theoretical Physics, 57:3242–3270, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [20] Yan, Fei & Iliyasu, Abdullah & Le, Phuc & Sun, Bo & Dong, Fangyan & Hirota,  Kaoru.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' A Parallel Comparison of Multiple Pairs of Images on Quantum Computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  International Journal of Innovative Computing and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 199-212, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [21] S¸ ahin, Engin, and ˙Ihsan Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' Quantum Information Processing 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='7: 1-30, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [22] Lidar, Daniel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', and Todd A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Brun, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum error correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Cambridge  University Press, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [23] IBM Quantum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' https://quantum-computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='  [24] Miranda, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Computer Sound Design: Synthesis techniques and programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  Focal Press;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' 2nd edition, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [25] QuTune Project - Quantum Computer Music Resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' https://iccmr-  quantum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content='io/, Last Accessed 01 Feb 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [26] Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Dai, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Errando-Herranz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Lloyd, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+page_content=' Scalable and  High-Fidelity Quantum Random Access Memory in Spin-Photon Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' PRX  Quantum, 2, 030319, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  [27] Asaka, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=', Sakai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' and Yahagi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum random access memory via quantum  walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content=' Quantum Science and Technology, 6(3): 035004, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
+page_content='  29  RealHardwareReconstructed OPAM  010  001-  000-  Amplitude  111 -  110-  101-  100  0  1  2  3  4  5  6  7  Sample' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNAzT4oBgHgl3EQfoP3V/content/2301.01595v1.pdf'}
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+Model reduction for stochastic systems with nonlinear drift
+Martin Redmann∗
+February 1, 2023
+Abstract
+In this paper, we study dimension reduction techniques for large-scale controlled stochastic
+differential equations (SDEs). The drift of the considered SDEs contains a polynomial term
+satisfying a one-sided growth condition. Such nonlinearities in high dimensional settings occur,
+e.g., when stochastic reaction diffusion equations are discretized in space. We provide a brief
+discussion around existence, uniqueness and stability of solutions. (Almost) stability then is
+the basis for new concepts of Gramians that we introduce and study in this work. With the
+help of these Gramians, dominant subspace are identified leading to a balancing related highly
+accurate reduced order SDE. We provide an algebraic error criterion and an error analysis of
+the propose model reduction schemes. The paper is concluded by applying our method to
+spatially discretized reaction diffusion equations.
+Keywords: model order reduction· nonlinear stochastic systems · Gramians · L´evy processes
+MSC classification: 60G51 · 60H10 · 65C30 · 93C10 · 93E03 · 93E15
+1
+Introduction
+Model order reduction (MOR) aims to find low-order approximations for high-/infinite-dimensional
+systems of differential equations reducing the complexity of the original problem. Many MOR
+schemes are based on projections (Galerkin or Petrov-Galerkin type). In this context, the first
+goal is to identify solution manifolds and approximate them by low-dimensional linear subspaces.
+A reduced state variable, taking values in this subspace, is subsequently constructed in order
+to ensure an accurate estimation of the original dynamics. There is a rich selection of different
+MOR strategies. Proper orthogonal decomposition (POD) [20] is an approach, where solution
+spaces are learned from data. Methods like the iterative rational Krylov algorithm (IRKA) [13]
+rely on interpolation or on the minimization of certain error measures between systems. More-
+over, there are Gramian based techniques like balanced truncation (BT) [25], where dominant
+subspaces of the original dynamics are associated to eigenspaces of these (algebraic) Gramians.
+Recently, there has been an enormous interest in dimension reduction for large-scale nonlinear
+systems. Data-driven [12, 18, 28] or interpolation/optimization based methods [3, 6] were applied
+to such equations in a deterministic framework. Generalizing BT to nonlinear systems was first
+addressed in [32]. Alternatives, where the reduced order model can be computed easier, can be
+found in [5, 19].
+MOR in probabilistic settings is even more essential than in the deterministic context discussed
+above. This is due to an enormous amount of system evaluations required, e.g., for conducting
+Monte-Carlo simulations. On the other hand, it is also about the feasibility of certain algorithms.
+E.g., a stochastic differential equation (SDE) in dimension n is in some sense equivalent to a partial
+differential equation (PDE) with n spatial variables using the formula of Feynman-Kac. Knowing
+how hard it is to solve high-dimensional PDEs in general, it becomes clear how vital MOR for
+SDEs is. A POD approach for SDEs is studied in [34]. Balancing related or optimization based
+MOR techniques are, for instance, investigated in [2, 4, 7, 31] for the linear case. The advantage
+∗Martin Luther University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Str.
+5, 06120 Halle
+(Saale), Germany, Email: martin.redmann@mathematik.uni-halle.de.
+1
+arXiv:2301.13722v1  [math.PR]  31 Jan 2023
+
+2
+M. REDMANN
+of the latter schemes is the possibility for detailed error and stability analysis.
+However, an
+extension to nonlinear stochastic systems seems very challenging. A first approach for stochastic
+bilinear equations is presented in [29] but it might not work for more complex nonlinearities.
+The goal of this paper is to extend BT to stochastic systems, e.g., with certain polynomial
+nonlinearities. In the deterministic case, a wide focus is on quadratic systems, see for instance
+[5, 19]. This is because many nonlinear terms in a differential equation can be transformed to
+a quadratic expression using additional dummy variables. This approach is called lifting in the
+literature. It has the advantage that a large set of nonlinear systems can be covered if we know
+how to handle quadratic ones. However, this is also the drawback of this ansatz, since differential
+equations involving quadratic terms range from globally stable to finite time explosion systems,
+i.e., the existence of a global solution is not guaranteed. This large variety of properties makes it
+seem infeasible to develop a general theory like for example an error analysis with sharp bounds.
+For that reason, we do not intend to apply to technique of lifting the dynamics to a quadratic
+system in this paper, because one might loose track of essential properties that are usually not
+visible anymore in a transformed SDE. Instead we exploit the structure of our locally Lipschitz
+nonlinearity that we assume to be of one-sided linear growth.
+This also involves interesting
+polynomials that play a role in reaction diffusion equations. This type of growth will be reflected
+linearly in the associated Lyapunov operator that defines the Gramians that we propose in our
+MOR procedure.
+The paper is now structured as follows. Section 2 deals with the setting and the first details
+concerning the goals of this work. In Section 3, we recall facts about existence and uniqueness
+of solutions to the considered nonlinear SDE. We further investigate global asymptotic stability
+as the basis of the Gramians that we introduce in Section 4. There, it is explained and reasoned
+how Gramians need to be chosen in order to find a good dominant subspace characterization
+and hence an accurate reduced system. We also discuss on properties of Gramians that need
+to be fulfilled to ensure the classical error bound for BT known for deterministic linear systems
+[10, 11].
+Having computed the desired Gramians based on the strategy that we provide, we
+explain how to compute the reduced system in Section 5. Finally, Section 6 delivers an error
+bound analysis for the balancing related MOR scheme, also involving a discussion on criteria for
+a high approximation quality. Section 7 illustrates the performance of the MOR technique by
+applying it to spatially discretized stochastic reaction diffusion equations.
+2
+Setting, notation and goal
+Let
+�
+Ω, F, (Ft)t∈[0,T], P
+�1 be a filtered probability space on which every stochastic process ap-
+pearing in this paper is defined. Given an Rd-valued and square integrable L´evy process M =
+�
+M1
+. . .
+Md
+�⊤ with mean zero, we assume that it is is (Ft)t∈[0,T]-adapted and its increments
+M(t + h) − M(t) are independent of Ft for t, h ≥ 0 and t + h ≤ T. Exploiting the independent
+and stationary increments, there exists a positive semidefinite matrix K = (kij)i,j=1,...,d, so that
+E[M(t)M(t)⊤] = Kt, see [27, Theorem 4.44] for a proof. We call K covariance matrix of M.
+Now, we consider the following large-scale nonlinear stochastic dynamics driven by M:
+dx(t) = [Ax(t) + Bu(t) + f (x(t))]dt + N (x(t−)) dM(t),
+x(0) = x0,
+(1a)
+y(t) = Cx(t),
+t ∈ [0, T],
+(1b)
+where x(t−) := lims↑t x(s), A ∈ Rn×n, B ∈ Rn×m, C ∈ Rp×n, N : Rn → Rn×d is a linear mapping
+defined by N(x) =
+�
+N1x
+. . .
+Ndx
+�
+for x ∈ Rn with N1, . . . , Nd ∈ Rn×n.
+The state vector
+x(t) ∈ Rn is assumed to be high-dimensional, whereas the quantity of interest y(t) ∈ Rp usually
+is a vector with a low number of entries. The nonlinear function f : Rn → Rn shall satisfy the
+following local Lipschitz condition
+∥f(x) − f(z)∥2 ≤ cR ∥x − z∥2 ,
+(2)
+1(Ft)t∈[0,T ] is right continuous and complete.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+3
+for ∥x∥2 , ∥z∥2 ≤ R, cR > 0 and any R > 0, where ⟨·, ·⟩2 denotes the Euclidean inner product
+with corresponding norm ∥·∥2. Further, we assume the special type of monotonicity condition
+⟨x, f(x)⟩2 ≤ cf ∥x∥2
+2 ,
+(3)
+for all x ∈ Rn and a constant cf. In the literature, (3) is called one-sided growth condition as
+well. In fact, cf can be negative. In this case, (3) is also known as dissipativity condition. Below,
+x(t, x0, B), t ∈ [0, T], represents the solution to (1a) with initial condition x0 ∈ Rn and matrix B
+determining the inhomogeneous part of the state equation. The associated control process u is
+assumed to be an (Ft)t∈[0,T]-adapted process with
+∥u∥2
+L2
+T := E
+� T
+0
+∥u(t)∥2
+2 dt < ∞.
+Moreover, suppose that f(0) = 0 to ensure that the uncontrolled state equation (1a) (B = 0) has
+an equilibrium at zero. If f(0) ̸= 0, we can replace f by f −f(0) as well as B and u by
+�
+B
+f(0)
+�
+and
+�
+u
+1
+�⊤, respectively. The above setting covers interesting polynomial nonlinearities. This
+is illustrated in the next example.
+Example 2.1. The local Lipschitz condition (2) is fulfilled by all functions f with continuous
+partial derivatives. This is particularly given for polynomials. If we assume f = f(i), i ∈ {1, 2, 3},
+to be special third order polynomial, where
+f(1)(x) = x ◦ (1n − x) ◦ (x − 1na) = (1 + a)x◦2 − x◦3 − ax,
+a ∈ R,
+f(2)(x) = x − x◦3
+and
+f(3)(x) = x − x ∥x∥2
+2 ,
+the monotonicity condition (3) holds. The products/powers involving “◦” have to be understood
+in the Hadamard (component wise) sense and 1n is the vector of ones having length n. Now, (3)
+can be verified by the following calculations
+⟨x, f(1)(x)⟩2 = −a ∥x∥2
+2 +
+n
+�
+i=1
+x2
+i [(1 + a)xi − x2
+i ] ≤ (a − 1)2
+4
+∥x∥2
+2 ,
+⟨x, f(2)(x)⟩2 = ∥x∥2
+2 −
+n
+�
+i=1
+x4
+i ≤ ∥x∥2
+2 ,
+⟨x, f(3)(x)⟩2 = ∥x∥2
+2 − ∥x∥4
+2 ≤ ∥x∥2
+2
+exploiting that (1 + a)xi − x2
+i ≤ (a+1)2
+4
+for all xi ∈ R.
+Our setting is not restricted to the functions of Example 2.1. However, we will frequently
+refer to these interesting cases. Let us point out that the component-wise functions f(1) and f(2)
+occur if the nonlinear part of certain (stochastic) reaction diffusion equations are evaluated on a
+spatial grid. To be more precise, a finite difference discretization of Zeldovich-Frank-Kamenetsky
+(or FitzHugh-Nagano) and Chafee-Infante equations would lead to such a setting. This paper
+does not intend to discuss finite difference schemes for stochastic partial differential equations
+in detail. However, the interested reader may find more information regarding these methods in
+[14, 15, 16, 33]. We also refer to, e.g., [8, 21, 24, 27] for a theoretical treatment of stochastic
+reaction diffusion equations.
+The goal of this paper is to drastically reduce the dimension of the high-dimensional system (1)
+in order to lower the computational complexity when solving this system of stochastic differential
+equations. Therefore, the solution manifold of (1a) shall be approximated by an r-dimensional
+subspace im[V ] of Rn (V ∈ Rn×r is a full-rank matrix), so that we find a process xr yielding
+V xr(t) ≈ x(t). Inserting this estimate into (1) leads to
+V xr(t) = x0 +
+� t
+0
+AV xr(s) + Bu(s) + f(V xr(s))ds +
+� t
+0
+N (V xr(s−)) dM(s) + e(t)
+(4)
+
+4
+M. REDMANN
+with y(t) ≈ yr(t) := CV xr(t) and where e(t) is the state equation error. Now, we enforce the
+residual e(t) to be orthogonal to a second subspace im[W] (W ∈ Rn×r has full rank). We further
+assume that our choice of W provides W ⊤V = I. Multiplying (4) with W ⊤, we obtain
+dxr(t) = [Arxr(t) + Bru(t) + fr(xr(t))]dt + Nr(xr(t−))dM(t),
+(5a)
+yr(t) = Crxr(t),
+t ∈ [0, T],
+(5b)
+with xr(0) = W ⊤x0 ∈ Rr, r ≪ n and y ≈ yr. Generally, we have that xr(t) ∈ Rr, Ar ∈ Rr×r,
+Br ∈ Rr×m, Cr ∈ Rp×r, Nr : Rr → Rr×d defined by Nr(xr) =
+�
+Nr,1xr
+. . .
+Nr,dxr
+�
+for xr ∈ Rr,
+where Nr,i ∈ Rr×r (i = 1, . . . , d) and fr : Rr → Rr. In particular, the reduced coefficients are of
+the following form
+Ar = W ⊤AV,
+Br = W ⊤B,
+fr(·) = W ⊤f(V ·),
+Nr,i = W ⊤NiV,
+Cr = CV.
+(6)
+The goal of this paper is to provide a reduced order method for which we can compute the
+projection matrices V and W and for which we find an accurate approximation of (1). Here,
+the main focus will be on the control dynamics and not on the initial state. Therefore, we study
+reduced order modelling when x0 = 0. Moreover, we aim to investigate Gramian based schemes
+which often heavily rely on stability of the state equation. Therefore, we discuss global asymptotic
+stability in the next section. Before doing so, we briefly point out that there is a unique solution
+to (1a) by referring to the existing literature.
+3
+Existence and uniqueness as well as global asymptotic stability
+3.1
+Existence and uniqueness for (1a)
+We briefly discuss that our setting is well-posed. We define the drift function F(t, x) := Ax +
+Bu(t) + f(x) of (1a). Using (3) and exploiting that the remaining parts in the drift and diffusion
+are either linear in x or solely time dependent, we can find a constant cF,N, so that
+2⟨x, F(t, x)⟩2 + ∥N(x)K
+1
+2 ∥2
+F ≤ cF,N
+�
+1 + ∥x∥2
+2
+�
+(7)
+given that the control u is bounded by a constant independent of t ∈ [0, T] and ω ∈ Ω. Here, ∥·∥F
+denotes the Frobenius norm. Moreover, the drift F is locally Lipschitz continuous (uniformly
+in (t, ω)) in the sense of (2), since the same is true for f.
+As N is linear, it is particularly
+globally Lipschitz with respect to ∥ · K
+1
+2 ∥F . The monotonicity condition (7) and local Lipschitz
+continuity of drift and diffusion yield existence and uniqueness of a solution to (1a) by [23,
+Theorem 3.5] if M is a Brownian motion. On the other hand, the arguments of Mao [23] can
+immediately be transferred to our more general setting because the Ito-integral w.r.t M has
+essentially the same properties as the one in the Brownian case. The first property is the Ito
+isometry E
+���
+� T
+0 Ψ(s)dM(s)
+���
+2
+2 = E
+� T
+0 ∥Ψ(s)K
+1
+2 ∥2
+F ds =: ∥Ψ∥2 for predictable2 processes Ψ with
+∥Ψ∥ < ∞ which relies on the linear covariance function of M, see [27]. Secondly, the equation for
+the expected value of a quadratic form of the state variable has the same structure, see Lemma
+A.1. It is also worth mentioning that existence and uniqueness has been established in a more
+general setting than in [23] also covering ours, see [1]. There, the result was proved assuming a
+monotonicity condition, a local Lipschitz condition in the drift and the Brownian diffusion part
+as well as global Lipschitz continuity in the jump diffusion.
+3.2
+A note on global asymptotic stability
+Stability concepts are essential in order to define computational accessible Gramians which are
+vital for identifying less relevant information in a system like (1). We recall known facts for the
+linear part of (1) based on the results in [17].
+2Predictable means that the process is measurable w.r.t. the σ algebra that is generated by left-continuous and
+(Ft)t∈[0,T ]-adapted processes.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+5
+Proposition 3.1. Let f ≡ 0 and B = 0 in (1a), then the following statements are equivalent:
+(a) The state in (1a) is exponentially mean square stable, i.e., there are k, β > 0, so that
+�
+E ∥x(t, x0, 0)∥2
+2 ≤ ∥x0∥2 k e−βt .
+(b) It holds that
+λ
+�
+I ⊗ A + A ⊗ I +
+d
+�
+i,j=1
+Ni ⊗ Njkij
+�
+⊂ C−,
+where λ(·) denotes the spectrum of a matrix.
+(c) There exists a matrix X > 0 with
+A⊤X + XA +
+d
+�
+i,j=1
+N⊤
+i XNjkij < 0.
+Proof. A proof of these statements can be found in [9, 30].
+Throughout the rest of the paper, we assume that
+λ
+�
+I ⊗ (A + c1I) + (A + c1I) ⊗ I +
+d
+�
+i,j=1
+Ni ⊗ Njkij
+�
+⊂ C−
+(8)
+for some constant c1. According to Proposition 3.1 this means that (1a) with the shifted linear
+drift coefficient A+c1I is mean square asymptotically stable for B = 0 and f ≡ 0. The associated
+state variable is of the form ec1t x(t), so that the original state x(t) (B = 0 and f ≡ 0) needs to
+have a decay rate β > c1, see Proposition 3.1 (a), given that c1 is positive. We desire, but do not
+assume, that we can choose c1 ≥ cf, i.e., the decay rate of the linear part shall outperform the
+one-sided linear growth constant in (3). This requires a sufficiently stable linear part if cf > 0,
+e.g., for the nonlinearities in Example 2.1. Since cf can also be negative, this means that the
+linear part of (1a) can even be exponentially increasing in some cases. Using classical arguments
+of [17, 23] based on quadratic Lyapunov-type functions, we provide the following criterion for the
+global mean square stability of the uncontrolled state equation (1a). This criterion is required
+around the discussion of the Gramians introduced later.
+Theorem 3.2. Suppose that B = 0 in (1a) and given constant c1, c2 ∈ R and a matrix X > 0.
+If we have
+(A + c1I)⊤X + X(A + c1I)+
+d
+�
+i,j=1
+N⊤
+i XNjkij < 0
+and
+(9)
+⟨x, Xf(x)⟩2 ≤ c2
+���X
+1
+2 x
+���
+2
+2
+(10)
+for all x ∈ Rn. Then, there exist constants k, β > 0, so that
+E ∥x(t, x0, 0)∥2
+2 ≤ ∥x0∥2
+2 k e(2(c2−c1)−β)t .
+Proof. A proof is stated in Appendix B
+Remark 3.3. If c1 ≥ c2 in Theorem 3.2, we obtain global mean square asymptotic stability for
+our nonlinear system. In particular, by assumption (3), (10) holds for X = I and c2 = cf. If (9)
+is now true for X = I and c1 = cf, mean square asymptotic stability follows.
+
+6
+M. REDMANN
+4
+Gramians and dominant subspace characterization
+In this section, algebraic objects, called Gramians, are introduced. We aim to construct them,
+so that their eigenspaces corresponding to small eigenvalues coincide with the information in
+(1) that can be neglected. It is not trivial to find the right notion for general nonlinearities f.
+However, the monotonicity condition in (3) will become essential for our concept. In particular,
+positive (semi)definite Gramian candidates X have to preserve (3) in a certain sense when ⟨·, ·⟩2
+is replaced by ⟨·, X·⟩2. We begin with a global Gramian concept to illustrate what we require.
+Subsequently, we immediately weaken it for practical reasons.
+4.1
+Monotonicity Gramians
+First, a pair of Gramians is defined that characterizes dominant subspaces of (1) for all u ∈ L2
+T .
+Definition 4.1. Let c1 and c2 be constants. Then, a pair of matrices (P, Q) with P, Q > 0 is
+called global monotonicity Gramians if they satisfy
+(A + c1I)⊤P −1 + P −1(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i P −1Njkij ≤ −P −1BB⊤P −1,
+(11)
+(A + c1I)⊤Q + Q(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i QNjkij ≤ −C⊤C,
+(12)
+and if further holds that
+⟨x, P −1f(x)⟩2 ≤ c2∥P − 1
+2 x∥2
+2
+and
+⟨x, Qf(x)⟩2 ≤ c2∥Q
+1
+2 x∥2
+2
+(13)
+for all x ∈ Rn.
+Notice that assumption (8) ensures the existence of solutions to (11) and (12), see [4, 30]. In
+the following, we state a sufficient criterion for the existence of Gramians also satisfying (13).
+Proposition 4.2. Suppose that (9) and (10) hold with some constants c1 and c2. Then, global
+monotonicity Gramians P and Q exist with the same constants.
+Proof. We denote the left hand side of (9) by −Y and multiply it with γ > 0. Hence, we have
+(A + c1I)⊤(γX) + (γX)(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i (γX)Njkij = −γY.
+(14)
+Since Y > 0, we can ensure that −γY ≤ −(γX)BB⊤(γX) if γ is sufficiently small. Therefore, P =
+(γX)−1 solves (11) for a potentially small γ. On the other hand, this P gives us ⟨x, P −1f(x)⟩2 =
+γ⟨x, Xf(x)⟩2 ≤ γc2∥X
+1
+2 x∥2
+2 = c2∥P − 1
+2 x∥2
+2. Now, we know that −γY ≤ −C⊤C if γ is sufficiently
+large. Consequently, Q = γX satisfies (12) for a potentially large γ. Moreover, we find that
+⟨x, Qf(x)⟩2 = γ⟨x, Xf(x)⟩2 ≤ γc2∥X
+1
+2 x∥2
+2 = c2∥Q
+1
+2 x∥2
+2 using (10). This concludes the proof.
+Remark 4.3. Certainly, the existence of global monotonicity Gramians is not sufficient for our
+considerations. As we will see later, it is important to find candidates P and Q that have a large
+number of small eigenvalues. Consequently, one might have to solve a problem of minimizing
+tr(P) and tr(Q) subject to (11), (12) and (13). Moreover, we allow c1 < c2 in Definition 4.1 to
+have an additional degree of freedom. However, this comes with a price. We will observe that
+c2 − c1 is supposed to be small. In fact, we desire to choose c1 = c2 if such a c1 ensures (8).
+Example 4.4.
+• Choosing f = f(3) from Example 2.1, we see that ⟨x, Xf(3)(x)⟩2 ≤ ∥X
+1
+2 x∥2
+2
+for any X ≥ 0 and all x ∈ Rn. Therefore, any solutions of (11) and (12) with c1 = c2 =
+cf = 1 are global monotonicity Gramians. In particular, we can choose the solution to the
+equality in (12) and the candidate with minimal trace in (11).
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+7
+• If f is globally Lipschitz in some norm, then there exist a Lipschitz constant cL, so that
+⟨x, Xf(x)⟩2 = ⟨X
+1
+2 x, X
+1
+2 f(x)⟩2 ≤ ∥X
+1
+2 x∥2∥X
+1
+2 f(x)∥2 ≤ cL∥X
+1
+2 x∥2
+2 given that X = P −1, Q >
+0 meaning that every positive solution to (11) and (12) can be picked. However, cL depends
+on X which shows that c1 and c2 influence each other. On the other hand, this cL might not
+be the optimal candidate for the one-sided Lipschitz constant c2 which can even be negative,
+i.e., it is also challenging to identify optimal constants.
+We emphasize further that, generally, we cannot derive P and Q independent of (13). For
+instance, fixing c1 = c2 ≥ cf, we can easily find a solution Q for (12) and a vector x ∈ Rn, so
+that ⟨x, Qf(1)(x)⟩2 > c2∥Q
+1
+2 x∥2
+2. Here, f = f(1) is the function defined in Example 2.1. Having
+in mind that we aim to fix c1 and c2 close to each other with associated Gramians P and Q
+having a large number of small eigenvalues, the concept of global Gramians might generally be
+too restrictive. Therefore, it is more reasonable to seek for solutions of (11) and (12) that satisfy
+(13) on average instead of point-wise. This means, we aim to allow for positive values of the
+monotonicity gaps
+GP −1(x) := ⟨x, P −1(f(x) − c2x)⟩2
+and
+GQ(x) := ⟨x, Q(f(x) − c2x)⟩2
+(15)
+as long as GP −1 and GQ are mainly non-positive on the essential parts of Rn. We specify the above
+arguments in the following definition. In this context, we introduce the set U of controls u ∈ L2
+T
+for which we desire to evaluate system (1). The following pair of Gramians (P, Q) identifies less
+important direction for controls in U. Therefore, it is meaningful to pick Gramian candidates
+that ensure a large set U.
+Definition 4.5. Let c1, c2 be constants and U ⊆ L2
+T be the set of controls we are interested in.
+Then, a pair of matrices (P, Q) with P, Q > 0 is called average monotonicity Gramians for U if
+(11) and (12) are satisfied, respectively, and if instead of (13) it holds that
+E
+� t
+0
+⟨x(s), P −1f(x(s))⟩2ds ≤ c2 E
+� t
+0
+∥P − 1
+2 x(s)∥2
+2ds
+and
+(16)
+E
+� t
+0
+⟨x(s), Qf(x(s))⟩2ds ≤ c2 E
+� t
+0
+∥Q
+1
+2 x(s)∥2
+2ds
+(17)
+for all t ∈ [0, T] and all state variables x(t) = x(t, 0, u) with u ∈ U.
+Certainly, a global is also an average monotonicity Gramian with U = L2
+T . Suppose that there
+are areas, where one of the functions in (15) is positive. Then, controls u concentrating the state
+variable x in such areas for a long time will violate (16) or (17).
+Remark 4.6. In Definitions 4.1 and 4.5, Gramians are constructed as solutions to (shifted)
+linear matrix inequalities in order to allow a practical computation. This is possible due to the
+monotonicity condition for f in (3) which shall be preserved in some sense under the inner
+products defined by the Gramians P and Q.
+A more general version of global monotonicity
+Gramians is obtained by adding twice the estimates in (13) to (11) and (12) resulting in
+x⊤�
+A⊤P −1 + P −1A +
+d
+�
+i,j=1
+N⊤
+i P −1Njkij
+�
+x + 2⟨x, P −1f(x)⟩2 ≤ −∥B⊤P −1x∥2
+2 + c∥P − 1
+2 x∥2
+2, (18)
+x⊤�
+A⊤Q + QA +
+d
+�
+i,j=1
+N⊤
+i QNjkij
+�
+x + 2⟨x, Qf(x)⟩2 ≤ −∥Cx∥2
+2 + c∥Q
+1
+2 x∥2
+2
+(19)
+for all x ∈ Rn, where c ≥ 0 is some “small” constant. The same way, average monotonicity
+Gramians can be generalized setting x = x(s) in (18) and (19), taking the expected value and
+integrating both sides of these inequalities over each subinterval [0, t] with 0 < t ≤ T. However,
+we will not discuss this generalization in detail below.
+
+8
+M. REDMANN
+4.2
+Relevance of monotonicity Gramians
+In the following, we state in which sense the Gramians of Definition 4.5 help to identify the
+dominant subspaces of (1). This then motivates a truncation procedure resulting in a special
+type of reduced system (5). Below, let us assume that x0 = 0, i.e., x(t) = x(t, 0, u). By definition,
+Gramians are positive (semi)definite matrices. Consequently, we can find an orthonormal basis
+(pk) for Rn consisting of eigenvalues of P with corresponding eigenvalues (λP,k). The same is true
+for Q, where the basis is denoted by (qk) with associated eigenvalues (λQ,k). Hence, the state
+variable can be represented as
+x(t) =
+n
+�
+k=1
+⟨x(t), pk⟩2 pk
+and
+x(t) =
+n
+�
+k=1
+⟨x(t), qk⟩2 qk.
+(20)
+Based on this representation, we aim to answer which directions pk are less relevant in (1a) and
+which directions qk can be neglected in (1b).
+Theorem 4.7. Let P and Q be average monotonicity Gramians for the set of controls U ⊆ L2
+T and
+constants c1, c2 according to Definition 4.5. Moreover, let (pk, λP,k) and (qk, λQ,k) be associated
+bases of eigenvectors giving us (20). Then, given a zero initial state, we have
+sup
+t∈[0,T]
+E⟨x(t), pk⟩2
+2 ≤ λP,k ecT ∥u∥2
+L2
+T ,
+(21)
+E
+� t
+0
+∥y(s)∥2
+2 ds ≤ 2E
+� t
+0
+⟨Qx(s), Bu(s)⟩2 ec(t−s) ds
+= 2
+n
+�
+k=1
+λQ,kE
+� t
+0
+⟨qk, x(s)⟩2⟨qk, Bu(s)⟩2 ec(t−s) ds
+(22)
+for all t ∈ [0, T] and u ∈ U, where c = max{0, 2(c2 − c1)}.
+Proof. We find inequalities for E
+�
+x(t)⊤Xx(t)
+�
+, where X ∈ {P −1, Q}. To do so, we apply Lemma
+A.1 to X
+1
+2 x(t) and obtain
+d
+dtE
+�
+x(t)⊤Xx(t)
+�
+= 2E
+�
+x(t)⊤X[Ax(t) + Bu(t) + f(x(t))]
+�
++
+d
+�
+i,j=1
+E
+�
+x(t)⊤N⊤
+i XNjx(t)
+�
+kij.
+We integrate this equation over [0, t] with t ≤ T yielding
+E
+�
+x(t)⊤Xx(t)
+�
+= E
+� t
+0
+�
+x(s)⊤�
+A⊤X + XA +
+d
+�
+i,j=1
+N⊤
+i XNjkij
+�
+x(s)
+�
+ds
++ 2
+� t
+0
+E
+�
+x(s)⊤X
+�
+Bu(s) + f(x(s))
+��
+ds
+≤ E
+� t
+0
+�
+x(s)⊤�
+(A + c1I)⊤X + X(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i XNjkij
+�
+x(s)
+�
+ds
++ 2
+� t
+0
+E
+�
+x(s)⊤XBu(s)
+�
+ds + c
+� t
+0
+E
+�
+x(s)⊤Xx(s)
+�
+ds
+(23)
+exploiting (16), (17) and that x0 = 0. Setting α(t) := 2
+� t
+0 E
+�
+x(s)⊤XBu(s)
+�
+ds and X = Q, we
+obtain
+E
+�
+x(t)⊤Qx(t)
+�
+≤ −
+� t
+0
+E
+�
+x(s)⊤C⊤Cx(s)
+�
+ds + 2
+� t
+0
+E
+�
+x(s)⊤QBu(s)
+�
+ds + c
+� t
+0
+E
+�
+x(s)⊤Qx(s)
+�
+ds
+= − ∥y∥2
+L2
+t + α(t) + c
+� t
+0
+E
+�
+x(s)⊤Qx(s)
+�
+ds
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+9
+using (12). Therefore, by (50), we have
+E
+�
+x(t)⊤Qx(t)
+�
+≤
+� t
+0
+( ˙α(s) − E ∥y(s)∥2
+2) ec(t−s) ds,
+and hence
+� t
+0 E ∥y(s)∥2
+2 ds ≤
+� t
+0 ˙α(s) ec(t−s) ds. Inserting the representation for x(s) in (20) yields
+∥y∥2
+L2
+t ≤ 2
+� t
+0
+E
+�
+x(s)⊤QBu(s)
+�
+ec(t−s) ds = 2
+� t
+0
+E
+��
+Q
+n
+�
+k=1
+⟨x(s), qk⟩2 qk
+�⊤
+Bu(s)
+�
+ec(t−s) ds
+= 2
+n
+�
+k=1
+λQ,k
+� t
+0
+E
+�
+⟨x(s), qk⟩2 q⊤
+k Bu(s)
+�
+ec(t−s) ds
+leading to (22). With X = P −1 in (23), it holds that
+E
+�
+x(t)⊤P −1x(t)
+�
+≤ −
+� t
+0
+E
+�
+x(s)⊤P −1BB⊤P −1x(s)
+�
+ds + 2
+� t
+0
+E
+�
+x(s)⊤P −1Bu(s)
+�
+ds
++ c
+� t
+0
+E
+�
+x(s)⊤P −1x(s)
+�
+ds
+= E
+� t
+0
+∥u(s)∥2
+2 − ∥B⊤P −1x(s) − u(s)∥2
+2ds + c
+� t
+0
+E
+�
+x(s)⊤P −1x(s)
+�
+ds
+exploiting (11). Applying (49), we obtain
+E
+�
+x(t)⊤P −1x(t)
+�
+≤ E
+� t
+0
+∥u(s)∥2
+2 ds +
+� t
+0
+� s
+0
+E ∥u(v)∥2
+2 dv c ec(t−s) ds
+≤ ect E
+� t
+0
+∥u(s)∥2
+2 ds.
+We further observe that
+⟨x(t), pk⟩2
+2 ≤ λP,k
+n
+�
+i=1
+λ−1
+P,i⟨x(t), pi⟩2
+2 = λP,k
+���
+n
+�
+i=1
+λ
+− 1
+2
+P,i ⟨x(t), pi⟩2 pi
+���
+2
+2 = λP,k
+���P − 1
+2 x(t)
+���
+2
+2
+= λP,k x(t)⊤P −1x(t),
+so that (21) follows. This concludes the proof.
+Estimate (21) tells us that the state variable is small in the direction of pk if λP,k is small and
+in case c T is not too large (c2 −c1 is supposed to be little). Consequently, these eigenspaces of P
+can be neglected in our considerations. The eigenspaces spanned by vectors qk that are associated
+to small eigenvalues of Q are also of minor relevance due to (22). This inequality shows that such
+qk barely contribute to the energy of the output y on each subinterval [0, t].
+Remark 4.8.
+• Following basically the same steps, the result of Theorem 4.7 holds also true
+if the more general notion of Gramians in Remark 4.6 is used.
+• Theorem 4.7 is formulated for u ∈ U since it is based on (16) and (17). This does not mean
+that a reduced order model based on neglecting eigenspaces of P and Q associated to small
+eigenvalues leads to a bad approximation for u ∈ L2
+T \ U. This is because (16) and (17)
+might still almost hold in that cases since suitable Gramians lead to GQ and GP −1 in (15)
+being small when they are positive. Then, the estimates in Theorem 4.7 will approximately
+hold.
+
+10
+M. REDMANN
+4.3
+Computation of monotonicity Gramians
+We aim to compute average monotonicity Gramians P and Q for a large set U of controls. We
+choose them as solutions to (11) and (12), so that GP −1 and GQ in (15) have a local maximum
+in the origin or a saddle point with very few increasing directions. Else, we might have several
+cases in which the monotonicity condition is immediately violated. This would not allow (16)
+and (17) to hold for a large U.
+On the other hand, it is essential that the area where the
+monotonicity condition is fulfilled clearly dominates the one where it does not hold. A possible
+and acceptable scenario in dimension n = 2 is illustrated in Figure 1. Here, the monotonicity gap
+GQ is depicted for f = f(2), c2 = cf = 1 and Q = [ 0.49426 0.58159
+0.58159 0.68542 ], a matrix with a large and a
+small eigenvalue. The blue color stands for small absolute values and red for large ones. GQ is
+non positive except for the black areas, where the monotonicity condition is slightly violated. In
+−2
+−1.5
+−1
+−0.5
+0
+0.5
+1
+1.5
+2
+−2
+−1.5
+−1
+−0.5
+0
+0.5
+1
+1.5
+2
+Figure 1: GQ for a special choice of Q, n = 2, f = f(2) and c2 = cf = 1. The area in black marks
+the regions, where GQ is positive.
+the following proposition, a simple criterion for local optimality for GP −1 and GQ is given.
+Proposition 4.9. Define the function g(x) = ⟨x, X(f(x) − c2x)⟩2 with a constant c2, f being
+twice differentiable and X > 0. We assume that
+fxj(x)|x=0 − c2ej = −˜c2ej
+(24)
+for all j ∈ {1, . . . , n} and ˜c2 > 0, where ej is the j-th unit vector in Rn. Then, g has a local
+maximum in x = 0.
+Proof. It is easy to check that x = 0 is an extreme value since gxi(x) = ⟨ei, X(f(x) − c2x)⟩2 +
+⟨x, X(fxi(x)−c2ei)⟩2 is zero at the origin. Moreover, we derive gxixj(x) = ⟨ei, X(fxj(x)−c2ej)⟩2+
+⟨ej, X(fxi(x)−c2ei)⟩2+⟨x, Xfxixj(x)⟩2. Therefore, we find
+�
+gxixj(0)
+�
+i,j=1,...,n = −2˜c2X < 0 which
+concludes the proof.
+Condition (24) is, e.g., satisfied if polynomials are considered. We can therefore observe that
+GP −1 and GQ have a local maximum for the choices of f given in Example 2.1 in case c2 is
+sufficiently large. In particular, we fix c2 ≥ cf, since this means that GP −1 and GQ are non-
+positive along the bases of eigenvectors used in (20). This is a consequence of assumption (3).
+Theorem 4.7 motivates to choose c1, so that c2 − c1 is a small positive number. If possible, we
+even set c1 = c2 providing c = 0. If c1 > 0, the possibility of this choice also depends on weather
+(8) is satisfied. We then compute the solution to (11) having a minimal trace and the solution to
+the equality in (12). This provides that GP −1 and GQ are non-positive on large parts of Rn for
+the particular functions introduced in Example 2.1 and only small positive values are taken on
+the other area. This leads to (16) and (17) for a large U. This is what we observe from numerical
+experiments, where A is a discrete Laplacian. Let us now briefly sketch how such a minimal trace
+monotonicity Gramian P is computed. We reformulate (11) by multiplying it with P from the
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+11
+left and from the right leading to
+(A + c1I)P + P(A + c1I)⊤ + BB⊤ +
+d
+�
+i,j=1
+PN⊤
+i P −1NjkijP ≤ 0.
+(25)
+Since �d
+i,j=1 PN⊤
+i kijP −1NjP = P [ N⊤
+1
+... N⊤
+d ] (K ⊗ P −1) [ N⊤
+1
+... N⊤
+d ]⊤ P, we obtain the following
+equivalent representation
+�(A + c1I)P + P(A + c1I)⊤ + BB⊤
+P [ N⊤
+1
+... N⊤
+d ]
+[ N⊤
+1
+... N⊤
+d ]⊤ P
+−K−1 ⊗ P
+�
+≤ 0
+(26)
+for (25) based on Schur complement conditions for the definiteness of a matrix. Here, we need to
+further assume that K is invertible. Now, we can use a linear matrix inequality solver to find a
+solution to the minimization of tr(P) subject to (26) and P > 0. In this paper, we use YALMIP
+and MOSEK [26, 22] for an efficient computation of P.
+In general, a good choice for P and Q guaranteeing (16) and (17) for many different controls
+always depends on the particular nonlinearity f. Therefore, no universal recommendation can be
+given here.
+4.4
+Extension under one-sided Lipschitz continuity
+Many functions f satisfying (3) are also one-sided Lipschitz continuous. However, we require an
+extended version of this continuity concept in the context of the error analysis in Section 6. In
+detail the following inequalities are supposed to hold:
+⟨x ± z, f(x) ± f(z)⟩2 ≤ cf ∥x ± z∥2
+2 ,
+(27)
+for all x, z ∈ Rn and a constant cf. Condition (27) will later inspire the extended definition of
+Gramians. Notice that one-sided Lipschitz continuity is defined with a minus in (27) but we
+additionally ask for this property when replacing each minus by a plus. In this context, let us
+look at the functions of Example 2.1 again. We begin with f(2) and f(3) and show that (27) is
+satisfied.
+Example 4.10. Inserting f(3)(x) = x − ∥x∥2
+2 x below yields
+⟨x ± z, f(3)(x) ± f(3)(z)⟩2 = ∥x ± z∥2
+2 − ⟨x ± z, ∥x∥2
+2 x ± ∥z∥2
+2 z⟩2.
+Now, we find that
+⟨x ± z, ∥x∥2
+2 x ± ∥z∥2
+2 z⟩2 = ∥x∥4
+2 + ∥z∥4
+2 ± ⟨x, z⟩2(∥x∥2
+2 + ∥z∥2
+2) ≥ ∥x∥4
+2 + ∥z∥4
+2 − 0.5(∥x∥2
+2 + ∥z∥2
+2)2
+= 0.5(∥x∥2
+2 − ∥z∥2
+2)2 ≥ 0
+and hence (27) holds with cf = 1 in case f = f(3). We obtain from f(2)(x) = x − x◦3 that
+⟨x − z, f(2)(x) − f(2)(z)⟩2 = ∥x − z∥2
+2 − ⟨x − z, x◦3 − z◦3⟩2.
+Since we have that
+⟨x − z, x◦3 − z◦3⟩2 =
+n
+�
+i=1
+(x4
+i + z4
+i − zix3
+i − xiz3
+i ) =
+n
+�
+i=1
+(xi − zi)2(x2
+i + z2
+i + zixi)
+≥
+n
+�
+i=1
+(xi − zi)20.5(x2
+i + z2
+i + 2zixi) ≥ 0,
+we obtain ⟨x−z, f(2)(x)−f(2)(z)⟩2 ≤ ∥x − z∥2
+2 and consequently the point symmetry of f(2) yields
+⟨x + z, f(2)(x) + f(2)(z)⟩2 = ⟨x − (−z), f(2)(x) − f(2)(−z)⟩2 ≤ ∥x − (−z)∥2
+2 = ∥x + z∥2
+2 .
+Therefore, cf = 1 in (27) for f = f(2).
+
+12
+M. REDMANN
+As we will see below, f(1) is also one-sided Lipschitz but (27) is not fulfilled if a plus is
+considered.
+Example 4.11. Using f(1)(x) = (1 + a)x◦2 − x◦3 − ax leads to
+⟨x − z, f(1)(x) − f(1)(z)⟩2 = −a ∥x − z∥2
+2 + ⟨x − z, (1 + a)(x◦2 − z◦2) − (x◦3 − z◦3)⟩2.
+We obtain that
+⟨x − z, (1 + a)(x◦2 − z◦2) − (x◦3 − z◦3)⟩2 =
+n
+�
+i=1
+[(1 + a)(x3
+i − zix2
+i − xiz2
+i + z3
+i ) − x4
+i + xiz3
+i + zix3
+i − z4
+i ]
+=
+n
+�
+i=1
+(xi − zi)2[(1 + a)(xi + zi) − x2
+i − z2
+i − xizi] ≤ (1 + a)2
+3
+∥x − z∥2
+2
+exploiting that (1 + a)(xi + zi) − x2
+i − z2
+i − xizi ≤ (1+a)2
+3
+for all i ∈ {1, . . . , n}. Therefore, we have
+⟨x − z, f(1)(x) − f(1)(z)⟩2 ≤ a2 − a + 1
+3
+∥x − z∥2
+2 .
+We observe that the one-sided Lipschitz constant is different from the monotonicity constant in
+Example 2.1. Moreover, we show that (27) does not hold with a plus. Let n = 1 and cf be an
+arbitrary constant. We fix x = 1 and z = ϵ − 1 with ϵ > 0. We obtain
+⟨x + z, f(1)(x) + f(1)(z)⟩2 = ϵ[−aϵ + (1 + a)(1 + (ϵ − 1)2) − (1 + (ϵ − 1)3)]
+= ϵ[2(1 + a) − ϵ3 + (4 + a)ϵ2 − (5 + 3a)ϵ] > cfϵ2 = cf ∥x + z∥2
+2 ,
+if ϵ is sufficiently small and a > −1.
+Motivated by the one-sided Lipschitz continuity (27), a Gramian based inner product shall
+preserve this property leading to the following extension of Definition 4.1.
+Definition 4.12. Let c1 and c2 be constants. Then, a pair of matrices (P, Q) with P, Q > 0 is
+called global one-sided Lipschitz Gramians if they satisfy (11), (12) and
+⟨x + z, P −1(f(x) + f(z))⟩2 ≤ c2∥P − 1
+2 (x + z)∥2
+2,
+⟨x − z, Q(f(x) − f(z))⟩2 ≤ c2∥Q
+1
+2 (x − z)∥2
+2
+(28)
+for all x, z ∈ Rn.
+Example 4.13. Let P, Q > 0 be solutions to (11), (12) and f be globally Lipschitz with −f(x) =
+f(−x).
+Then, we can always construct global one-sided Lipschitz Gramians, since for X ∈
+{P −1, Q} satisfying (11) and (12), we have that
+⟨X
+1
+2 (x ± z), X
+1
+2 (f(x) ± f(z))⟩2 ≤ ∥X
+1
+2 (x ± z)∥2∥X
+1
+2 (f(x) ± f(z))∥2 ≤ c2∥X
+1
+2 (x ± z)∥2
+2
+for some suitable constant c2.
+If (28) is satisfied for z = 0, P and Q are global monotonicity Gramians. We will see later
+that a reduced order model based on the Gramians introduced in Definition 4.12 will lead to error
+estimates for all controls u ∈ L2
+T . However, as in the global monotonicity Gramian case, it might
+be inefficient to choose a Gramian allowing to derive estimates for all u. The error analysis will
+show that it is actually enough to have (28) for large/essential sets of pairs (x, z) ∈ Rn × Rn in
+order to find a reasonable error criterion for a large number of different controls, i.e., the one-sided
+Lipschitz gaps
+G+
+P −1(x, z) := ⟨x + z, P −1(f(x) + f(z))⟩2 − c2∥P − 1
+2 (x + z)∥2
+2,
+G−
+Q(x, z) := ⟨x − z, Q(f(x) − f(z))⟩2 − c2∥Q
+1
+2 (x − z)∥2
+2
+(29)
+in (28) are mainly negative but also small positive values will be allowed.
+We postpone the
+discussion of a weaker version of Definition 4.12 to Section 6.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+13
+Remark 4.14. One-sided Lipschitz Gramians are again special solutions of linear matrix in-
+equalities for reasons of accessibility. Analogue to Remark 4.6 this concept can be formulated
+more generally. Adding twice (28) to the respective inequality in (11) and (12) leads to
+(x + z)⊤�
+A⊤P −1 + P −1A +
+d
+�
+i,j=1
+N⊤
+i P −1Njkij
+�
+(x + z) + 2⟨x + z, P −1(f(x) + f(z))⟩2
+(30)
+≤ −∥B⊤P −1(x + z)∥2
+2 + c∥P − 1
+2 (x + z)∥2
+2,
+(x − z)⊤�
+A⊤Q + QA +
+d
+�
+i,j=1
+N⊤
+i QNjkij
+�
+(x − z) + 2⟨x − z, Q(f(x) − f(z))⟩2
+(31)
+≤ −∥C(x − z)∥2
+2 + c∥Q
+1
+2 (x − z)∥2
+2
+for all x, z ∈ Rn with c ≥ 0. We will see that this structure is what one requires to achieve a
+suitable global error bound for all u ∈ L2
+T . Notice that z = 0 leads to (18) and (19), respectively.
+We will not discuss a definition of Gramians P and Q via (30) and (31) in further detail but will
+refer to them within the error analysis.
+Now, let us briefly discuss the existence of global one-sided Lipschitz Gramians.
+Proposition 4.15. Given a matrix X > 0 satisfying (9) for some constant c1 and
+⟨x ± z, X(f(x) ± f(z))⟩2 ≤ c2∥X
+1
+2 (x ± z)∥2
+2
+for all x, z ∈ Rn and a constant c2. Then, global one-sided Lipschitz Gramians exist with these
+constants.
+Proof. The proof uses the same argument as in Proposition 4.2 and is therefore omitted.
+Example 4.11 indicates that the global one-sided Lipschitz Gramian P might not be well-
+defined in case f = f(1).
+5
+Particular reduced order model
+We select a nonsingular S ∈ Rn×n that we use to simultaneously diagonalize Gramians P and
+Q. This means that the bases of eigenvectors (pk) and (qk) in (20) will be the canonical basis of
+Rn. Consequently, by Theorem 4.7, unimportant directions can be identified with components in
+the transformed state variable that are associated with small diagonal entries of the diagonalized
+Gramians. In particular, the transformation matrix defines the new state by xn = Sx. Inserting
+this into (1) leads to an equivalent stochastic system with coefficients
+(An, Bn, fn, Nn,i, Cn) := (SAS−1, SB, Sf(S−1·), SNiS−1, CS−1)
+(32)
+instead of the original ones (A, B, f, Ni, C), i.e.,
+dxn(t) = [Anxn(t) + Bnu(t) + fn (xn(t))]dt +
+d
+�
+i=1
+Nn,i (xn(t−)) dMi(t),
+y(t) = Cnxn(t),
+(33)
+with t ∈ [0, T] and xn(0) = 0. The new system (33) has the same input u and output y. Moreover,
+properties like asymptotic stability are not affected. However, the Gramians are different. These
+are given in the following proposition, where the precise diagonalizing transformation is stated.
+Proposition 5.1. Suppose that S is an invertible matrix. If P and Q are global/average mono-
+tonicity or one-sided Lipschitz Gramians of (1) according to Definitions 4.1, 4.5 or 4.12. Then,
+Pn = SPS⊤ and Qn = S−⊤QS−1 are the respective Gramians in the transformed setting (33).
+
+14
+M. REDMANN
+Given that P, Q > 0, we find that Pn = Qn = Σn = diag(σ1, . . . , σn) using the balancing transfor-
+mation
+S = Σ
+1
+2nU ⊤L−1
+P ,
+(34)
+where P = LP L⊤
+P and L⊤
+P QLP = UΣ2
+nU ⊤ is a spectral factorization with an orthogonal U.
+Proof. We multiply (11) and (12) with S−⊤ from the left and with S−1 from the right hand side.
+Consequently, we see that SPS⊤ and S−⊤QS−1 satisfy these inequalities under the coefficients
+in (32). Moreover, (13) is preserved under this transformation, since
+⟨x, P −1
+n fn(x)⟩2 = ⟨x, S−⊤P −1S−1Sf(S−1x)⟩2 = ⟨S−1x, P −1f(S−1x)⟩2 ≤ c2∥P − 1
+2 S−1x∥2
+2
+= c2∥P
+− 1
+2
+n
+x∥2
+2
+and
+⟨x, Qnfn(x)⟩2 = ⟨x, S−⊤QS−1Sf(S−1x)⟩2 = ⟨S−1x, Qf(S−1x)⟩2 ≤ c2∥Q
+1
+2 S−1x∥2
+2 = c2∥Q
+1
+2nx∥2
+2.
+Analogue, we can prove that the one-sided Lipschitz conditions (28) hold under the transforma-
+tion. With xn(s) = xn(s, 0, u) given u ∈ U, we now find
+⟨xn(s), P −1
+n fn(xn(s))⟩2 = ⟨x(s), P −1f(x(s))⟩2
+and
+⟨xn(s), Qnfn(xn(s))⟩2 = ⟨x(s), Qf(x(s))⟩2,
+as well as
+∥P
+− 1
+2
+n
+xn(s)∥2
+2 = ∥P − 1
+2 x(s)∥2
+2
+and
+∥Q
+− 1
+2
+n xn(s)∥2
+2 = ∥Q
+1
+2 x(s)∥2
+2,
+so that the average monotonicity conditions (16) and (17) still hold for the same set U. We use
+(34) and obtain Pn = Σ
+1
+2nU ⊤L−1
+P PL−⊤
+P UΣ
+1
+2n = Σn as well as Qn = Σ
+− 1
+2
+n U ⊤L⊤
+P QLP UΣ
+− 1
+2
+n
+= Σn
+which concludes the proof.
+We observe that the diagonal entries of the balanced Gramians are σi =
+�
+λi(PQ).
+We
+call them Hankel singular values (HSVs) from now on. Now, we partition the balanced state
+xn =
+�xn,1
+xn,2
+�
+and Σn = diag(Σr, Σ2,n−r), where Σr = diag(σ1, . . . , σr) contains the large and
+Σ2,n−r = diag(σr+1, . . . , σn), r < n, the small HSVs. The same is done for (32) yielding
+An =
+�Ar
+⋆
+⋆
+⋆
+�
+,
+Bn =
+�Br
+⋆
+�
+,
+Nn,i =
+�Nr,i
+⋆
+⋆
+⋆
+�
+,
+Cn =
+�
+Cr
+⋆
+�
+and
+fr(xr) : = ˜fr([ xr
+0 ]),
+where
+fn =
+� ˜fr
+⋆
+�
+,
+xr ∈ Rr,
+0 ∈ Rn−r.
+(35)
+Since xn,2 is associated to small values in Σ2,n−r, we truncate the equation for these variables
+and remove them from the dynamics of xn,1 and y. This results in a reduced system (5) with
+coefficients given by (35). Setting V = Vr and W = Wr, where
+S−1 =
+�
+Vr
+⋆
+�
+and
+S⊤ =
+�
+Wr
+⋆
+�
+,
+we see that our reduced system’s structure is of the form as in (6). Here, S is given by (34).
+6
+Error analysis of Gramian based reduced system
+We consider the reduced system (5) with state dimension r and coefficients like in (35).
+As
+an intermediate step, let us introduce the same type of reduced model with dimension k =
+r, r + 1, . . . , n which we write as follows:
+dxk(t) = [Akxk(t) + Bku(t) + fk(xk(t))]dt +
+d
+�
+i=1
+Nk,ixk(t−)dMi(t),
+yk(t) = Ckxk(t).
+(36)
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+15
+Setting yn := y, we then observe that
+∥y − yr∥ ≤
+n
+�
+i=r+1
+∥yk − yk−1∥ ,
+(37)
+where ∥·∥ is some function space norm.
+This means that we have to investigate the error
+∥yk − yk−1∥ of removing a single HSV. We can derive the reduced system of order k −1 from (36)
+by setting the last entry of xk equal to zero. Doing so, we obtain
+d
+�
+xk−1(t)
+0
+�
+=
+�
+Ak
+�
+xk−1(t)
+0
+�
++ Bku(t) + fk
+� �
+xk−1(t)
+0
+� �
+−
+�
+0
+v0(t)
+� �
+dt
++
+d
+�
+i=1
+�
+Nk,i
+�
+xk−1(t−)
+0
+�
+−
+�
+0
+vi(t−)
+� �
+dMi(t),
+yk−1(t) = Ck
+�
+xk−1(t)
+0
+�
+,
+(38)
+where the first k − 1 rows in the state equation of (38) represent the reduced order model of
+dimension k − 1 and v0, . . . , vd are (non specified) scalar processes that are introduced to ensure
+the equality in the last line which can be read as d0 = 0dt + �d
+i=1 0dMi(t).
+Theorem 6.1. Let y be the output of (1) with x(0) = 0 and given the r-dimensional reduced
+system (5) with output yr, coefficients as in (35) and xr(0) = 0. If this reduced system is based
+on Gramians P and Q satisfying (11) and (12) for a constant c1. Then, for all u ∈ L2
+T , we have
+�
+E
+� T
+0
+∥y(s) − yr(s)∥2
+2 ec(T−s) ds ≤
+n
+�
+k=r+1
+�
+E
+� T
+0
+�
+2G−
+Q
+�
+Vkxk(s), Vk−1xk−1(s)
+�
++ σ2
+k
+�
+2G+
+P −1
+�
+Vkxk(s), Vk−1xk−1(s)
+�
++ 4 ∥u(s)∥2
+2
+��
+ec(T−s) ds.
+where c = max{0, 2(c2 − c1)} is defined by another constant c2 (e.g. the parameter of Definitions
+4.1, 4.5 or 4.12) and G+
+P −1, G−
+Q are the associated one-sided Lipschitz gaps in (29). Moreover, xk
+is the reduced state variable of order k = r, r + 1. . . . , n and Vk is the associated projection matrix
+being the first k columns of the inverse S−1 of the balancing transformation defined by (34).
+Corollary 6.2. Given the assumptions of Theorem 6.1, let P and Q be global one-sided Lipschitz
+Gramians according to Definition 4.12. Then, the following bound holds:
+�
+E
+� T
+0
+∥y(s) − yr(s)∥2
+2 ec(T−s) ds ≤ 2
+n
+�
+k=r+1
+σk
+�
+E
+� T
+0
+∥u(s)∥2
+2 ec(T−s) ds
+(39)
+for all u ∈ L2
+T . The same bound is established if the Gramians are defined by (30) and (31).
+Proof. The functions G+
+P −1 and G−
+Q are non positive by construction of the global one-sided
+Lipschitz Gramians. Consequently, the result immediately follows from the one of Theorem 6.1.
+It is not an immediate consequence of Theorem 6.1 that (30) and (31) lead to the same result.
+However, the proof uses exactly the same ideas. Therefore, it is omitted.
+Remark 6.3.
+• We found the classical bound for reduced order systems based on balanced
+truncation in Corollary 6.2 up to the exponential terms in (39), see [10, 11] for the deter-
+ministic and [4] for the stochastic linear case. As mentioned before, choices of Gramians
+are only acceptable if c is sufficiently small, i.e., the exponentials do not dominate. On the
+other hand, global one-sided Lipschitz Gramians might not be a optimal in terms of their
+spectrum, so that a weaker concept is more reasonable.
+
+16
+M. REDMANN
+• As mentioned in Section 4.4, we can allow for small positive one-sided Lipschitz gaps G−
+Q
+and G+
+P −1, see (29), in certain (small) regions. If we pick P and Q accordingly, Theorem
+6.1 then tells us that the averages
+E
+� T
+0
+G−
+Q
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ec(T−s) ds
+and
+E
+� T
+0
+G+
+P −1
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ec(T−s) ds
+will be non positive for a large number of controls u ∈ L2
+T and slightly positive in many of
+the other scenarios. This means that (39) will (approximately) hold for many controls.
+• In case we have a priori information concerning the solution space of the system, we can say
+even more. This is given if P and Q are monotonicity Gramians according to Definitions
+4.1 or 4.5, because of (21) in Theorem 4.7. This estimate provides that we obtain a small
+state approximation error, i.e., x(t) ≈ Vkxk(t) for k ∈ {r, . . . , n − 1}, if the truncated HSVs
+σk+1, . . . , σn are of low order. In particular, we have Vk+1xk+1(t) ≈ Vkxk(t) since this is the
+error of just removing σk+1. Therefore, we can conclude that we need G−
+Q and G+
+P −1 to be
+mainly negative solely on sets of pairs (x, z) ∈ Rn×Rn with x ≈ z. In general, monotonicity
+Gramians do not ensure (39), but due to the continuity of f, we can say that
+E
+� T
+0
+G−
+Q
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ec(T−s) ds ≈ E
+� T
+0
+G−
+Q
+�
+Vkxk(s), Vkxk(s)
+�
+ec(T−s) ds = 0,
+E
+� T
+0
+G+
+P −1
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ec(T−s) ds ≈ E
+� T
+0
+G+
+P −1
+�
+Vkxk(s), Vkxk(s)
+�
+�
+��
+�
+= 4GP −1
+�
+Vkxk(s)
+�
+ec(T−s) ds.
+Now, the monotonicity gap GP −1 defined in (15) is non positive on average for u ∈ U
+by construction of the average monotonicity Gramian P. This ensures that the bound of
+Corollary 6.2 might still deliver a reasonable error criterion although it does not hold.
+Proof of Theorem 6.1. We introduce x−(t) := xk(t) −
+�
+xk−1(t)
+0
+�
+and x+(t) := xk(t) +
+�
+xk−1(t)
+0
+�
+,
+for which the dynamics are obtained by subtracting/adding (36) and (38), i.e.,
+dx−(t) = [Akx−(t) +
+�
+0
+v0(t)
+�
++ fk(xk(t)) − fk
+�� xk−1(t)
+0
+��]dt +
+d
+�
+i=1
+�Nk,ix−(t−) +
+�
+0
+vi(t−)
+� �dMi(t)
+(40)
+dx+(t) = [Akx+(t) + 2Bku(t) −
+�
+0
+v0(t)
+�
++ fk(xk(t)) + fk
+�� xk−1(t)
+0
+��]dt +
+d
+�
+i=1
+�Nk,ix+(t−) −
+�
+0
+vi(t−)
+� �dMi(t)
+(41)
+Recalling that Σk = diag(σ1, . . . , σk) denotes the diagonal matrix of the k largest HSVs of the
+original system, we know, by Proposition 5.1, that Σn satisfies (11) and (12) with the balanced
+realization (32). Evaluating the left upper k × k block of the equations associated to Σn, we
+obtain
+(Ak + c1I)⊤Σ−1
+k
++ Σ−1
+k (Ak + c1I) +
+d
+�
+i,j=1
+N⊤
+k,iΣ−1
+k Nk,jkij ≤ −Σ−1
+k BkB⊤
+k Σ−1
+k ,
+(42)
+(Ak + c1I)⊤Σk + Σk(Ak + c1I) +
+d
+�
+i,j=1
+N⊤
+k,iΣkNk,jkij ≤ −C⊤
+k Ck.
+(43)
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+17
+Taking (40) into account, Lemma A.1 is applied to Σ
+1
+2
+k x−(t) to obtain
+d
+dtE
+�
+x−(t)⊤Σkx−(t)
+�
+=2E
+�
+x−(t)⊤Σk[Akx−(t) +
+�
+0
+v0(t)
+�
++ fk(xk(t)) − fk
+�� xk−1(t)
+0
+��]
+�
++
+d
+�
+i,j=1
+E
+��
+Nk,ix−(t) +
+�
+0
+vi(t)
+� �⊤Σk
+�
+Nk,jx−(t) +
+�
+0
+vj(t)
+� ��
+kij.
+Integrating this equation over [0, t] with t ≤ T yields
+E
+�
+x−(t)⊤Σkx−(t)
+�
+= E
+� t
+0
+x−(s)⊤�
+A⊤
+k Σk + ΣkAk +
+d
+�
+i,j=1
+N⊤
+k,iΣkNk,jkij
+�
+x−(s)ds
++ 2E
+� t
+0
+x−(s)⊤Σk
+�
+fk(xk(s)) − fk
+�� xk−1(s)
+0
+���ds + R−(t),
+where R−(t) = E
+� t
+0 2x−(s)⊤Σk
+�
+0
+v0(s)
+�
++�d
+i,j=1
+�
+2Nk,ix−(s) +
+�
+0
+vi(s)
+��⊤
+Σk
+�
+0
+vj(s)
+�
+kijds. Let xk,2
+be the last entry of xk and hence also of x−. Moreover, nk,i shall denote the last line of Nk,i. There-
+fore, we obtain that x−(s)⊤Σk
+�
+0
+v0(s)
+�
+= σkxk,2(s)v0(s) and
+�
+2Nk,ix−(s) +
+�
+0
+vi(s)
+��⊤
+Σk
+�
+0
+vj(s)
+�
+kij =
+σk (2nk,ix−(s) + vi(s)) vj(s)kij. By construction of vi in (38), we have −2nk,i
+�
+xk−1(s)
+0
+�
++2vi(s) =
+0, so that σk (2nk,ix−(s) + vi(s)) vj(s)kij = σk (2nk,ixk(s) − vi(s)) vj(s)kij. Therefore, it holds
+that
+R−(t) ≤ σkE
+� t
+0
+2xk,2(s)v0(s) +
+d
+�
+i,j=1
+(2nk,ixk(s) + vi(s)) vj(s)kijds
+exploiting that �d
+i,j=1 vi(s)vj(s)kij ≥ 0, because K = (kij) is positive semidefinite. Hence,
+E
+�
+x−(t)⊤Σkx−(t)
+�
+≤ E
+� t
+0
+x−(s)⊤�
+(Ak + c1I)⊤Σk + Σk(Ak + c1I) +
+d
+�
+i,j=1
+N⊤
+k,iΣkNk,jkij
+�
+x−(s)ds
++ 2E
+� t
+0
+x−(s)⊤Σk
+�
+fk(xk(s)) − fk
+�� xk−1(s)
+0
+�� − c2x−(s)
+�ds
++ σkE
+� t
+0
+2xk,2(s)v0(s) +
+d
+�
+i,j=1
+(2nk,ixk(s) + vi(s)) vj(s)kijds
++ c
+� t
+0
+E
+�
+x−(s)⊤Σkx−(s)
+�
+ds.
+We set Tk,−(t) := 2E
+� t
+0 x−(s)⊤Σk
+�
+fk(xk(s))−fk
+�� xk−1(s)
+0
+��−c2x−(s)
+�ds and αk(t) := E
+� t
+0 2xk,2(s)v0(s)+
+�d
+i,j=1 (2nk,ixk(s) + vi(s)) vj(s)kijds. Based on (43) combined with the definitions of the outputs
+in (36) and (38), we have
+E
+�
+x−(t)⊤Σkx−(t)
+�
+≤ − ∥yk − yk−1∥2
+L2
+t + Tk,−(t) + σkαk(t) + c
+� t
+0
+E
+�
+x−(s)⊤Σkx−(s)
+�
+ds.
+We obtain by (50) that
+E
+� t
+0
+∥yk(s) − yk−1(s)∥2
+2 ec(t−s) ds ≤
+� t
+0
+� ˙Tk,−(s) + σk ˙αk(s)
+�
+ec(t−s) ds.
+(44)
+
+18
+M. REDMANN
+Now, exploiting Lemma A.1 for the process Σ
+− 1
+2
+k x+(t) together with (41) yields
+E
+�
+x+(t)⊤Σ−1
+k x+(t)
+�
+= E
+� t
+0
+x+(s)⊤�
+A⊤
+k Σ−1
+k
++ Σ−1
+k Ak +
+d
+�
+i,j=1
+N⊤
+k,iΣ−1
+k Nk,jkij
+�
+x+(s)ds
++ 2E
+� t
+0
+x+(s)⊤Σ−1
+k
+�
+fk(xk(s)) + fk
+�� xk−1(s)
+0
+���ds
++ E
+� t
+0
+4x+(s)⊤Σ−1
+k Bku(s)ds − R+(t),
+where R+(t) = E
+� t
+0 2x+(s)⊤Σ−1
+k
+�
+0
+v0(s)
+�
++ �d
+i,j=1
+�
+2Nk,ix+(s) −
+�
+0
+vi(s)
+��⊤
+Σ−1
+k
+�
+0
+vj(s)
+�
+kijds. We
+observe that x+(s)⊤Σ−1
+k
+�
+0
+v0(s)
+�
+= σ−1
+k xk,2v0(s) and
+�
+2Nk,ix+(s) −
+�
+0
+vi(s)
+��⊤
+Σ−1
+k
+�
+0
+vj(s)
+�
+kij =
+σ−1
+k (2nk,ix+(s)−vi(s))vj(s)kij = σ−1
+k (2nk,ixk(s)+vi(s))vj(s)kij telling us that R+(t) = σ−1
+k αk(t).
+Defining Tk,+(t) := 2E
+� t
+0 x+(s)⊤Σ−1
+k
+�
+fk(xk(s)) + fk
+�� xk−1(s)
+0
+�� − c2x+(s)
+�ds results in
+E
+�
+x+(t)⊤Σ−1
+k x+(t)
+�
+= E
+� t
+0
+x+(s)⊤�
+(Ak + c1I)⊤Σ−1
+k
++ Σ−1
+k (Ak + c1I) +
+d
+�
+i,j=1
+N⊤
+k,iΣ−1
+k Nk,jkij
+�
+x+(s)ds
++ Tk,+(t) + E
+� t
+0
+4x+(s)⊤Σ−1
+k Bku(s)ds − σ−1
+k αk(t)
++ c
+� t
+0
+E
+�
+x+(s)⊤Σ−1
+k x+(s)
+�
+ds.
+We exploit the estimate
+4 ∥u(s)∥2
+2 ≥ ∥2u(s)∥2
+2 −
+���B⊤
+k Σ−1
+k x+(s) − 2u(s)
+���
+2
+2
+= −x+(s)⊤Σ−1
+k BkB⊤
+k Σ−1
+k x+(s) + 4x+(s)⊤Σ−1
+k Bku(s)
+and insert (42) in order to find
+E
+�
+x+(t)⊤Σ−1
+k x+(t)
+�
+≤ 4 ∥u∥2
+L2
+t + Tk,+(t) − σ−1
+k αk(t) + c
+� t
+0
+E
+�
+x+(s)⊤Σ−1
+k x+(s)
+�
+ds.
+We apply (50) providing
+� t
+0
+˙αk(s) ec(t−s) ds ≤ σk
+� t
+0
+� ˙Tk,+(s) + 4E ∥u(s)∥2
+2
+�
+ec(t−s) ds.
+Combining this with (44) leads to
+E
+� t
+0
+∥yk(s) − yk−1(s)∥2
+2 ec(t−s) ds ≤
+� t
+0
+�
+˙Tk,−(s) + σ2
+k
+� ˙Tk,+(s) + 4E ∥u(s)∥2
+2
+��
+ec(t−s) ds.
+The last step is to find different representations for Tk,− and Tk,+ inserting the definitions of x+
+and x−. We recall that fk(xk) := ˜fk(
+�
+xk
+0n−k
+�
+), xk ∈ Rk and 0n−k ∈ Rn−k by (35). Since ˜fk are
+the first k entries of the balanced nonlinearity fn, we have
+�
+xk(s) ±
+� xk−1(s)
+0
+��⊤Dk
+�fk(xk(s)) ± fk
+�� xk−1(s)
+0
+�� − c2
+�xk(s) ±
+� xk−1(s)
+0
+���
+=
+��
+xk(s)
+0n−k
+�
+±
+�
+xk−1(s)
+0n−k+1
+��⊤Dn
+�fn(
+�
+xk(s)
+0n−k
+�
+) ± fn
+��
+xk−1(s)
+0n−k+1
+�� − c2
+��
+xk(s)
+0n−k
+�
+±
+�
+xk−1(s)
+0n−k+1
+���,
+where Dk ∈ {Σk, Σ−1
+k }. By Proposition 5.1 and (32), we know that Σn = S−⊤QS−1, Σ−1
+n
+=
+S−⊤P −1S−1 and fn = Sf(S−1·).
+Moreover, S−1�
+xk(s)
+0n−k
+�
+= Vkxk(s), since Vk are the first k
+columns of the inverse S−1 of the balancing transformation. Hence,
+Tk,−(t) = 2E
+� t
+0
+G−
+Q
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ds,
+Tk,+(t) = 2E
+� t
+0
+G+
+P −1
+�
+Vkxk(s), Vk−1xk−1(s)
+�
+ds
+according to the definition of the one-sided Lipschitz gaps in (29). This concludes the proof using
+(37) and setting t = T.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+19
+7
+Numerical experiments
+Below, let L > 0 defining a “step size” parameter h :=
+L
+(n+1). Based on this, we introduce a grid
+by ζj = jh for j = 0, 1, . . . , n + 1. Now, we mainly focus on an example for (1) that is given by
+dx1(t) =
+�x2(t) − 2x1(t)
+h2
++ u1(t)
+h2
++ f(x1(t))
+�
+dt +
+d
+�
+i=1
+gi(ζ1)x1(t−)dMi(t),
+dxj(t) =
+�xj+1(t) − 2xj(t) + xj−1(t)
+h2
++ f(xj(t))
+�
+dt +
+d
+�
+i=1
+gi(ζj)xj(t−)dMi(t),
+dxn(t) =
+�−2xn(t) + xn−1(t)
+h2
++ u2(t)
+h2
++ f(xn(t))
+�
+dt +
+d
+�
+i=1
+gi(ζn)xn(t−)dMi(t)
+(45)
+for j ∈ {2, . . . , n − 1}. We have that u = [ u1
+u2 ] (m = 2) and f(x) = [ f(x1) ... f(xn) ]⊤, where f and
+gi are scalar functions. Formally, (45) can interpreted as a finite difference discretization of the
+stochastic reaction diffusion equation
+dvt(ζ) =
+� ∂2
+∂ζ2 vt(ζ) + f
+�
+vt(ζ)
+��
++
+d
+�
+i=1
+gi(ζ)vt−(ζ)dMi(t),
+ζ ∈ (0, L),
+t ∈ (0, T),
+v0(ζ) ≡ 0,
+vt(0) = u1(t)
+and
+vt(L) = u2(t)
+(46)
+with controlled boundaries and the intuition that xj(t) ≈ vt(ζj). Let us specify the other pa-
+rameter and the noise profile. Below, M is a Wiener process in dimension d = 2 with covariance
+K =
+�
+1
+−0.5
+−0.5
+1
+�
+and n = 100. We study the nonlinearities f(v) = (1+a)v2 −v3 −av with a = 0.1
+and f(v) = v − v3, so that f = f(1) or f = f(2) introduced in Example 2.1. The particular noise
+scaling functions are g1(ζ) = 4 sin(ζ) and g2(ζ) = 4 cos(ζ). Moreover, the terminal time is T = 1
+and the quantity of interest shall be the following average:
+y(t) = 1
+n
+n
+�
+j=1
+xj(t).
+(47)
+For illustration we show two typical paths of (47) for f = f(1), f(2) and two different inputs in
+Figures 2 and 3.
+0
+0.2
+0.4
+0.6
+0.8
+1
+−1
+0
+1
+2
+3
+Time t
+Output path y(·, ω)
+Figure 2: Path of (47) with f = f(1) and
+u = ˜u in (48).
+0
+0.2
+0.4
+0.6
+0.8
+1
+−2
+−1.5
+−1
+−0.5
+0
+0.5
+Time t
+Output path y(·, ω)
+Figure 3: Path of (47) with f = f(2) and
+u = ˆu in (48).
+For f = f(2), we know that (10) holds with X = I and c2 ≥ cf = 1. Further, we observe
+that (9) is true for X = I and c1 = cf = 1. Therefore, the system is globally mean square
+asymptotically stable according to Theorem 3.2 and the concept of monotonicity Gramians with
+
+20
+M. REDMANN
+c1 = c2 = 1 is well-defined by Proposition 4.2. We can even guarantee the existence of a one-sided
+Lipschitz Gramian by Proposition 4.15 since the one-sided Lipschitz condition (27) holds with
+cf = 1 using Example 4.10. The choice of f = f(2) also yields a mean square asymptotically
+stable system since (9) particularly holds for X = I if c1 = cf =
+(a−1)2
+4
+= 0.20250 is used
+and since we know, by Example 2.1, that (10) is true setting X = I and c2 ≥ cf. Therefore,
+monotonicity Gramians also exist here for c1 = c2 = 0.20250. On the other hand, a one-sided
+Lipschitz Gramian Q exists with c1 = c2 = a2−a+1
+3
+= 0.30¯3 due to Proposition 4.15 (X = I)
+exploiting Example 4.11. The same example, however, indicates that P might not be available
+as a one-sided Lipschitz Gramian.
+The goal of this section is to construct average monotonicity Gramians P and Q according
+to Definition 4.5 for a large set of controls U. In detail, we choose the monotonicity/one-sided
+Lipschitz constant to define c1 = c2 = 1 for f = f(2) and we set c1 = c2 = 0.30¯3 for f = f(1) which
+is a number dominating the monotonicity constant 0.20250. Consequently, Theorems 4.7 and 6.1
+hold for c = 0. We choose Q to be the solution to the equality in (12) and P the candidate with
+minimal trace satisfying (11). We refer to Section 4.3 for the particular computation strategy.
+We observe that these P and Q do not satisfy (13) for all x ∈ Rn but for the essential ones.
+In fact, we run experiments for a large variety of controls involving increasing, decreasing and
+(highly) oscillating u as well as a combination of all of them. In all cases, conditions (16) and
+(17) were fulfilled indicating that these P and Q are average monotonicity Gramians for a large
+set of controls U ⊂ L2
+T . We present the experiments solely for two representatives ˜u, ˆu ∈ U which
+are given by
+˜u(t) =
+�
+−3 cos(20t)
+2 sin(10t)
+�
+and
+ˆu(t) =
+�
+−3 e−t
+2
+√
+t
+�
+.
+(48)
+These are chosen since they also steer the state x(t) to regions of Rn, where the monotonicity
+conditions in (13) are violated. The constructed monotonicity Gramians have the advantage that
+the HSVs provide a reliable criterion for the reduction error according to Theorem 4.7. Here,
+we have c = 0. We depict these algebraic values for f = f(1) in Figure 4 and observe a strong
+decay telling us that we can expect a low approximation error for small r. The HSVs for f = f(2)
+behave very similarly and are therefore omitted. As discussed in Remark 6.3, we cannot expect
+1
+20
+40
+60
+80
+100
+0
+−5
+−10
+−15
+−20
+−25
+−30
+i (index)
+log10
+��
+λi(PQ)
+�
+Figure 4: Logarithmic HSVs based on monotonicity Gramians for f = f(1) with c1 = c2 = 0.30¯3,
+where Q satisfies the equality in (12) and P is the minimal trace solution of (11).
+the bound in Corollary 6.2 (with c = 0) to hold if average monotonicity Gramians are used.
+However, we expect the error to not be far from this bound, since the one-sided Lipschitz gaps
+G+
+P −1 and G−
+Q in Theorem 6.1 are expected to be small when they are positive. We compute the
+output yr of the reduced order model (5) introduced in Section 5 for different reduced dimensions
+r = 3, 6, 10, 20. The relative output error for f = f(1) can be found in Table 1 for the controls
+˜u and ˆu. We observe a decreasing behaviour for growing r yielding a very high accuracy for
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+21
+∥y − yr∥L2
+T / ∥y∥L2
+T for f = f(1)
+r
+u = ˜u
+u = ˆu
+3
+4.4077e−02
+3.8041e−02
+6
+4.0903e−03
+3.7334e−03
+10
+3.1233e−04
+2.5745e−04
+20
+2.7327e−07
+3.5013e−07
+Table 1: Relative output error dimension
+reduction with controls in (48) and f = f(1).
+2 �n
+k=r+1 σk ∥u∥L2
+T / ∥y∥L2
+T for f = f(1)
+r
+u = ˜u
+u = ˆu
+3
+aa 1.0240e−01aa
+1.8031e−01
+6
+aa 8.6029e−03 aa
+1.5112e−02
+10
+aa 4.6198e−04 aa
+8.1347e−04
+20
+aa 1.3487e−07 aa
+2.3709e−07
+Table 2: Relative error criterion of Corollary 6.2
+with c = 0 and f = f(1).
+∥y − yr∥L2
+T / ∥y∥L2
+T for f = f(2)
+r
+u = ˜u
+u = ˆu
+3
+4.3380e−02
+3.5840e−02
+6
+3.7409e−03
+2.9983e−03
+10
+3.1507e−04
+2.3924e−04
+20
+1.8514e−07
+3.8720e−07
+Table 3: Relative output error dimension
+reduction with controls in (48) and f = f(2).
+2 �n
+k=r+1 σk ∥u∥L2
+T / ∥y∥L2
+T for f = f(2)
+r
+u = ˜u
+u = ˆu
+3
+aa1.0494e−01aa
+1.6369e−01
+6
+aa7.2186e−03 aa
+1.3624e−02
+10
+aa4.7378e−04aa
+7.3326e−04
+20
+aa1.3493e−07aa
+2.1019e−07
+Table 4: Relative error criterion of Corollary 6.2
+with c = 0 and f = f(2).
+r ≥ 6. Table 2 shows the bound of Corollary 6.2 which generally is no upper bound for the error
+calculated in Table 1, see the case of r = 20. This is because the one-sided Lipschitz gaps are not
+always non positive. However, 2 �n
+k=r+1 σk is close to the actual error. This is an observation
+made also in additional simulations that are not presented here. The intuition for 2 �n
+k=r+1 σk
+being an upper bound for dimensions r = 3, 6, 10 but not for r = 20 might be the low order of
+a positive one-sided Lipschitz gap. For that reason, it becomes only visible when 2 �n
+k=r+1 σk is
+very small. We repeat the error calculations for f = f(2) and obtain basically the same results,
+see Tables 3 and 4. This is due to a similar path behaviour of y for both nonlinearities f(1) and
+f(2). Let us finally mention that we conducted the same experiments also when the right Dirichlet
+boundary condition in (46) is replaced by the Neumann condition
+∂
+∂ζ vt(ζ)|ζ=L = u2(t) leading to
+dxn(t) =
+�−xn(t) + xn−1(t)
+h2
++ u2(t)
+h
++ f(xn(t))
+�
+dt +
+d
+�
+i=1
+gi(ζn)xn(t)dMi(t)
+instead of the last line in (45). Here, analog results can be seen using the same kind of parameters.
+A
+Supporting lemmas
+This Section contains several useful auxiliary results.
+Lemma A.1. Suppose that a, b1, . . . , bd are Rn-valued processes with a being (Ft)-adapted and
+almost surely Lebesgue integrable and bi being integrable w.r.t the mean zero square integrable
+L´evy process M =
+�
+M1
+. . .
+Md
+�⊤ with covariance matrix K = (kij). If x is represented by
+dx(t) = a(t)dt + b(t)dM = a(t)dt +
+d
+�
+i=1
+bi(t)dMi,
+where b =
+�
+b1
+. . .
+bd
+�
+. Then, we have
+d
+dtE
+�
+x(t)⊤x(t)
+�
+= 2E
+�
+x(t)⊤a(t)
+�
++ E
+���b(t)K
+1
+2
+���
+2
+F = 2E
+�
+x(t)⊤a(t)
+�
++
+d
+�
+i,j=1
+E
+�
+bi(t)⊤bj(t)
+�
+kij.
+We introduce two classical versions of Gronwall’s lemma below.
+
+22
+M. REDMANN
+Lemma A.2 (Gronwall lemma – differential form). Given T > 0 let z : [0, T] → R be differen-
+tiable functions and β ∈ R. Given that
+˙z(t) ≤ βz(t),
+t ∈ [0, T],
+then for all t ∈ [0, T], it holds that
+z(t) ≤ z(0) eβt .
+The corresponding integral version follows next.
+Lemma A.3 (Gronwall lemma – integral form). Given T > 0 let z, α : [0, T] → R be continuous
+functions and β ≥ 0. Given that
+z(t) ≤ α(t) +
+� t
+0
+βz(s)ds,
+t ∈ [0, T],
+then for all t ∈ [0, T], it holds that
+z(t) ≤ α(t) +
+� t
+0
+α(s)β eβ(t−s) ds.
+(49)
+If α further is absolutely continuous, we have
+z(t) ≤ α(0) eβt +
+� t
+0
+˙α(s) eβ(t−s) ds,
+(50)
+where ˙α is the derivative of α Lebesgue almost everywhere.
+Proof. The first part is a very classical result and is not proved here. Given that α is absolutely
+continuous, we can apply integration by parts yielding
+� t
+0
+α(s)β eβ(t−s) ds = −α(s) eβ(t−s) ��t
+0 +
+� t
+0
+˙α(s) eβ(t−s) ds
+Hence, we obtain (50) from (49).
+B
+Proof of Theorem 3.2
+We define
+−Y := (A + c1I)⊤X + X(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i XNjkij < 0.
+(51)
+We apply Lemma A.1 to the uncontrolled process X
+1
+2 x(t) and obtain
+d
+dtE
+�
+x(t)⊤Xx(t)
+�
+= 2E
+�
+x(t)⊤X[Ax(t) + f(x(t))]
+�
++
+d
+�
+i,j=1
+E
+�
+x(t)⊤N⊤
+i XNjx(t)
+�
+kij
+≤ 2E
+�
+x(t)⊤X[Ax(t) + c2Ix(t)]
+�
++
+d
+�
+i,j=1
+E
+�
+x(t)⊤N⊤
+i XNjx(t)
+�
+kij
+= E
+�
+x(t)⊤�
+(A + c1I)⊤X + X(A + c1I) +
+d
+�
+i,j=1
+N⊤
+i XNjkij
+�
+x(t)
+�
++ 2(c2 − c1)E
+�
+x(t)⊤Xx(t)
+�
+= 2(c2 − c1)E
+�
+x(t)⊤Xx(t)
+�
+− E
+�
+x(t)⊤Y x(t)
+�
+.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+23
+exploiting inequality (10) and inserting (51). We define k and k to be the smallest the largest
+eigenvalue of X, respectively, yielding kI ≤ X ≤ kI. With the smallest eigenvalue kY of Y giving
+−Y ≤ −kY I, we obtain −E
+�
+x(t)⊤Y x(t)
+�
+≤ −kY E
+�
+x(t)⊤x(t)
+�
+≤ − kY
+k E
+�
+x(t)⊤Xx(t)
+�
+. Setting
+β := kY
+k , we hence find
+d
+dtE
+�
+x(t)⊤Xx(t)
+�
+≤ (2(c2 − c1) − β)E
+�
+x(t)⊤Xx(t)
+�
+.
+By the differential version of Gronwall’s inequality in Lemma A.2, we have
+E
+�
+x(t)⊤x(t)
+�
+≤ 1
+kE
+�
+x⊤(t)Xx(t)
+�
+≤ 1
+kx⊤
+0 Xx0 exp {(2(c2 − c1) − β)t}
+≤ k
+kx⊤
+0 x0 exp {(2(c2 − c1) − β)t}
+concluding the proof.
+Acknowledgments
+MR is supported by the DFG via the individual grant “Low-order approximations for large-scale
+problems arising in the context of high-dimensional PDEs and spatially discretized SPDEs”–
+project number 499366908.
+References
+[1] S. Albeverio, Z. Brze´zniak, and J.-L. Wu. Existence of global solutions and invariant mea-
+sures for stochastic differential equations driven by Poisson type noise with non-Lipschitz
+coefficients. Journal of Mathematical Analysis and Applications, 371(1):309–322, 2010.
+[2] S. Becker and C. Hartmann. Infinite-dimensional bilinear and stochastic balanced truncation
+with error bounds. Math. Control. Signals, Syst., 31:1–37, 2019.
+[3] P. Benner and T. Breiten. Two-Sided Projection Methods for Nonlinear Model Order Re-
+duction. SIAM J. Sci. Comput., 37(2), 2015.
+[4] P. Benner, T. Damm, and Y. R. Rodriguez Cruz. Dual pairs of generalized Lyapunov in-
+equalities and balanced truncation of stochastic linear systems. IEEE Trans. Autom. Contr.,
+62(2):782–791, 2017.
+[5] P. Benner and P. Goyal. Balanced truncation model order reduction for quadratic-bilinear
+systems. Technical Report 1705.00160, arXiv, 2017.
+[6] P. Benner, P. Goyal, and S. Gugercin.
+H2-Quasi-Optimal Model Order Reduction for
+Quadratic-Bilinear Control Systems. SIAM J. Matrix Anal. Appl., 39(2), 2018.
+[7] P. Benner and M. Redmann. Model Reduction for Stochastic Systems. Stoch PDE: Anal
+Comp, 3(3):291–338, 2015.
+[8] G. Da Prato. Kolmogorov Equations for Stochastic PDEs. Number VII. Birkh¨auser Basel,
+2004.
+[9] T. Damm. Rational Matrix Equations in Stochastic Control. Lecture Notes in Control and
+Information Sciences 297. Berlin: Springer, 2004.
+[10] D. F. Enns. Model reduction with balanced realizations: An error bound and a frequency
+weighted generalization. In Proc. 23rd IEEE Conf. Decision and Control, 1984.
+
+24
+M. REDMANN
+[11] K. Glover. All optimal Hankel-norm approximations of linear multivariable systems and
+their L∞-error bounds. Int. J. Control, 39(6):1115–1193, 1984.
+[12] I. V. Gosea and A. C. Antoulas. Data-driven model order reduction of quadratic-bilinear
+systems. Numerical Linear Algebra with Applications, 25(6), 2018.
+[13] S. Gugercin, A. C. Antoulas, and C. Beattie. H2 Model Reduction for Large-Scale Linear
+Dynamical Systems. SIAM J. Matrix Anal. Appl., 30(2):609–638, 2008.
+[14] I. Gy¨ongy. Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential
+Equations Driven by Space-Time White Noise I. Potential Analysis, 9:1–25, 1998.
+[15] I. Gy¨ongy. Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential
+Equations Driven by Space-Time White Noise II. Potential Analysis, 11:1–37, 1999.
+[16] I. Gy¨ongy. On stochastic finite difference schemes. Stoch PDE: Anal Comp, 2:539–583, 2014.
+[17] R. Z. Khasminskii.
+Stochastic stability of differential equations, volume 66 of Stochastic
+Modelling and Applied Probability. Springer, Heidelberg, second edition, 2012.
+[18] B. Kramer and K. E. Willcox. Nonlinear Model Order Reduction via Lifting Transformations
+and Proper Orthogonal Decomposition. AIAA Journal, 57(6):2297–2307, 2019.
+[19] B. Kramer and K. E. Willcox. Balanced Truncation Model Reduction for Lifted Nonlinear
+Systems, pages 157–174. Springer International Publishing, Cham, 2022.
+[20] K. Kunisch and S. Volkwein.
+Galerkin proper orthogonal decomposition methods for
+parabolic problems. Numer. Math., 90(1):117–148, 2001.
+[21] C. K¨uhn and A. Neamt¸u.
+Dynamics of Stochastic Reaction-Diffusion Equations.
+In
+W. Grecksch and H. Lisei, editors, Infinite Dimensional and Finite Dimensional Stochastic
+Equations and Applications in Physics, chapter 1, pages 1–60. World Scientific Publishing,
+2020.
+[22] J. L¨ofberg. YALMIP: A Toolbox for Modeling and Optimization in MATLAB. In In Pro-
+ceedings of the CACSD Conference, Taipei, Taiwan, 2004.
+[23] X. Mao. Stochastic Differential Equations and Applications (Second Edition). Woodhead
+Publishing, 2007.
+[24] C. Marinelli and M. R¨ockner. On uniqueness of mild solutions for dissipative stochastic
+evolution equations. Infinite Dimensional Analysis, Quantum Probability and Related Topics,
+13(3):363–376, 2010.
+[25] B. Moore. Principal component analysis in linear systems: Controllability, observability, and
+model reduction. IEEE transactions on automatic control, 26(1):17–32, 1981.
+[26] MOSEK ApS. The MOSEK optimization toolbox for MATLAB manual. Version 10.0., 2022.
+[27] S. Peszat and J. Zabczyk. Stochastic Partial Differential Equations with L´evy Noise. An evo-
+lution equation approach. Encyclopedia of Mathematics and Its Applications 113. Cambridge
+University Press, 2007.
+[28] E. Qian, B. Kramer, B. Peherstorfer, and K. E. Wilcox. Lift & Learn: Physics-informed
+machine learning for large-scale nonlinear dynamical systems. Physica D: Nonlinear Phe-
+nomena, 2020.
+[29] M. Redmann. Energy estimates and model order reduction for stochastic bilinear systems.
+Int. J. Control, 93(8):1954–1963, 2018.
+
+MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT
+25
+[30] M. Redmann. Type II singular perturbation approximation for linear systems with L´evy
+noise. SIAM J. Control Optim., 56(3):2120–2158, 2018.
+[31] M. Redmann and M. A. Freitag. Optimization based model order reduction for stochastic
+systems. Appl. Math. Comput., Volume 398, 2021.
+[32] J. M. A. Scherpen. Balancing for nonlinear systems. Syst. Control. Lett., 21:143–153, 1993.
+[33] T. Shardlow.
+Numerical methods for stochastic parabolic PDEs.
+Numerical Functional
+Analysis and Optimization, 20(1-2):121–145, 1999.
+[34] T. M. Tyranowski. Data-driven structure-preserving model reduction for stochastic Hamil-
+tonian systems. arXiv preprint:2201.13391, 2022.
+
diff --git a/fNFST4oBgHgl3EQfGjh7/content/tmp_files/load_file.txt b/fNFST4oBgHgl3EQfGjh7/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf,len=1019
+page_content='Model reduction for stochastic systems with nonlinear drift  Martin Redmann∗  February 1, 2023  Abstract  In this paper, we study dimension reduction techniques for large-scale controlled stochastic  differential equations (SDEs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The drift of the considered SDEs contains a polynomial term  satisfying a one-sided growth condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Such nonlinearities in high dimensional settings occur,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', when stochastic reaction diffusion equations are discretized in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We provide a brief  discussion around existence, uniqueness and stability of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' (Almost) stability then is  the basis for new concepts of Gramians that we introduce and study in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' With the  help of these Gramians, dominant subspace are identified leading to a balancing related highly  accurate reduced order SDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We provide an algebraic error criterion and an error analysis of  the propose model reduction schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The paper is concluded by applying our method to  spatially discretized reaction diffusion equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Keywords: model order reduction· nonlinear stochastic systems · Gramians · L´evy processes  MSC classification: 60G51 · 60H10 · 65C30 · 93C10 · 93E03 · 93E15  1  Introduction  Model order reduction (MOR) aims to find low-order approximations for high-/infinite-dimensional  systems of differential equations reducing the complexity of the original problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Many MOR  schemes are based on projections (Galerkin or Petrov-Galerkin type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In this context, the first  goal is to identify solution manifolds and approximate them by low-dimensional linear subspaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  A reduced state variable, taking values in this subspace, is subsequently constructed in order  to ensure an accurate estimation of the original dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' There is a rich selection of different  MOR strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Proper orthogonal decomposition (POD) [20] is an approach, where solution  spaces are learned from data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Methods like the iterative rational Krylov algorithm (IRKA) [13]  rely on interpolation or on the minimization of certain error measures between systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' More-  over, there are Gramian based techniques like balanced truncation (BT) [25], where dominant  subspaces of the original dynamics are associated to eigenspaces of these (algebraic) Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Recently, there has been an enormous interest in dimension reduction for large-scale nonlinear  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Data-driven [12, 18, 28] or interpolation/optimization based methods [3, 6] were applied  to such equations in a deterministic framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Generalizing BT to nonlinear systems was first  addressed in [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Alternatives, where the reduced order model can be computed easier, can be  found in [5, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MOR in probabilistic settings is even more essential than in the deterministic context discussed  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is due to an enormous amount of system evaluations required, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', for conducting  Monte-Carlo simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the other hand, it is also about the feasibility of certain algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', a stochastic differential equation (SDE) in dimension n is in some sense equivalent to a partial  differential equation (PDE) with n spatial variables using the formula of Feynman-Kac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Knowing  how hard it is to solve high-dimensional PDEs in general, it becomes clear how vital MOR for  SDEs is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A POD approach for SDEs is studied in [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Balancing related or optimization based  MOR techniques are, for instance, investigated in [2, 4, 7, 31] for the linear case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The advantage  ∗Martin Luther University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  5, 06120 Halle  (Saale), Germany, Email: martin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='redmann@mathematik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='uni-halle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='de.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='13722v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='PR]  31 Jan 2023  2  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  of the latter schemes is the possibility for detailed error and stability analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  However, an  extension to nonlinear stochastic systems seems very challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A first approach for stochastic  bilinear equations is presented in [29] but it might not work for more complex nonlinearities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The goal of this paper is to extend BT to stochastic systems, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', with certain polynomial  nonlinearities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In the deterministic case, a wide focus is on quadratic systems, see for instance  [5, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is because many nonlinear terms in a differential equation can be transformed to  a quadratic expression using additional dummy variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This approach is called lifting in the  literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' It has the advantage that a large set of nonlinear systems can be covered if we know  how to handle quadratic ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, this is also the drawback of this ansatz, since differential  equations involving quadratic terms range from globally stable to finite time explosion systems,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', the existence of a global solution is not guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This large variety of properties makes it  seem infeasible to develop a general theory like for example an error analysis with sharp bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  For that reason, we do not intend to apply to technique of lifting the dynamics to a quadratic  system in this paper, because one might loose track of essential properties that are usually not  visible anymore in a transformed SDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Instead we exploit the structure of our locally Lipschitz  nonlinearity that we assume to be of one-sided linear growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  This also involves interesting  polynomials that play a role in reaction diffusion equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This type of growth will be reflected  linearly in the associated Lyapunov operator that defines the Gramians that we propose in our  MOR procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The paper is now structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Section 2 deals with the setting and the first details  concerning the goals of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In Section 3, we recall facts about existence and uniqueness  of solutions to the considered nonlinear SDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We further investigate global asymptotic stability  as the basis of the Gramians that we introduce in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' There, it is explained and reasoned  how Gramians need to be chosen in order to find a good dominant subspace characterization  and hence an accurate reduced system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We also discuss on properties of Gramians that need  to be fulfilled to ensure the classical error bound for BT known for deterministic linear systems  [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Having computed the desired Gramians based on the strategy that we provide, we  explain how to compute the reduced system in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Finally, Section 6 delivers an error  bound analysis for the balancing related MOR scheme, also involving a discussion on criteria for  a high approximation quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Section 7 illustrates the performance of the MOR technique by  applying it to spatially discretized stochastic reaction diffusion equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  2  Setting, notation and goal  Let  �  Ω, F, (Ft)t∈[0,T], P  �1 be a filtered probability space on which every stochastic process ap-  pearing in this paper is defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given an Rd-valued and square integrable L´evy process M =  �  M1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Md  �⊤ with mean zero, we assume that it is is (Ft)t∈[0,T]-adapted and its increments  M(t + h) − M(t) are independent of Ft for t, h ≥ 0 and t + h ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Exploiting the independent  and stationary increments, there exists a positive semidefinite matrix K = (kij)i,j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=',d, so that  E[M(t)M(t)⊤] = Kt, see [27, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='44] for a proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We call K covariance matrix of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Now, we consider the following large-scale nonlinear stochastic dynamics driven by M:  dx(t) = [Ax(t) + Bu(t) + f (x(t))]dt + N (x(t−)) dM(t),  x(0) = x0,  (1a)  y(t) = Cx(t),  t ∈ [0, T],  (1b)  where x(t−) := lims↑t x(s), A ∈ Rn×n, B ∈ Rn×m, C ∈ Rp×n, N : Rn → Rn×d is a linear mapping  defined by N(x) =  �  N1x  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Ndx  �  for x ∈ Rn with N1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , Nd ∈ Rn×n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The state vector  x(t) ∈ Rn is assumed to be high-dimensional, whereas the quantity of interest y(t) ∈ Rp usually  is a vector with a low number of entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The nonlinear function f : Rn → Rn shall satisfy the  following local Lipschitz condition  ∥f(x) − f(z)∥2 ≤ cR ∥x − z∥2 ,  (2)  1(Ft)t∈[0,T ] is right continuous and complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  3  for ∥x∥2 , ∥z∥2 ≤ R, cR > 0 and any R > 0, where ⟨·, ·⟩2 denotes the Euclidean inner product  with corresponding norm ∥·∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Further, we assume the special type of monotonicity condition  ⟨x, f(x)⟩2 ≤ cf ∥x∥2  2 ,  (3)  for all x ∈ Rn and a constant cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In the literature, (3) is called one-sided growth condition as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In fact, cf can be negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In this case, (3) is also known as dissipativity condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Below,  x(t, x0, B), t ∈ [0, T], represents the solution to (1a) with initial condition x0 ∈ Rn and matrix B  determining the inhomogeneous part of the state equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The associated control process u is  assumed to be an (Ft)t∈[0,T]-adapted process with  ∥u∥2  L2  T := E  � T  0  ∥u(t)∥2  2 dt < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Moreover, suppose that f(0) = 0 to ensure that the uncontrolled state equation (1a) (B = 0) has  an equilibrium at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If f(0) ̸= 0, we can replace f by f −f(0) as well as B and u by  �  B  f(0)  �  and  �  u  1  �⊤, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The above setting covers interesting polynomial nonlinearities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This  is illustrated in the next example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The local Lipschitz condition (2) is fulfilled by all functions f with continuous  partial derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is particularly given for polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If we assume f = f(i), i ∈ {1, 2, 3},  to be special third order polynomial, where  f(1)(x) = x ◦ (1n − x) ◦ (x − 1na) = (1 + a)x◦2 − x◦3 − ax,  a ∈ R,  f(2)(x) = x − x◦3  and  f(3)(x) = x − x ∥x∥2  2 ,  the monotonicity condition (3) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The products/powers involving “◦” have to be understood  in the Hadamard (component wise) sense and 1n is the vector of ones having length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, (3)  can be verified by the following calculations  ⟨x, f(1)(x)⟩2 = −a ∥x∥2  2 +  n  �  i=1  x2  i [(1 + a)xi − x2  i ] ≤ (a − 1)2  4  ∥x∥2  2 ,  ⟨x, f(2)(x)⟩2 = ∥x∥2  2 −  n  �  i=1  x4  i ≤ ∥x∥2  2 ,  ⟨x, f(3)(x)⟩2 = ∥x∥2  2 − ∥x∥4  2 ≤ ∥x∥2  2  exploiting that (1 + a)xi − x2  i ≤ (a+1)2  4  for all xi ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Our setting is not restricted to the functions of Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, we will frequently  refer to these interesting cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let us point out that the component-wise functions f(1) and f(2)  occur if the nonlinear part of certain (stochastic) reaction diffusion equations are evaluated on a  spatial grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' To be more precise, a finite difference discretization of Zeldovich-Frank-Kamenetsky  (or FitzHugh-Nagano) and Chafee-Infante equations would lead to such a setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This paper  does not intend to discuss finite difference schemes for stochastic partial differential equations  in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, the interested reader may find more information regarding these methods in  [14, 15, 16, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We also refer to, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', [8, 21, 24, 27] for a theoretical treatment of stochastic  reaction diffusion equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The goal of this paper is to drastically reduce the dimension of the high-dimensional system (1)  in order to lower the computational complexity when solving this system of stochastic differential  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, the solution manifold of (1a) shall be approximated by an r-dimensional  subspace im[V ] of Rn (V ∈ Rn×r is a full-rank matrix), so that we find a process xr yielding  V xr(t) ≈ x(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Inserting this estimate into (1) leads to  V xr(t) = x0 +  � t  0  AV xr(s) + Bu(s) + f(V xr(s))ds +  � t  0  N (V xr(s−)) dM(s) + e(t)  (4)  4  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  with y(t) ≈ yr(t) := CV xr(t) and where e(t) is the state equation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, we enforce the  residual e(t) to be orthogonal to a second subspace im[W] (W ∈ Rn×r has full rank).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We further  assume that our choice of W provides W ⊤V = I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Multiplying (4) with W ⊤, we obtain  dxr(t) = [Arxr(t) + Bru(t) + fr(xr(t))]dt + Nr(xr(t−))dM(t),  (5a)  yr(t) = Crxr(t),  t ∈ [0, T],  (5b)  with xr(0) = W ⊤x0 ∈ Rr, r ≪ n and y ≈ yr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Generally, we have that xr(t) ∈ Rr, Ar ∈ Rr×r,  Br ∈ Rr×m, Cr ∈ Rp×r, Nr : Rr → Rr×d defined by Nr(xr) =  �  Nr,1xr  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Nr,dxr  �  for xr ∈ Rr,  where Nr,i ∈ Rr×r (i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , d) and fr : Rr → Rr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, the reduced coefficients are of  the following form  Ar = W ⊤AV,  Br = W ⊤B,  fr(·) = W ⊤f(V ·),  Nr,i = W ⊤NiV,  Cr = CV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (6)  The goal of this paper is to provide a reduced order method for which we can compute the  projection matrices V and W and for which we find an accurate approximation of (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here,  the main focus will be on the control dynamics and not on the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, we study  reduced order modelling when x0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, we aim to investigate Gramian based schemes  which often heavily rely on stability of the state equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, we discuss global asymptotic  stability in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Before doing so, we briefly point out that there is a unique solution  to (1a) by referring to the existing literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  3  Existence and uniqueness as well as global asymptotic stability  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1  Existence and uniqueness for (1a)  We briefly discuss that our setting is well-posed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We define the drift function F(t, x) := Ax +  Bu(t) + f(x) of (1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Using (3) and exploiting that the remaining parts in the drift and diffusion  are either linear in x or solely time dependent, we can find a constant cF,N, so that  2⟨x, F(t, x)⟩2 + ∥N(x)K  1  2 ∥2  F ≤ cF,N  �  1 + ∥x∥2  2  �  (7)  given that the control u is bounded by a constant independent of t ∈ [0, T] and ω ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, ∥·∥F  denotes the Frobenius norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, the drift F is locally Lipschitz continuous (uniformly  in (t, ω)) in the sense of (2), since the same is true for f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  As N is linear, it is particularly  globally Lipschitz with respect to ∥ · K  1  2 ∥F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The monotonicity condition (7) and local Lipschitz  continuity of drift and diffusion yield existence and uniqueness of a solution to (1a) by [23,  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5] if M is a Brownian motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the other hand, the arguments of Mao [23] can  immediately be transferred to our more general setting because the Ito-integral w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='t M has  essentially the same properties as the one in the Brownian case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The first property is the Ito  isometry E  ���  � T  0 Ψ(s)dM(s)  ���  2  2 = E  � T  0 ∥Ψ(s)K  1  2 ∥2  F ds =: ∥Ψ∥2 for predictable2 processes Ψ with  ∥Ψ∥ < ∞ which relies on the linear covariance function of M, see [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Secondly, the equation for  the expected value of a quadratic form of the state variable has the same structure, see Lemma  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' It is also worth mentioning that existence and uniqueness has been established in a more  general setting than in [23] also covering ours, see [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' There, the result was proved assuming a  monotonicity condition, a local Lipschitz condition in the drift and the Brownian diffusion part  as well as global Lipschitz continuity in the jump diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  A note on global asymptotic stability  Stability concepts are essential in order to define computational accessible Gramians which are  vital for identifying less relevant information in a system like (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We recall known facts for the  linear part of (1) based on the results in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  2Predictable means that the process is measurable w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' the σ algebra that is generated by left-continuous and  (Ft)t∈[0,T ]-adapted processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  5  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let f ≡ 0 and B = 0 in (1a), then the following statements are equivalent:  (a) The state in (1a) is exponentially mean square stable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', there are k, β > 0, so that  �  E ∥x(t, x0, 0)∥2  2 ≤ ∥x0∥2 k e−βt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (b) It holds that  λ  �  I ⊗ A + A ⊗ I +  d  �  i,j=1  Ni ⊗ Njkij  �  ⊂ C−,  where λ(·) denotes the spectrum of a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (c) There exists a matrix X > 0 with  A⊤X + XA +  d  �  i,j=1  N⊤  i XNjkij < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A proof of these statements can be found in [9, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Throughout the rest of the paper, we assume that  λ  �  I ⊗ (A + c1I) + (A + c1I) ⊗ I +  d  �  i,j=1  Ni ⊗ Njkij  �  ⊂ C−  (8)  for some constant c1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' According to Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 this means that (1a) with the shifted linear  drift coefficient A+c1I is mean square asymptotically stable for B = 0 and f ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The associated  state variable is of the form ec1t x(t), so that the original state x(t) (B = 0 and f ≡ 0) needs to  have a decay rate β > c1, see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 (a), given that c1 is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We desire, but do not  assume, that we can choose c1 ≥ cf, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', the decay rate of the linear part shall outperform the  one-sided linear growth constant in (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This requires a sufficiently stable linear part if cf > 0,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', for the nonlinearities in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Since cf can also be negative, this means that the  linear part of (1a) can even be exponentially increasing in some cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Using classical arguments  of [17, 23] based on quadratic Lyapunov-type functions, we provide the following criterion for the  global mean square stability of the uncontrolled state equation (1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This criterion is required  around the discussion of the Gramians introduced later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Suppose that B = 0 in (1a) and given constant c1, c2 ∈ R and a matrix X > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  If we have  (A + c1I)⊤X + X(A + c1I)+  d  �  i,j=1  N⊤  i XNjkij < 0  and  (9)  ⟨x, Xf(x)⟩2 ≤ c2  ���X  1  2 x  ���  2  2  (10)  for all x ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, there exist constants k, β > 0, so that  E ∥x(t, x0, 0)∥2  2 ≤ ∥x0∥2  2 k e(2(c2−c1)−β)t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A proof is stated in Appendix B  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If c1 ≥ c2 in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2, we obtain global mean square asymptotic stability for  our nonlinear system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, by assumption (3), (10) holds for X = I and c2 = cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If (9)  is now true for X = I and c1 = cf, mean square asymptotic stability follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  6  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  4  Gramians and dominant subspace characterization  In this section, algebraic objects, called Gramians, are introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We aim to construct them,  so that their eigenspaces corresponding to small eigenvalues coincide with the information in  (1) that can be neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' It is not trivial to find the right notion for general nonlinearities f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  However, the monotonicity condition in (3) will become essential for our concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular,  positive (semi)definite Gramian candidates X have to preserve (3) in a certain sense when ⟨·, ·⟩2  is replaced by ⟨·, X·⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We begin with a global Gramian concept to illustrate what we require.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Subsequently, we immediately weaken it for practical reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1  Monotonicity Gramians  First, a pair of Gramians is defined that characterizes dominant subspaces of (1) for all u ∈ L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let c1 and c2 be constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, a pair of matrices (P, Q) with P, Q > 0 is  called global monotonicity Gramians if they satisfy  (A + c1I)⊤P −1 + P −1(A + c1I) +  d  �  i,j=1  N⊤  i P −1Njkij ≤ −P −1BB⊤P −1,  (11)  (A + c1I)⊤Q + Q(A + c1I) +  d  �  i,j=1  N⊤  i QNjkij ≤ −C⊤C,  (12)  and if further holds that  ⟨x, P −1f(x)⟩2 ≤ c2∥P − 1  2 x∥2  2  and  ⟨x, Qf(x)⟩2 ≤ c2∥Q  1  2 x∥2  2  (13)  for all x ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Notice that assumption (8) ensures the existence of solutions to (11) and (12), see [4, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In  the following, we state a sufficient criterion for the existence of Gramians also satisfying (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Suppose that (9) and (10) hold with some constants c1 and c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, global  monotonicity Gramians P and Q exist with the same constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We denote the left hand side of (9) by −Y and multiply it with γ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Hence, we have  (A + c1I)⊤(γX) + (γX)(A + c1I) +  d  �  i,j=1  N⊤  i (γX)Njkij = −γY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (14)  Since Y > 0, we can ensure that −γY ≤ −(γX)BB⊤(γX) if γ is sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, P =  (γX)−1 solves (11) for a potentially small γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the other hand, this P gives us ⟨x, P −1f(x)⟩2 =  γ⟨x, Xf(x)⟩2 ≤ γc2∥X  1  2 x∥2  2 = c2∥P − 1  2 x∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, we know that −γY ≤ −C⊤C if γ is sufficiently  large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, Q = γX satisfies (12) for a potentially large γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, we find that  ⟨x, Qf(x)⟩2 = γ⟨x, Xf(x)⟩2 ≤ γc2∥X  1  2 x∥2  2 = c2∥Q  1  2 x∥2  2 using (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Certainly, the existence of global monotonicity Gramians is not sufficient for our  considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' As we will see later, it is important to find candidates P and Q that have a large  number of small eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, one might have to solve a problem of minimizing  tr(P) and tr(Q) subject to (11), (12) and (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, we allow c1 < c2 in Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 to  have an additional degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, this comes with a price.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We will observe that  c2 − c1 is supposed to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In fact, we desire to choose c1 = c2 if such a c1 ensures (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Choosing f = f(3) from Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, we see that ⟨x, Xf(3)(x)⟩2 ≤ ∥X  1  2 x∥2  2  for any X ≥ 0 and all x ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, any solutions of (11) and (12) with c1 = c2 =  cf = 1 are global monotonicity Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, we can choose the solution to the  equality in (12) and the candidate with minimal trace in (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  7  If f is globally Lipschitz in some norm, then there exist a Lipschitz constant cL, so that  ⟨x, Xf(x)⟩2 = ⟨X  1  2 x, X  1  2 f(x)⟩2 ≤ ∥X  1  2 x∥2∥X  1  2 f(x)∥2 ≤ cL∥X  1  2 x∥2  2 given that X = P −1, Q >  0 meaning that every positive solution to (11) and (12) can be picked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, cL depends  on X which shows that c1 and c2 influence each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the other hand, this cL might not  be the optimal candidate for the one-sided Lipschitz constant c2 which can even be negative,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', it is also challenging to identify optimal constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We emphasize further that, generally, we cannot derive P and Q independent of (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' For  instance, fixing c1 = c2 ≥ cf, we can easily find a solution Q for (12) and a vector x ∈ Rn, so  that ⟨x, Qf(1)(x)⟩2 > c2∥Q  1  2 x∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, f = f(1) is the function defined in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Having  in mind that we aim to fix c1 and c2 close to each other with associated Gramians P and Q  having a large number of small eigenvalues, the concept of global Gramians might generally be  too restrictive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, it is more reasonable to seek for solutions of (11) and (12) that satisfy  (13) on average instead of point-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This means, we aim to allow for positive values of the  monotonicity gaps  GP −1(x) := ⟨x, P −1(f(x) − c2x)⟩2  and  GQ(x) := ⟨x, Q(f(x) − c2x)⟩2  (15)  as long as GP −1 and GQ are mainly non-positive on the essential parts of Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We specify the above  arguments in the following definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In this context, we introduce the set U of controls u ∈ L2  T  for which we desire to evaluate system (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The following pair of Gramians (P, Q) identifies less  important direction for controls in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, it is meaningful to pick Gramian candidates  that ensure a large set U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let c1, c2 be constants and U ⊆ L2  T be the set of controls we are interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Then, a pair of matrices (P, Q) with P, Q > 0 is called average monotonicity Gramians for U if  (11) and (12) are satisfied, respectively, and if instead of (13) it holds that  E  � t  0  ⟨x(s), P −1f(x(s))⟩2ds ≤ c2 E  � t  0  ∥P − 1  2 x(s)∥2  2ds  and  (16)  E  � t  0  ⟨x(s), Qf(x(s))⟩2ds ≤ c2 E  � t  0  ∥Q  1  2 x(s)∥2  2ds  (17)  for all t ∈ [0, T] and all state variables x(t) = x(t, 0, u) with u ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Certainly, a global is also an average monotonicity Gramian with U = L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Suppose that there  are areas, where one of the functions in (15) is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, controls u concentrating the state  variable x in such areas for a long time will violate (16) or (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In Definitions 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5, Gramians are constructed as solutions to (shifted)  linear matrix inequalities in order to allow a practical computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is possible due to the  monotonicity condition for f in (3) which shall be preserved in some sense under the inner  products defined by the Gramians P and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  A more general version of global monotonicity  Gramians is obtained by adding twice the estimates in (13) to (11) and (12) resulting in  x⊤�  A⊤P −1 + P −1A +  d  �  i,j=1  N⊤  i P −1Njkij  �  x + 2⟨x, P −1f(x)⟩2 ≤ −∥B⊤P −1x∥2  2 + c∥P − 1  2 x∥2  2, (18)  x⊤�  A⊤Q + QA +  d  �  i,j=1  N⊤  i QNjkij  �  x + 2⟨x, Qf(x)⟩2 ≤ −∥Cx∥2  2 + c∥Q  1  2 x∥2  2  (19)  for all x ∈ Rn, where c ≥ 0 is some “small” constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The same way, average monotonicity  Gramians can be generalized setting x = x(s) in (18) and (19), taking the expected value and  integrating both sides of these inequalities over each subinterval [0, t] with 0 < t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However,  we will not discuss this generalization in detail below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  8  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  Relevance of monotonicity Gramians  In the following, we state in which sense the Gramians of Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5 help to identify the  dominant subspaces of (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This then motivates a truncation procedure resulting in a special  type of reduced system (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Below, let us assume that x0 = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', x(t) = x(t, 0, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' By definition,  Gramians are positive (semi)definite matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, we can find an orthonormal basis  (pk) for Rn consisting of eigenvalues of P with corresponding eigenvalues (λP,k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The same is true  for Q, where the basis is denoted by (qk) with associated eigenvalues (λQ,k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Hence, the state  variable can be represented as  x(t) =  n  �  k=1  ⟨x(t), pk⟩2 pk  and  x(t) =  n  �  k=1  ⟨x(t), qk⟩2 qk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (20)  Based on this representation, we aim to answer which directions pk are less relevant in (1a) and  which directions qk can be neglected in (1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let P and Q be average monotonicity Gramians for the set of controls U ⊆ L2  T and  constants c1, c2 according to Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, let (pk, λP,k) and (qk, λQ,k) be associated  bases of eigenvectors giving us (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, given a zero initial state, we have  sup  t∈[0,T]  E⟨x(t), pk⟩2  2 ≤ λP,k ecT ∥u∥2  L2  T ,  (21)  E  � t  0  ∥y(s)∥2  2 ds ≤ 2E  � t  0  ⟨Qx(s), Bu(s)⟩2 ec(t−s) ds  = 2  n  �  k=1  λQ,kE  � t  0  ⟨qk, x(s)⟩2⟨qk, Bu(s)⟩2 ec(t−s) ds  (22)  for all t ∈ [0, T] and u ∈ U, where c = max{0, 2(c2 − c1)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We find inequalities for E  �  x(t)⊤Xx(t)  �  , where X ∈ {P −1, Q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' To do so, we apply Lemma  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 to X  1  2 x(t) and obtain  d  dtE  �  x(t)⊤Xx(t)  �  = 2E  �  x(t)⊤X[Ax(t) + Bu(t) + f(x(t))]  �  +  d  �  i,j=1  E  �  x(t)⊤N⊤  i XNjx(t)  �  kij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We integrate this equation over [0, t] with t ≤ T yielding  E  �  x(t)⊤Xx(t)  �  = E  � t  0  �  x(s)⊤�  A⊤X + XA +  d  �  i,j=1  N⊤  i XNjkij  �  x(s)  �  ds  + 2  � t  0  E  �  x(s)⊤X  �  Bu(s) + f(x(s))  ��  ds  ≤ E  � t  0  �  x(s)⊤�  (A + c1I)⊤X + X(A + c1I) +  d  �  i,j=1  N⊤  i XNjkij  �  x(s)  �  ds  + 2  � t  0  E  �  x(s)⊤XBu(s)  �  ds + c  � t  0  E  �  x(s)⊤Xx(s)  �  ds  (23)  exploiting (16), (17) and that x0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Setting α(t) := 2  � t  0 E  �  x(s)⊤XBu(s)  �  ds and X = Q, we  obtain  E  �  x(t)⊤Qx(t)  �  ≤ −  � t  0  E  �  x(s)⊤C⊤Cx(s)  �  ds + 2  � t  0  E  �  x(s)⊤QBu(s)  �  ds + c  � t  0  E  �  x(s)⊤Qx(s)  �  ds  = − ∥y∥2  L2  t + α(t) + c  � t  0  E  �  x(s)⊤Qx(s)  �  ds  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  9  using (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, by (50), we have  E  �  x(t)⊤Qx(t)  �  ≤  � t  0  ( ˙α(s) − E ∥y(s)∥2  2) ec(t−s) ds,  and hence  � t  0 E ∥y(s)∥2  2 ds ≤  � t  0 ˙α(s) ec(t−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Inserting the representation for x(s) in (20) yields  ∥y∥2  L2  t ≤ 2  � t  0  E  �  x(s)⊤QBu(s)  �  ec(t−s) ds = 2  � t  0  E  ��  Q  n  �  k=1  ⟨x(s), qk⟩2 qk  �⊤  Bu(s)  �  ec(t−s) ds  = 2  n  �  k=1  λQ,k  � t  0  E  �  ⟨x(s), qk⟩2 q⊤  k Bu(s)  �  ec(t−s) ds  leading to (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' With X = P −1 in (23), it holds that  E  �  x(t)⊤P −1x(t)  �  ≤ −  � t  0  E  �  x(s)⊤P −1BB⊤P −1x(s)  �  ds + 2  � t  0  E  �  x(s)⊤P −1Bu(s)  �  ds  + c  � t  0  E  �  x(s)⊤P −1x(s)  �  ds  = E  � t  0  ∥u(s)∥2  2 − ∥B⊤P −1x(s) − u(s)∥2  2ds + c  � t  0  E  �  x(s)⊤P −1x(s)  �  ds  exploiting (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Applying (49), we obtain  E  �  x(t)⊤P −1x(t)  �  ≤ E  � t  0  ∥u(s)∥2  2 ds +  � t  0  � s  0  E ∥u(v)∥2  2 dv c ec(t−s) ds  ≤ ect E  � t  0  ∥u(s)∥2  2 ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We further observe that  ⟨x(t), pk⟩2  2 ≤ λP,k  n  �  i=1  λ−1  P,i⟨x(t), pi⟩2  2 = λP,k  ���  n  �  i=1  λ  − 1  2  P,i ⟨x(t), pi⟩2 pi  ���  2  2 = λP,k  ���P − 1  2 x(t)  ���  2  2  = λP,k x(t)⊤P −1x(t),  so that (21) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Estimate (21) tells us that the state variable is small in the direction of pk if λP,k is small and  in case c T is not too large (c2 −c1 is supposed to be little).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, these eigenspaces of P  can be neglected in our considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The eigenspaces spanned by vectors qk that are associated  to small eigenvalues of Q are also of minor relevance due to (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This inequality shows that such  qk barely contribute to the energy of the output y on each subinterval [0, t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Following basically the same steps, the result of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7 holds also true  if the more general notion of Gramians in Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6 is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7 is formulated for u ∈ U since it is based on (16) and (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This does not mean  that a reduced order model based on neglecting eigenspaces of P and Q associated to small  eigenvalues leads to a bad approximation for u ∈ L2  T \\ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is because (16) and (17)  might still almost hold in that cases since suitable Gramians lead to GQ and GP −1 in (15)  being small when they are positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, the estimates in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7 will approximately  hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  10  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3  Computation of monotonicity Gramians  We aim to compute average monotonicity Gramians P and Q for a large set U of controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We  choose them as solutions to (11) and (12), so that GP −1 and GQ in (15) have a local maximum  in the origin or a saddle point with very few increasing directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Else, we might have several  cases in which the monotonicity condition is immediately violated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This would not allow (16)  and (17) to hold for a large U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  On the other hand, it is essential that the area where the  monotonicity condition is fulfilled clearly dominates the one where it does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A possible  and acceptable scenario in dimension n = 2 is illustrated in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, the monotonicity gap  GQ is depicted for f = f(2), c2 = cf = 1 and Q = [ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='49426 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='58159  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='58159 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='68542 ], a matrix with a large and a  small eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The blue color stands for small absolute values and red for large ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' GQ is  non positive except for the black areas, where the monotonicity condition is slightly violated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In  −2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  2  −2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  2  Figure 1: GQ for a special choice of Q, n = 2, f = f(2) and c2 = cf = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The area in black marks  the regions, where GQ is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  the following proposition, a simple criterion for local optimality for GP −1 and GQ is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Define the function g(x) = ⟨x, X(f(x) − c2x)⟩2 with a constant c2, f being  twice differentiable and X > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We assume that  fxj(x)|x=0 − c2ej = −˜c2ej  (24)  for all j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n} and ˜c2 > 0, where ej is the j-th unit vector in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, g has a local  maximum in x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' It is easy to check that x = 0 is an extreme value since gxi(x) = ⟨ei, X(f(x) − c2x)⟩2 +  ⟨x, X(fxi(x)−c2ei)⟩2 is zero at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, we derive gxixj(x) = ⟨ei, X(fxj(x)−c2ej)⟩2+  ⟨ej, X(fxi(x)−c2ei)⟩2+⟨x, Xfxixj(x)⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, we find  �  gxixj(0)  �  i,j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=',n = −2˜c2X < 0 which  concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Condition (24) is, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', satisfied if polynomials are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We can therefore observe that  GP −1 and GQ have a local maximum for the choices of f given in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 in case c2 is  sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, we fix c2 ≥ cf, since this means that GP −1 and GQ are non-  positive along the bases of eigenvectors used in (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is a consequence of assumption (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7 motivates to choose c1, so that c2 − c1 is a small positive number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If possible, we  even set c1 = c2 providing c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If c1 > 0, the possibility of this choice also depends on weather  (8) is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We then compute the solution to (11) having a minimal trace and the solution to  the equality in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This provides that GP −1 and GQ are non-positive on large parts of Rn for  the particular functions introduced in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 and only small positive values are taken on  the other area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This leads to (16) and (17) for a large U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is what we observe from numerical  experiments, where A is a discrete Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let us now briefly sketch how such a minimal trace  monotonicity Gramian P is computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We reformulate (11) by multiplying it with P from the  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  11  left and from the right leading to  (A + c1I)P + P(A + c1I)⊤ + BB⊤ +  d  �  i,j=1  PN⊤  i P −1NjkijP ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (25)  Since �d  i,j=1 PN⊤  i kijP −1NjP = P [ N⊤  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' N⊤  d ] (K ⊗ P −1) [ N⊤  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' N⊤  d ]⊤ P, we obtain the following  equivalent representation  �(A + c1I)P + P(A + c1I)⊤ + BB⊤  P [ N⊤  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' N⊤  d ]  [ N⊤  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' N⊤  d ]⊤ P  −K−1 ⊗ P  �  ≤ 0  (26)  for (25) based on Schur complement conditions for the definiteness of a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, we need to  further assume that K is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, we can use a linear matrix inequality solver to find a  solution to the minimization of tr(P) subject to (26) and P > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In this paper, we use YALMIP  and MOSEK [26, 22] for an efficient computation of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  In general, a good choice for P and Q guaranteeing (16) and (17) for many different controls  always depends on the particular nonlinearity f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, no universal recommendation can be  given here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4  Extension under one-sided Lipschitz continuity  Many functions f satisfying (3) are also one-sided Lipschitz continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, we require an  extended version of this continuity concept in the context of the error analysis in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In  detail the following inequalities are supposed to hold:  ⟨x ± z, f(x) ± f(z)⟩2 ≤ cf ∥x ± z∥2  2 ,  (27)  for all x, z ∈ Rn and a constant cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Condition (27) will later inspire the extended definition of  Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Notice that one-sided Lipschitz continuity is defined with a minus in (27) but we  additionally ask for this property when replacing each minus by a plus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In this context, let us  look at the functions of Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We begin with f(2) and f(3) and show that (27) is  satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Inserting f(3)(x) = x − ∥x∥2  2 x below yields  ⟨x ± z, f(3)(x) ± f(3)(z)⟩2 = ∥x ± z∥2  2 − ⟨x ± z, ∥x∥2  2 x ± ∥z∥2  2 z⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Now, we find that  ⟨x ± z, ∥x∥2  2 x ± ∥z∥2  2 z⟩2 = ∥x∥4  2 + ∥z∥4  2 ± ⟨x, z⟩2(∥x∥2  2 + ∥z∥2  2) ≥ ∥x∥4  2 + ∥z∥4  2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5(∥x∥2  2 + ∥z∥2  2)2  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5(∥x∥2  2 − ∥z∥2  2)2 ≥ 0  and hence (27) holds with cf = 1 in case f = f(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We obtain from f(2)(x) = x − x◦3 that  ⟨x − z, f(2)(x) − f(2)(z)⟩2 = ∥x − z∥2  2 − ⟨x − z, x◦3 − z◦3⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Since we have that  ⟨x − z, x◦3 − z◦3⟩2 =  n  �  i=1  (x4  i + z4  i − zix3  i − xiz3  i ) =  n  �  i=1  (xi − zi)2(x2  i + z2  i + zixi)  ≥  n  �  i=1  (xi − zi)20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5(x2  i + z2  i + 2zixi) ≥ 0,  we obtain ⟨x−z, f(2)(x)−f(2)(z)⟩2 ≤ ∥x − z∥2  2 and consequently the point symmetry of f(2) yields  ⟨x + z, f(2)(x) + f(2)(z)⟩2 = ⟨x − (−z), f(2)(x) − f(2)(−z)⟩2 ≤ ∥x − (−z)∥2  2 = ∥x + z∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Therefore, cf = 1 in (27) for f = f(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  12  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  As we will see below, f(1) is also one-sided Lipschitz but (27) is not fulfilled if a plus is  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Using f(1)(x) = (1 + a)x◦2 − x◦3 − ax leads to  ⟨x − z, f(1)(x) − f(1)(z)⟩2 = −a ∥x − z∥2  2 + ⟨x − z, (1 + a)(x◦2 − z◦2) − (x◦3 − z◦3)⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We obtain that  ⟨x − z, (1 + a)(x◦2 − z◦2) − (x◦3 − z◦3)⟩2 =  n  �  i=1  [(1 + a)(x3  i − zix2  i − xiz2  i + z3  i ) − x4  i + xiz3  i + zix3  i − z4  i ]  =  n  �  i=1  (xi − zi)2[(1 + a)(xi + zi) − x2  i − z2  i − xizi] ≤ (1 + a)2  3  ∥x − z∥2  2  exploiting that (1 + a)(xi + zi) − x2  i − z2  i − xizi ≤ (1+a)2  3  for all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, we have  ⟨x − z, f(1)(x) − f(1)(z)⟩2 ≤ a2 − a + 1  3  ∥x − z∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We observe that the one-sided Lipschitz constant is different from the monotonicity constant in  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, we show that (27) does not hold with a plus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let n = 1 and cf be an  arbitrary constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We fix x = 1 and z = ϵ − 1 with ϵ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We obtain  ⟨x + z, f(1)(x) + f(1)(z)⟩2 = ϵ[−aϵ + (1 + a)(1 + (ϵ − 1)2) − (1 + (ϵ − 1)3)]  = ϵ[2(1 + a) − ϵ3 + (4 + a)ϵ2 − (5 + 3a)ϵ] > cfϵ2 = cf ∥x + z∥2  2 ,  if ϵ is sufficiently small and a > −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Motivated by the one-sided Lipschitz continuity (27), a Gramian based inner product shall  preserve this property leading to the following extension of Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let c1 and c2 be constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, a pair of matrices (P, Q) with P, Q > 0 is  called global one-sided Lipschitz Gramians if they satisfy (11), (12) and  ⟨x + z, P −1(f(x) + f(z))⟩2 ≤ c2∥P − 1  2 (x + z)∥2  2,  ⟨x − z, Q(f(x) − f(z))⟩2 ≤ c2∥Q  1  2 (x − z)∥2  2  (28)  for all x, z ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let P, Q > 0 be solutions to (11), (12) and f be globally Lipschitz with −f(x) =  f(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Then, we can always construct global one-sided Lipschitz Gramians, since for X ∈  {P −1, Q} satisfying (11) and (12), we have that  ⟨X  1  2 (x ± z), X  1  2 (f(x) ± f(z))⟩2 ≤ ∥X  1  2 (x ± z)∥2∥X  1  2 (f(x) ± f(z))∥2 ≤ c2∥X  1  2 (x ± z)∥2  2  for some suitable constant c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  If (28) is satisfied for z = 0, P and Q are global monotonicity Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We will see later  that a reduced order model based on the Gramians introduced in Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12 will lead to error  estimates for all controls u ∈ L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, as in the global monotonicity Gramian case, it might  be inefficient to choose a Gramian allowing to derive estimates for all u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The error analysis will  show that it is actually enough to have (28) for large/essential sets of pairs (x, z) ∈ Rn × Rn in  order to find a reasonable error criterion for a large number of different controls, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', the one-sided  Lipschitz gaps  G+  P −1(x, z) := ⟨x + z, P −1(f(x) + f(z))⟩2 − c2∥P − 1  2 (x + z)∥2  2,  G−  Q(x, z) := ⟨x − z, Q(f(x) − f(z))⟩2 − c2∥Q  1  2 (x − z)∥2  2  (29)  in (28) are mainly negative but also small positive values will be allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We postpone the  discussion of a weaker version of Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12 to Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  13  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' One-sided Lipschitz Gramians are again special solutions of linear matrix in-  equalities for reasons of accessibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Analogue to Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6 this concept can be formulated  more generally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Adding twice (28) to the respective inequality in (11) and (12) leads to  (x + z)⊤�  A⊤P −1 + P −1A +  d  �  i,j=1  N⊤  i P −1Njkij  �  (x + z) + 2⟨x + z, P −1(f(x) + f(z))⟩2  (30)  ≤ −∥B⊤P −1(x + z)∥2  2 + c∥P − 1  2 (x + z)∥2  2,  (x − z)⊤�  A⊤Q + QA +  d  �  i,j=1  N⊤  i QNjkij  �  (x − z) + 2⟨x − z, Q(f(x) − f(z))⟩2  (31)  ≤ −∥C(x − z)∥2  2 + c∥Q  1  2 (x − z)∥2  2  for all x, z ∈ Rn with c ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We will see that this structure is what one requires to achieve a  suitable global error bound for all u ∈ L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Notice that z = 0 leads to (18) and (19), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We will not discuss a definition of Gramians P and Q via (30) and (31) in further detail but will  refer to them within the error analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Now, let us briefly discuss the existence of global one-sided Lipschitz Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given a matrix X > 0 satisfying (9) for some constant c1 and  ⟨x ± z, X(f(x) ± f(z))⟩2 ≤ c2∥X  1  2 (x ± z)∥2  2  for all x, z ∈ Rn and a constant c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, global one-sided Lipschitz Gramians exist with these  constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The proof uses the same argument as in Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 and is therefore omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='11 indicates that the global one-sided Lipschitz Gramian P might not be well-  defined in case f = f(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  5  Particular reduced order model  We select a nonsingular S ∈ Rn×n that we use to simultaneously diagonalize Gramians P and  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This means that the bases of eigenvectors (pk) and (qk) in (20) will be the canonical basis of  Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, by Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7, unimportant directions can be identified with components in  the transformed state variable that are associated with small diagonal entries of the diagonalized  Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, the transformation matrix defines the new state by xn = Sx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Inserting  this into (1) leads to an equivalent stochastic system with coefficients  (An, Bn, fn, Nn,i, Cn) := (SAS−1, SB, Sf(S−1·), SNiS−1, CS−1)  (32)  instead of the original ones (A, B, f, Ni, C), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=',  dxn(t) = [Anxn(t) + Bnu(t) + fn (xn(t))]dt +  d  �  i=1  Nn,i (xn(t−)) dMi(t),  y(t) = Cnxn(t),  (33)  with t ∈ [0, T] and xn(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The new system (33) has the same input u and output y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover,  properties like asymptotic stability are not affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, the Gramians are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' These  are given in the following proposition, where the precise diagonalizing transformation is stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Suppose that S is an invertible matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If P and Q are global/average mono-  tonicity or one-sided Lipschitz Gramians of (1) according to Definitions 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5 or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then,  Pn = SPS⊤ and Qn = S−⊤QS−1 are the respective Gramians in the transformed setting (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  14  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  Given that P, Q > 0, we find that Pn = Qn = Σn = diag(σ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , σn) using the balancing transfor-  mation  S = Σ  1  2nU ⊤L−1  P ,  (34)  where P = LP L⊤  P and L⊤  P QLP = UΣ2  nU ⊤ is a spectral factorization with an orthogonal U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We multiply (11) and (12) with S−⊤ from the left and with S−1 from the right hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Consequently, we see that SPS⊤ and S−⊤QS−1 satisfy these inequalities under the coefficients  in (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, (13) is preserved under this transformation, since  ⟨x, P −1  n fn(x)⟩2 = ⟨x, S−⊤P −1S−1Sf(S−1x)⟩2 = ⟨S−1x, P −1f(S−1x)⟩2 ≤ c2∥P − 1  2 S−1x∥2  2  = c2∥P  − 1  2  n  x∥2  2  and  ⟨x, Qnfn(x)⟩2 = ⟨x, S−⊤QS−1Sf(S−1x)⟩2 = ⟨S−1x, Qf(S−1x)⟩2 ≤ c2∥Q  1  2 S−1x∥2  2 = c2∥Q  1  2nx∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Analogue, we can prove that the one-sided Lipschitz conditions (28) hold under the transforma-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' With xn(s) = xn(s, 0, u) given u ∈ U, we now find  ⟨xn(s), P −1  n fn(xn(s))⟩2 = ⟨x(s), P −1f(x(s))⟩2  and  ⟨xn(s), Qnfn(xn(s))⟩2 = ⟨x(s), Qf(x(s))⟩2,  as well as  ∥P  − 1  2  n  xn(s)∥2  2 = ∥P − 1  2 x(s)∥2  2  and  ∥Q  − 1  2  n xn(s)∥2  2 = ∥Q  1  2 x(s)∥2  2,  so that the average monotonicity conditions (16) and (17) still hold for the same set U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We use  (34) and obtain Pn = Σ  1  2nU ⊤L−1  P PL−⊤  P UΣ  1  2n = Σn as well as Qn = Σ  − 1  2  n U ⊤L⊤  P QLP UΣ  − 1  2  n  = Σn  which concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We observe that the diagonal entries of the balanced Gramians are σi =  �  λi(PQ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We  call them Hankel singular values (HSVs) from now on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, we partition the balanced state  xn =  �xn,1  xn,2  �  and Σn = diag(Σr, Σ2,n−r), where Σr = diag(σ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , σr) contains the large and  Σ2,n−r = diag(σr+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , σn), r < n, the small HSVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The same is done for (32) yielding  An =  �Ar  ⋆  ⋆  ⋆  �  ,  Bn =  �Br  ⋆  �  ,  Nn,i =  �Nr,i  ⋆  ⋆  ⋆  �  ,  Cn =  �  Cr  ⋆  �  and  fr(xr) : = ˜fr([ xr  0 ]),  where  fn =  � ˜fr  ⋆  �  ,  xr ∈ Rr,  0 ∈ Rn−r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (35)  Since xn,2 is associated to small values in Σ2,n−r, we truncate the equation for these variables  and remove them from the dynamics of xn,1 and y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This results in a reduced system (5) with  coefficients given by (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Setting V = Vr and W = Wr, where  S−1 =  �  Vr  ⋆  �  and  S⊤ =  �  Wr  ⋆  �  ,  we see that our reduced system’s structure is of the form as in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, S is given by (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  6  Error analysis of Gramian based reduced system  We consider the reduced system (5) with state dimension r and coefficients like in (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  As  an intermediate step, let us introduce the same type of reduced model with dimension k =  r, r + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n which we write as follows:  dxk(t) = [Akxk(t) + Bku(t) + fk(xk(t))]dt +  d  �  i=1  Nk,ixk(t−)dMi(t),  yk(t) = Ckxk(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (36)  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  15  Setting yn := y, we then observe that  ∥y − yr∥ ≤  n  �  i=r+1  ∥yk − yk−1∥ ,  (37)  where ∥·∥ is some function space norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  This means that we have to investigate the error  ∥yk − yk−1∥ of removing a single HSV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We can derive the reduced system of order k −1 from (36)  by setting the last entry of xk equal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Doing so, we obtain  d  �  xk−1(t)  0  �  =  �  Ak  �  xk−1(t)  0  �  + Bku(t) + fk  � �  xk−1(t)  0  � �  −  �  0  v0(t)  � �  dt  +  d  �  i=1  �  Nk,i  �  xk−1(t−)  0  �  −  �  0  vi(t−)  � �  dMi(t),  yk−1(t) = Ck  �  xk−1(t)  0  �  ,  (38)  where the first k − 1 rows in the state equation of (38) represent the reduced order model of  dimension k − 1 and v0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , vd are (non specified) scalar processes that are introduced to ensure  the equality in the last line which can be read as d0 = 0dt + �d  i=1 0dMi(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let y be the output of (1) with x(0) = 0 and given the r-dimensional reduced  system (5) with output yr, coefficients as in (35) and xr(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If this reduced system is based  on Gramians P and Q satisfying (11) and (12) for a constant c1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, for all u ∈ L2  T , we have  �  E  � T  0  ∥y(s) − yr(s)∥2  2 ec(T−s) ds ≤  n  �  k=r+1  �  E  � T  0  �  2G−  Q  �  Vkxk(s), Vk−1xk−1(s)  �  + σ2  k  �  2G+  P −1  �  Vkxk(s), Vk−1xk−1(s)  �  + 4 ∥u(s)∥2  2  ��  ec(T−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  where c = max{0, 2(c2 − c1)} is defined by another constant c2 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' the parameter of Definitions  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5 or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12) and G+  P −1, G−  Q are the associated one-sided Lipschitz gaps in (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, xk  is the reduced state variable of order k = r, r + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n and Vk is the associated projection matrix  being the first k columns of the inverse S−1 of the balancing transformation defined by (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given the assumptions of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, let P and Q be global one-sided Lipschitz  Gramians according to Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, the following bound holds:  �  E  � T  0  ∥y(s) − yr(s)∥2  2 ec(T−s) ds ≤ 2  n  �  k=r+1  σk  �  E  � T  0  ∥u(s)∥2  2 ec(T−s) ds  (39)  for all u ∈ L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The same bound is established if the Gramians are defined by (30) and (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The functions G+  P −1 and G−  Q are non positive by construction of the global one-sided  Lipschitz Gramians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, the result immediately follows from the one of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  It is not an immediate consequence of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 that (30) and (31) lead to the same result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  However, the proof uses exactly the same ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, it is omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We found the classical bound for reduced order systems based on balanced  truncation in Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 up to the exponential terms in (39), see [10, 11] for the deter-  ministic and [4] for the stochastic linear case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' As mentioned before, choices of Gramians  are only acceptable if c is sufficiently small, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', the exponentials do not dominate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the  other hand, global one-sided Lipschitz Gramians might not be a optimal in terms of their  spectrum, so that a weaker concept is more reasonable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  16  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  As mentioned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4, we can allow for small positive one-sided Lipschitz gaps G−  Q  and G+  P −1, see (29), in certain (small) regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If we pick P and Q accordingly, Theorem  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 then tells us that the averages  E  � T  0  G−  Q  �  Vkxk(s), Vk−1xk−1(s)  �  ec(T−s) ds  and  E  � T  0  G+  P −1  �  Vkxk(s), Vk−1xk−1(s)  �  ec(T−s) ds  will be non positive for a large number of controls u ∈ L2  T and slightly positive in many of  the other scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This means that (39) will (approximately) hold for many controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  In case we have a priori information concerning the solution space of the system, we can say  even more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is given if P and Q are monotonicity Gramians according to Definitions  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5, because of (21) in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This estimate provides that we obtain a small  state approximation error, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', x(t) ≈ Vkxk(t) for k ∈ {r, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n − 1}, if the truncated HSVs  σk+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , σn are of low order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In particular, we have Vk+1xk+1(t) ≈ Vkxk(t) since this is the  error of just removing σk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, we can conclude that we need G−  Q and G+  P −1 to be  mainly negative solely on sets of pairs (x, z) ∈ Rn×Rn with x ≈ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In general, monotonicity  Gramians do not ensure (39), but due to the continuity of f, we can say that  E  � T  0  G−  Q  �  Vkxk(s), Vk−1xk−1(s)  �  ec(T−s) ds ≈ E  � T  0  G−  Q  �  Vkxk(s), Vkxk(s)  �  ec(T−s) ds = 0,  E  � T  0  G+  P −1  �  Vkxk(s), Vk−1xk−1(s)  �  ec(T−s) ds ≈ E  � T  0  G+  P −1  �  Vkxk(s), Vkxk(s)  �  �  ��  �  = 4GP −1  �  Vkxk(s)  �  ec(T−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Now, the monotonicity gap GP −1 defined in (15) is non positive on average for u ∈ U  by construction of the average monotonicity Gramian P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This ensures that the bound of  Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 might still deliver a reasonable error criterion although it does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We introduce x−(t) := xk(t) −  �  xk−1(t)  0  �  and x+(t) := xk(t) +  �  xk−1(t)  0  �  ,  for which the dynamics are obtained by subtracting/adding (36) and (38), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=',  dx−(t) = [Akx−(t) +  �  0  v0(t)  �  + fk(xk(t)) − fk  �� xk−1(t)  0  ��]dt +  d  �  i=1  �Nk,ix−(t−) +  �  0  vi(t−)  � �dMi(t)  (40)  dx+(t) = [Akx+(t) + 2Bku(t) −  �  0  v0(t)  �  + fk(xk(t)) + fk  �� xk−1(t)  0  ��]dt +  d  �  i=1  �Nk,ix+(t−) −  �  0  vi(t−)  � �dMi(t)  (41)  Recalling that Σk = diag(σ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , σk) denotes the diagonal matrix of the k largest HSVs of the  original system, we know, by Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, that Σn satisfies (11) and (12) with the balanced  realization (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Evaluating the left upper k × k block of the equations associated to Σn, we  obtain  (Ak + c1I)⊤Σ−1  k  + Σ−1  k (Ak + c1I) +  d  �  i,j=1  N⊤  k,iΣ−1  k Nk,jkij ≤ −Σ−1  k BkB⊤  k Σ−1  k ,  (42)  (Ak + c1I)⊤Σk + Σk(Ak + c1I) +  d  �  i,j=1  N⊤  k,iΣkNk,jkij ≤ −C⊤  k Ck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (43)  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  17  Taking (40) into account, Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 is applied to Σ  1  2  k x−(t) to obtain  d  dtE  �  x−(t)⊤Σkx−(t)  �  =2E  �  x−(t)⊤Σk[Akx−(t) +  �  0  v0(t)  �  + fk(xk(t)) − fk  �� xk−1(t)  0  ��]  �  +  d  �  i,j=1  E  ��  Nk,ix−(t) +  �  0  vi(t)  � �⊤Σk  �  Nk,jx−(t) +  �  0  vj(t)  � ��  kij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Integrating this equation over [0, t] with t ≤ T yields  E  �  x−(t)⊤Σkx−(t)  �  = E  � t  0  x−(s)⊤�  A⊤  k Σk + ΣkAk +  d  �  i,j=1  N⊤  k,iΣkNk,jkij  �  x−(s)ds  + 2E  � t  0  x−(s)⊤Σk  �  fk(xk(s)) − fk  �� xk−1(s)  0  ���ds + R−(t),  where R−(t) = E  � t  0 2x−(s)⊤Σk  �  0  v0(s)  �  +�d  i,j=1  �  2Nk,ix−(s) +  �  0  vi(s)  ��⊤  Σk  �  0  vj(s)  �  kijds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let xk,2  be the last entry of xk and hence also of x−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, nk,i shall denote the last line of Nk,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' There-  fore, we obtain that x−(s)⊤Σk  �  0  v0(s)  �  = σkxk,2(s)v0(s) and  �  2Nk,ix−(s) +  �  0  vi(s)  ��⊤  Σk  �  0  vj(s)  �  kij =  σk (2nk,ix−(s) + vi(s)) vj(s)kij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' By construction of vi in (38), we have −2nk,i  �  xk−1(s)  0  �  +2vi(s) =  0, so that σk (2nk,ix−(s) + vi(s)) vj(s)kij = σk (2nk,ixk(s) − vi(s)) vj(s)kij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, it holds  that  R−(t) ≤ σkE  � t  0  2xk,2(s)v0(s) +  d  �  i,j=1  (2nk,ixk(s) + vi(s)) vj(s)kijds  exploiting that �d  i,j=1 vi(s)vj(s)kij ≥ 0, because K = (kij) is positive semidefinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Hence,  E  �  x−(t)⊤Σkx−(t)  �  ≤ E  � t  0  x−(s)⊤�  (Ak + c1I)⊤Σk + Σk(Ak + c1I) +  d  �  i,j=1  N⊤  k,iΣkNk,jkij  �  x−(s)ds  + 2E  � t  0  x−(s)⊤Σk  �  fk(xk(s)) − fk  �� xk−1(s)  0  �� − c2x−(s)  �ds  + σkE  � t  0  2xk,2(s)v0(s) +  d  �  i,j=1  (2nk,ixk(s) + vi(s)) vj(s)kijds  + c  � t  0  E  �  x−(s)⊤Σkx−(s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We set Tk,−(t) := 2E  � t  0 x−(s)⊤Σk  �  fk(xk(s))−fk  �� xk−1(s)  0  ��−c2x−(s)  �ds and αk(t) := E  � t  0 2xk,2(s)v0(s)+  �d  i,j=1 (2nk,ixk(s) + vi(s)) vj(s)kijds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Based on (43) combined with the definitions of the outputs  in (36) and (38), we have  E  �  x−(t)⊤Σkx−(t)  �  ≤ − ∥yk − yk−1∥2  L2  t + Tk,−(t) + σkαk(t) + c  � t  0  E  �  x−(s)⊤Σkx−(s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We obtain by (50) that  E  � t  0  ∥yk(s) − yk−1(s)∥2  2 ec(t−s) ds ≤  � t  0  � ˙Tk,−(s) + σk ˙αk(s)  �  ec(t−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (44)  18  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  Now, exploiting Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 for the process Σ  − 1  2  k x+(t) together with (41) yields  E  �  x+(t)⊤Σ−1  k x+(t)  �  = E  � t  0  x+(s)⊤�  A⊤  k Σ−1  k  + Σ−1  k Ak +  d  �  i,j=1  N⊤  k,iΣ−1  k Nk,jkij  �  x+(s)ds  + 2E  � t  0  x+(s)⊤Σ−1  k  �  fk(xk(s)) + fk  �� xk−1(s)  0  ���ds  + E  � t  0  4x+(s)⊤Σ−1  k Bku(s)ds − R+(t),  where R+(t) = E  � t  0 2x+(s)⊤Σ−1  k  �  0  v0(s)  �  + �d  i,j=1  �  2Nk,ix+(s) −  �  0  vi(s)  ��⊤  Σ−1  k  �  0  vj(s)  �  kijds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We  observe that x+(s)⊤Σ−1  k  �  0  v0(s)  �  = σ−1  k xk,2v0(s) and  �  2Nk,ix+(s) −  �  0  vi(s)  ��⊤  Σ−1  k  �  0  vj(s)  �  kij =  σ−1  k (2nk,ix+(s)−vi(s))vj(s)kij = σ−1  k (2nk,ixk(s)+vi(s))vj(s)kij telling us that R+(t) = σ−1  k αk(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Defining Tk,+(t) := 2E  � t  0 x+(s)⊤Σ−1  k  �  fk(xk(s)) + fk  �� xk−1(s)  0  �� − c2x+(s)  �ds results in  E  �  x+(t)⊤Σ−1  k x+(t)  �  = E  � t  0  x+(s)⊤�  (Ak + c1I)⊤Σ−1  k  + Σ−1  k (Ak + c1I) +  d  �  i,j=1  N⊤  k,iΣ−1  k Nk,jkij  �  x+(s)ds  + Tk,+(t) + E  � t  0  4x+(s)⊤Σ−1  k Bku(s)ds − σ−1  k αk(t)  + c  � t  0  E  �  x+(s)⊤Σ−1  k x+(s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We exploit the estimate  4 ∥u(s)∥2  2 ≥ ∥2u(s)∥2  2 −  ���B⊤  k Σ−1  k x+(s) − 2u(s)  ���  2  2  = −x+(s)⊤Σ−1  k BkB⊤  k Σ−1  k x+(s) + 4x+(s)⊤Σ−1  k Bku(s)  and insert (42) in order to find  E  �  x+(t)⊤Σ−1  k x+(t)  �  ≤ 4 ∥u∥2  L2  t + Tk,+(t) − σ−1  k αk(t) + c  � t  0  E  �  x+(s)⊤Σ−1  k x+(s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We apply (50) providing  � t  0  ˙αk(s) ec(t−s) ds ≤ σk  � t  0  � ˙Tk,+(s) + 4E ∥u(s)∥2  2  �  ec(t−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Combining this with (44) leads to  E  � t  0  ∥yk(s) − yk−1(s)∥2  2 ec(t−s) ds ≤  � t  0  �  ˙Tk,−(s) + σ2  k  � ˙Tk,+(s) + 4E ∥u(s)∥2  2  ��  ec(t−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The last step is to find different representations for Tk,− and Tk,+ inserting the definitions of x+  and x−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We recall that fk(xk) := ˜fk(  �  xk  0n−k  �  ), xk ∈ Rk and 0n−k ∈ Rn−k by (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Since ˜fk are  the first k entries of the balanced nonlinearity fn, we have  �  xk(s) ±  � xk−1(s)  0  ��⊤Dk  �fk(xk(s)) ± fk  �� xk−1(s)  0  �� − c2  �xk(s) ±  � xk−1(s)  0  ���  =  ��  xk(s)  0n−k  �  ±  �  xk−1(s)  0n−k+1  ��⊤Dn  �fn(  �  xk(s)  0n−k  �  ) ± fn  ��  xk−1(s)  0n−k+1  �� − c2  ��  xk(s)  0n−k  �  ±  �  xk−1(s)  0n−k+1  ���,  where Dk ∈ {Σk, Σ−1  k }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' By Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 and (32), we know that Σn = S−⊤QS−1, Σ−1  n  =  S−⊤P −1S−1 and fn = Sf(S−1·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Moreover, S−1�  xk(s)  0n−k  �  = Vkxk(s), since Vk are the first k  columns of the inverse S−1 of the balancing transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Hence,  Tk,−(t) = 2E  � t  0  G−  Q  �  Vkxk(s), Vk−1xk−1(s)  �  ds,  Tk,+(t) = 2E  � t  0  G+  P −1  �  Vkxk(s), Vk−1xk−1(s)  �  ds  according to the definition of the one-sided Lipschitz gaps in (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This concludes the proof using  (37) and setting t = T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  19  7  Numerical experiments  Below, let L > 0 defining a “step size” parameter h :=  L  (n+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Based on this, we introduce a grid  by ζj = jh for j = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Now, we mainly focus on an example for (1) that is given by  dx1(t) =  �x2(t) − 2x1(t)  h2  + u1(t)  h2  + f(x1(t))  �  dt +  d  �  i=1  gi(ζ1)x1(t−)dMi(t),  dxj(t) =  �xj+1(t) − 2xj(t) + xj−1(t)  h2  + f(xj(t))  �  dt +  d  �  i=1  gi(ζj)xj(t−)dMi(t),  dxn(t) =  �−2xn(t) + xn−1(t)  h2  + u2(t)  h2  + f(xn(t))  �  dt +  d  �  i=1  gi(ζn)xn(t−)dMi(t)  (45)  for j ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , n − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We have that u = [ u1  u2 ] (m = 2) and f(x) = [ f(x1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' f(xn) ]⊤, where f and  gi are scalar functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Formally, (45) can interpreted as a finite difference discretization of the  stochastic reaction diffusion equation  dvt(ζ) =  � ∂2  ∂ζ2 vt(ζ) + f  �  vt(ζ)  ��  +  d  �  i=1  gi(ζ)vt−(ζ)dMi(t),  ζ ∈ (0, L),  t ∈ (0, T),  v0(ζ) ≡ 0,  vt(0) = u1(t)  and  vt(L) = u2(t)  (46)  with controlled boundaries and the intuition that xj(t) ≈ vt(ζj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let us specify the other pa-  rameter and the noise profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Below, M is a Wiener process in dimension d = 2 with covariance  K =  �  1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  1  �  and n = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We study the nonlinearities f(v) = (1+a)v2 −v3 −av with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1  and f(v) = v − v3, so that f = f(1) or f = f(2) introduced in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The particular noise  scaling functions are g1(ζ) = 4 sin(ζ) and g2(ζ) = 4 cos(ζ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moreover, the terminal time is T = 1  and the quantity of interest shall be the following average:  y(t) = 1  n  n  �  j=1  xj(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (47)  For illustration we show two typical paths of (47) for f = f(1), f(2) and two different inputs in  Figures 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8  1  −1  0  1  2  3  Time t  Output path y(·, ω)  Figure 2: Path of (47) with f = f(1) and  u = ˜u in (48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8  1  −2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5  Time t  Output path y(·, ω)  Figure 3: Path of (47) with f = f(2) and  u = ˆu in (48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  For f = f(2), we know that (10) holds with X = I and c2 ≥ cf = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Further, we observe  that (9) is true for X = I and c1 = cf = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore, the system is globally mean square  asymptotically stable according to Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 and the concept of monotonicity Gramians with  20  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  c1 = c2 = 1 is well-defined by Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We can even guarantee the existence of a one-sided  Lipschitz Gramian by Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='15 since the one-sided Lipschitz condition (27) holds with  cf = 1 using Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The choice of f = f(2) also yields a mean square asymptotically  stable system since (9) particularly holds for X = I if c1 = cf =  (a−1)2  4  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='20250 is used  and since we know, by Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1, that (10) is true setting X = I and c2 ≥ cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Therefore,  monotonicity Gramians also exist here for c1 = c2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='20250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On the other hand, a one-sided  Lipschitz Gramian Q exists with c1 = c2 = a2−a+1  3  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='30¯3 due to Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='15 (X = I)  exploiting Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The same example, however, indicates that P might not be available  as a one-sided Lipschitz Gramian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The goal of this section is to construct average monotonicity Gramians P and Q according  to Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5 for a large set of controls U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In detail, we choose the monotonicity/one-sided  Lipschitz constant to define c1 = c2 = 1 for f = f(2) and we set c1 = c2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='30¯3 for f = f(1) which  is a number dominating the monotonicity constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='20250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Consequently, Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1  hold for c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We choose Q to be the solution to the equality in (12) and P the candidate with  minimal trace satisfying (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We refer to Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3 for the particular computation strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We observe that these P and Q do not satisfy (13) for all x ∈ Rn but for the essential ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  In fact, we run experiments for a large variety of controls involving increasing, decreasing and  (highly) oscillating u as well as a combination of all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In all cases, conditions (16) and  (17) were fulfilled indicating that these P and Q are average monotonicity Gramians for a large  set of controls U ⊂ L2  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We present the experiments solely for two representatives ˜u, ˆu ∈ U which  are given by  ˜u(t) =  �  −3 cos(20t)  2 sin(10t)  �  and  ˆu(t) =  �  −3 e−t  2  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (48)  These are chosen since they also steer the state x(t) to regions of Rn, where the monotonicity  conditions in (13) are violated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The constructed monotonicity Gramians have the advantage that  the HSVs provide a reliable criterion for the reduction error according to Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here,  we have c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We depict these algebraic values for f = f(1) in Figure 4 and observe a strong  decay telling us that we can expect a low approximation error for small r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The HSVs for f = f(2)  behave very similarly and are therefore omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' As discussed in Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3, we cannot expect  1  20  40  60  80  100  0  −5  −10  −15  −20  −25  −30  i (index)  log10  ��  λi(PQ)  �  Figure 4: Logarithmic HSVs based on monotonicity Gramians for f = f(1) with c1 = c2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='30¯3,  where Q satisfies the equality in (12) and P is the minimal trace solution of (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  the bound in Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 (with c = 0) to hold if average monotonicity Gramians are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  However, we expect the error to not be far from this bound, since the one-sided Lipschitz gaps  G+  P −1 and G−  Q in Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 are expected to be small when they are positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We compute the  output yr of the reduced order model (5) introduced in Section 5 for different reduced dimensions  r = 3, 6, 10, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The relative output error for f = f(1) can be found in Table 1 for the controls  ˜u and ˆu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We observe a decreasing behaviour for growing r yielding a very high accuracy for  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  21  ∥y − yr∥L2  T / ∥y∥L2  T for f = f(1)  r  u = ˜u  u = ˆu  3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='4077e−02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8041e−02  6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='0903e−03  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7334e−03  10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1233e−04  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5745e−04  20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7327e−07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5013e−07  Table 1: Relative output error dimension  reduction with controls in (48) and f = f(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  2 �n  k=r+1 σk ∥u∥L2  T / ∥y∥L2  T for f = f(1)  r  u = ˜u  u = ˆu  3  aa 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='0240e−01aa  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8031e−01  6  aa 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6029e−03 aa  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5112e−02  10  aa 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6198e−04 aa  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1347e−04  20  aa 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3487e−07 aa  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3709e−07  Table 2: Relative error criterion of Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  with c = 0 and f = f(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  ∥y − yr∥L2  T / ∥y∥L2  T for f = f(2)  r  u = ˜u  u = ˆu  3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3380e−02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='5840e−02  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7409e−03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='9983e−03  10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1507e−04  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3924e−04  20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8514e−07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='8720e−07  Table 3: Relative output error dimension  reduction with controls in (48) and f = f(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  2 �n  k=r+1 σk ∥u∥L2  T / ∥y∥L2  T for f = f(2)  r  u = ˜u  u = ˆu  3  aa1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='0494e−01aa  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='6369e−01  6  aa7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2186e−03 aa  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3624e−02  10  aa4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='7378e−04aa  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3326e−04  20  aa1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3493e−07aa  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1019e−07  Table 4: Relative error criterion of Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  with c = 0 and f = f(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  r ≥ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Table 2 shows the bound of Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 which generally is no upper bound for the error  calculated in Table 1, see the case of r = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is because the one-sided Lipschitz gaps are not  always non positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' However, 2 �n  k=r+1 σk is close to the actual error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is an observation  made also in additional simulations that are not presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The intuition for 2 �n  k=r+1 σk  being an upper bound for dimensions r = 3, 6, 10 but not for r = 20 might be the low order of  a positive one-sided Lipschitz gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' For that reason, it becomes only visible when 2 �n  k=r+1 σk is  very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We repeat the error calculations for f = f(2) and obtain basically the same results,  see Tables 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' This is due to a similar path behaviour of y for both nonlinearities f(1) and  f(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Let us finally mention that we conducted the same experiments also when the right Dirichlet  boundary condition in (46) is replaced by the Neumann condition  ∂  ∂ζ vt(ζ)|ζ=L = u2(t) leading to  dxn(t) =  �−xn(t) + xn−1(t)  h2  + u2(t)  h  + f(xn(t))  �  dt +  d  �  i=1  gi(ζn)xn(t)dMi(t)  instead of the last line in (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Here, analog results can be seen using the same kind of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  A  Supporting lemmas  This Section contains several useful auxiliary results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Suppose that a, b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' , bd are Rn-valued processes with a being (Ft)-adapted and  almost surely Lebesgue integrable and bi being integrable w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='t the mean zero square integrable  L´evy process M =  �  M1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Md  �⊤ with covariance matrix K = (kij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' If x is represented by  dx(t) = a(t)dt + b(t)dM = a(t)dt +  d  �  i=1  bi(t)dMi,  where b =  �  b1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  bd  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Then, we have  d  dtE  �  x(t)⊤x(t)  �  = 2E  �  x(t)⊤a(t)  �  + E  ���b(t)K  1  2  ���  2  F = 2E  �  x(t)⊤a(t)  �  +  d  �  i,j=1  E  �  bi(t)⊤bj(t)  �  kij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  We introduce two classical versions of Gronwall’s lemma below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  22  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2 (Gronwall lemma – differential form).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given T > 0 let z : [0, T] → R be differen-  tiable functions and β ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given that  ˙z(t) ≤ βz(t),  t ∈ [0, T],  then for all t ∈ [0, T], it holds that  z(t) ≤ z(0) eβt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  The corresponding integral version follows next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='3 (Gronwall lemma – integral form).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given T > 0 let z, α : [0, T] → R be continuous  functions and β ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given that  z(t) ≤ α(t) +  � t  0  βz(s)ds,  t ∈ [0, T],  then for all t ∈ [0, T], it holds that  z(t) ≤ α(t) +  � t  0  α(s)β eβ(t−s) ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (49)  If α further is absolutely continuous, we have  z(t) ≤ α(0) eβt +  � t  0  ˙α(s) eβ(t−s) ds,  (50)  where ˙α is the derivative of α Lebesgue almost everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The first part is a very classical result and is not proved here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Given that α is absolutely  continuous, we can apply integration by parts yielding  � t  0  α(s)β eβ(t−s) ds = −α(s) eβ(t−s) ��t  0 +  � t  0  ˙α(s) eβ(t−s) ds  Hence, we obtain (50) from (49).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  B  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2  We define  −Y := (A + c1I)⊤X + X(A + c1I) +  d  �  i,j=1  N⊤  i XNjkij < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  (51)  We apply Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='1 to the uncontrolled process X  1  2 x(t) and obtain  d  dtE  �  x(t)⊤Xx(t)  �  = 2E  �  x(t)⊤X[Ax(t) + f(x(t))]  �  +  d  �  i,j=1  E  �  x(t)⊤N⊤  i XNjx(t)  �  kij  ≤ 2E  �  x(t)⊤X[Ax(t) + c2Ix(t)]  �  +  d  �  i,j=1  E  �  x(t)⊤N⊤  i XNjx(t)  �  kij  = E  �  x(t)⊤�  (A + c1I)⊤X + X(A + c1I) +  d  �  i,j=1  N⊤  i XNjkij  �  x(t)  �  + 2(c2 − c1)E  �  x(t)⊤Xx(t)  �  = 2(c2 − c1)E  �  x(t)⊤Xx(t)  �  − E  �  x(t)⊤Y x(t)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  23  exploiting inequality (10) and inserting (51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' We define k and k to be the smallest the largest  eigenvalue of X, respectively, yielding kI ≤ X ≤ kI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' With the smallest eigenvalue kY of Y giving  −Y ≤ −kY I, we obtain −E  �  x(t)⊤Y x(t)  �  ≤ −kY E  �  x(t)⊤x(t)  �  ≤ − kY  k E  �  x(t)⊤Xx(t)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Setting  β := kY  k , we hence find  d  dtE  �  x(t)⊤Xx(t)  �  ≤ (2(c2 − c1) − β)E  �  x(t)⊤Xx(t)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  By the differential version of Gronwall’s inequality in Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='2, we have  E  �  x(t)⊤x(t)  �  ≤ 1  kE  �  x⊤(t)Xx(t)  �  ≤ 1  kx⊤  0 Xx0 exp {(2(c2 − c1) − β)t}  ≤ k  kx⊤  0 x0 exp {(2(c2 − c1) − β)t}  concluding the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Acknowledgments  MR is supported by the DFG via the individual grant “Low-order approximations for large-scale  problems arising in the context of high-dimensional PDEs and spatially discretized SPDEs”–  project number 499366908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Albeverio, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Brze´zniak, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Existence of global solutions and invariant mea-  sures for stochastic differential equations driven by Poisson type noise with non-Lipschitz  coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Journal of Mathematical Analysis and Applications, 371(1):309–322, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Becker and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Hartmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Infinite-dimensional bilinear and stochastic balanced truncation  with error bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Signals, Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 31:1–37, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Benner and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Breiten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Two-Sided Projection Methods for Nonlinear Model Order Re-  duction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 37(2), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [4] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Benner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Damm, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Rodriguez Cruz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Dual pairs of generalized Lyapunov in-  equalities and balanced truncation of stochastic linear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Autom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Contr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=',  62(2):782–791, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Benner and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Goyal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Balanced truncation model order reduction for quadratic-bilinear  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Technical Report 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='00160, arXiv, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Benner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Goyal, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gugercin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  H2-Quasi-Optimal Model Order Reduction for  Quadratic-Bilinear Control Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Matrix Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 39(2), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Benner and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Redmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Model Reduction for Stochastic Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Stoch PDE: Anal  Comp, 3(3):291–338, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Da Prato.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Kolmogorov Equations for Stochastic PDEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Number VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Birkh¨auser Basel,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [9] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Damm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Rational Matrix Equations in Stochastic Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lecture Notes in Control and  Information Sciences 297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Berlin: Springer, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Enns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Model reduction with balanced realizations: An error bound and a frequency  weighted generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' 23rd IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Decision and Control, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  24  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' REDMANN  [11] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Glover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' All optimal Hankel-norm approximations of linear multivariable systems and  their L∞-error bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Control, 39(6):1115–1193, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [12] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gosea and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Antoulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Data-driven model order reduction of quadratic-bilinear  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Numerical Linear Algebra with Applications, 25(6), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gugercin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Antoulas, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Beattie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' H2 Model Reduction for Large-Scale Linear  Dynamical Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Matrix Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 30(2):609–638, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [14] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gy¨ongy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential  Equations Driven by Space-Time White Noise I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Potential Analysis, 9:1–25, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [15] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gy¨ongy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential  Equations Driven by Space-Time White Noise II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Potential Analysis, 11:1–37, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [16] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Gy¨ongy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On stochastic finite difference schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Stoch PDE: Anal Comp, 2:539–583, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Khasminskii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Stochastic stability of differential equations, volume 66 of Stochastic  Modelling and Applied Probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Springer, Heidelberg, second edition, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Kramer and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Willcox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Nonlinear Model Order Reduction via Lifting Transformations  and Proper Orthogonal Decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' AIAA Journal, 57(6):2297–2307, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Kramer and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Willcox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Balanced Truncation Model Reduction for Lifted Nonlinear  Systems, pages 157–174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Springer International Publishing, Cham, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Kunisch and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Volkwein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Galerkin proper orthogonal decomposition methods for  parabolic problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 90(1):117–148, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [21] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' K¨uhn and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Neamt¸u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Dynamics of Stochastic Reaction-Diffusion Equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  In  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Grecksch and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lisei, editors, Infinite Dimensional and Finite Dimensional Stochastic  Equations and Applications in Physics, chapter 1, pages 1–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' World Scientific Publishing,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' L¨ofberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' YALMIP: A Toolbox for Modeling and Optimization in MATLAB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' In In Pro-  ceedings of the CACSD Conference, Taipei, Taiwan, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [23] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Mao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Stochastic Differential Equations and Applications (Second Edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Woodhead  Publishing, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [24] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Marinelli and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' R¨ockner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' On uniqueness of mild solutions for dissipative stochastic  evolution equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Infinite Dimensional Analysis, Quantum Probability and Related Topics,  13(3):363–376, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [25] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Moore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Principal component analysis in linear systems: Controllability, observability, and  model reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' IEEE transactions on automatic control, 26(1):17–32, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [26] MOSEK ApS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' The MOSEK optimization toolbox for MATLAB manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Version 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [27] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Peszat and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Zabczyk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Stochastic Partial Differential Equations with L´evy Noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' An evo-  lution equation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Encyclopedia of Mathematics and Its Applications 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Cambridge  University Press, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [28] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Qian, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Kramer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Peherstorfer, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Wilcox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lift & Learn: Physics-informed  machine learning for large-scale nonlinear dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Physica D: Nonlinear Phe-  nomena, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Redmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Energy estimates and model order reduction for stochastic bilinear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Control, 93(8):1954–1963, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  MODEL REDUCTION FOR STOCHASTIC SYSTEMS WITH NONLINEAR DRIFT  25  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Redmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Type II singular perturbation approximation for linear systems with L´evy  noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Control Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 56(3):2120–2158, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Redmann and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Freitag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Optimization based model order reduction for stochastic  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', Volume 398, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Scherpen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Balancing for nonlinear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=', 21:143–153, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [33] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Shardlow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Numerical methods for stochastic parabolic PDEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  Numerical Functional  Analysis and Optimization, 20(1-2):121–145, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='  [34] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Tyranowski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' Data-driven structure-preserving model reduction for stochastic Hamil-  tonian systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content=' arXiv preprint:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
+page_content='13391, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fNFST4oBgHgl3EQfGjh7/content/2301.13722v1.pdf'}
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+IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+1
+Split Boot - True Network-Based Booting on
+Heterogeneous MPSoCs
+Marvin Fuchs, Luis E. Ardila-Perez, Torben Mehner, and Oliver Sander
+Abstract—In the context of the High-Luminosity (HL) up-
+grade of the LHC, many custom ATCA electronics boards are
+being designed containing heterogeneous System-on-Chip (SoC)
+devices, more specifically the Xilinx Zynq UltraScale+ (ZUS+)
+family. While the application varies greatly, these devices are
+regularly used for performing board management tasks, making
+them a fundamental element in the correct operation of the
+board. The large number of hundreds of SoC devices creates
+significant challenges in their firmware deployment, maintenance,
+and accessibility.
+Even though U-Boot on ZUS+ devices supports network boot
+through the Preboot Execution Environment (PXE), the standard
+ZUS+ boot process contains application-specific information at
+earlier boot steps, particularly within the First Stage Bootloader
+(FSBL). This prevents the initialization of several devices from
+a universal image. Inspired by the PXE boot process on desktop
+PCs, this paper describes split boot, a novel boot method
+tailored to the specific needs of the ZUS+. All application-
+specific configuration is moved to a network storage device and
+automatically fetched during the boot process. We considered
+the entire process, from firmware and software development to
+binary distribution in a large-scale system. The developed method
+nicely integrates with the standard Xilinx development toolset
+workflow.
+Index Terms—Booting, Large-Scale Experiments, MPSoC, Net-
+work Booting, PXE, System-on-Chip, Zynq Ultrascale+
+I. INTRODUCTION
+T
+HE Xilinx Zynq UltraScale+ (ZUS+) devices are het-
+erogeneous Multi-Processor System-on-Chips (MPSoCs)
+that, in addition to the Programmable Logic (PL), contain a
+Processing System (PS) with a number of hard processing
+units, such as an ARM Cortex-A53 named Application Pro-
+cessing Unit (APU), an ARM Cortex-R5 named Real-Time
+Processing Unit (RPU), and the Platform Management Unit
+(PMU) based on the MicroBlaze architecture [1]. Even though
+not all processors have to be involved in the boot process, it
+usually relies on several of them. To make the ZUS+ devices
+deployable in a wide range of applications, they are designed
+to be highly configurable. To a certain extent, this also applies
+to the boot process, as shown in Fig. 1. For example, it is
+possible to load both, the bitfile for the PL and the firmware
+for the RPU, in either the First Stage Bootloader (FSBL), the
+second-stage boot loader U-Boot or from Linux. In some cases
+it is also possible to change the order, for example to load the
+PMU firmware either before or after the FSBL.
+Manuscript submitted September 10, 2022; revised November 11, 2022.
+This research acknowledges the support by the Doctoral School “Karlsruhe
+School of Elementary and Astroparticle Physics: Science and Technology”
+M. Fuchs (corresponding author, email: marvin.fuchs at kit.edu), L. E.
+Ardila-Perez, T. Mehner and O. Sander are with the Institute for Data Process-
+ing and Electronics (IPE) of the Karlsruhe Institute of Technology, Hermann-
+von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
+The first stage in the boot process that contains application-
+specific information is the FSBL. Vivado generates C code
+to configure the PS and to optionally divide it in multiple
+subsystems via an isolation-configuration according to the set-
+tings selected in the Vivado PS Configuration Wizard (PCW)
+GUI [2]. When the FSBL software project is set up, this source
+code is automatically integrated.
+The FSBL contains information on how to configure the
+various internal clocks, the interfaces to the PL, and external
+interfaces such as the UARTs or the network. The application-
+specific code contained in it to do this, is one of the reasons
+why the FSBL cannot be factory-saved to a non-volatile mem-
+ory within the MPSoC. Thus, it is one of the first components
+loaded from an external storage (e.g. a QSPI memory or an
+SD Card). The same storage location is usually also used for
+the PMU firmware, the Arm Trusted Firmware (ATF), and U-
+Boot. In contrast, entirely generic software like the PMU ROM
+and the Configuration Security Unit (CSU) ROM is stored on
+non-volatile memory within the ZUS+ [3].
+The goal of the modified boot process presented in this
+paper is to fetch all application-specific data including the
+PS configuration from a network source. This is, however,
+not trivial because the FSBL itself is a low-level stage in
+the boot process and it is not designated to communicate
+via a network connection. Just as with PCs that boot via
+Preboot Execution Environment (PXE), the greatest advantage
+for MPSoCs that obtain all application-specific data from the
+Fig. 1. Default software stack used to boot Xilinx Zynq UltraScale+ devices.
+The solid lines describe one possible example of a boot process, whereas the
+dashed lines show alternative possibilities to load a bitfile for the PL and the
+firmware for the RPU.
+arXiv:2301.05642v1  [physics.ins-det]  13 Jan 2023
+
+Real-Time
+Bit File
+Linux
+Firmware
+U-Boot
+ATF
+PMUFirmware
+FSBL
+APU
+IRPU
+CSUROM
+PL
+PMU
+PMUROM
+ICSUIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+2
+network appears in large systems where many devices need to
+be maintained. One example is the distribution of updates in
+a large and distributed system, comprised of many identically
+configured boards. In its most efficient implementation, split
+boot enables accomplishing the task by only updating the
+single network storage and rebooting the devices. Significant
+time is saved compared to having to flash the local storage of
+each board. In the remainder of this contribution, we present a
+two-step approach that essentially supports fetching the entire
+PS configuration via network and applying it to the PS.
+II. RELATED WORK
+U-Boot already features PXE, which allows devices to boot
+into an operating system such as Linux via the network. How-
+ever, it does not cover the configuration of the PS [4]. Such
+a functionality is not provided, because PXE was originally
+designed for computer networks rather than networks of highly
+configurable System-on-Chips (SoCs) such as the ZUS+ fam-
+ily. Modifications to the FSBL on MPSoC devices might be
+required on a regular basis due to containing application-
+specific information. This is a major drawback compared to
+the boot of a desktop PC, where updates to the BIOS and all
+other software used before the second-stage boot loader are
+very rarely necessary. Research regarding PXE usually targets
+desktop PCs [5] or servers [6], but not embedded devices.
+Xilinx provides means to adapt the boot process based on the
+application domain [1] and further describes in a patent the
+boot process possibilities of MPSoC devices [7]. However, the
+ability to load the PS configuration from a remote location
+is not mentioned. In the context of the High-Luminosity
+(HL) upgrade of the LHC, active research is being conducted
+about the boot process of MPSoC devices. To date, though,
+work has focused primarily on investigating and securing the
+possibilities provided by Xilinx [8] and building the Linux
+distribution for use on the device [9].
+III. SPLIT CONFIGURATION APPROACH
+Simply moving the entire configuration of the PS part of
+a ZUS+ MPSoC to a network storage is not feasible. Some
+initial configuration is needed to bring up the essential func-
+tionality of the device. This includes, first and foremost, the
+network interface and the configuration of the DDR memory
+controller, but also some internal configuration. While this
+configuration is board-specific, it is not application-specific.
+As a conclusion, we propose using a base configuration which
+is static and reduced to the absolute minimum to boot into U-
+Boot with network access. This approach is similar in many
+ways to that of a PC BIOS. Updates to the base firmware are
+possible, but they are expected to happen rarely.
+The application-specific data for the PS can be split into
+two tasks. The first one includes the configuration of all the
+individual components like clocks within the PS, the PS-
+PL interfaces, and some peripherals like the DDR memory.
+The second task is the application of the so-called isolation-
+configuration, which divides the PS into multiple subsystems
+and defines access permissions between them. For both, we
+propose to move the application-specific data into separate bi-
+nary configuration files, which are then fetched from a network
+source and applied by U-Boot during the boot process. Fig. 2
+shows how removing the application-specific configuration
+data from the FSBL leads to a system where only generic
+software remains on the local boot medium and everything
+application-specific is stored on the network.
+IV. THE MODIFIED BOOT PROCESS
+Xilinx ZUS+ devices require multiple tweaks in the default
+boot process to allow for changes to the PS configuration after
+it has been initially configured in the FSBL. An overview of
+these modifications is provided by the example boot sequence
+in Fig. 3, where the changes are shown as white boxes with red
+frames. The boot procedure starts as usual with the software
+components PMU ROM and CSU ROM stored on non-volatile
+memory within the ZUS+. Afterwards, the PMU firmware is
+started, in this case, before the FSBL.
+The FSBL contains the first modification in the proposed
+boot process. Usually, at this stage, the PS gets initialized
+with its complete configuration. During the split boot process,
+however, this is where the PS receives its base configuration
+(psu init base), which includes the boot related peripheral and
+memory configuration.
+The source code that is used to configure the PS is generated
+by Vivado according to the options selected in the PCW and
+inserted into the FSBL automatically. Because of this, the
+software architecture of the FSBL allows us to easily replace
+this part of the source code, for example with that of our
+generic base configuration.
+When the FSBL has finished its execution, it hands over
+to the ATF. The ATF is a reference implementation of an
+ARM secure world software provided by Xilinx and in the
+example depicted in Fig. 3 the first software executed on the
+APU. Such a software is necessary to utilize the Armv8-A
+Exception Model that is implemented in the APU [10].
+When the ATF is running, U-Boot can be started. It contains
+the remaining modifications to the original boot process. The
+first modification (Fetch Cfg.) loads all the required config-
+uration data using standard U-Boot features from a TFTP
+server. This includes, in addition to the regular Linux kernel, a
+Fig. 2.
+The split boot approach removes from the FSBL the application-
+specific PS configuration and the isolation configuration. As a result, only
+generic information remains on the local boot medium.
+
+Linux Kernel & RootFS
+Remote
+Remote
+Linux Kernel & RootFS
+Bitstream
+PS Isolation Configuration
+Bitstream
+PS Extended Configuration
+U-Boot
+Local
+U-Boot
+Local
+ATF
+ATF
+FSBL
+psu_init
+FSBL
+psu_init_base
+PMU Firmware
+PMU Firmware
+Application Specific
+GenericIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+3
+Fig. 3. Modified boot process for Xilinx Zynq UltraScale+ devices. The modifications are represented by the red bordered boxes. The first modification in the
+boot process, psu init base, marks were usually the configuration of the PS would happen. Here, the source code to completely configure the PS is replaced
+by source code that applies a base configuration, allowing to continue the boot process and using a network interface later on. The remaining modifications
+can all be found in U-Boot. They include fetching configuration data, modifying the configuration of the PS (psu init ext), and optionally configuring the
+isolation within the PS.
+custom binary file for the modification of the PS configuration,
+a file to configure the isolation within the PS, and the PL
+bitstream. The next step is to extend the configuration of
+the PS to its complete state (psu init ext). U-Boot running
+on ARM Exception Level 2 is not allowed to access the
+required configuration registers directly. Instead, it is possible
+to request the ATF running at Exception Level 3 via a Secure
+Monitor Call (SMC) to instruct the PMU firmware to access
+a configuration register. The PMU has unrestricted access
+to all configuration registers within the PS [3]. Using this
+methodology, the ATF can remain unmodified, while only
+a minor modification to the PMU firmware is required to
+temporarily allow U-Boot to make all these requests until the
+PS is fully configured.
+After the reconfiguration of the PS is finished, it might be
+necessary to rebind some U-Boot drivers, for example the one
+used for Ethernet. Then, the bitstream can be written to the
+PL. It is also possible to configure an isolation within the PS
+(Setup isolation) if desired. At this point, the system is fully
+configured, operational, and behaves exactly the same as it
+would with the traditional boot. Finally, U-Boot can continue
+to boot Linux on the APU. In the example boot process shown
+in Fig. 3, PXE is used to load the Linux kernel, and the kernel
+itself uses NFS to mount the rootfs.
+Modifying the configuration of some critical components
+within the PS is not possible from U-Boot. This applies
+to the DDR interface and a very limited number of other
+configuration registers as shown in Table I. However, for many
+resources that are used by U-Boot but are not essential for it to
+run, it is possible to overwrite the configuration. Activating the
+isolation within the PS from U-Boot brings some limitations as
+well. All software that is running while the isolation is being
+activated must observe the restrictions enforced by it. If the
+isolation includes a restriction of the memory ranges used by
+the APU for instance, it is mandatory that U-Boot observes
+this restriction before the activation of the isolation. Otherwise
+U-Boot might lose access to essential data when the isolation
+is activated, which can lead to undesired behaviour or even to
+a crash of the system.
+V. CUSTOM CONFIGURATION FILES
+The PS configuration files that are stored and later fetched
+from the network are encoded using a binary format. This is
+done to efficiently process them in U-Boot. Despite the many
+features of U-Boot, it is still low-level software. Therefore,
+working with more complex data formats based on ASCII like
+XML would significantly increase the overhead. While human
+readable code would be an advantage, the wish to manually
+change about one thousand 32-bit registers is rather unlikely.
+The internal structure of the binary configuration files is
+strongly inspired by the architecture of the source code that
+is used in the FSBL to configure the PS. This code can be
+unwrapped to a long list of calls of eight different functions
+listed in Table II [11]. The configuration of the PS is therefore
+fully represented by this list of function calls including the
+respective call arguments. Therefore, this is the only infor-
+mation that must be stored in the binary configuration files.
+Listing 1 and Listing 2 show the encoding of the function
+calls in the binary format. All call arguments of the functions
+in Table II are 32-bit values, which can also be realized by
+macros in the source code. It is possible to represent each of
+the eight different functions with an unique 32-bit ID. As seen
+in Listing 1 and Listing 2 the function PSU_Mask_Write
+has the ID 0x00000001. The binary file is now composed of
+the list of function calls from the FSBL encoded in this format.
+It is possible to navigate through the different function calls
+
+Network access
+PMU ROM
+PMU
+PMU RAM
+PMU Firmware
+CSU RAM
+CSU
+CSU ROM
+RPU
+FSBL
+psu_init_base
+OCM
+ATF
+U-Boot
+Fetch Cfg.psu init_ext
+Setup Isolation
+APU
+PXE
+TFTP
+DDR
+--
+Linux Kernel -NFS→ F
+RootFS
+PL
+Bitstream
+CRAM
+--
+TimeIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+4
+PSU_Mask_Write(CRL_APB_RPLL_CFG_OFFSET,
+0xFE7FEDEFU, 0x7E4B0C82U);
+PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,
+0x00717F00U, 0x00015400U);
+PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,
+0x00000008U, 0x00000008U);
+PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,
+0x00000001U, 0x00000001U);
+PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,
+0x00000001U, 0x00000000U);
+mask_poll(CRL_APB_PLL_STATUS_OFFSET,
+0x00000002U);
+Listing 1. Source code snippet from psu init.c.
+00000001 FF5E0034 FE7FEDEF 7E4B0C82
+00000001 FF5E0030 00717F00 00015400
+00000001 FF5E0030 00000008 00000008
+00000001 FF5E0030 00000001 00000001
+00000001 FF5E0030 00000001 00000000
+00000003 FF5E0040 00000002 0000000F
+Listing 2. Encoding of the source code in Listing 1 in a binary configuration
+file.
+in such a binary file because the number of arguments of each
+function is constant and known. Finally, a distinct unique ID
+0x0000000F is used to mark the end of the file, as can be
+seen at the end of the file in Listing 2.
+VI. PSU CONFIGURATION GENERATOR
+A Python tool called the PSU Configuration Generator
+was developed to keep the effort of developing a project
+using the split boot mechanism to a minimum. This tool
+handles, among other things, the generation of the binary
+configuration files. It was designed to integrate seamlessly
+with the development tools provided by Xilinx. Thus, the
+*.xsa (Xilinx Support Archive) files exported from Vivado
+are used as input data. Within this archive, psu init.c and
+psu init.h contain the C source code which is used in the
+FSBL to configure the PS. They also contain a more abstract
+description of the configuration of the PS and the PL in
+the XML file zusys.hwh. The current implementation of the
+TABLE I
+LIST OF REGISTERS THAT CANNOT BE MODIFIED FROM U-BOOT [11].
+Register
+Mask
+Reason
+0xFD1A0030
+0xFE7FEDEF
+Part of the configuration of the
+DDR.
+0xFD1A002C
+0x00717F00
+0xFD1A002C
+0x00000008
+0xFD1A002C
+0x00000001
+0xFD1A0044
+0x00000002
+0xFD1A004C
+0x00003F00
+0xFD1A0080
+0x00003F07
+0xFF260020
+0xFFFFFFFF
+Can be read from the ATF.
+0xFF260000
+0x00000001
+0xFD0C00AC
+0xFFFFFFFF
+SATA Port Phy configuration
+registers initialized with reset
+values [12]. Modifying these
+registers causes a crash.
+0xFD0C00B0
+0xFFFFFFFF
+0xFD0C00B4
+0xFFFFFFFF
+0xFD0C00B8
+0xFFFFFFFF
+TABLE II
+LIST OF FUNCTIONS REPRESENTED IN THE BINARY CONFIGURATION
+FILES.
+Name
+Action
+PSU_Mask_Write
+Read-modify-write
+mask_poll
+Polls until a 1 occurs in the
+masked part of the register
+or a specified number of at-
+tempts in exceeded
+mask_pollOnValue
+Polls until the masked part
+of the register matches the
+desired value, or until a cer-
+tain number of attempts is
+exceeded
+mask_delay
+Delay for a specified duration
+serdes_illcalib
+Calibration
+algorithm
+for
+SerDes
+serdes_fixcal_code
+Calibration algorithm
+serdes_enb_coarse_saturation
+Activates the coarse satura-
+tion logic for PLLs of all four
+GT lanes of the MPSoC
+psu_init_xppu_aper_ram
+Initialization of the PPU
+PSU Configuration Generator uses the *.xsa file containing
+the complete PS configuration as input.
+The files psu init.c and psu init.h are parsed to identify
+the function calls that need to be written to the configuration
+files. The parser uses a depth-first search to find all calls of
+the eight functions listed in Table II, starting by the functions
+that can be called directly from the FSBL. If a function call is
+allowed in U-Boot, or in other words, if the addressed registers
+can be modified from U-Boot, the function call is encoded
+in the binary format, resolving all macros contained in it,
+and appended to the binary output file. Furthermore, to be
+adaptable, the PSU Configuration Generator allows skipping
+selected registers or ignoring some function calls specified in
+a JSON file. There are only a few interfaces to the FSBL that
+represent root nodes. Using the functions in Table II, all nodes
+representing termination conditions for the depth-first search
+are identified. Both, the root and termination nodes form the
+boundary conditions for the search algorithm.
+The file psu init.c contains two main interfaces to the FSBL.
+One to configure the PS and one to set up the isolation.
+To execute these two actions separately from U-Boot, the
+PSU Configuration Generator offers the possibility to export
+separate configuration files. Additionally, it provides the option
+to extract the bitfile for the PL from the *.xsa archive.
+Therefore, achieving a higher degree of automation as all these
+files need to be copied to the same TFTP server.
+VII. DEVELOPMENT WORKFLOW
+To make split boot usable in real world applications, it
+is important to integrate the required modifications to the
+different software components and the additional steps in the
+development process with the default workflow of the Xilinx
+development tools. To achieve this, an approach based on
+
+IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+5
+Fig. 4. Creation flow of all software and firmware components to be stored
+on the local boot medium. They are based on a Vivado project representing
+the base configuration of the PS and optionally also the PL. Output files are
+packed in the single boot image called BOOT.bin.
+two Vivado projects was chosen. One project represents the
+base configuration of the PS, and optionally also of the PL,
+which are applied at the FSBL. The other project contains the
+complete configuration, which is fetched by U-Boot via the
+network. Both Vivado projects are integrated into a workflow
+that is divided into two independent sub-processes. The first
+one leads to the generation of all files that are needed in the
+boot routine before network access is possible. The second
+sub-process produces the necessary files that can be loaded
+from the network. This distinct separation enables only the
+second sub-process to be required for each new project. The
+first sub-process, containing only generic data, is only executed
+once per hardware platform. As a result, the development
+effort with split boot is comparable to a project without it.
+A. Creation of the Base Configuration
+The creation of all files needed for the early stages of the
+boot process, before a network connection can be utilized,
+are depicted in Fig. 4. In particular, they also contain the base
+configuration for the PS. As can be seen, these files are entirely
+based on the *.xsa file exported from the Vivado project rep-
+resenting the base configuration base.xsa. The PetaLinux tools
+are the only additional tools from the Xilinx development suite
+that are required in the process. After creating a respective
+PetaLinux project, the tools automate the process of building
+all individual software components. However, one manual step
+might be required if the complete configuration includes an
+isolation setting because the memory regions used by U-Boot
+need to be restricted according to it. This can be achieved in
+the device tree, and it is the only limitation we have thus far
+observed as a result of the activation of the isolation within
+the PS from U-Boot. As can be seen in Fig. 4, patches are
+used to apply the required modifications to U-Boot and the
+PMU firmware. The use of patch files is an integral part of
+developing with the PetaLinux software suite, and thus both
+the creation and the application during the build process is
+automated.
+The patch applied to the U-Boot source code is used to
+add the functionality to modify the configuration of the PS
+and to apply the isolation. This functionality is packaged in
+the custom U-Boot-command psuinite. As an argument this
+command needs the address of the configuration file to be ap-
+plied in memory. It then iterates over the configuration file and
+executes the function calls listed there. The command contains
+implementations of all functions listed in Table II. The source
+code is derived from the implementations in psu init.c and
+only slightly modified to use the drivers available in U-Boot
+and to request access to the required configuration registers
+via SMC from the PMU firmware instead of accessing them
+directly. A flag can be passed to the command if the access
+to the configuration registers from the APU should be locked
+in the PMU firmware after the configuration file is applied.
+Finally, a debugging flag exists that enables print outputs for
+each register access made. Another patch applied to the U-
+Boot source code inserts all the additional steps required by
+split boot to the regular steps U-Boot performs to boot the
+system. This patch also includes checks if the additional steps
+were executed successfully or not. If a failure is detected, the
+boot process is immediately aborted with an error message
+because the errorless execution of each of these steps is
+essential for a successful boot.
+The patch applied to the PMU firmware is required to allow
+U-Boot to access all needed configuration registers via SMC
+calls. By default, the PMU firmware verifies that the requesting
+instance is authorized to access the requested resource. This
+mechanism must be temporarily disabled until U-Boot has
+completed all required configuration register accesses. The
+patch enables all such accesses from the start of the PMU
+firmware and gives U-Boot the option to restore the default
+access control when the configuration has been extended to its
+complete state.
+PetaLinux tools are able to build the PMU firmware, the
+FSBL, the ATF, and U-Boot once the patches have been
+applied. Since this FSBL is based on the base.xsa, it already
+contains the desired configuration for the PS in psu init.c and
+psu init.h, so modifying these files is not necessary. However,
+the FSBL contains one more application-specific section. The
+structure XPm ConfigObject contains, among other things,
+the information about which components in the PS will be
+used in the given configuration. One of the final steps in
+the FSBL is to send this information to the PMU firmware.
+If a component is not marked as active in this structure, it
+is not possible to activate it later purely via configuration
+registers. One workaround for this limitation is to mark every
+node in the XPm ConfigObject as active. The downside is that
+this increases the power consumption of the MPSoC as all
+nodes will be powered, which also leads to potential security
+vulnerabilities. Therefore, it is still being investigated if this
+structure can be modified at a later stage of the boot process.
+Having the PMU firmware, the FSBL, the ATF, and U-Boot
+ready, the final step is to use the Xilinx tool bootgen to package
+them in a boot image. This file can then be copied to a local
+boot medium such as an SD Card.
+
+Create the base configuration in Vivado
+(PS and PL)
+base.xsa
+Create new PetaLinux project
+Patch U-Boot and the PMU Firmware
+Build PetaLinux project
+pmufw.elf
+fsbl.elf
+bl31.elf
+u-boot.elf
+Create BOOT.bin using bootgen
+BOOT.binIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+6
+Fig. 5.
+Creation of all software and firmware components that are fetched
+from the network during boot. They are based on a Vivado project representing
+the complete configuration of the PS and PL. The tool PSU Configuration
+Generator was developed to automate the creation of the binary configuration
+files, it could optionally also use the file base.xsa.
+B. Creation of the Complete Configuration
+Fig. 5 shows the process to create all files used for the
+later stages of the boot process that can be fetched from a
+TFTP server in the network, including the binary configuration
+files to extend the configuration of the PS. It can be seen that
+two paths are used to create the files. One uses PetaLinux
+tools to build the Linux kernel and the other path uses the
+custom tool PSU Configuration Generator to generate the two
+custom binary configuration files and to extract the bitfile for
+the PL. In contrast to the files created for the early stages
+of the boot process, the files created here contain application-
+specific information and are thus mainly based on the *.xsa file
+exported from the Vivado project representing the complete
+configuration complete.xsa. The information in base.xsa can
+be used optionally to achieve a higher degree of automation.
+The path in Fig. 5 for building the Linux kernel uses solely
+the file complete.xsa as input. This archive is used as the
+basis to set up a PetaLinux project. Afterwards, the PetaLinux
+framework fully automates the process of building the kernel.
+The tools provided by the PetaLinux software suite can be
+used to customize the kernel as usual.
+To prevent redundant reconfigurations, the path in Fig. 5
+showing the usage of the PSU Configuration Generator could
+use both, complete.xsa and base.xsa. However, currently only
+the complete configuration is used as input. The redundant
+reconfigurations that occur because of this, have not caused
+any problems so far. However, the registers that can not be
+modified from U-Boot (see Table I) must be declared in the
+JSON configuration files. Fig. 5 also makes clear why it is
+efficient to use the PSU Configuration Generator to extract the
+bitfile for the PL from complete.xsa. This feature helps to have
+as many of the files that must be copied to the remote server
+ready at the same time and at the same location. Only the
+Linux kernel needs to be collected from a different location.
+VIII. IMPLEMENTATION AND TESTING
+The split boot mechanism as described here was developed
+and tested on a Trenz Electronic TE0803-03-4BE11-A MP-
+SoC System-on-Module (SoM) plugged onto a custom carrier
+board [13] that included, among other things, an SSD, two
+UART interfaces, and two network interfaces, one via SGMII
+and one via RGMII. On the software side, the development
+tools of the Xilinx toolset 2020.2 were used.
+Because the split boot process in its most efficient imple-
+mentation loads the configuration for the PL from a network
+server, the ability to configure the interfaces between PS and
+PL at run time is of great interest. Two independent tests were
+run for validation. With the clocks generated in the PS directly
+connected to Multiplexed Input/Output (MIO) pins of the PL,
+the ability of activating the signal and changing the frequency
+was confirmed with an externally connected oscilloscope. The
+second test targets the AXI interfaces. A BRAM IP core
+instantiated in the PL was used to confirm the possibility to
+activate them at run time and to change the width of the bus.
+Fig. 6 shows the setup used for both tests.
+The reconfigurability of interfaces using SerDes was ex-
+amined using the connected SSD. SerDes interfaces are high-
+lighted in particular here, because they are not only configured
+but also calibrated by the FSBL and this calibration step was
+also relocated to U-Boot. After changing the configuration and
+perform the calibrating in U-Boot, read and write access to
+the SSD from Linux was possible without any limitations.
+Another interface using SerDes is Ethernet via SGMII. The
+Ethernet interface, however, needs to be configured in the
+FSBL because it is used in the split boot mechanism. Thus,
+the only test possible was to use U-Boot to clear the respective
+configuration registers with zeros before restoring the config-
+uration values. This test was also successful. After rebinding
+the Ethernet driver in U-Boot, the interface could be used
+normally. The same procedure was also successfully tested
+with the Ethernet interface based on RGMII that consequently
+does not use SerDes. In addition, it was also tested whether
+the configuration of the MIO pins of the PS can be changed.
+For this purpose two MIO pins were assigned to one of the
+UARTs in the PS at run time. After that, the UART could be
+used without restrictions for input and output.
+Aside from these tests aiming at the configurability of a
+single component, booting Linux on the MPSoC after extend-
+ing the configuration in U-Boot was used as a comprehensive
+test. This is possible because the majority of components in the
+PS that are configured as part of the complete configuration
+Fig. 6.
+Setup used to test the reconfigurability of the AXI and clock
+interfaces between PS and PL by the split boot mechanism. After the initial
+configuration, both interfaces were enabled with 32-bit AXI width and 100
+MHz clock. Later they were changed to 128-bit and 200 MHz.
+
+Create the complete
+configuration in Vivado
+(PS and PL)
+complete.xsa
+base.xsa
+Create a new PetaLinux project or
+PSU Configuration
+Generator
+update the hardware description of
+an existing one
+Build PetaLinux project
+image.ub
+pl.bit
+psu_config.bin
+en isolation.binMPSoC
+PS
+32 bit /
+A
+PL
+128 bit
+ARM
+I/
+A53
+BRAM
+V
+0
+Clock
+Clk
+gen.
+100MHz/200MHz
+OscilloscopeIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. XX, NO. XX, XXXX 2022
+7
+Fig. 7.
+Custom Zynq Ultrascale+ MPSoC based FMC+ mezzanine board
+designed for slow control tasks.
+are targeted and initialized by a Linux driver loaded during
+the kernel’s boot process. Linux was able to boot on the
+reconfigured MPSoC in the same way as if the PS had been
+fully configured in the FSBL. This supports the claim that
+after reconfiguration in U-Boot, the MPSoC behaves exactly
+as if the configuration had been done completely in the FSBL.
+To investigate whether the isolation configured in U-Boot
+behaves the same way as if it had been configured in the
+FSBL, two types of tests were run. The access to different
+regions in the address range of the DDR memory, separated
+by the isolation, was examined before and after the isolation
+was enabled. A similar access check was also performed for
+multiple registers belonging to different isolated components
+within the PS. In both cases, the isolation behaved the same
+way as if it had been activated in the FSBL. This outcome was
+expected because, despite the fact that the configuration of the
+isolation is handled in software, the actual separation of the
+PS into multiple subsystems is enforced directly by hardware
+and thus unaffected by the order in which the software is
+executed [3].
+In addition to the Trenz Electronic MPSoC, split boot based
+on version 2020.2 of the Xilinx development tools was also
+implemented on a Xilinx ZCU102 evaluation board and on
+a custom ZUS+ based FMC+ mezzanine board, depicted in
+Fig. 7 [14]. Furthermore it was implemented on a Xilinx Kria
+K26 SoM plugged onto a KV260 development platform using
+version 2020.2.2 of the Xilinx toolset. Despite some minor
+changes to the patches required due to the different version of
+the toolset used for the Kria K26, the test results were iden-
+tical. The implementation process on these different hardware
+platforms was also used to estimate the effort required to create
+all the projects and files needed for a new platform. Due to
+the two Vivado and PetaLinux projects used, the process takes
+longer than with the regular boot process, but the additional
+time required was typically well under an hour, especially
+when the patches for the version of the toolset used were
+already available.
+IX. CONCLUSION
+The large number of hundreds of SoC devices used within
+the LHC upgrade creates significant challenges in their
+firmware deployment, maintenance, and accessibility. Booting
+from a singular source would be beneficial and would signifi-
+cantly ease maintenance. This functionality is supported by the
+modified boot process presented in this paper. The split boot
+process enables a clear separation by having all application-
+specific data on a remote server and just a generic base
+layer of software remaining on the local boot medium. The
+proposed workflow minimizes the overhead of implementing
+the modified boot process while relying on official Xilinx tools
+wherever possible. Split boot was implemented and tested
+on four different hardware platforms with two versions of
+the Xilinx development tools. Although the boot sequence is
+already fully functional, there is still room for improvement.
+A higher level of automation could be attained and will be
+addressed in future work.
+REFERENCES
+[1] Zynq UltraScale+ MPSoC Software Developer Guide, version 2020.2,
+Xilinx. [Online]. Available: https://docs.xilinx.com/r/2020.2-English/u
+g1137-zynq-ultrascale-mpsoc-swdev. Accessed on: August 2, 2022.
+[2] “Vivado PS Configuration Wizard Overview”. [Online]. Available: https:
+//www.xilinx.com/video/hardware/vivado-ps-configuration-wizard-ove
+rview.html. Accessed on: August 23, 2022.
+[3] Zynq UltraScale+ Device Technical Reference Manual, version 2.3,
+Xilinx. [Online]. Available: https://docs.xilinx.com/r/en-US/ug1085-zyn
+q-ultrascale-trm/Zynq-UltraScale-Device-Technical-Reference-Manual.
+Accessed on: November 11, 2022.
+[4] PetaLinux Tools Documentation Reference Guide, version 2022.1, Xil-
+inx. [Online]. Available: https://docs.xilinx.com/r/en-US/ug1144-petal
+inux-tools-reference-guide. Accessed on: August 9, 2022.
+[5] T.
+Cruz,
+P.
+Simoes,
+F.
+Bastos,
+and
+E.
+Monteiro,
+“Integra-
+tion of PXE-based desktop solutions into broadband access net-
+works,”
+in
+Proc.
+CNSM
+2010,
+Niagara
+Falls,
+Canada,
+2010.
+doi:10.1109/CNSM.2010.5691309.
+[6] L. Guojie and Z. Jianbiao, “A TPCM-Based Trusted PXE Boot Method
+For Servers,” in Proc. ICSIP 2020, Nanjing, China, 2020, pp. 996–1000.
+doi:10.1109/ICSIP49896.2020.9339366.
+[7] B. Abhiram Sai Krishna, M. J. Sarmah, and A. Kumar A V, “Multi-
+stage Boot Image Loading and Configuration of Programmable Logic
+Devices,” International Publication WO 2017/062479 A1, Apr. 13, 2017.
+[8] N. Dzemaili, “A reliable booting system for Zynq Ultrascale+ MPSoC
+devices,” B.S. thesis, HU University of Applied Sciences Utrecht, 2021.
+[9] K. S. Mor, “An Embedded Linux Distribution for the Data Acquisition
+Hardware of the Compact Muon Solenoid Experiment at CERN,” M.S.
+thesis, Eindhoven University of Technology, 2020.
+[10] “ARM privilege and exception levels”. [Online]. Available: https://deve
+loper.arm.com/documentation/102412/0102/Privilege-and-Exception-le
+vels. Accessed on: August 2, 2022.
+[11] M. Fuchs, “Highly integrated slow control on heterogeneous SoC
+architectures,” M.S. thesis, Karlsruhe Institute of Technology, 2021.
+[12] “Zynq ultrascale+ devices register reference”. [Online]. Available: https:
+//www.xilinx.com/htmldocs/registers/ug1087/ug1087-zynq-ultrascale-re
+gisters.html. Accessed on: August 16, 2022.
+[13] Ardila-Perez, Luis, Cascadan, Andre, Calligaris, Luigi, Tcherniakhovski,
+Denis, Balzer, Matthias, Weber, Marc et al., “A novel centralized slow
+control and board management solution for ATCA blades based on
+the Zynq Ultrascale+ System-on-Chip,” CHEP 2019, vol. 245, Art. no.
+01015, Nov. 2020. doi:10.1051/epjconf/202024501015.
+[14] T. Mehner, L. E. Ardila-Perez, M. N. Balzer, O. Sander, D. Tcher-
+niakhovski, M. Schleicher et al., “ZynqMP-based board-management
+mezzanines for Serenity ATCA-blades,” J. Instrum., vol. 17, no. 3, Mar.
+2022. doi:10.1088/1748-0221/17/03/C03009.
+
+2021
+oooao
+O
+101001
+EE0808
+C
+401
+C
+0044
+1023
+10
+一
+工
+L09
+ZynqMP Mezzanine FMC+ (BuZZyBoard)
+v1.0
+October 2020
+:0
+R19
+018
+KIT
+Luls Ardita
+O
\ No newline at end of file
diff --git a/gNE5T4oBgHgl3EQfhg_G/content/tmp_files/load_file.txt b/gNE5T4oBgHgl3EQfhg_G/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,480 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf,len=479
+page_content='IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  1  Split Boot - True Network-Based Booting on  Heterogeneous MPSoCs  Marvin Fuchs, Luis E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Ardila-Perez, Torben Mehner, and Oliver Sander  Abstract—In the context of the High-Luminosity (HL) up-  grade of the LHC, many custom ATCA electronics boards are  being designed containing heterogeneous System-on-Chip (SoC)  devices, more specifically the Xilinx Zynq UltraScale+ (ZUS+)  family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' While the application varies greatly, these devices are  regularly used for performing board management tasks, making  them a fundamental element in the correct operation of the  board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The large number of hundreds of SoC devices creates  significant challenges in their firmware deployment, maintenance,  and accessibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Even though U-Boot on ZUS+ devices supports network boot  through the Preboot Execution Environment (PXE), the standard  ZUS+ boot process contains application-specific information at  earlier boot steps, particularly within the First Stage Bootloader  (FSBL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This prevents the initialization of several devices from  a universal image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Inspired by the PXE boot process on desktop  PCs, this paper describes split boot, a novel boot method  tailored to the specific needs of the ZUS+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' All application-  specific configuration is moved to a network storage device and  automatically fetched during the boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' We considered  the entire process, from firmware and software development to  binary distribution in a large-scale system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The developed method  nicely integrates with the standard Xilinx development toolset  workflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Index Terms—Booting, Large-Scale Experiments, MPSoC, Net-  work Booting, PXE, System-on-Chip, Zynq Ultrascale+  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' INTRODUCTION  T  HE Xilinx Zynq UltraScale+ (ZUS+) devices are het-  erogeneous Multi-Processor System-on-Chips (MPSoCs)  that, in addition to the Programmable Logic (PL), contain a  Processing System (PS) with a number of hard processing  units, such as an ARM Cortex-A53 named Application Pro-  cessing Unit (APU), an ARM Cortex-R5 named Real-Time  Processing Unit (RPU), and the Platform Management Unit  (PMU) based on the MicroBlaze architecture [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Even though  not all processors have to be involved in the boot process, it  usually relies on several of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' To make the ZUS+ devices  deployable in a wide range of applications, they are designed  to be highly configurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' To a certain extent, this also applies  to the boot process, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' For example, it is  possible to load both, the bitfile for the PL and the firmware  for the RPU, in either the First Stage Bootloader (FSBL), the  second-stage boot loader U-Boot or from Linux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In some cases  it is also possible to change the order, for example to load the  PMU firmware either before or after the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Manuscript submitted September 10, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' revised November 11, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  This research acknowledges the support by the Doctoral School “Karlsruhe  School of Elementary and Astroparticle Physics: Science and Technology”  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Fuchs (corresponding author, email: marvin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='fuchs at kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='edu), L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Ardila-Perez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Mehner and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Sander are with the Institute for Data Process-  ing and Electronics (IPE) of the Karlsruhe Institute of Technology, Hermann-  von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany  The first stage in the boot process that contains application-  specific information is the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Vivado generates C code  to configure the PS and to optionally divide it in multiple  subsystems via an isolation-configuration according to the set-  tings selected in the Vivado PS Configuration Wizard (PCW)  GUI [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' When the FSBL software project is set up, this source  code is automatically integrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The FSBL contains information on how to configure the  various internal clocks, the interfaces to the PL, and external  interfaces such as the UARTs or the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The application-  specific code contained in it to do this, is one of the reasons  why the FSBL cannot be factory-saved to a non-volatile mem-  ory within the MPSoC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Thus, it is one of the first components  loaded from an external storage (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' a QSPI memory or an  SD Card).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The same storage location is usually also used for  the PMU firmware, the Arm Trusted Firmware (ATF), and U-  Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In contrast, entirely generic software like the PMU ROM  and the Configuration Security Unit (CSU) ROM is stored on  non-volatile memory within the ZUS+ [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The goal of the modified boot process presented in this  paper is to fetch all application-specific data including the  PS configuration from a network source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This is, however,  not trivial because the FSBL itself is a low-level stage in  the boot process and it is not designated to communicate  via a network connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Just as with PCs that boot via  Preboot Execution Environment (PXE), the greatest advantage  for MPSoCs that obtain all application-specific data from the  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Default software stack used to boot Xilinx Zynq UltraScale+ devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The solid lines describe one possible example of a boot process, whereas the  dashed lines show alternative possibilities to load a bitfile for the PL and the  firmware for the RPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='05642v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='ins-det]  13 Jan 2023  Real-Time  Bit File  Linux  Firmware  U-Boot  ATF  PMUFirmware  FSBL  APU  IRPU  CSUROM  PL  PMU  PMUROM  ICSUIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  2  network appears in large systems where many devices need to  be maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' One example is the distribution of updates in  a large and distributed system, comprised of many identically  configured boards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In its most efficient implementation, split  boot enables accomplishing the task by only updating the  single network storage and rebooting the devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Significant  time is saved compared to having to flash the local storage of  each board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In the remainder of this contribution, we present a  two-step approach that essentially supports fetching the entire  PS configuration via network and applying it to the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' RELATED WORK  U-Boot already features PXE, which allows devices to boot  into an operating system such as Linux via the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' How-  ever, it does not cover the configuration of the PS [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Such  a functionality is not provided, because PXE was originally  designed for computer networks rather than networks of highly  configurable System-on-Chips (SoCs) such as the ZUS+ fam-  ily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Modifications to the FSBL on MPSoC devices might be  required on a regular basis due to containing application-  specific information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This is a major drawback compared to  the boot of a desktop PC, where updates to the BIOS and all  other software used before the second-stage boot loader are  very rarely necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Research regarding PXE usually targets  desktop PCs [5] or servers [6], but not embedded devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Xilinx provides means to adapt the boot process based on the  application domain [1] and further describes in a patent the  boot process possibilities of MPSoC devices [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However, the  ability to load the PS configuration from a remote location  is not mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In the context of the High-Luminosity  (HL) upgrade of the LHC, active research is being conducted  about the boot process of MPSoC devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' To date, though,  work has focused primarily on investigating and securing the  possibilities provided by Xilinx [8] and building the Linux  distribution for use on the device [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' SPLIT CONFIGURATION APPROACH  Simply moving the entire configuration of the PS part of  a ZUS+ MPSoC to a network storage is not feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Some  initial configuration is needed to bring up the essential func-  tionality of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This includes, first and foremost, the  network interface and the configuration of the DDR memory  controller, but also some internal configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' While this  configuration is board-specific, it is not application-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  As a conclusion, we propose using a base configuration which  is static and reduced to the absolute minimum to boot into U-  Boot with network access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This approach is similar in many  ways to that of a PC BIOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Updates to the base firmware are  possible, but they are expected to happen rarely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The application-specific data for the PS can be split into  two tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The first one includes the configuration of all the  individual components like clocks within the PS, the PS-  PL interfaces, and some peripherals like the DDR memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The second task is the application of the so-called isolation-  configuration, which divides the PS into multiple subsystems  and defines access permissions between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' For both, we  propose to move the application-specific data into separate bi-  nary configuration files, which are then fetched from a network  source and applied by U-Boot during the boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 2  shows how removing the application-specific configuration  data from the FSBL leads to a system where only generic  software remains on the local boot medium and everything  application-specific is stored on the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' THE MODIFIED BOOT PROCESS  Xilinx ZUS+ devices require multiple tweaks in the default  boot process to allow for changes to the PS configuration after  it has been initially configured in the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' An overview of  these modifications is provided by the example boot sequence  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 3, where the changes are shown as white boxes with red  frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The boot procedure starts as usual with the software  components PMU ROM and CSU ROM stored on non-volatile  memory within the ZUS+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Afterwards, the PMU firmware is  started, in this case, before the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The FSBL contains the first modification in the proposed  boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Usually, at this stage, the PS gets initialized  with its complete configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' During the split boot process,  however, this is where the PS receives its base configuration  (psu init base), which includes the boot related peripheral and  memory configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The source code that is used to configure the PS is generated  by Vivado according to the options selected in the PCW and  inserted into the FSBL automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Because of this, the  software architecture of the FSBL allows us to easily replace  this part of the source code, for example with that of our  generic base configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  When the FSBL has finished its execution, it hands over  to the ATF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The ATF is a reference implementation of an  ARM secure world software provided by Xilinx and in the  example depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 3 the first software executed on the  APU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Such a software is necessary to utilize the Armv8-A  Exception Model that is implemented in the APU [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  When the ATF is running, U-Boot can be started.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It contains  the remaining modifications to the original boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  first modification (Fetch Cfg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=') loads all the required config-  uration data using standard U-Boot features from a TFTP  server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This includes, in addition to the regular Linux kernel, a  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The split boot approach removes from the FSBL the application-  specific PS configuration and the isolation configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As a result, only  generic information remains on the local boot medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Linux Kernel & RootFS  Remote  Remote  Linux Kernel & RootFS  Bitstream  PS Isolation Configuration  Bitstream  PS Extended Configuration  U-Boot  Local  U-Boot  Local  ATF  ATF  FSBL  psu_init  FSBL  psu_init_base  PMU Firmware  PMU Firmware  Application Specific  GenericIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Modified boot process for Xilinx Zynq UltraScale+ devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The modifications are represented by the red bordered boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The first modification in the  boot process, psu init base, marks were usually the configuration of the PS would happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Here, the source code to completely configure the PS is replaced  by source code that applies a base configuration, allowing to continue the boot process and using a network interface later on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The remaining modifications  can all be found in U-Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' They include fetching configuration data, modifying the configuration of the PS (psu init ext), and optionally configuring the  isolation within the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  custom binary file for the modification of the PS configuration,  a file to configure the isolation within the PS, and the PL  bitstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The next step is to extend the configuration of  the PS to its complete state (psu init ext).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' U-Boot running  on ARM Exception Level 2 is not allowed to access the  required configuration registers directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Instead, it is possible  to request the ATF running at Exception Level 3 via a Secure  Monitor Call (SMC) to instruct the PMU firmware to access  a configuration register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The PMU has unrestricted access  to all configuration registers within the PS [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Using this  methodology, the ATF can remain unmodified, while only  a minor modification to the PMU firmware is required to  temporarily allow U-Boot to make all these requests until the  PS is fully configured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  After the reconfiguration of the PS is finished, it might be  necessary to rebind some U-Boot drivers, for example the one  used for Ethernet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Then, the bitstream can be written to the  PL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It is also possible to configure an isolation within the PS  (Setup isolation) if desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' At this point, the system is fully  configured, operational, and behaves exactly the same as it  would with the traditional boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Finally, U-Boot can continue  to boot Linux on the APU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In the example boot process shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 3, PXE is used to load the Linux kernel, and the kernel  itself uses NFS to mount the rootfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Modifying the configuration of some critical components  within the PS is not possible from U-Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This applies  to the DDR interface and a very limited number of other  configuration registers as shown in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However, for many  resources that are used by U-Boot but are not essential for it to  run, it is possible to overwrite the configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Activating the  isolation within the PS from U-Boot brings some limitations as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' All software that is running while the isolation is being  activated must observe the restrictions enforced by it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' If the  isolation includes a restriction of the memory ranges used by  the APU for instance, it is mandatory that U-Boot observes  this restriction before the activation of the isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Otherwise  U-Boot might lose access to essential data when the isolation  is activated, which can lead to undesired behaviour or even to  a crash of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' CUSTOM CONFIGURATION FILES  The PS configuration files that are stored and later fetched  from the network are encoded using a binary format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This is  done to efficiently process them in U-Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Despite the many  features of U-Boot, it is still low-level software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Therefore,  working with more complex data formats based on ASCII like  XML would significantly increase the overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' While human  readable code would be an advantage, the wish to manually  change about one thousand 32-bit registers is rather unlikely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The internal structure of the binary configuration files is  strongly inspired by the architecture of the source code that  is used in the FSBL to configure the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This code can be  unwrapped to a long list of calls of eight different functions  listed in Table II [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The configuration of the PS is therefore  fully represented by this list of function calls including the  respective call arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Therefore, this is the only infor-  mation that must be stored in the binary configuration files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Listing 1 and Listing 2 show the encoding of the function  calls in the binary format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' All call arguments of the functions  in Table II are 32-bit values, which can also be realized by  macros in the source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It is possible to represent each of  the eight different functions with an unique 32-bit ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As seen  in Listing 1 and Listing 2 the function PSU_Mask_Write  has the ID 0x00000001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The binary file is now composed of  the list of function calls from the FSBL encoded in this format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  It is possible to navigate through the different function calls  Network access  PMU ROM  PMU  PMU RAM  PMU Firmware  CSU RAM  CSU  CSU ROM  RPU  FSBL  psu_init_base  OCM  ATF  U-Boot  Fetch Cfg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='psu init_ext  Setup Isolation  APU  PXE  TFTP  DDR  --  Linux Kernel -NFS→ F  RootFS  PL  Bitstream  CRAM  --  TimeIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  4  PSU_Mask_Write(CRL_APB_RPLL_CFG_OFFSET,  0xFE7FEDEFU, 0x7E4B0C82U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,  0x00717F00U, 0x00015400U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,  0x00000008U, 0x00000008U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,  0x00000001U, 0x00000001U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  PSU_Mask_Write(CRL_APB_RPLL_CTRL_OFFSET,  0x00000001U, 0x00000000U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  mask_poll(CRL_APB_PLL_STATUS_OFFSET,  0x00000002U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Source code snippet from psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  00000001 FF5E0034 FE7FEDEF 7E4B0C82  00000001 FF5E0030 00717F00 00015400  00000001 FF5E0030 00000008 00000008  00000001 FF5E0030 00000001 00000001  00000001 FF5E0030 00000001 00000000  00000003 FF5E0040 00000002 0000000F  Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Encoding of the source code in Listing 1 in a binary configuration  file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  in such a binary file because the number of arguments of each  function is constant and known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Finally, a distinct unique ID  0x0000000F is used to mark the end of the file, as can be  seen at the end of the file in Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' PSU CONFIGURATION GENERATOR  A Python tool called the PSU Configuration Generator  was developed to keep the effort of developing a project  using the split boot mechanism to a minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This tool  handles, among other things, the generation of the binary  configuration files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It was designed to integrate seamlessly  with the development tools provided by Xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Thus, the  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa (Xilinx Support Archive) files exported from Vivado  are used as input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Within this archive, psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c and  psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='h contain the C source code which is used in the  FSBL to configure the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' They also contain a more abstract  description of the configuration of the PS and the PL in  the XML file zusys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='hwh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The current implementation of the  TABLE I  LIST OF REGISTERS THAT CANNOT BE MODIFIED FROM U-BOOT [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Register  Mask  Reason  0xFD1A0030  0xFE7FEDEF  Part of the configuration of the  DDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  0xFD1A002C  0x00717F00  0xFD1A002C  0x00000008  0xFD1A002C  0x00000001  0xFD1A0044  0x00000002  0xFD1A004C  0x00003F00  0xFD1A0080  0x00003F07  0xFF260020  0xFFFFFFFF  Can be read from the ATF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  0xFF260000  0x00000001  0xFD0C00AC  0xFFFFFFFF  SATA Port Phy configuration  registers initialized with reset  values [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Modifying these  registers causes a crash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  0xFD0C00B0  0xFFFFFFFF  0xFD0C00B4  0xFFFFFFFF  0xFD0C00B8  0xFFFFFFFF  TABLE II  LIST OF FUNCTIONS REPRESENTED IN THE BINARY CONFIGURATION  FILES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Name  Action  PSU_Mask_Write  Read-modify-write  mask_poll  Polls until a 1 occurs in the  masked part of the register  or a specified number of at-  tempts in exceeded  mask_pollOnValue  Polls until the masked part  of the register matches the  desired value,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' or until a cer-  tain number of attempts is  exceeded  mask_delay  Delay for a specified duration  serdes_illcalib  Calibration  algorithm  for  SerDes  serdes_fixcal_code  Calibration algorithm  serdes_enb_coarse_saturation  Activates the coarse satura-  tion logic for PLLs of all four  GT lanes of the MPSoC  psu_init_xppu_aper_ram  Initialization of the PPU  PSU Configuration Generator uses the *.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa file containing  the complete PS configuration as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The files psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c and psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='h are parsed to identify  the function calls that need to be written to the configuration  files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The parser uses a depth-first search to find all calls of  the eight functions listed in Table II, starting by the functions  that can be called directly from the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' If a function call is  allowed in U-Boot, or in other words, if the addressed registers  can be modified from U-Boot, the function call is encoded  in the binary format, resolving all macros contained in it,  and appended to the binary output file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Furthermore, to be  adaptable, the PSU Configuration Generator allows skipping  selected registers or ignoring some function calls specified in  a JSON file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' There are only a few interfaces to the FSBL that  represent root nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Using the functions in Table II, all nodes  representing termination conditions for the depth-first search  are identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Both, the root and termination nodes form the  boundary conditions for the search algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The file psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c contains two main interfaces to the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  One to configure the PS and one to set up the isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  To execute these two actions separately from U-Boot, the  PSU Configuration Generator offers the possibility to export  separate configuration files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Additionally, it provides the option  to extract the bitfile for the PL from the *.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Therefore, achieving a higher degree of automation as all these  files need to be copied to the same TFTP server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' DEVELOPMENT WORKFLOW  To make split boot usable in real world applications, it  is important to integrate the required modifications to the  different software components and the additional steps in the  development process with the default workflow of the Xilinx  development tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' To achieve this, an approach based on  IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  5  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Creation flow of all software and firmware components to be stored  on the local boot medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' They are based on a Vivado project representing  the base configuration of the PS and optionally also the PL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Output files are  packed in the single boot image called BOOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  two Vivado projects was chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' One project represents the  base configuration of the PS, and optionally also of the PL,  which are applied at the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The other project contains the  complete configuration, which is fetched by U-Boot via the  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Both Vivado projects are integrated into a workflow  that is divided into two independent sub-processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The first  one leads to the generation of all files that are needed in the  boot routine before network access is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The second  sub-process produces the necessary files that can be loaded  from the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This distinct separation enables only the  second sub-process to be required for each new project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  first sub-process, containing only generic data, is only executed  once per hardware platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As a result, the development  effort with split boot is comparable to a project without it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Creation of the Base Configuration  The creation of all files needed for the early stages of the  boot process, before a network connection can be utilized,  are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In particular, they also contain the base  configuration for the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As can be seen, these files are entirely  based on the *.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa file exported from the Vivado project rep-  resenting the base configuration base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The PetaLinux tools  are the only additional tools from the Xilinx development suite  that are required in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' After creating a respective  PetaLinux project, the tools automate the process of building  all individual software components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However, one manual step  might be required if the complete configuration includes an  isolation setting because the memory regions used by U-Boot  need to be restricted according to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This can be achieved in  the device tree, and it is the only limitation we have thus far  observed as a result of the activation of the isolation within  the PS from U-Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 4, patches are  used to apply the required modifications to U-Boot and the  PMU firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The use of patch files is an integral part of  developing with the PetaLinux software suite, and thus both  the creation and the application during the build process is  automated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The patch applied to the U-Boot source code is used to  add the functionality to modify the configuration of the PS  and to apply the isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This functionality is packaged in  the custom U-Boot-command psuinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' As an argument this  command needs the address of the configuration file to be ap-  plied in memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It then iterates over the configuration file and  executes the function calls listed there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The command contains  implementations of all functions listed in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The source  code is derived from the implementations in psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c and  only slightly modified to use the drivers available in U-Boot  and to request access to the required configuration registers  via SMC from the PMU firmware instead of accessing them  directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' A flag can be passed to the command if the access  to the configuration registers from the APU should be locked  in the PMU firmware after the configuration file is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Finally, a debugging flag exists that enables print outputs for  each register access made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Another patch applied to the U-  Boot source code inserts all the additional steps required by  split boot to the regular steps U-Boot performs to boot the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This patch also includes checks if the additional steps  were executed successfully or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' If a failure is detected, the  boot process is immediately aborted with an error message  because the errorless execution of each of these steps is  essential for a successful boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The patch applied to the PMU firmware is required to allow  U-Boot to access all needed configuration registers via SMC  calls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' By default, the PMU firmware verifies that the requesting  instance is authorized to access the requested resource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This  mechanism must be temporarily disabled until U-Boot has  completed all required configuration register accesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  patch enables all such accesses from the start of the PMU  firmware and gives U-Boot the option to restore the default  access control when the configuration has been extended to its  complete state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  PetaLinux tools are able to build the PMU firmware, the  FSBL, the ATF, and U-Boot once the patches have been  applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Since this FSBL is based on the base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa, it already  contains the desired configuration for the PS in psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='c and  psu init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='h, so modifying these files is not necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However,  the FSBL contains one more application-specific section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  structure XPm ConfigObject contains, among other things,  the information about which components in the PS will be  used in the given configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' One of the final steps in  the FSBL is to send this information to the PMU firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  If a component is not marked as active in this structure, it  is not possible to activate it later purely via configuration  registers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' One workaround for this limitation is to mark every  node in the XPm ConfigObject as active.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The downside is that  this increases the power consumption of the MPSoC as all  nodes will be powered, which also leads to potential security  vulnerabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Therefore, it is still being investigated if this  structure can be modified at a later stage of the boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Having the PMU firmware, the FSBL, the ATF, and U-Boot  ready, the final step is to use the Xilinx tool bootgen to package  them in a boot image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This file can then be copied to a local  boot medium such as an SD Card.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Create the base configuration in Vivado  (PS and PL)  base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa  Create new PetaLinux project  Patch U-Boot and the PMU Firmware  Build PetaLinux project  pmufw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='elf  fsbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='elf  bl31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='elf  u-boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='elf  Create BOOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='bin using bootgen  BOOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='binIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  6  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Creation of all software and firmware components that are fetched  from the network during boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' They are based on a Vivado project representing  the complete configuration of the PS and PL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The tool PSU Configuration  Generator was developed to automate the creation of the binary configuration  files, it could optionally also use the file base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Creation of the Complete Configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 5 shows the process to create all files used for the  later stages of the boot process that can be fetched from a  TFTP server in the network, including the binary configuration  files to extend the configuration of the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' It can be seen that  two paths are used to create the files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' One uses PetaLinux  tools to build the Linux kernel and the other path uses the  custom tool PSU Configuration Generator to generate the two  custom binary configuration files and to extract the bitfile for  the PL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In contrast to the files created for the early stages  of the boot process, the files created here contain application-  specific information and are thus mainly based on the *.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa file  exported from the Vivado project representing the complete  configuration complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The information in base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa can  be used optionally to achieve a higher degree of automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The path in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 5 for building the Linux kernel uses solely  the file complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This archive is used as the  basis to set up a PetaLinux project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Afterwards, the PetaLinux  framework fully automates the process of building the kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The tools provided by the PetaLinux software suite can be  used to customize the kernel as usual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  To prevent redundant reconfigurations, the path in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 5  showing the usage of the PSU Configuration Generator could  use both, complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa and base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However, currently only  the complete configuration is used as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The redundant  reconfigurations that occur because of this, have not caused  any problems so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' However, the registers that can not be  modified from U-Boot (see Table I) must be declared in the  JSON configuration files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 5 also makes clear why it is  efficient to use the PSU Configuration Generator to extract the  bitfile for the PL from complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This feature helps to have  as many of the files that must be copied to the remote server  ready at the same time and at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Only the  Linux kernel needs to be collected from a different location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' IMPLEMENTATION AND TESTING  The split boot mechanism as described here was developed  and tested on a Trenz Electronic TE0803-03-4BE11-A MP-  SoC System-on-Module (SoM) plugged onto a custom carrier  board [13] that included, among other things, an SSD, two  UART interfaces, and two network interfaces, one via SGMII  and one via RGMII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' On the software side, the development  tools of the Xilinx toolset 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2 were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Because the split boot process in its most efficient imple-  mentation loads the configuration for the PL from a network  server, the ability to configure the interfaces between PS and  PL at run time is of great interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Two independent tests were  run for validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' With the clocks generated in the PS directly  connected to Multiplexed Input/Output (MIO) pins of the PL,  the ability of activating the signal and changing the frequency  was confirmed with an externally connected oscilloscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  second test targets the AXI interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' A BRAM IP core  instantiated in the PL was used to confirm the possibility to  activate them at run time and to change the width of the bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 6 shows the setup used for both tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  The reconfigurability of interfaces using SerDes was ex-  amined using the connected SSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' SerDes interfaces are high-  lighted in particular here, because they are not only configured  but also calibrated by the FSBL and this calibration step was  also relocated to U-Boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' After changing the configuration and  perform the calibrating in U-Boot, read and write access to  the SSD from Linux was possible without any limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Another interface using SerDes is Ethernet via SGMII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  Ethernet interface, however, needs to be configured in the  FSBL because it is used in the split boot mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Thus,  the only test possible was to use U-Boot to clear the respective  configuration registers with zeros before restoring the config-  uration values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This test was also successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' After rebinding  the Ethernet driver in U-Boot, the interface could be used  normally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The same procedure was also successfully tested  with the Ethernet interface based on RGMII that consequently  does not use SerDes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In addition, it was also tested whether  the configuration of the MIO pins of the PS can be changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  For this purpose two MIO pins were assigned to one of the  UARTs in the PS at run time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' After that, the UART could be  used without restrictions for input and output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Aside from these tests aiming at the configurability of a  single component, booting Linux on the MPSoC after extend-  ing the configuration in U-Boot was used as a comprehensive  test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This is possible because the majority of components in the  PS that are configured as part of the complete configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Setup used to test the reconfigurability of the AXI and clock  interfaces between PS and PL by the split boot mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' After the initial  configuration, both interfaces were enabled with 32-bit AXI width and 100  MHz clock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Later they were changed to 128-bit and 200 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Create the complete  configuration in Vivado  (PS and PL)  complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa  base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xsa  Create a new PetaLinux project or  PSU Configuration  Generator  update the hardware description of  an existing one  Build PetaLinux project  image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='ub  pl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='bit  psu_config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='bin  en isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='binMPSoC  PS  32 bit /  A  PL  128 bit  ARM  I/  A53  BRAM  V  0  Clock  Clk  gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  100MHz/200MHz  OscilloscopeIEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' XX, XXXX 2022  7  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Custom Zynq Ultrascale+ MPSoC based FMC+ mezzanine board  designed for slow control tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  are targeted and initialized by a Linux driver loaded during  the kernel’s boot process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Linux was able to boot on the  reconfigured MPSoC in the same way as if the PS had been  fully configured in the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This supports the claim that  after reconfiguration in U-Boot, the MPSoC behaves exactly  as if the configuration had been done completely in the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  To investigate whether the isolation configured in U-Boot  behaves the same way as if it had been configured in the  FSBL, two types of tests were run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The access to different  regions in the address range of the DDR memory, separated  by the isolation, was examined before and after the isolation  was enabled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' A similar access check was also performed for  multiple registers belonging to different isolated components  within the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' In both cases, the isolation behaved the same  way as if it had been activated in the FSBL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This outcome was  expected because, despite the fact that the configuration of the  isolation is handled in software, the actual separation of the  PS into multiple subsystems is enforced directly by hardware  and thus unaffected by the order in which the software is  executed [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  In addition to the Trenz Electronic MPSoC, split boot based  on version 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2 of the Xilinx development tools was also  implemented on a Xilinx ZCU102 evaluation board and on  a custom ZUS+ based FMC+ mezzanine board, depicted in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 7 [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Furthermore it was implemented on a Xilinx Kria  K26 SoM plugged onto a KV260 development platform using  version 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2 of the Xilinx toolset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Despite some minor  changes to the patches required due to the different version of  the toolset used for the Kria K26, the test results were iden-  tical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The implementation process on these different hardware  platforms was also used to estimate the effort required to create  all the projects and files needed for a new platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Due to  the two Vivado and PetaLinux projects used, the process takes  longer than with the regular boot process, but the additional  time required was typically well under an hour, especially  when the patches for the version of the toolset used were  already available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' CONCLUSION  The large number of hundreds of SoC devices used within  the LHC upgrade creates significant challenges in their  firmware deployment, maintenance, and accessibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Booting  from a singular source would be beneficial and would signifi-  cantly ease maintenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' This functionality is supported by the  modified boot process presented in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The split boot  process enables a clear separation by having all application-  specific data on a remote server and just a generic base  layer of software remaining on the local boot medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' The  proposed workflow minimizes the overhead of implementing  the modified boot process while relying on official Xilinx tools  wherever possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Split boot was implemented and tested  on four different hardware platforms with two versions of  the Xilinx development tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Although the boot sequence is  already fully functional, there is still room for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  A higher level of automation could be attained and will be  addressed in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  REFERENCES  [1] Zynq UltraScale+ MPSoC Software Developer Guide, version 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2,  Xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/r/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2-English/u  g1137-zynq-ultrascale-mpsoc-swdev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Accessed on: August 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [2] “Vivado PS Configuration Wizard Overview”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https:  //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/video/hardware/vivado-ps-configuration-wizard-ove  rview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Accessed on: August 23, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [3] Zynq UltraScale+ Device Technical Reference Manual, version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='3,  Xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/r/en-US/ug1085-zyn  q-ultrascale-trm/Zynq-UltraScale-Device-Technical-Reference-Manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Accessed on: November 11, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [4] PetaLinux Tools Documentation Reference Guide, version 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='1, Xil-  inx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/r/en-US/ug1144-petal  inux-tools-reference-guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Accessed on: August 9, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Cruz,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Simoes,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Bastos,  and  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  Monteiro,  “Integra-  tion of PXE-based desktop solutions into broadband access net-  works,”  in  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  CNSM  2010,  Niagara  Falls,  Canada,  2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='1109/CNSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='5691309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Guojie and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Jianbiao, “A TPCM-Based Trusted PXE Boot Method  For Servers,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' ICSIP 2020, Nanjing, China, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 996–1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='1109/ICSIP49896.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='9339366.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Abhiram Sai Krishna, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Sarmah, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Kumar A V, “Multi-  stage Boot Image Loading and Configuration of Programmable Logic  Devices,” International Publication WO 2017/062479 A1, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 13, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Dzemaili, “A reliable booting system for Zynq Ultrascale+ MPSoC  devices,” B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' thesis, HU University of Applied Sciences Utrecht, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [9] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Mor, “An Embedded Linux Distribution for the Data Acquisition  Hardware of the Compact Muon Solenoid Experiment at CERN,” M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  thesis, Eindhoven University of Technology, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [10] “ARM privilege and exception levels”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https://deve  loper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/documentation/102412/0102/Privilege-and-Exception-le  vels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Accessed on: August 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Fuchs, “Highly integrated slow control on heterogeneous SoC  architectures,” M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' thesis, Karlsruhe Institute of Technology, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [12] “Zynq ultrascale+ devices register reference”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Available: https:  //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='com/htmldocs/registers/ug1087/ug1087-zynq-ultrascale-re  gisters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Accessed on: August 16, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [13] Ardila-Perez, Luis, Cascadan, Andre, Calligaris, Luigi, Tcherniakhovski,  Denis, Balzer, Matthias, Weber, Marc et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=', “A novel centralized slow  control and board management solution for ATCA blades based on  the Zynq Ultrascale+ System-on-Chip,” CHEP 2019, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 245, Art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  01015, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='1051/epjconf/202024501015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  [14] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Mehner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Ardila-Perez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Balzer, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Sander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Tcher-  niakhovski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Schleicher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=', “ZynqMP-based board-management  mezzanines for Serenity ATCA-blades,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' 3, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='1088/1748-0221/17/03/C03009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='  2021  oooao  O  101001  EE0808  C  401  C  0044  1023  10  一  工  L09  ZynqMP Mezzanine FMC+ (BuZZyBoard)  v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
+page_content='0  October 2020  :0  R19  018  KIT  Luls Ardita  O' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNE5T4oBgHgl3EQfhg_G/content/2301.05642v1.pdf'}
diff --git a/hdE1T4oBgHgl3EQffQTi/content/tmp_files/2301.03217v1.pdf.txt b/hdE1T4oBgHgl3EQffQTi/content/tmp_files/2301.03217v1.pdf.txt
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+arXiv:2301.03217v1  [math.DG]  9 Jan 2023
+Induced para-Kähler Einstein metrics
+on cotangent bundles
+Andreas Čap and Thomas Mettler
+Abstract. In earlier work we have shown that for certain geometric
+structures on a smooth manifold M of dimension n, one obtains a para-
+Kähler–Einstein metric on a manifold A of dimension 2n associated to
+the structure on M.
+The geometry also provides a family of diffeo-
+morphisms between A and T ∗M, so one can use this construction to
+obtain metrics on the cotangent bundle of M. In this short article, we
+discuss the relation of these metrics to Patterson–Walker metrics and
+derive explicit formulae for them in the cases of projective, conformal
+and Grassmannian structures.
+1. Introduction
+An almost para-Kähler structure on a 2n-manifold N consists of a pseudo-
+Riemannian metric h of split-signature (n, n) and a symplectic form Ω such
+that the endomorphism I : TN → TN defined by Ω = h(I·, ·) satisfies
+I2 = IdTN. Almost para-Kähler structures are sometimes also called almost
+bi-Lagrangian structures, see for instance [3, 12, 13]. In [5], generalising the
+results from [11], we showed how to canonically construct an almost para-
+Kähler structure (h, Ω) on a manifold of dimension 2n, which is naturally
+associated to a geometric structure (from a certain class) on an n-manifold
+M. The structures in question admit a description in terms of a so-called
+torsion-free |1|-graded parabolic geometry. This class of geometric structures
+includes in particular projective, conformal and Grassmannian (i.e. torsion-
+free almost Grassmannian) structures. What makes the construction remark-
+able is that h is always an Einstein metric.
+The almost para-Kähler structure is defined on the total space of an affine
+bundle µ : A → M whose sections can be interpreted as the Weyl structures
+of the parabolic geometry and whose associated vector bundle is the cotan-
+gent bundle ν : T ∗M → M. In [5] it is also shown that the choice of a Weyl
+structure s : M → A induces a diffeomorphism ϕs : T ∗M → A satisfying
+(ϕs)∗Ω = dτ − ν∗(Alt Ps),
+where τ denotes the tautological 1-form of T ∗M and Alt Ps the alternating
+part of the Rho-tensor Ps of s.
+This Rho-tensor is a curvature quantity
+associated to s which is an analog of the Ricci curvature.
+Date: January 9, 2023.
+1
+
+2
+A. ČAP AND T. METTLER
+The purpose of this short note is to relate the resulting metrics to classi-
+cally known metrics on the cotangent bundle. In particular, we show – see
+Theorem 3.3 below – that the pullback of the metric has a universal structure
+given by
+(1.1)
+(ϕs)∗h = hϑs − ν∗(Sym Ps) + q,
+where hϑs is the Patterson–Walker metric of the Weyl connection ϑs deter-
+mined by s (see below for details). Further, Sym Ps denotes the symmetric
+part of the Rho-tensor of s and q is a symmetric covariant 2-tensor field on
+T ∗M which only depends on the underlying geometric structure and which
+is semibasic for the projection ν : T ∗M → M.
+Moreover, q is homoge-
+neous of degree 2 in the fibres of T ∗M, that is, satisfies (St)∗q = t2q where
+St : T ∗M → T ∗M denotes scaling of a cotangent vector by the factor t ∈ R∗.
+We work out explicit expressions for (1.1) in the case of projective, confor-
+mal and Grassmannian structures. In the case of projective and conformal
+geometry, expressions for the Rho tensor are well-known, so this amounts
+to computing q. For projective structures, we recover the result from [11],
+where it is shown that q = −τ ⊗ τ. Additionally, we show that in the case
+of a conformal structure [g] on M, the tensor field q is given by
+q = −τ ⊗ τ + 1
+2| · |2
+g♯ν∗g
+where g ∈ [g], g♯ ∈ Γ(S2(TM)) denotes the dual metric of g and | · |2
+g♯ :
+T ∗M → R is defined by ξ �→ g♯(ξ, ξ). Notice that q does only depend on [g].
+In the Grassmannian case, we derive a similar explicit description of q in
+terms of an “improved” version of the tautological one form obtained from
+the structure and we show how to compute the Rho tensor.
+Acknowledgements. A.Č. acknowledges support by the Austrian Science
+Fund (FWF): P 33559-N. T.M. is partially supported by the DFG priority
+programme “Geometry at infinity” SPP 2026. The authors are grateful to
+M. Dunajski for helpful correspondence.
+2. Preliminaries
+We start by briefly collecting some basic facts about soldering forms,
+Patterson–Walker metrics, |1|-graded parabolic geometries and Weyl struc-
+tures. Throughout this article all manifolds and mappings are assumed to
+be smooth, that is, C∞.
+2.1. Soldering forms. Let M be an n-manifold and V a real n-dimensional
+vector space. We consider a right principal G0-bundle π0 : G0 → M for some
+Lie group G0 and ρ : G0 → GL(V ) a representation of G0 on the vector
+space V . Suppose that we have a 1-form ω ∈ Ω1(G0, V ) on G0 with values
+in V which is semibasic and ρ-equivariant.
+The former condition means
+that ω vanishes on all vectors of TG0 that are tangent to the fibres of π0
+and the latter condition means that ω satisfies R∗
+aω = ρ(a−1)(ω) for all
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+3
+a ∈ G0, where Ra : G0 → G0 denotes the right action by a. Recall that
+such a form defines a 1-form ω ∈ Ω1(M, E) on M with values in the vector
+bundle ν : G0 ×ρ V =: E → M associated to ρ. Indeed, for all v ∈ TM
+the element ω(v) ∈ E is represented by (u, ω(˜v)) ∈ G0 × V for any choice
+of u ∈ G0 having the same basepoint as v and any ˜v ∈ TuG0 such that
+π′
+u(˜v) = v, where π′
+u : TuG0 → Tπ(u)M denotes the derivative of π at u. The
+1-form ω ∈ Ω1(G0, V ) is called a soldering form if ω – thought of as a map
+TM → E – is a vector bundle isomorphism. Recall that this is equivalent to
+the fact that ω is strictly horizontal in the sense that its kernel in any point
+of G0 is the vertical subbundle.
+2.2. The Patterson–Walker metric. We review the construction of the
+Patterson–Walker metric, adapted to our setting. To this end suppose, as
+above, that π : G0 → M is a right principal G0-bundle equipped with a
+soldering form ω ∈ Ω1(G0, V ) which is equivariant with respect to a repre-
+sentation ρ : G0 → GL(V ). Assume in addition that ρ is infinitesimally
+effective, that is, the induced Lie algebra representation ̺ : g0 → gl(V ) is in-
+jective. Using ω, the tangent bundle of M can be identified with the bundle
+associated to ρ, that is, TM ≃ G0 ×ρ V .
+Now let ϑ ∈ Ω1(G0, g0) be a principal G0-connection on G0. Let us denote
+by V ∗ the dual space to V and by ̺∗ : g0 → gl(V ∗) the the dual repre-
+sentation to ̺. Then on the product G0 × V ∗ we consider the V ∗-valued
+1-form
+ζϑ = dξ + (̺∗ ◦ ϑ)(ξ),
+where ξ : G0 × V ∗ → V ∗ denotes the second projection. By construction,
+the V ∗-valued 1-form is equivariant with respect to the dual representation
+ρ∗ : G0 → GL(V ∗) and it is easy to check that it is semibasic for the
+projection G0×V ∗ → T ∗M ≃ G0×ρ∗V ∗. Consequently, it represents a 1-form
+ζϑ ∈ Ω1(T ∗M, ν∗T ∗M) on T ∗M with values in the pullback of the cotangent
+bundle ν : T ∗M → M of M. The pullback bundle ν∗T ∗M is naturally a
+subbundle of T ∗(T ∗M) and hence we may interpret ζϑ as a 1-form on T ∗M
+with values in T ∗(T ∗M), or equivalently, as a section of T ∗(T ∗M)⊗T ∗(T ∗M).
+The symmetric part hϑ = Sym ζϑ is a pseudo-Riemannian metric of split-
+signature (n, n) known as the Patterson–Walker metric associated to the
+connection ϑ, see [17] for the original construction and [14, 15] for recent
+applications.
+2.3. Parabolic geometries. Recall that a Cartan geometry of type (G, P)
+for some Lie group G and closed subgroup P ⊂ G is a pair (π : G → M, θ)
+consisting of a right principal P-bundle π : G → M together with a Cartan
+connection θ taking values in the Lie algebra g of G. We let R : G × P → G
+denote the right action of P and we write Rg = R(·, g) for all g ∈ P and
+ιu = R(u, ·) for all u ∈ G. The 1-form θ ∈ Ω1(G, g) being a Cartan connection
+means that for all u ∈ G the linear map θu : TuG → g is an isomorphism and
+
+4
+A. ČAP AND T. METTLER
+moreover
+(2.1)
+(R∗θ)(u,g) = (ι∗
+uθ)g + (R∗
+gθ)u = (ΥP )g + Ad(g−1) ◦ θu,
+for all (u, g) ∈ G × P, where ΥP denotes the Maurer–Cartan form of P and
+Ad : G → GL(g) the adjoint action of G. In addition, the curvature 2-form
+Θ = dθ+ 1
+2[θ, θ] of θ satisfies a further condition called normality. The details
+of this conditions are not important for our purposes, some consequences
+will be discussed below. We will always assume that the Cartan geometry is
+torsion-free, that is, Θ has values in p ⊂ g, the Lie algebra of P.
+Here we consider the special case of |1|-graded parabolic geometries. This
+means that G is assumed to be semisimple and that its Lie algebra g is
+endowed with a so-called |1|-grading. This is a decomposition
+g = g−1 ⊕ g0 ⊕ g1
+into a direct sum of linear subspaces gi for i = −1, 0, 1 such that [gi, gj] ⊂
+gi+j with the convention that gℓ = {0} for ℓ = ±2. Furthermore, no simple
+ideal of g is allowed to be contained in g0 and the Lie algebra p of P satisfies
+p = g0 ⊕ g1. In particular, this implies that P ⊂ G is a parabolic subgroup
+in the sense of representation theory.
+These properties have some nice consequences. First, the exponential map
+of g – restricted to g1 – is a diffeomorphism from g1 onto a closed normal
+subgroup P+ ⊂ P. Second, defining G0 ⊂ P to consist of those elements
+g so that the adjoint action Ad(g) ∈ GL(g) preserves the grading of g, one
+can show that the Lie algebra of G0 is g0 and that G0 is isomorphic to the
+quotient P/P+. Third, every element g of P can be written as g = g0 exp(Z)
+for unique elements g0 ∈ G0 and Z ∈ g1.
+Since P+ ⊂ P is a normal subgroup, we obtain a principal P/P+ ≃ G0-
+bundle G/P+ → M whose total space we denote by G0 and whose basepoint
+projection we denote by π0. We can project the values of the Cartan con-
+nection θ to g/p ∼= g−1. Equivariancy of θ then easily implies that the result
+descends to a 1-form ω ∈ Ω1(G0, g−1). Equivariancy of θ also implies that
+ω is equivariant with respect to the G0-representation ρ : G0 → GL(g−1)
+obtained by restricting the adjoint representation to g−1;
+(2.2)
+ρ = Ad( · )|g−1 : G0 → GL(g−1),
+g0 �→ Ad(g0)|g−1.
+This representation is infinitesimally effective. The construction then easily
+implies that ω is a soldering form in the sense of Section 2.1. Hence we obtain
+a G0-structure on the manifold M and it turns out that, apart from the
+case of projective structures, the normality condition on Θ ensures that the
+Cartan geometry (G → M, θ) is an equivalent encoding of this G0-structure.
+2.4. Weyl structures. In order to work explicitly with a parabolic geome-
+try it is often advantageous to fix a Weyl structure for the parabolic geometry.
+This gives a description of the Cartan geometry (G → M, θ) in terms of the
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+5
+underlying G0-structure (G0 → M, ω) defined above.
+Here we briefly re-
+view the key facts and refer the reader to [5, 6, 7] for details and additional
+context.
+Following [6], we define a Weyl structure for (π : G → M, θ) to be a G0-
+equivariant section σ : G0 → G of the projection G → G0. Writing the Cartan
+connection θ as θ = (θ−1, θ0, θ1) with θi taking values in gi, a choice of Weyl
+structure σ gives three 1-forms on G0
+(2.3)
+ω = σ∗θ−1 ∈ Ω1(G0, g−1),
+ϑσ = σ∗θ0 ∈ Ω1(G0, g0),
+Pσ = −ψB ◦ (σ∗θ1) ∈ Ω1(G0, g∗
+−1).
+Here ω is just the soldering form from Section 2.3 above. The form ϑσ is a
+principal G0-connection on π0 : G0 → M referred to as the Weyl connection
+determined by σ. For the last component, we let B denotes a suitable con-
+stant multiple of the Killing form of g and ψB : g1 → g∗
+−1 the linear map
+defined by the rule
+ψB(Z)(X) = B(Z, X)
+for all Z ∈ g1 and all X ∈ g−1. It is well-known that ψB is an isomorphism.
+In the literature on parabolic geometries, ψB is usually suppressed from the
+notation and g1 is simply identified with (g−1)∗.
+The multiple B of the Killing form is chosen so that the form Pσ represents
+the so-called Rho tensor Pσ of the Weyl structure σ, thought of as a 1-form on
+M with values in T ∗M. Notice that here our convention for the Rho tensor
+agrees with the classical definitions for conformal an projective structures
+and hence differs by a sign from [5, 6, 7].
+2.5. On the Rho tensor. Here we briefly explain how the normalization
+condition on the curvature of a |1|-graded parabolic geometry leads to a way
+to explicitly determine the Rho tensor associated to a Weyl structure. We
+start by introducing a canonical object on M, which will also be useful for
+other purposes. This comes from the component
+(2.4)
+[ , ] : g−1 × g1 → g0
+of the Lie bracket in g, which is a G0-equivariant bilinear map. Observe
+further that the derivative of the representation ρ from (2.2) defines an in-
+clusion g0 → End(g−1, g−1), which by construction is again induced by the
+Lie bracket. Together with ψB, this shows that (2.4) induces a
+�2
+2
+�
+-tensor field
+on M. We will interpret this below as associating to a vector field X ∈ X(M)
+and a one-form α ∈ Ω1(M) a
+�1
+1
+�
+-tensor field {X, α} which in particular can
+be viewed as a section of End(TM, TM) or of End(T ∗M, T ∗M).
+Now given two vector fields X, Y ∈ X(M) and a T ∗M-valued one form P,
+we define a
+�1
+3
+�
+-tensor field ∂P by
+(2.5)
+∂P(X, Y ) := {X, P(Y )} − {Y, P(X)}.
+
+6
+A. ČAP AND T. METTLER
+By construction, this is skew symmetric in X and Y and thus defines a two-
+form with values in End(TM, TM), so this looks like the curvature of a linear
+connection on TM. Now for a Weyl structure σ, we consider the induced
+Weyl connection θσ. The curvature of this Weyl connection is equivalently
+encoded by a two-form Rσ with values in End(TM, TM).
+Now it turns
+out that the normalization condition on the Cartan connection implies that
+the Rho tensor Pσ is uniquely characterized by the fact that Rσ − ∂Pσ has
+vanishing Ricci type contraction, see [8] or Section 5.2.3 of [6]. Throughout
+the article we follow the convention of defining the Ricci curvature Ric(∇)
+of a torsion-free connection ∇ as
+(X, Y ) �→ Ric(∇)(X, Y ) = tr
+�
+Z �→ R∇(Z, X)(Y )
+�
+where the curvature operator R∇ is defined as usual by
+R∇(X, Y )(Z) = ∇X∇Y Z − ∇Y ∇XZ − ∇[X,Y ]Z.
+Notice that this convention, while common in projective differential geom-
+etry, differs (by a swap of the arguments) from the standard convention in
+Riemannian geometry.
+3. The almost para-Kähler structure of a Weyl structure
+3.1. Construction of the almost para-Kähler structure. We briefly
+review the construction of the almost para-Kähler structure associated to a
+torsion-free |1|-graded parabolic geometry given in [5]. Notice that we may
+think of a torsion-free |1|-graded parabolic geometry (π : G → M, θ) of type
+(G, P) on M as a Cartan geometry (Π : G → A, θ) of type (G, G0) on the
+quotient A := G/G0. In doing so, the tangent bundle of A becomes TA =
+G ×G0 (g/g0), where G0 acts via the adjoint action on g and hence on g/g0.
+The G0-module g/g0 is isomorphic to g−1 ⊕ g1, where again G0 acts on both
+summands via the adjoint representation. Consequently, the tangent bundle
+of A decomposes into a direct sum of rank n vector bundles TA = L+ ⊕ L−,
+where L± = G ×G0 g±1. We consider the 1-form η = ψB ◦ θ1 ∈ Ω1(G, g∗
+−1).
+Explicitly, we have
+η(v)(X) = B(θ1(v), X)
+for all v ∈ TG and all X ∈ g−1. It follows from the properties of the Cartan
+connection and the invariance of B under the adjoint representation that
+the 1-form η is G0-equivariant and semibasic for the projection Π : G → A.
+Consequently, η represents a 1-form η on A with values in (L−)∗ ⊂ T ∗A.
+Hence we may view η as a section of T ∗A ⊗ T ∗A.
+The symmetric part
+h = Sym η is then a pseudo-Riemannian metric of split-signature on A. This
+uses that ψB : g1 → g∗
+−1 is an isomorphism. The alternating part Ω = Alt η
+turns out to be a symplectic form by torsion-freeness (see [5, Theorem 3.1]),
+and the pair (h, Ω) is an almost para-Kähler structure. Furthermore, the
+sections of A → M are in bijective correspondence with the Weyl structures
+for (π : G → M, θ). Remarkably, by [5, Theorem 3.5], the normalization
+conditions for |1|-graded parabolic geometries imply that the metric h always
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+7
+is Einstein and hence (h, Ω) is an almost para-Kähler Einstein structure. We
+refer to [5] for further details and to [2] for recent results about the geometry
+of 4-dimensional para-Kähler Einstein structures.
+3.2. The choice of a Weyl structure. In this section we shall prove the
+main structural identity (1.1). We start by identifying G with the product
+G0 × g1 equipped with a suitable right action.
+An element of G0 will be
+denoted by [u], where u ∈ G. On G0 × g1 a P-right action ˆR is defined by
+the rule
+([u], Z) · g = ([u · g0], Ad(g−1
+0 )(Z) + W)
+for all ([u], Z) ∈ G0 × g1 and all g = g0 exp(W) in P and as the basepoint
+projection we take the map
+ˆπ : G0 × g1 → M,
+([u], Z) �→ π0([u]).
+With these definitions, ˆπ : G0 × g1 → M is indeed a right principal P-bundle
+and moreover, the choice of a Weyl structure identifies this bundle with
+π : G → M:
+Proposition 3.1. Let (π : G → M, θ) be a |1|-graded parabolic geometry of
+type (G, P). Then every Weyl structure σ : G0 → G induces an isomorphism
+of principal P-bundles
+Φσ : G0 × g1 → G,
+([u], Z) �→ σ([u]) · exp(Z)
+satisfying
+(Φσ)∗θ = dZ + σ∗θ + [σ∗θ, Z] + 1
+2[[σ∗θ, Z], Z],
+where Z : G0 × g1 → g1 denotes the projection onto the second factor, the
+brackets are in g, and we omit writing the pullbacks from the first factor.
+For the proof we need the following elementary lemma on the Maurer-
+Cartan form ΥP ∈ Ω1(P, p):
+Lemma 3.2. The exponential map exp : g1 → P satisfies exp∗ ΥP = d Idg1,
+where Idg1 denotes the identity map on g1.
+Proof. For X, Y ∈ g1, we compute
+(exp∗ ΥP)X(Y ) = (ΥP )exp(X)(exp′
+X(Y )) = (Lexp(X)−1)′
+exp(X)(exp′
+X(Y ))
+= (Lexp(X)−1 ◦ exp)′
+X(Y )
+= d
+dt
+����
+t=0
+exp(−X) exp(X + tY ) = d
+dt
+����
+t=0
+exp(tY ) = Y,
+where we use that [X, X + tY ] = 0 since [g1, g1] = {0}.
+□
+Proof of Proposition 3.1. First observe that since [g1, g1] = {0}, we have
+exp(Z) exp(W) = exp(Z + W)
+for all Z, W ∈ g1. As a consequence, the standard identity
+g exp(X)g−1 = exp(Ad(g)(X)),
+g ∈ G, X ∈ g
+
+8
+A. ČAP AND T. METTLER
+implies that for all g0 exp(W) ∈ P and h0 exp(Z) ∈ P, we have
+(3.1)
+g0 exp(Z)h0 exp(W) = g0h0 exp(Ad(h−1
+0 )(Z) + W),
+where we use that Ad(h−1
+0 ) preserves g1.
+Since exp : g1 → P+ is a diffeomorphism and σ : G0 → G is equivariant, it
+easily follows that Φσ is a diffeomorphism. In order to verify the equivariancy
+of Φσ, we compute for all ([u], Z) ∈ G0 × g1 and for all g = g0 exp(W) ∈ P
+Φσ(([u], Z) · g) = Φσ(([u · g0], Ad(g−1
+0 )(Z) + W))
+= σ([u · g0]) · exp(Ad(g−1
+0 )(Z) + W)
+= σ([u]) · g0 exp(Ad(g−1
+0 )(Z) + W)
+= σ([u]) · exp(Z)g0 exp(W)
+= σ([u]) · exp(Z)g = Φσ(([u], Z)) · g,
+where we used the definitions of the various mappings as well as (3.1) and the
+equivariancy of σ. It follows that Φσ is a principal P-bundle isomorphism.
+For the second part of the lemma we denote by Ad−1 the composition of
+Ad with the inversion in P and compute
+(3.2)
+(Φσ)∗θ = (σ, exp)∗(R∗θ) = (σ, exp)∗ �
+ΥP + Ad−1 ◦ θ
+�
+= exp∗ ΥP + σ∗ �
+Ad−1 ◦ θ
+�
+where we used (2.1) and think of (σ, exp) as a map G0 × g1 → G × P. Now
+for Z, W ∈ g we have the standard identity
+Ad(exp(Z))(W) =
+∞
+�
+k=0
+ad(Z)k
+k!
+(W) = W + [Z, W] + 1
+2[Z, [Z, W]] + · · · .
+As a consequence, we obtain for all Z ∈ g1
+(3.3)
+(Rexp(Z))∗θ = Ad(exp(−Z)) ◦ θ = θ + [θ, Z] + 1
+2[[θ, Z], Z],
+where we use that the sum terminates after three summands, since [g1, g1] =
+0. Combining (3.2), (3.3) and Lemma 3.2, we obtain
+(3.4)
+(Φσ)∗θ = dZ + σ∗θ + [σ∗θ, Z] + 1
+2[[σ∗θ, Z], Z],
+as claimed.
+□
+Recall from Section 2.4 that for every choice of Weyl structure σ : G0 → G,
+ω = σ∗θ−1 ∈ Ω1(G0, g−1) is the soldering form of the G0-structure π0 :
+G′ → M. Moreover, ϑσ = σ∗θ0 ∈ Ω1(G0, g0) is a principal connection on
+π0 : G0 → M. Using (2.3) and (3.4) we thus obtain
+(Φσ)∗θ1 = dZ + σ∗θ1 + [ϑσ, Z] + 1
+2[[ω, Z], Z]
+and hence, using (2.3) again, we have
+(3.5)
+(Φσ)∗(ψB ◦ θ1) = ψB ◦ (dZ + [ϑσ, Z]) − Pσ + 1
+2ψB ◦ ([[ω, Z], Z]) .
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+9
+In order to relate this to the Patterson–Walker metric associated to ϑσ,
+we first observe that via ψB, the map Z corresponds to the second projection
+G0 × g∗
+−1 → g∗
+−1. Moreover, in the notation of Section 2.2, the expression
+[ϑσ, Z] can be written as (ad ◦ϑσ)(Z).
+Invariance of the bilinear form B
+implies that for X ∈ g−1, Y ∈ g0 and Z ∈ g1, we get
+B(ad(Y )(X), Z) = −B(X, ad(Y )(Z)).
+This exactly says that, via ψB, the adjoint action on g1 corresponds to the
+dual of the adjoint action on g−1, which was denoted by ̺∗ in Section 2.2.
+Together, this shows that the term ψB ◦ (dZ + [ϑσ, Z]) exactly gives the
+g∗
+−1-valued 1-form ζϑσ defined there.
+Combining this with (3.5), we obtain
+(3.6)
+(Φσ)∗(ψB ◦ θ1) = ζϑσ − Pσ + q
+where q ∈ Ω1(G0 × g∗
+−1, g∗
+−1) is given by
+(3.7)
+q = 1
+2ψB ◦
+�
+[[ω, ψ−1
+B ◦ ξ], ψ−1
+B ◦ ξ]
+�
+.
+By construction, q represents a 1-form q on T ∗M with values in the pullback
+of the cotangent bundle of M, which is evidently closely related to the op-
+eration on M introduced in Section 2.5. More precisely, for α ∈ T ∗M with
+ν(α) = x and a tangent vector X ∈ TαT ∗M, we get
+(3.8)
+q(α)(X) = 1
+2{ν′
+α(X), α}(α) ∈ T ∗
+xM = (ν∗T ∗M)α.
+In particular, this shows that q is semibasic for the projection ν : T ∗M → M
+and satisfies (St)∗q = t2q, where St : T ∗M → T ∗M denotes scaling of a
+cotangent vector by the factor t ∈ R∗.
+Finally, notice that using ψB to identify g1 with g∗
+−1, we get T ∗M ≃
+G0 ×G0 g1. But then the G0-equivariant diffeomorphism Φσ : G0 × g1 → G
+induces a diffeomorphism ϕσ : T ∗M → G/G0 = A and we have
+(ϕσ)∗η = ζϑσ − ν∗Pσ + q.
+Recall that η is the (L−)∗-valued 1-form on A whose symmetric and alter-
+nating part give the almost para-Kähler structure (h, Ω) of the parabolic
+geometry (π : G → M, θ). Recall also that the symmetric part of the form
+ζϑσ is the Patterson–Walker metric hϑs of the Weyl connection ϑσ deter-
+mined by σ. Finally, viewed as a bilinear form on TαT ∗M, q(α) turns out
+to be symmetric. By construction, q(α) is the pullback of a bilinear form on
+TxM with x = ν(α). The latter is induced by the bilinear form on g−1 that,
+for some fixed Z ∈ g1, maps (X1, X2) to
+1
+2B([[X1, Z], Z], X2) = − 1
+2B([X1, Z], [Z, X2]) = 1
+2B([X1, Z], [X2, Z]),
+so this is obviously symmetric. In summary, we have thus shown:
+Theorem 3.3. Let (π : G → M, θ) be a torsion-free |1|-graded parabolic
+geometry with associated almost para-Kähler structure (h, Ω) on A and σ :
+
+10
+A. ČAP AND T. METTLER
+G0 → G a choice of Weyl structure. Then we have
+(ϕσ)∗h = hϑσ − ν∗ Sym(Pσ) + q,
+where q is given by formula (3.8).
+Remark 3.4 (Local coordinate expression). In terms of a choice of local coor-
+dinates (xi) : U → Rn on some open subset U ⊂ M, the metric (ϕσ)∗h takes
+the following explicit form. Let (xi, ξi) : ν−1(U) → R2n denote the canonical
+coordinates induced on ν−1(U) ⊂ T ∗M. The Weyl connection ϑσ induces a
+torsion-free connection ∇ on TM whose Christoffel symbols with respect to
+the coordinates (xi) we denote by Γi
+jk. The Patterson–Walker metric of ϑσ
+can then be expressed as
+(dξi − Γk
+ijξkdxj) ⊙ dxi,
+where ⊙ denotes the symmetric tensor product. On ν−1(U) we thus obtain
+(ϕσ)∗h =
+�
+dξi − Γk
+ijξkdxj − P(ij) + qij
+�
+⊙ dxi,
+where we write q = qijdxi ⊗ dxj for unique real-valued functions qij = qji :
+U → R and Pσ = Pijdxi ⊗ dxj for unique real-valued functions Pij : U → R.
+Here and henceforth, we employ the summation convention and P(ij) denotes
+symmetrization in the indices i, j.
+4. Examples
+4.1. Projective geometry. Consider an n-dimensional manifold M endowed
+with a projective structure [∇], a class of torsion-free connections that have
+the same geodesics up to parametrization. This determines a |1|-graded par-
+abolic geometry (π : G → M, θ), where G = SL±(n+1, R) is the subgroup of
+GL(n + 1, R) consisting of matrices whose determinant is ±1. The grading
+of its Lie algebra g = sl(n + 1, R) = {B ∈ gl(n + 1, R), tr B = 0} is given by
+g−1 =
+��
+0
+0
+x
+0
+����� x ∈ Rn
+�
+,
+g1 =
+��
+0
+y
+0
+0
+����� y ∈ Rn∗
+�
+and
+g0 =
+��
+− tr A
+0
+0
+A
+����� A ∈ gl(n, R)
+�
+.
+Here B is normalised so that
+B
+��
+0
+0
+x
+0
+�
+,
+�
+0
+y
+0
+0
+��
+= yx = y(x).
+Next, one computes that for x ∈ Rn and y, z ∈ Rn∗ we get
+(4.1)
+���
+0
+0
+x
+0
+�
+,
+�
+0
+y
+0
+0
+��
+,
+�
+0
+z
+0
+0
+��
+=
+�
+0
+−(yx)z − (zx)y
+0
+0
+�
+.
+This shows that for ξ ∈ TxM and α ∈ T ∗
+xM we get {ξ, α}(α) = −2α(ξ)α.
+Together with formula (3.8) and the definition of the tautological form τ on
+T ∗M, this shows that
+q = −τ ⊗ τ,
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+11
+in agreement with [11].
+The Weyl connection ϑσ = σ∗θ0 determines a torsion-free connection ∇
+on TM which is a representative connection of the projective structure. To
+compute the associated Rho tensor a similar computation as for formula
+(4.1) shows that for X, Z ∈ X(M) and α ∈ Ω1(M), we get {X, α}(Z) =
+α(X)Z +α(Z)X. Using this and formula (2.5) from Section 2.5 we conclude
+that for X, Y, Z ∈ X(M), we obtain
+∂Pσ(X, Y )(Z) = Pσ(Y, X)Z − Pσ(X, Y )Z + Pσ(Y, Z)X − Pσ(X, Z)Y.
+This easily implies that the Ricci type contraction of ∂Pσ maps X, Y to
+nPσ(X, Y ) − Pσ(Y, X). Now let Ric(∇) the Ricci type contraction of the
+curvature of ϑσ. Then the discussion in Section 2.5 shows that we must have
+Ric(∇)(X, Y ) = nPσ(X, Y ) − Pσ(Y, X).
+Symmetrizing and alternating, we conclude that Sym Ric(∇) = (n−1) Sym Pσ
+and Alt Ric(∇) = (n + 1) Alt Pσ, and hence
+Pσ =
+1
+(n − 1) Sym Ric(∇) +
+1
+(n + 1) Alt Ric(∇).
+Remark 4.1 (Dancing metric). Starting from the standard projective struc-
+ture on RP2, the resulting para-Kähler–Einstein structure is defined on
+A = SL(3, R)/GL(2, R). In this case the Einstein metric is referred to as
+the dancing metric [1, 9] because of its significance in the “rolling” of the
+projective planes RP2 and RP2∗. This para-Kähler–Einstein structure was
+first constructed in [16] (in any dimension).
+Remark 4.2 (para-c-projective compactification). In the projective case, the
+almost para-Kähler structure on A admits a so-called para-c-projective com-
+pactification, see [10], an analog of a c-projective compactification, see [4].
+4.2. Conformal geometry. A conformal manifold (M, [g]) of dimension
+n ⩾ 3 gives rise to a |1|-graded parabolic geometry (π : G → M, θ) where G
+is defined as follows: Consider the matrix
+J =
+
+
+0
+0
+−1
+0
+In
+0
+−1
+0
+0
+
+
+of size n + 2 and let G = O(n + 1, 1) denote the subgroup of GL(n + 2, R)
+consisting of matrices a satisfying atJa = J. The Lie algebra g = o(n + 1, 1)
+of G consists of matrices of the form
+
+
+s
+z
+0
+x
+A
+zt
+0
+xt
+−s
+
+
+
+12
+A. ČAP AND T. METTLER
+where s ∈ R, x ∈ Rn, z ∈ Rn∗ and A ∈ o(n) is a skew-symmetric matrix of
+size n. The grading of g is given by
+g−1 =
+
+
+
+
+
+0
+0
+0
+x
+0
+0
+0
+xt
+0
+
+
+������
+x ∈ Rn
+
+
+ ,
+g1 =
+
+
+
+
+
+0
+z
+0
+0
+0
+zt
+0
+0
+0
+
+
+������
+y ∈ Rn
+
+
+
+and
+g0 =
+
+
+
+
+
+s
+0
+0
+0
+A
+0
+0
+0
+−s
+
+
+������
+s ∈ R, A ∈ o(n)
+
+
+ .
+We normalise B such that
+B
+
+
+
+
+0
+0
+0
+x
+0
+0
+0
+xt
+0
+
+ ,
+
+
+0
+z
+0
+0
+0
+zt
+0
+0
+0
+
+
+
+ = z(x) = zx.
+Computing triple brackets as for formula (4.1) one verifies that (with
+obvious notation) we get for x, y ∈ Rn and z, w ∈ Rn∗ the expressions
+[[x, z], w] = −z(x)w − w(x)z + (wt · zt)xt
+(4.2)
+[[x, z], y] = z(x)y + z(y)x − (x · y)zt
+(4.3)
+Now formula (4.2) shows that for ξ ∈ TxM and α ∈ T ∗
+xM we get
+{ξ, α}(α) = 2α(ξ)α + g#
+x (α, α)gx(ξ, ·).
+Here g is some metric from the conformal class and g# is its dual metric,
+which immediately implies that the operation is conformally invariant. To-
+gether with formula (3.8) and the definition of the tautological form τ on
+T ∗M, this shows that
+q = −τ ⊗ τ + 1
+2| · |2
+g♯ν∗g.
+Here | · |2
+g♯ is interpreted as a real-valued smooth function on T ∗M and the
+pullback ν∗g is interpreted as a one-form on T ∗M with values in ν∗T ∗M.
+The Weyl connection ϑσ = σ∗θ0 determines a torsion-free connection ∇
+on TM which preserves [g] in the sense that for some (any hence any) rep-
+resentative metric g ∈ [g] there exists a 1-form β such that
+∇g = β ⊗ g.
+To compute the Rho-tensor, we first conclude from formula (4.3) that for
+vector fields X, Y ∈ X(M) and a one-form α ∈ Ω1(M), we get
+{X, α}(Y ) = α(X)Y + α(Y )X − g(X, Y )g#(α, ·).
+Using this and formula (2.5) from Section 2.5 we conclude that for X, Y, Z ∈
+X(M), we can write ∂Pσ(X, Y )(Z) as
+Pσ(Y, X)Z + Pσ(Y, Z)X − g(X, Z)g#(Pσ(Y ))
+−Pσ(X, Y )Z − Pσ(X, Z)Y + g(Y, Z)g#(Pσ(X)).
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+13
+To form the Ricci-type contraction of this, we have to take a local orthonor-
+mal frame, insert each element for X and then take the inner product with
+the same element and sum the results. This sends (Y, Z) to
+(n − 1)Pσ(Y, Z) − Pσ(Z, Y ) + g(Y, Z) trg#(Pσ).
+Observe that in the literature on conformal geometry usually only the case
+of Levi-Civita connections of metrics in the conformal class is discussed, for
+which Pσ is automatically symmetric. Anyway, the discussion in Section 2.5
+shows that the above expression has to coincide with Ric(∇). To conclude the
+discussion as in Section 4.1 above, we now have to compute the alternation,
+and the trace-free part and the trace part of the symmetrization, which gives
+Sym0 Ric(∇) = (n − 2) Sym0 Pσ
+Alt Ric(∇) = n Alt Pσ
+g trg#(Ric(∇)) = (2n − 2)g trg#(Pσ).
+Observe that for a Levi-Civita connection trg#(Ric(∇)) is the scalar curva-
+ture of the metric g. In any case, we immediately get the general formula
+Pσ =
+1
+n − 2 Sym0 Ric(∇) + 1
+n Alt Ric(∇) +
+1
+n(n − 2)g trg#(Ric(∇)).
+4.3. Grassmannian geometry. An almost Grassmannian structure of type
+(m, n) on a manifold M consists of two real vector bundles E and F on M, of
+rank m and n and vector bundle isomorphisms TM ≃ E∗ ⊗ F ≃ Hom(E, F)
+and ΛmE∗ ∼= ΛnF. Here E∗ denotes the dual of E and the isomorphism
+between the top exterior powers will not be relevant for us.
+An almost
+Grassmannian structure on M gives rise to a |1|-graded parabolic geometry
+(π : G → M, θ) where G = SL(n + m, R). The structure is called Grass-
+mannian if it admits a compatible torsion-free connection on TM, which is
+equivalent to torsion-freeness of the parabolic geometry. The grading of the
+Lie algebra g = sl(n + m, R) of G is given by
+g−1 =
+��
+0
+0
+x
+0
+����� x ∈ M(n × m, R)
+�
+,
+g1 =
+��
+0
+z
+0
+0
+����� y ∈ M(m × n, R)
+�
+and
+g0 =
+��
+B
+0
+0
+A
+����� A ∈ gl(n, R), B ∈ gl(m, R), tr(A) + tr(B) = 0
+�
+,
+where M(n × m, R) denotes the vector space of (n × m)-matrices with real
+entries.
+The main case of interest for our purpose is m = 2, n ≥ 2, for
+which there are examples of such geometries that are torsion-free but not
+locally isomorphic to G/P. For m = n = 2 such a structure is equivalent
+to a conformal structure of neutral signature. For m, n > 2, any torsion-free
+structure is locally isomorphic to G/P, but our results still are of interest,
+since there is the freedom in the choice of Weyl structure.
+
+14
+A. ČAP AND T. METTLER
+As the invariant form B we use the trace form, which leads to
+B
+��
+0
+0
+x
+0
+�
+,
+�
+0
+z
+0
+0
+��
+= tr(zx) = tr(xz).
+Formally, the setup looks very similar to projective structures (which corre-
+spond to the case m = 1). This is also reflected in the structure of the triple
+brackets, which formally look very similar to (4.1): For x, y ∈ M(n × m, R)
+and z, w ∈ M(m × n, R) we get (in obvious notation)
+(4.4)
+[[x, z], w] = −zxw − wxz
+[[x, z], y] = xzy + yzx.
+However, here we have matrix multiplications so for example xz is a 2 × 2-
+matrix and zxw is not simply a multiple of w.
+The easiest way to encode our operations geometrically is to define one
+additional operation on a manifold M endowed with an almost Grassmannian
+structure. Since TM ∼= E∗ ⊗ F, we get T ∗M ∼= E ⊗ F ∗ ∼= Hom(F, E) and
+thus composition of linear maps induces a bilinear bundle map T ∗M×TM →
+End(E, E), which we denote by (α, X) �→ α ◦ X both on elements and on
+sections. This can be viewed as an “refinement” of the dual pairing, since by
+definition we get α(X) = tr(α ◦ X), where tr denotes the point-wise trace.
+There clearly are analogous composition operations TM ×End(E, E) → TM
+and End(E, E) × T ∗M → T ∗M (and others that we don’t need here). In
+this language, the first formula in (4.4) readily shows that for α ∈ T ∗
+xM and
+ξ ∈ TxM, we get {ξ, α}(α) = −2(α ◦ ξ) ◦ α.
+Next, we get a corresponding refinement τ G ∈ Ω1(T ∗M, End(ν∗E, ν∗E))
+of the tautological one-form τ on T ∗M. By definition, for α ∈ T ∗M with
+ν(α) = x ∈ M, the fiber of End(ν∗E, ν∗E) over α equals End(Ex, Ex), so
+for ξ ∈ TαT ∗M, we can define
+τ G(α)(ξ) := α ◦ ν′
+α(ξ).
+By definition, the tautological form τ is then recovered as τ = tr(τ G), where
+again tr denotes a point-wise trace in the values of the form. Using formula
+(3.8) we readily conclude that for α ∈ T ∗M and ξ, η ∈ TαT ∗M we get
+q(α)(ξ, η) = − tr((α ◦ ν′
+α(ξ)) ◦ (α ◦ ν′
+α(η))),
+which is evidently symmetric in ξ and η. To connect more closely to the
+other cases, we can write this as q = − tr(τ G ⊗ τ G), where we agree that
+the tensor product of one-forms with values in End(ν∗E, ν∗E) includes a
+composition of the values, i.e. (A ⊗ B)(ξ, η) = A(ξ) ◦ B(η).
+The description of the Rho tensor is also similar to the projective case,
+with some complications caused by the matrix multiplications.The Weyl con-
+nection ϑσ = σ∗θ0 determines a torsion-free connection ∇ on TM which
+is induced by connections on E and F that are compatible with the iso-
+morphism of the top exterior powers.
+Now the second equation in (4.4)
+readily shows that for X, Y ∈ X(M) and α ∈ Ω1(M) we get {α, X}(Y ) =
+X ◦ (α ◦ Y ) + Y ◦ (α ◦ X). Using this and formula (2.5) from Section 2.5 we
+
+EINSTEIN METRICS ON COTANGENT BUNDLES
+15
+conclude that for X, Y, Z ∈ X(M), ∂Pσ(X, Y )(Z) is given by
+X ◦ (Pσ(Y ) ◦ Z) + Z ◦ (Pσ(Y ) ◦ X) − Y ◦ (Pσ(X) ◦ Z) − Z ◦ (Pσ(X) ◦ Y )
+To compute the action of the Ricci type contraction on Y and Z, we have
+to insert the elements of a basis for X and contract (i.e. take the trace of
+the composition) with the dual basis element and sum up over the basis. To
+write up the result, we need additional notation. We have to view Pσ(x)
+as an element in ⊗2T ∗
+xM and identifying TxM with Hom(Fx, Ex) such an
+element defines a linear map Fx ⊗ Fx → Ex ⊗ Ex.
+But for such a map,
+we can separately swap the input or the output and hence independently
+symmetrize or alternate in the input and the output. Writing tE for the
+twist map on E ⊗ E and tF for the twist map on F ⊗ F, one verifies that
+the Ricci type contraction of ∂Pσ can be written as
+(mn + 1)Pσ − tE ◦ Pσ − Pσ ◦ tF .
+Observe that this is consistent with the result in the projective case, since for
+m = 1, we have tE = id. By the discussion in Section 2.5, this again has to
+coincide with the Ricci type contraction Ric(∇) of the curvature of ∇. Now
+we can compose this equation on both sides with either a symmetrization or
+an alternation to obtain
+Sym ◦ Ric(∇) ◦ Sym = (mn − 1) Sym ◦Pσ ◦ Sym
+Alt ◦ Ric(∇) ◦ Alt = (mn + 3) Alt ◦Pσ ◦ Alt
+Sym ◦ Ric(∇) ◦ Alt = (mn + 1) Sym ◦Pσ ◦ Alt
+Alt ◦ Ric(∇) ◦ Sym = (mn + 1) Alt ◦Pσ ◦ Sym .
+From this, one deduces an explicit formula for Pσ as before.
+References
+[1] G. Bor, L. Hernández Lamoneda, P. Nurowski, The dancing metric, G2-
+symmetry and projective rolling, Trans. Amer. Math. Soc. 370 (2018), 4433–4481.
+DOI 10.1090/tran/7277 MR 3811534 11
+[2] G. Bor, O. Makhmali, P. Nurowski, Para-Kähler-Einstein 4-manifolds and
+non-integrable twistor distributions, Geom. Dedicata 216 (2022), Paper No. 9, 48.
+DOI 10.1007/s10711-021-00665-4 MR 4366946 7
+[3] R. L. Bryant, Bochner-Kähler metrics, J. Amer. Math. Soc. 14 (2001), 623–715.
+DOI 10.1090/S0894-0347-01-00366-6 MR 1824987 1
+[4] A. Čap, A. R. Gover, c-projective compactification; (quasi-)Kähler metrics and
+CR boundaries, Amer. J. Math. 141 (2019), 813–856. DOI 10.1353/ajm.2019.0017
+MR 3956522 11
+[5] A. Čap, T. Mettler, Geometric theory of Weyl structures, Commun. Contemp.
+Math. (2022), to appear. DOI 10.1142/s0219199722500262 1, 5, 6, 7
+[6] A. Čap, J. Slovák, Weyl structures for parabolic geometries, Math. Scand. 93 (2003),
+53–90. DOI 10.7146/math.scand.a-14413 MR 1997873 5, 6
+[7] A. Čap, J. Slovák, Parabolic geometries. I, Mathematical Surveys and Monographs
+154, American Mathematical Society, Providence, RI, 2009, Background and general
+theory. DOI 10.1090/surv/154 MR 2532439 5
+
+16
+A. ČAP AND T. METTLER
+[8] A. Čap, J. Slovák, V. Souček, Invariant operators on manifolds with almost Hermit-
+ian symmetric structures. II. Normal Cartan connections, Acta Math. Univ. Comenian.
+(N.S.) 66 (1997), 203–220. MR 1620484 6
+[9] M. Dunajski, Twistor theory of dancing paths, SIGMA Symmetry Integrability Geom.
+Methods Appl. 18 (2022), Paper No. 027, 13. DOI 10.3842/SIGMA.2022.027 MR 4401805
+11
+[10] M. Dunajski, A. R. Gover, A. Waterhouse, Some examples of projective and
+c-projective compactifications of Einstein metrics, Ann. Henri Poincaré 21 (2020), 1113–
+1133. DOI 10.1007/s00023-020-00903-7 MR 4078278 11
+[11] M. Dunajski, T. Mettler, Gauge theory on projective surfaces and anti-self-
+dual Einstein metrics in dimension four,
+J. Geom. Anal. 28 (2018),
+2780–2811.
+DOI 10.1007/s12220-017-9934-9 MR 3833818 1, 2, 11
+[12] F. Etayo, R. Santamaría, U. R. Trías, The geometry of a bi-Lagrangian
+manifold, Differential Geom. Appl. 24 (2006), 33–59. DOI 10.1016/j.difgeo.2005.07.002
+MR 2193747 1
+[13] M. J. D. Hamilton, Bi-Lagrangian structures on nilmanifolds, J. Geom. Phys. 140
+(2019), 10–25. DOI 10.1016/j.geomphys.2019.01.008 MR 3916049 1
+[14] M. Hammerl, K. Sagerschnig, J. Šilhan, A. Taghavi-Chabert, V. Žádník,
+Fefferman-Graham ambient metrics of Patterson-Walker metrics, Bull. Lond. Math. Soc.
+50 (2018), 316–320. DOI 10.1112/blms.12136 MR 3830122 3
+[15] M. Hammerl, K. Sagerschnig, J. Šilhan, A. Taghavi-Chabert, V. Žád-
+ník,
+Conformal Patterson-Walker metrics,
+Asian J. Math. 23 (2019),
+703–734.
+DOI 10.4310/ajm.2019.v23.n5.a1 MR 4095182 3
+[16] P. Libermann, Sur le problème d’équivalence de certaines structures infinitésimales,
+Ann. Mat. Pura Appl. (4) 36 (1954), 27–120. DOI 10.1007/BF02412833 MR 66020 11
+[17] E. M. Patterson, A. G. Walker, Riemann extensions, Quart. J. Math. Oxford
+Ser. (2) 3 (1952), 19–28. DOI 10.1093/qmath/3.1.19 MR 48131 3
+A.Č.: Faculty of Mathematics, University of Vienna, Vienna, Austria
+Email address: Andreas.Cap@univie.ac.at
+T.M.: Faculty of Mathematics and Computer Science, UniDistance Suisse,
+Brig, Switzerland
+Email address: thomas.mettler@fernuni.ch
+
diff --git a/hdE1T4oBgHgl3EQffQTi/content/tmp_files/load_file.txt b/hdE1T4oBgHgl3EQffQTi/content/tmp_files/load_file.txt
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@@ -0,0 +1,535 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf,len=534
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='03217v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='DG]  9 Jan 2023  Induced para-Kähler Einstein metrics  on cotangent bundles  Andreas Čap and Thomas Mettler  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In earlier work we have shown that for certain geometric  structures on a smooth manifold M of dimension n, one obtains a para-  Kähler–Einstein metric on a manifold A of dimension 2n associated to  the structure on M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The geometry also provides a family of diffeo-  morphisms between A and T ∗M, so one can use this construction to  obtain metrics on the cotangent bundle of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In this short article, we  discuss the relation of these metrics to Patterson–Walker metrics and  derive explicit formulae for them in the cases of projective, conformal  and Grassmannian structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Introduction  An almost para-Kähler structure on a 2n-manifold N consists of a pseudo-  Riemannian metric h of split-signature (n, n) and a symplectic form Ω such  that the endomorphism I : TN → TN defined by Ω = h(I·, ·) satisfies  I2 = IdTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Almost para-Kähler structures are sometimes also called almost  bi-Lagrangian structures, see for instance [3, 12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In [5], generalising the  results from [11], we showed how to canonically construct an almost para-  Kähler structure (h, Ω) on a manifold of dimension 2n, which is naturally  associated to a geometric structure (from a certain class) on an n-manifold  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The structures in question admit a description in terms of a so-called  torsion-free |1|-graded parabolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This class of geometric structures  includes in particular projective, conformal and Grassmannian (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' torsion-  free almost Grassmannian) structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' What makes the construction remark-  able is that h is always an Einstein metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The almost para-Kähler structure is defined on the total space of an affine  bundle µ : A → M whose sections can be interpreted as the Weyl structures  of the parabolic geometry and whose associated vector bundle is the cotan-  gent bundle ν : T ∗M → M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In [5] it is also shown that the choice of a Weyl  structure s : M → A induces a diffeomorphism ϕs : T ∗M → A satisfying  (ϕs)∗Ω = dτ − ν∗(Alt Ps),  where τ denotes the tautological 1-form of T ∗M and Alt Ps the alternating  part of the Rho-tensor Ps of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This Rho-tensor is a curvature quantity  associated to s which is an analog of the Ricci curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Date: January 9, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  1  2  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  The purpose of this short note is to relate the resulting metrics to classi-  cally known metrics on the cotangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In particular, we show – see  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3 below – that the pullback of the metric has a universal structure  given by  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1)  (ϕs)∗h = hϑs − ν∗(Sym Ps) + q,  where hϑs is the Patterson–Walker metric of the Weyl connection ϑs deter-  mined by s (see below for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Further, Sym Ps denotes the symmetric  part of the Rho-tensor of s and q is a symmetric covariant 2-tensor field on  T ∗M which only depends on the underlying geometric structure and which  is semibasic for the projection ν : T ∗M → M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Moreover, q is homoge-  neous of degree 2 in the fibres of T ∗M, that is, satisfies (St)∗q = t2q where  St : T ∗M → T ∗M denotes scaling of a cotangent vector by the factor t ∈ R∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  We work out explicit expressions for (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1) in the case of projective, confor-  mal and Grassmannian structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In the case of projective and conformal  geometry, expressions for the Rho tensor are well-known, so this amounts  to computing q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' For projective structures, we recover the result from [11],  where it is shown that q = −τ ⊗ τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Additionally, we show that in the case  of a conformal structure [g] on M, the tensor field q is given by  q = −τ ⊗ τ + 1  2| · |2  g♯ν∗g  where g ∈ [g], g♯ ∈ Γ(S2(TM)) denotes the dual metric of g and | · |2  g♯ :  T ∗M → R is defined by ξ �→ g♯(ξ, ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Notice that q does only depend on [g].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  In the Grassmannian case, we derive a similar explicit description of q in  terms of an “improved” version of the tautological one form obtained from  the structure and we show how to compute the Rho tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='Č.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' acknowledges support by the Austrian Science  Fund (FWF): P 33559-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' is partially supported by the DFG priority  programme “Geometry at infinity” SPP 2026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The authors are grateful to  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Dunajski for helpful correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Preliminaries  We start by briefly collecting some basic facts about soldering forms,  Patterson–Walker metrics, |1|-graded parabolic geometries and Weyl struc-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Throughout this article all manifolds and mappings are assumed to  be smooth, that is, C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Soldering forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Let M be an n-manifold and V a real n-dimensional  vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We consider a right principal G0-bundle π0 : G0 → M for some  Lie group G0 and ρ : G0 → GL(V ) a representation of G0 on the vector  space V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Suppose that we have a 1-form ω ∈ Ω1(G0, V ) on G0 with values  in V which is semibasic and ρ-equivariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The former condition means  that ω vanishes on all vectors of TG0 that are tangent to the fibres of π0  and the latter condition means that ω satisfies R∗  aω = ρ(a−1)(ω) for all  EINSTEIN METRICS ON COTANGENT BUNDLES  3  a ∈ G0, where Ra : G0 → G0 denotes the right action by a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Recall that  such a form defines a 1-form ω ∈ Ω1(M, E) on M with values in the vector  bundle ν : G0 ×ρ V =: E → M associated to ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Indeed, for all v ∈ TM  the element ω(v) ∈ E is represented by (u, ω(˜v)) ∈ G0 × V for any choice  of u ∈ G0 having the same basepoint as v and any ˜v ∈ TuG0 such that  π′  u(˜v) = v, where π′  u : TuG0 → Tπ(u)M denotes the derivative of π at u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The  1-form ω ∈ Ω1(G0, V ) is called a soldering form if ω – thought of as a map  TM → E – is a vector bundle isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Recall that this is equivalent to  the fact that ω is strictly horizontal in the sense that its kernel in any point  of G0 is the vertical subbundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The Patterson–Walker metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We review the construction of the  Patterson–Walker metric, adapted to our setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To this end suppose, as  above, that π : G0 → M is a right principal G0-bundle equipped with a  soldering form ω ∈ Ω1(G0, V ) which is equivariant with respect to a repre-  sentation ρ : G0 → GL(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Assume in addition that ρ is infinitesimally  effective, that is, the induced Lie algebra representation ̺ : g0 → gl(V ) is in-  jective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Using ω, the tangent bundle of M can be identified with the bundle  associated to ρ, that is, TM ≃ G0 ×ρ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Now let ϑ ∈ Ω1(G0, g0) be a principal G0-connection on G0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Let us denote  by V ∗ the dual space to V and by ̺∗ : g0 → gl(V ∗) the the dual repre-  sentation to ̺.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Then on the product G0 × V ∗ we consider the V ∗-valued  1-form  ζϑ = dξ + (̺∗ ◦ ϑ)(ξ),  where ξ : G0 × V ∗ → V ∗ denotes the second projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' By construction,  the V ∗-valued 1-form is equivariant with respect to the dual representation  ρ∗ : G0 → GL(V ∗) and it is easy to check that it is semibasic for the  projection G0×V ∗ → T ∗M ≃ G0×ρ∗V ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Consequently, it represents a 1-form  ζϑ ∈ Ω1(T ∗M, ν∗T ∗M) on T ∗M with values in the pullback of the cotangent  bundle ν : T ∗M → M of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The pullback bundle ν∗T ∗M is naturally a  subbundle of T ∗(T ∗M) and hence we may interpret ζϑ as a 1-form on T ∗M  with values in T ∗(T ∗M), or equivalently, as a section of T ∗(T ∗M)⊗T ∗(T ∗M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The symmetric part hϑ = Sym ζϑ is a pseudo-Riemannian metric of split-  signature (n, n) known as the Patterson–Walker metric associated to the  connection ϑ, see [17] for the original construction and [14, 15] for recent  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Parabolic geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Recall that a Cartan geometry of type (G, P)  for some Lie group G and closed subgroup P ⊂ G is a pair (π : G → M, θ)  consisting of a right principal P-bundle π : G → M together with a Cartan  connection θ taking values in the Lie algebra g of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We let R : G × P → G  denote the right action of P and we write Rg = R(·, g) for all g ∈ P and  ιu = R(u, ·) for all u ∈ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The 1-form θ ∈ Ω1(G, g) being a Cartan connection  means that for all u ∈ G the linear map θu : TuG → g is an isomorphism and  4  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  moreover  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1)  (R∗θ)(u,g) = (ι∗  uθ)g + (R∗  gθ)u = (ΥP )g + Ad(g−1) ◦ θu,  for all (u, g) ∈ G × P, where ΥP denotes the Maurer–Cartan form of P and  Ad : G → GL(g) the adjoint action of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In addition, the curvature 2-form  Θ = dθ+ 1  2[θ, θ] of θ satisfies a further condition called normality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The details  of this conditions are not important for our purposes, some consequences  will be discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We will always assume that the Cartan geometry is  torsion-free, that is, Θ has values in p ⊂ g, the Lie algebra of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here we consider the special case of |1|-graded parabolic geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This  means that G is assumed to be semisimple and that its Lie algebra g is  endowed with a so-called |1|-grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This is a decomposition  g = g−1 ⊕ g0 ⊕ g1  into a direct sum of linear subspaces gi for i = −1, 0, 1 such that [gi, gj] ⊂  gi+j with the convention that gℓ = {0} for ℓ = ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Furthermore, no simple  ideal of g is allowed to be contained in g0 and the Lie algebra p of P satisfies  p = g0 ⊕ g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In particular, this implies that P ⊂ G is a parabolic subgroup  in the sense of representation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  These properties have some nice consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' First, the exponential map  of g – restricted to g1 – is a diffeomorphism from g1 onto a closed normal  subgroup P+ ⊂ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Second, defining G0 ⊂ P to consist of those elements  g so that the adjoint action Ad(g) ∈ GL(g) preserves the grading of g, one  can show that the Lie algebra of G0 is g0 and that G0 is isomorphic to the  quotient P/P+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Third, every element g of P can be written as g = g0 exp(Z)  for unique elements g0 ∈ G0 and Z ∈ g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Since P+ ⊂ P is a normal subgroup, we obtain a principal P/P+ ≃ G0-  bundle G/P+ → M whose total space we denote by G0 and whose basepoint  projection we denote by π0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We can project the values of the Cartan con-  nection θ to g/p ∼= g−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Equivariancy of θ then easily implies that the result  descends to a 1-form ω ∈ Ω1(G0, g−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Equivariancy of θ also implies that  ω is equivariant with respect to the G0-representation ρ : G0 → GL(g−1)  obtained by restricting the adjoint representation to g−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2)  ρ = Ad( · )|g−1 : G0 → GL(g−1),  g0 �→ Ad(g0)|g−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This representation is infinitesimally effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The construction then easily  implies that ω is a soldering form in the sense of Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Hence we obtain  a G0-structure on the manifold M and it turns out that, apart from the  case of projective structures, the normality condition on Θ ensures that the  Cartan geometry (G → M, θ) is an equivalent encoding of this G0-structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Weyl structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In order to work explicitly with a parabolic geome-  try it is often advantageous to fix a Weyl structure for the parabolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This gives a description of the Cartan geometry (G → M, θ) in terms of the  EINSTEIN METRICS ON COTANGENT BUNDLES  5  underlying G0-structure (G0 → M, ω) defined above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here we briefly re-  view the key facts and refer the reader to [5, 6, 7] for details and additional  context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Following [6], we define a Weyl structure for (π : G → M, θ) to be a G0-  equivariant section σ : G0 → G of the projection G → G0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Writing the Cartan  connection θ as θ = (θ−1, θ0, θ1) with θi taking values in gi, a choice of Weyl  structure σ gives three 1-forms on G0  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3)  ω = σ∗θ−1 ∈ Ω1(G0, g−1),  ϑσ = σ∗θ0 ∈ Ω1(G0, g0),  Pσ = −ψB ◦ (σ∗θ1) ∈ Ω1(G0, g∗  −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here ω is just the soldering form from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3 above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The form ϑσ is a  principal G0-connection on π0 : G0 → M referred to as the Weyl connection  determined by σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' For the last component, we let B denotes a suitable con-  stant multiple of the Killing form of g and ψB : g1 → g∗  −1 the linear map  defined by the rule  ψB(Z)(X) = B(Z, X)  for all Z ∈ g1 and all X ∈ g−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' It is well-known that ψB is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  In the literature on parabolic geometries, ψB is usually suppressed from the  notation and g1 is simply identified with (g−1)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The multiple B of the Killing form is chosen so that the form Pσ represents  the so-called Rho tensor Pσ of the Weyl structure σ, thought of as a 1-form on  M with values in T ∗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Notice that here our convention for the Rho tensor  agrees with the classical definitions for conformal an projective structures  and hence differs by a sign from [5, 6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' On the Rho tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Here we briefly explain how the normalization  condition on the curvature of a |1|-graded parabolic geometry leads to a way  to explicitly determine the Rho tensor associated to a Weyl structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We  start by introducing a canonical object on M, which will also be useful for  other purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This comes from the component  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4)  [ , ] : g−1 × g1 → g0  of the Lie bracket in g, which is a G0-equivariant bilinear map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Observe  further that the derivative of the representation ρ from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2) defines an in-  clusion g0 → End(g−1, g−1), which by construction is again induced by the  Lie bracket.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Together with ψB, this shows that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4) induces a  �2  2  �  tensor field  on M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We will interpret this below as associating to a vector field X ∈ X(M)  and a one-form α ∈ Ω1(M) a  �1  1  �  tensor field {X, α} which in particular can  be viewed as a section of End(TM, TM) or of End(T ∗M, T ∗M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Now given two vector fields X, Y ∈ X(M) and a T ∗M-valued one form P,  we define a  �1  3  �  tensor field ∂P by  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5)  ∂P(X, Y ) := {X, P(Y )} − {Y, P(X)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  6  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  By construction, this is skew symmetric in X and Y and thus defines a two-  form with values in End(TM, TM), so this looks like the curvature of a linear  connection on TM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Now for a Weyl structure σ, we consider the induced  Weyl connection θσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The curvature of this Weyl connection is equivalently  encoded by a two-form Rσ with values in End(TM, TM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Now it turns  out that the normalization condition on the Cartan connection implies that  the Rho tensor Pσ is uniquely characterized by the fact that Rσ − ∂Pσ has  vanishing Ricci type contraction, see [8] or Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3 of [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Throughout  the article we follow the convention of defining the Ricci curvature Ric(∇)  of a torsion-free connection ∇ as  (X, Y ) �→ Ric(∇)(X, Y ) = tr  �  Z �→ R∇(Z, X)(Y )  �  where the curvature operator R∇ is defined as usual by  R∇(X, Y )(Z) = ∇X∇Y Z − ∇Y ∇XZ − ∇[X,Y ]Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Notice that this convention, while common in projective differential geom-  etry, differs (by a swap of the arguments) from the standard convention in  Riemannian geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The almost para-Kähler structure of a Weyl structure  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Construction of the almost para-Kähler structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We briefly  review the construction of the almost para-Kähler structure associated to a  torsion-free |1|-graded parabolic geometry given in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Notice that we may  think of a torsion-free |1|-graded parabolic geometry (π : G → M, θ) of type  (G, P) on M as a Cartan geometry (Π : G → A, θ) of type (G, G0) on the  quotient A := G/G0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In doing so, the tangent bundle of A becomes TA =  G ×G0 (g/g0), where G0 acts via the adjoint action on g and hence on g/g0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The G0-module g/g0 is isomorphic to g−1 ⊕ g1, where again G0 acts on both  summands via the adjoint representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Consequently, the tangent bundle  of A decomposes into a direct sum of rank n vector bundles TA = L+ ⊕ L−,  where L± = G ×G0 g±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We consider the 1-form η = ψB ◦ θ1 ∈ Ω1(G, g∗  −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Explicitly, we have  η(v)(X) = B(θ1(v), X)  for all v ∈ TG and all X ∈ g−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' It follows from the properties of the Cartan  connection and the invariance of B under the adjoint representation that  the 1-form η is G0-equivariant and semibasic for the projection Π : G → A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Consequently, η represents a 1-form η on A with values in (L−)∗ ⊂ T ∗A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Hence we may view η as a section of T ∗A ⊗ T ∗A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The symmetric part  h = Sym η is then a pseudo-Riemannian metric of split-signature on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This  uses that ψB : g1 → g∗  −1 is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The alternating part Ω = Alt η  turns out to be a symplectic form by torsion-freeness (see [5, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1]),  and the pair (h, Ω) is an almost para-Kähler structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Furthermore, the  sections of A → M are in bijective correspondence with the Weyl structures  for (π : G → M, θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Remarkably, by [5, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5], the normalization  conditions for |1|-graded parabolic geometries imply that the metric h always  EINSTEIN METRICS ON COTANGENT BUNDLES  7  is Einstein and hence (h, Ω) is an almost para-Kähler Einstein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We  refer to [5] for further details and to [2] for recent results about the geometry  of 4-dimensional para-Kähler Einstein structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The choice of a Weyl structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In this section we shall prove the  main structural identity (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We start by identifying G with the product  G0 × g1 equipped with a suitable right action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  An element of G0 will be  denoted by [u], where u ∈ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' On G0 × g1 a P-right action ˆR is defined by  the rule  ([u], Z) · g = ([u · g0], Ad(g−1  0 )(Z) + W)  for all ([u], Z) ∈ G0 × g1 and all g = g0 exp(W) in P and as the basepoint  projection we take the map  ˆπ : G0 × g1 → M,  ([u], Z) �→ π0([u]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  With these definitions, ˆπ : G0 × g1 → M is indeed a right principal P-bundle  and moreover, the choice of a Weyl structure identifies this bundle with  π : G → M:  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Let (π : G → M, θ) be a |1|-graded parabolic geometry of  type (G, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Then every Weyl structure σ : G0 → G induces an isomorphism  of principal P-bundles  Φσ : G0 × g1 → G,  ([u], Z) �→ σ([u]) · exp(Z)  satisfying  (Φσ)∗θ = dZ + σ∗θ + [σ∗θ, Z] + 1  2[[σ∗θ, Z], Z],  where Z : G0 × g1 → g1 denotes the projection onto the second factor, the  brackets are in g, and we omit writing the pullbacks from the first factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  For the proof we need the following elementary lemma on the Maurer-  Cartan form ΥP ∈ Ω1(P, p):  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The exponential map exp : g1 → P satisfies exp∗ ΥP = d Idg1,  where Idg1 denotes the identity map on g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' For X, Y ∈ g1, we compute  (exp∗ ΥP)X(Y ) = (ΥP )exp(X)(exp′  X(Y )) = (Lexp(X)−1)′  exp(X)(exp′  X(Y ))  = (Lexp(X)−1 ◦ exp)′  X(Y )  = d  dt  ����  t=0  exp(−X) exp(X + tY ) = d  dt  ����  t=0  exp(tY ) = Y,  where we use that [X, X + tY ] = 0 since [g1, g1] = {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  □  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' First observe that since [g1, g1] = {0}, we have  exp(Z) exp(W) = exp(Z + W)  for all Z, W ∈ g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' As a consequence, the standard identity  g exp(X)g−1 = exp(Ad(g)(X)),  g ∈ G, X ∈ g  8  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  implies that for all g0 exp(W) ∈ P and h0 exp(Z) ∈ P, we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1)  g0 exp(Z)h0 exp(W) = g0h0 exp(Ad(h−1  0 )(Z) + W),  where we use that Ad(h−1  0 ) preserves g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Since exp : g1 → P+ is a diffeomorphism and σ : G0 → G is equivariant, it  easily follows that Φσ is a diffeomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In order to verify the equivariancy  of Φσ, we compute for all ([u], Z) ∈ G0 × g1 and for all g = g0 exp(W) ∈ P  Φσ(([u], Z) · g) = Φσ(([u · g0], Ad(g−1  0 )(Z) + W))  = σ([u · g0]) · exp(Ad(g−1  0 )(Z) + W)  = σ([u]) · g0 exp(Ad(g−1  0 )(Z) + W)  = σ([u]) · exp(Z)g0 exp(W)  = σ([u]) · exp(Z)g = Φσ(([u], Z)) · g,  where we used the definitions of the various mappings as well as (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1) and the  equivariancy of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' It follows that Φσ is a principal P-bundle isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  For the second part of the lemma we denote by Ad−1 the composition of  Ad with the inversion in P and compute  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2)  (Φσ)∗θ = (σ, exp)∗(R∗θ) = (σ, exp)∗ �  ΥP + Ad−1 ◦ θ  �  = exp∗ ΥP + σ∗ �  Ad−1 ◦ θ  �  where we used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1) and think of (σ, exp) as a map G0 × g1 → G × P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Now  for Z, W ∈ g we have the standard identity  Ad(exp(Z))(W) =  ∞  �  k=0  ad(Z)k  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  (W) = W + [Z, W] + 1  2[Z, [Z, W]] + · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  As a consequence, we obtain for all Z ∈ g1  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3)  (Rexp(Z))∗θ = Ad(exp(−Z)) ◦ θ = θ + [θ, Z] + 1  2[[θ, Z], Z],  where we use that the sum terminates after three summands, since [g1, g1] =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Combining (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3) and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2, we obtain  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4)  (Φσ)∗θ = dZ + σ∗θ + [σ∗θ, Z] + 1  2[[σ∗θ, Z], Z],  as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  □  Recall from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4 that for every choice of Weyl structure σ : G0 → G,  ω = σ∗θ−1 ∈ Ω1(G0, g−1) is the soldering form of the G0-structure π0 :  G′ → M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Moreover, ϑσ = σ∗θ0 ∈ Ω1(G0, g0) is a principal connection on  π0 : G0 → M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4) we thus obtain  (Φσ)∗θ1 = dZ + σ∗θ1 + [ϑσ, Z] + 1  2[[ω, Z], Z]  and hence, using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3) again, we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5)  (Φσ)∗(ψB ◦ θ1) = ψB ◦ (dZ + [ϑσ, Z]) − Pσ + 1  2ψB ◦ ([[ω, Z], Z]) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  EINSTEIN METRICS ON COTANGENT BUNDLES  9  In order to relate this to the Patterson–Walker metric associated to ϑσ,  we first observe that via ψB, the map Z corresponds to the second projection  G0 × g∗  −1 → g∗  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Moreover, in the notation of Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2, the expression  [ϑσ, Z] can be written as (ad ◦ϑσ)(Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Invariance of the bilinear form B  implies that for X ∈ g−1, Y ∈ g0 and Z ∈ g1, we get  B(ad(Y )(X), Z) = −B(X, ad(Y )(Z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This exactly says that, via ψB, the adjoint action on g1 corresponds to the  dual of the adjoint action on g−1, which was denoted by ̺∗ in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Together, this shows that the term ψB ◦ (dZ + [ϑσ, Z]) exactly gives the  g∗  −1-valued 1-form ζϑσ defined there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Combining this with (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5), we obtain  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='6)  (Φσ)∗(ψB ◦ θ1) = ζϑσ − Pσ + q  where q ∈ Ω1(G0 × g∗  −1, g∗  −1) is given by  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='7)  q = 1  2ψB ◦  �  [[ω, ψ−1  B ◦ ξ], ψ−1  B ◦ ξ]  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  By construction, q represents a 1-form q on T ∗M with values in the pullback  of the cotangent bundle of M, which is evidently closely related to the op-  eration on M introduced in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' More precisely, for α ∈ T ∗M with  ν(α) = x and a tangent vector X ∈ TαT ∗M, we get  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='8)  q(α)(X) = 1  2{ν′  α(X), α}(α) ∈ T ∗  xM = (ν∗T ∗M)α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  In particular, this shows that q is semibasic for the projection ν : T ∗M → M  and satisfies (St)∗q = t2q, where St : T ∗M → T ∗M denotes scaling of a  cotangent vector by the factor t ∈ R∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Finally, notice that using ψB to identify g1 with g∗  −1, we get T ∗M ≃  G0 ×G0 g1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' But then the G0-equivariant diffeomorphism Φσ : G0 × g1 → G  induces a diffeomorphism ϕσ : T ∗M → G/G0 = A and we have  (ϕσ)∗η = ζϑσ − ν∗Pσ + q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Recall that η is the (L−)∗-valued 1-form on A whose symmetric and alter-  nating part give the almost para-Kähler structure (h, Ω) of the parabolic  geometry (π : G → M, θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Recall also that the symmetric part of the form  ζϑσ is the Patterson–Walker metric hϑs of the Weyl connection ϑσ deter-  mined by σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Finally, viewed as a bilinear form on TαT ∗M, q(α) turns out  to be symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' By construction, q(α) is the pullback of a bilinear form on  TxM with x = ν(α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The latter is induced by the bilinear form on g−1 that,  for some fixed Z ∈ g1, maps (X1, X2) to  1  2B([[X1, Z], Z], X2) = − 1  2B([X1, Z], [Z, X2]) = 1  2B([X1, Z], [X2, Z]),  so this is obviously symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In summary, we have thus shown:  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Let (π : G → M, θ) be a torsion-free |1|-graded parabolic  geometry with associated almost para-Kähler structure (h, Ω) on A and σ :  10  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  G0 → G a choice of Weyl structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Then we have  (ϕσ)∗h = hϑσ − ν∗ Sym(Pσ) + q,  where q is given by formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4 (Local coordinate expression).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In terms of a choice of local coor-  dinates (xi) : U → Rn on some open subset U ⊂ M, the metric (ϕσ)∗h takes  the following explicit form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Let (xi, ξi) : ν−1(U) → R2n denote the canonical  coordinates induced on ν−1(U) ⊂ T ∗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The Weyl connection ϑσ induces a  torsion-free connection ∇ on TM whose Christoffel symbols with respect to  the coordinates (xi) we denote by Γi  jk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The Patterson–Walker metric of ϑσ  can then be expressed as  (dξi − Γk  ijξkdxj) ⊙ dxi,  where ⊙ denotes the symmetric tensor product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' On ν−1(U) we thus obtain  (ϕσ)∗h =  �  dξi − Γk  ijξkdxj − P(ij) + qij  �  ⊙ dxi,  where we write q = qijdxi ⊗ dxj for unique real-valued functions qij = qji :  U → R and Pσ = Pijdxi ⊗ dxj for unique real-valued functions Pij : U → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here and henceforth, we employ the summation convention and P(ij) denotes  symmetrization in the indices i, j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Examples  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Projective geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Consider an n-dimensional manifold M endowed  with a projective structure [∇], a class of torsion-free connections that have  the same geodesics up to parametrization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This determines a |1|-graded par-  abolic geometry (π : G → M, θ), where G = SL±(n+1, R) is the subgroup of  GL(n + 1, R) consisting of matrices whose determinant is ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The grading  of its Lie algebra g = sl(n + 1, R) = {B ∈ gl(n + 1, R), tr B = 0} is given by  g−1 =  ��  0  0  x  0  ����� x ∈ Rn  �  ,  g1 =  ��  0  y  0  0  ����� y ∈ Rn∗  �  and  g0 =  ��  − tr A  0  0  A  ����� A ∈ gl(n, R)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here B is normalised so that  B  ��  0  0  x  0  �  ,  �  0  y  0  0  ��  = yx = y(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Next, one computes that for x ∈ Rn and y, z ∈ Rn∗ we get  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1)  ���  0  0  x  0  �  ,  �  0  y  0  0  ��  ,  �  0  z  0  0  ��  =  �  0  −(yx)z − (zx)y  0  0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This shows that for ξ ∈ TxM and α ∈ T ∗  xM we get {ξ, α}(α) = −2α(ξ)α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Together with formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='8) and the definition of the tautological form τ on  T ∗M, this shows that  q = −τ ⊗ τ,  EINSTEIN METRICS ON COTANGENT BUNDLES  11  in agreement with [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The Weyl connection ϑσ = σ∗θ0 determines a torsion-free connection ∇  on TM which is a representative connection of the projective structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To  compute the associated Rho tensor a similar computation as for formula  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1) shows that for X, Z ∈ X(M) and α ∈ Ω1(M), we get {X, α}(Z) =  α(X)Z +α(Z)X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Using this and formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5) from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5 we conclude  that for X, Y, Z ∈ X(M), we obtain  ∂Pσ(X, Y )(Z) = Pσ(Y, X)Z − Pσ(X, Y )Z + Pσ(Y, Z)X − Pσ(X, Z)Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  This easily implies that the Ricci type contraction of ∂Pσ maps X, Y to  nPσ(X, Y ) − Pσ(Y, X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Now let Ric(∇) the Ricci type contraction of the  curvature of ϑσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Then the discussion in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5 shows that we must have  Ric(∇)(X, Y ) = nPσ(X, Y ) − Pσ(Y, X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Symmetrizing and alternating, we conclude that Sym Ric(∇) = (n−1) Sym Pσ  and Alt Ric(∇) = (n + 1) Alt Pσ, and hence  Pσ =  1  (n − 1) Sym Ric(∇) +  1  (n + 1) Alt Ric(∇).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1 (Dancing metric).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Starting from the standard projective struc-  ture on RP2, the resulting para-Kähler–Einstein structure is defined on  A = SL(3, R)/GL(2, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In this case the Einstein metric is referred to as  the dancing metric [1, 9] because of its significance in the “rolling” of the  projective planes RP2 and RP2∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This para-Kähler–Einstein structure was  first constructed in [16] (in any dimension).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2 (para-c-projective compactification).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In the projective case, the  almost para-Kähler structure on A admits a so-called para-c-projective com-  pactification, see [10], an analog of a c-projective compactification, see [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Conformal geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' A conformal manifold (M, [g]) of dimension  n ⩾ 3 gives rise to a |1|-graded parabolic geometry (π : G → M, θ) where G  is defined as follows: Consider the matrix  J =  \uf8eb  \uf8ed  0  0  −1  0  In  0  −1  0  0  \uf8f6  \uf8f8  of size n + 2 and let G = O(n + 1, 1) denote the subgroup of GL(n + 2, R)  consisting of matrices a satisfying atJa = J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The Lie algebra g = o(n + 1, 1)  of G consists of matrices of the form  \uf8eb  \uf8ed  s  z  0  x  A  zt  0  xt  −s  \uf8f6  \uf8f8  12  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  where s ∈ R, x ∈ Rn, z ∈ Rn∗ and A ∈ o(n) is a skew-symmetric matrix of  size n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The grading of g is given by  g−1 =  \uf8f1  \uf8f2  \uf8f3  \uf8eb  \uf8ed  0  0  0  x  0  0  0  xt  0  \uf8f6  \uf8f8  ������  x ∈ Rn  \uf8fc  \uf8fd  \uf8fe ,  g1 =  \uf8f1  \uf8f2  \uf8f3  \uf8eb  \uf8ed  0  z  0  0  0  zt  0  0  0  \uf8f6  \uf8f8  ������  y ∈ Rn  \uf8fc  \uf8fd  \uf8fe  and  g0 =  \uf8f1  \uf8f2  \uf8f3  \uf8eb  \uf8ed  s  0  0  0  A  0  0  0  −s  \uf8f6  \uf8f8  ������  s ∈ R, A ∈ o(n)  \uf8fc  \uf8fd  \uf8fe .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  We normalise B such that  B  \uf8eb  \uf8ed  \uf8eb  \uf8ed  0  0  0  x  0  0  0  xt  0  \uf8f6  \uf8f8 ,  \uf8eb  \uf8ed  0  z  0  0  0  zt  0  0  0  \uf8f6  \uf8f8  \uf8f6  \uf8f8 = z(x) = zx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Computing triple brackets as for formula (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1) one verifies that (with  obvious notation) we get for x, y ∈ Rn and z, w ∈ Rn∗ the expressions  [[x, z], w] = −z(x)w − w(x)z + (wt · zt)xt  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2)  [[x, z], y] = z(x)y + z(y)x − (x · y)zt  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3)  Now formula (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2) shows that for ξ ∈ TxM and α ∈ T ∗  xM we get  {ξ, α}(α) = 2α(ξ)α + g#  x (α, α)gx(ξ, ·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here g is some metric from the conformal class and g# is its dual metric,  which immediately implies that the operation is conformally invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To-  gether with formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='8) and the definition of the tautological form τ on  T ∗M, this shows that  q = −τ ⊗ τ + 1  2| · |2  g♯ν∗g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Here | · |2  g♯ is interpreted as a real-valued smooth function on T ∗M and the  pullback ν∗g is interpreted as a one-form on T ∗M with values in ν∗T ∗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The Weyl connection ϑσ = σ∗θ0 determines a torsion-free connection ∇  on TM which preserves [g] in the sense that for some (any hence any) rep-  resentative metric g ∈ [g] there exists a 1-form β such that  ∇g = β ⊗ g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  To compute the Rho-tensor, we first conclude from formula (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3) that for  vector fields X, Y ∈ X(M) and a one-form α ∈ Ω1(M), we get  {X, α}(Y ) = α(X)Y + α(Y )X − g(X, Y )g#(α, ·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Using this and formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5) from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5 we conclude that for X, Y, Z ∈  X(M), we can write ∂Pσ(X, Y )(Z) as  Pσ(Y, X)Z + Pσ(Y, Z)X − g(X, Z)g#(Pσ(Y ))  −Pσ(X, Y )Z − Pσ(X, Z)Y + g(Y, Z)g#(Pσ(X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  EINSTEIN METRICS ON COTANGENT BUNDLES  13  To form the Ricci-type contraction of this, we have to take a local orthonor-  mal frame, insert each element for X and then take the inner product with  the same element and sum the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This sends (Y, Z) to  (n − 1)Pσ(Y, Z) − Pσ(Z, Y ) + g(Y, Z) trg#(Pσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Observe that in the literature on conformal geometry usually only the case  of Levi-Civita connections of metrics in the conformal class is discussed, for  which Pσ is automatically symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Anyway, the discussion in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5  shows that the above expression has to coincide with Ric(∇).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To conclude the  discussion as in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1 above, we now have to compute the alternation,  and the trace-free part and the trace part of the symmetrization, which gives  Sym0 Ric(∇) = (n − 2) Sym0 Pσ  Alt Ric(∇) = n Alt Pσ  g trg#(Ric(∇)) = (2n − 2)g trg#(Pσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Observe that for a Levi-Civita connection trg#(Ric(∇)) is the scalar curva-  ture of the metric g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In any case, we immediately get the general formula  Pσ =  1  n − 2 Sym0 Ric(∇) + 1  n Alt Ric(∇) +  1  n(n − 2)g trg#(Ric(∇)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Grassmannian geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' An almost Grassmannian structure of type  (m, n) on a manifold M consists of two real vector bundles E and F on M, of  rank m and n and vector bundle isomorphisms TM ≃ E∗ ⊗ F ≃ Hom(E, F)  and ΛmE∗ ∼= ΛnF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Here E∗ denotes the dual of E and the isomorphism  between the top exterior powers will not be relevant for us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  An almost  Grassmannian structure on M gives rise to a |1|-graded parabolic geometry  (π : G → M, θ) where G = SL(n + m, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The structure is called Grass-  mannian if it admits a compatible torsion-free connection on TM, which is  equivalent to torsion-freeness of the parabolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' The grading of the  Lie algebra g = sl(n + m, R) of G is given by  g−1 =  ��  0  0  x  0  ����� x ∈ M(n × m, R)  �  ,  g1 =  ��  0  z  0  0  ����� y ∈ M(m × n, R)  �  and  g0 =  ��  B  0  0  A  ����� A ∈ gl(n, R), B ∈ gl(m, R), tr(A) + tr(B) = 0  �  ,  where M(n × m, R) denotes the vector space of (n × m)-matrices with real  entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The main case of interest for our purpose is m = 2, n ≥ 2, for  which there are examples of such geometries that are torsion-free but not  locally isomorphic to G/P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' For m = n = 2 such a structure is equivalent  to a conformal structure of neutral signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' For m, n > 2, any torsion-free  structure is locally isomorphic to G/P, but our results still are of interest,  since there is the freedom in the choice of Weyl structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  14  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  As the invariant form B we use the trace form, which leads to  B  ��  0  0  x  0  �  ,  �  0  z  0  0  ��  = tr(zx) = tr(xz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Formally, the setup looks very similar to projective structures (which corre-  spond to the case m = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This is also reflected in the structure of the triple  brackets, which formally look very similar to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1): For x, y ∈ M(n × m, R)  and z, w ∈ M(m × n, R) we get (in obvious notation)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4)  [[x, z], w] = −zxw − wxz  [[x, z], y] = xzy + yzx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  However, here we have matrix multiplications so for example xz is a 2 × 2-  matrix and zxw is not simply a multiple of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The easiest way to encode our operations geometrically is to define one  additional operation on a manifold M endowed with an almost Grassmannian  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Since TM ∼= E∗ ⊗ F, we get T ∗M ∼= E ⊗ F ∗ ∼= Hom(F, E) and  thus composition of linear maps induces a bilinear bundle map T ∗M×TM →  End(E, E), which we denote by (α, X) �→ α ◦ X both on elements and on  sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' This can be viewed as an “refinement” of the dual pairing, since by  definition we get α(X) = tr(α ◦ X), where tr denotes the point-wise trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  There clearly are analogous composition operations TM ×End(E, E) → TM  and End(E, E) × T ∗M → T ∗M (and others that we don’t need here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' In  this language, the first formula in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4) readily shows that for α ∈ T ∗  xM and  ξ ∈ TxM, we get {ξ, α}(α) = −2(α ◦ ξ) ◦ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Next, we get a corresponding refinement τ G ∈ Ω1(T ∗M, End(ν∗E, ν∗E))  of the tautological one-form τ on T ∗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' By definition, for α ∈ T ∗M with  ν(α) = x ∈ M, the fiber of End(ν∗E, ν∗E) over α equals End(Ex, Ex), so  for ξ ∈ TαT ∗M, we can define  τ G(α)(ξ) := α ◦ ν′  α(ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  By definition, the tautological form τ is then recovered as τ = tr(τ G), where  again tr denotes a point-wise trace in the values of the form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Using formula  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='8) we readily conclude that for α ∈ T ∗M and ξ, η ∈ TαT ∗M we get  q(α)(ξ, η) = − tr((α ◦ ν′  α(ξ)) ◦ (α ◦ ν′  α(η))),  which is evidently symmetric in ξ and η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To connect more closely to the  other cases, we can write this as q = − tr(τ G ⊗ τ G), where we agree that  the tensor product of one-forms with values in End(ν∗E, ν∗E) includes a  composition of the values, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' (A ⊗ B)(ξ, η) = A(ξ) ◦ B(η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  The description of the Rho tensor is also similar to the projective case,  with some complications caused by the matrix multiplications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='The Weyl con-  nection ϑσ = σ∗θ0 determines a torsion-free connection ∇ on TM which  is induced by connections on E and F that are compatible with the iso-  morphism of the top exterior powers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Now the second equation in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='4)  readily shows that for X, Y ∈ X(M) and α ∈ Ω1(M) we get {α, X}(Y ) =  X ◦ (α ◦ Y ) + Y ◦ (α ◦ X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Using this and formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5) from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5 we  EINSTEIN METRICS ON COTANGENT BUNDLES  15  conclude that for X, Y, Z ∈ X(M), ∂Pσ(X, Y )(Z) is given by  X ◦ (Pσ(Y ) ◦ Z) + Z ◦ (Pσ(Y ) ◦ X) − Y ◦ (Pσ(X) ◦ Z) − Z ◦ (Pσ(X) ◦ Y )  To compute the action of the Ricci type contraction on Y and Z, we have  to insert the elements of a basis for X and contract (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' take the trace of  the composition) with the dual basis element and sum up over the basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' To  write up the result, we need additional notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' We have to view Pσ(x)  as an element in ⊗2T ∗  xM and identifying TxM with Hom(Fx, Ex) such an  element defines a linear map Fx ⊗ Fx → Ex ⊗ Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  But for such a map,  we can separately swap the input or the output and hence independently  symmetrize or alternate in the input and the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Writing tE for the  twist map on E ⊗ E and tF for the twist map on F ⊗ F, one verifies that  the Ricci type contraction of ∂Pσ can be written as  (mn + 1)Pσ − tE ◦ Pσ − Pσ ◦ tF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Observe that this is consistent with the result in the projective case, since for  m = 1, we have tE = id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' By the discussion in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='5, this again has to  coincide with the Ricci type contraction Ric(∇) of the curvature of ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Now  we can compose this equation on both sides with either a symmetrization or  an alternation to obtain  Sym ◦ Ric(∇) ◦ Sym = (mn − 1) Sym ◦Pσ ◦ Sym  Alt ◦ Ric(∇) ◦ Alt = (mn + 3) Alt ◦Pσ ◦ Alt  Sym ◦ Ric(∇) ◦ Alt = (mn + 1) Sym ◦Pσ ◦ Alt  Alt ◦ Ric(∇) ◦ Sym = (mn + 1) Alt ◦Pσ ◦ Sym .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  From this, one deduces an explicit formula for Pσ as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  References  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Bor, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Hernández Lamoneda, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Nurowski, The dancing metric, G2-  symmetry and projective rolling, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 370 (2018), 4433–4481.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1090/tran/7277 MR 3811534 11  [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Bor, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Makhmali, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Nurowski, Para-Kähler-Einstein 4-manifolds and  non-integrable twistor distributions, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Dedicata 216 (2022), Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 9, 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1007/s10711-021-00665-4 MR 4366946 7  [3] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Bryant, Bochner-Kähler metrics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 14 (2001), 623–715.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1090/S0894-0347-01-00366-6 MR 1824987 1  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Čap, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Gover, c-projective compactification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 141 (2019), 813–856.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1353/ajm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Čap, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Mettler, Geometric theory of Weyl structures, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Contemp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' (2022), to appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1142/s0219199722500262 1, 5, 6, 7  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Čap, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Slovák, Weyl structures for parabolic geometries, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Scand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 93 (2003),  53–90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='7146/math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Čap, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' ČAP AND T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' METTLER  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Normal Cartan connections, Acta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Comenian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=') 66 (1997), 203–220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' MR 1620484 6  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Dunajski, Twistor theory of dancing paths, SIGMA Symmetry Integrability Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  Methods Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 18 (2022), Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 027, 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='3842/SIGMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='027 MR 4401805  11  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Dunajski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Gover, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Waterhouse, Some examples of projective and  c-projective compactifications of Einstein metrics, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Henri Poincaré 21 (2020), 1113–  1133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1007/s00023-020-00903-7 MR 4078278 11  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Dunajski, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Mettler, Gauge theory on projective surfaces and anti-self-  dual Einstein metrics in dimension four,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 28 (2018),  2780–2811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1007/s12220-017-9934-9 MR 3833818 1, 2, 11  [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Etayo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Santamaría, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Trías, The geometry of a bi-Lagrangian  manifold, Differential Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 24 (2006), 33–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='difgeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='002  MR 2193747 1  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Hamilton, Bi-Lagrangian structures on nilmanifolds, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 140  (2019), 10–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='geomphys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content='008 MR 3916049 1  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Hammerl, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Sagerschnig, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Šilhan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Taghavi-Chabert, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Žádník,  Fefferman-Graham ambient metrics of Patterson-Walker metrics, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Lond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='  50 (2018), 316–320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1112/blms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='12136 MR 3830122 3  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Hammerl, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Sagerschnig, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Šilhan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Žád-  ník,  Conformal Patterson-Walker metrics,  Asian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' 23 (2019),  703–734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Libermann, Sur le problème d’équivalence de certaines structures infinitésimales,  Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' Pura Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' (4) 36 (1954), 27–120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content='1007/BF02412833 MR 66020 11  [17] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Patterson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' Walker, Riemann extensions, Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content=' DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content='Č.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' : Faculty of Mathematics, University of Vienna, Vienna, Austria  Email address: Andreas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
+page_content=' : Faculty of Mathematics and Computer Science, UniDistance Suisse,  Brig, Switzerland  Email address: thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hdE1T4oBgHgl3EQffQTi/content/2301.03217v1.pdf'}
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+Much Ado About Gender
+Current Practices and Future Recommendations for Appropriate Gender-Aware Information Access
+Christine Pinney
+Amifa Raj
+christinepinney@u.boisestate.edu
+amifaraj@u.boisestate.edu
+People & Information Research Team
+Boise State University
+Boise, Idaho, USA
+Alex Hanna
+alex@dair-institute.org
+DAIR Institute
+USA
+Michael D. Ekstrand
+ekstrand@acm.org
+People & Information Research Team
+Boise State University
+Boise, Idaho, USA
+ABSTRACT
+Information access research (and development) sometimes makes
+use of gender, whether to report on the demographics of partici-
+pants in a user study, as inputs to personalized results or recommen-
+dations, or to make systems gender-fair, amongst other purposes.
+This work makes a variety of assumptions about gender, however,
+that are not necessarily aligned with current understandings of
+what gender is, how it should be encoded, and how a gender vari-
+able should be ethically used. In this work, we present a systematic
+review of papers on information retrieval and recommender sys-
+tems that mention gender in order to document how gender is
+currently being used in this field. We find that most papers men-
+tioning gender do not use an explicit gender variable, but most
+of those that do either focus on contextualizing results of model
+performance, personalizing a system based on assumptions of user
+gender, or auditing a model’s behavior for fairness or other privacy-
+related issues. Moreover, most of the papers we review rely on
+a binary notion of gender, even if they acknowledge that gender
+cannot be split into two categories. We connect these findings with
+scholarship on gender theory and recent work on gender in human-
+computer interaction and natural language processing. We conclude
+by making recommendations for ethical and well-grounded use of
+gender in building and researching information access systems.
+CCS CONCEPTS
+• Social and professional topics → Gender; • Information sys-
+tems → Information retrieval.
+KEYWORDS
+information access, gender, auditing, systematic review
+ACM Reference Format:
+Christine Pinney, Amifa Raj, Alex Hanna, and Michael D. Ekstrand. 2023.
+Much Ado About Gender: Current Practices and Future Recommenda-
+tions for Appropriate Gender-Aware Information Access. In ACM SIGIR
+Conference on Human Information Interaction and Retrieval (CHIIR ’23),
+March 19–23, 2023, Austin, TX, USA. ACM, New York, NY, USA, 11 pages.
+https://doi.org/10.1145/3576840.3578316
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+© 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.
+This is the author’s version of the work. It is posted here for your personal use. Not for
+redistribution. The definitive Version of Record was published in ACM SIGIR Conference
+on Human Information Interaction and Retrieval (CHIIR ’23), March 19–23, 2023, Austin,
+TX, USA, https://doi.org/10.1145/3576840.3578316.
+1
+INTRODUCTION
+Research and development of information access systems (IAS) —
+search engines, recommender systems, and similar systems that
+facilitate access to information, often studied in conferences on in-
+formation retrieval (IR) and related topics such as recommendation
+and user modeling — often engage with gender in some way or
+another. These uses vary, from reporting the demographic distribu-
+tion of participants in a user study to using gender as a feature in
+personalized results to seeking to ensure the system treats users or
+content providers of various genders fairly, among other objectives.
+There has been little explicit consideration in this literature, how-
+ever, about how gender should be used in information access. Most
+work takes gender as a categorical feature that can be obtained from
+users or inferred from the underlying data set and uses it as any
+other feature in the system. There are several important questions
+about the use of gender in information access research, including:
+• When should gender be used, and when is it inappropriate,
+unhelpful, or harmful to use gender in research or practice?
+• When it is appropriate to use gender, how should gender be
+defined and operationalized?
+• Where and how should gender data be obtained? Are there
+methods that are best avoided?
+Our goal in this paper is to document the current state of research
+practice with respect to these questions and provide a foundation
+for discussion, further research, and well-grounded practice among
+information access researchers, practitioners, affected parties, and
+others that moves the community towards thoughtful, principled
+use and non-use of gender. We agree that it is indeed crucial for
+search engines, recommender systems (RS), and other information
+access systems to provide effective, appropriate, and useful results
+to users of all genders and other demographic affiliations. We argue
+that this is best done through careful attention to the meaning of
+gender and how its use and operationalization affects the people the
+system is aiming to assist, particularly people with marginalized
+gender identities and adverse experiences with computational and
+datafied representations of gender.
+To that end, we organize this paper in two parts. First, we pro-
+vide a systematic review and analysis of the use of gender in recent
+publications in key information access research venues. We then
+identify goals for which gender is used, ways it is encoded, and the
+data sources used to obtain gender information for users, content
+providers, and other affected people. Finally, we build on this survey
+arXiv:2301.04780v1  [cs.IR]  12 Jan 2023
+
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Pinney et al.
+and relevant literature from other domains to provide recommenda-
+tions for improving research and implementation practices around
+gender in information access.
+We are certainly not the first to question how gender is used
+in computing systems. Hamidi et al. [29] and Scheuerman et al.
+[66] have done crucial work on the (mis)use of gender in human-
+computer interaction, and [14] have looked at how it is used in
+natural language processing (NLP) research. This highlights how
+this issue is not unique to IAS; indeed, this is a common issue in
+quantitative social sciences writ large [75]. We complement their
+work by specifically investigating information access applications,
+including search and recommendation.
+2
+MOTIVATING VIGNETTES
+The use of gender as a variable in information access systems may
+be becoming more ubiquitous. Gender may be used as an input to
+a recommender system or information retrieval model. Some of
+the uses of gender may present themselves as more insidious than
+others. To motivate our interest in understanding the use of gender,
+we present two vignettes.
+In China, Kentucky Fried Chicken partnered with Baidu to offer
+a product which provided food recommendations based on details
+inferred from a customer’s face at 300 stores in Beijing [23]. In
+addition to inferring gender, the facial analysis product also inferred
+age and “beauty” [33]. The tool recommends different meals which
+are seemingly based on these factors. For instance, the author of the
+Guardian article was read as a woman in her 30s, and the system
+recommended a chicken hamburger meal. A press release from
+Baidu suggested that “‘a male customer in his early 20s’ would be
+offered ‘a set meal of crispy chicken hamburger, roasted chicken
+wings and coke’, while ‘a female customer in her 50s’ would get a
+recommendation of ‘porridge and soybean milk for breakfast’.”
+Gender itself is inferred in this system from gender expression,
+which has been criticized in the literature which we discuss be-
+low. Moreover, strong assumptions are made about the role gender
+should play in product recommendation. It’s not clear how, prima
+facie, how these meals correlate with these inferred features. In
+what way does it make sense for features such as inferred gender,
+beauty, or age to serve as a suggestion for meal items? Are those
+features indicative of purchasing behavior or desired products? To
+us, these features, inferred from personal appearance, make spuri-
+ous product recommendations. However, what we do know is that
+the system presents a new avenue for massive collection of facial
+images and purchasing patterns, which could be used by Baidu to
+monetize other aspects of social and economic life in China.
+Another, more positive, use of gender can be found in an audit
+conducted by Spotify to assess how female artists are represented
+and made visible to listeners through the platform’s discovery tools
+[21]. The authors of this study found that recommendations had
+a slightly higher proportion of female artists than users’ “organic”
+behavior (i.e. behavior which was not recommendation-driven),
+and further, that recommending more female artists correlated with
+increases in later user-initiated streaming of music by female artists.
+In this case, gender as a variable is used as an identifying fea-
+ture of a recommended product. Such work can be valuable in
+understanding how information access technologies interact with
+societal discrimination, when they propagate such biases, and how
+they may be deployed as interventions to promote more equitable
+information economies [17].
+3
+BACKGROUND
+Gender has been discussed in various ways in information access
+research throughout the history of the relevant fields, and there is
+also a rich literature on the construct of gender and its interaction
+with data and computation. To set the stage for our formal review
+in Section 4, we first briefly outline some of that background here.
+3.1
+The Uses of Demographics in IAS
+As noted in the introduction and explored much more thoroughly
+in our systematic review, there are a variety of ways that gender
+appears in information access research. One of the earliest recom-
+mender systems, Grundy [57], explicitly used a user’s gender as
+a component of its model of their preferences and incorporated
+gender stereotypes into its initial recommendations (which the
+user could refine through subsequent conversational interaction);
+in modern personalization, gender is one of the many attributes
+data brokers routinely collect and sell to companies to use for a
+variety of purposes [13]. Early work on matrix factorization for
+collaborative filtering used a gender affinity axis (“geared toward
+females” vs. “males”) to illustrate the idea of embedding movies
+[38]. A more recent line of work seeks to understand information
+access systems’ differential impacts to see if they are treating people
+of different genders “fairly” as users [20, 44], as producers of the
+information being retrieved [18, 21, 25], or as the subjects of that
+information [19, 34, 45].
+Aside from discussions in limitations sections of some of these
+papers, there is little work on when, why, and how gender is and
+should be used in information access research, or putting this work
+in the context of discussions about gender in social science or other
+computing fields such as human-computer interaction. This is the
+gap we seek to fill in this paper.
+3.2
+Gender as a Category
+Much of the literature within sociology and gender studies has
+focused on the differences between gender and sex. Typically, “sex”
+is used to refer to biological characteristics while “gender” is re-
+lated to internal perceptions of self and how external society sees
+individuals. However, gender and sex are entangled, and sex itself is
+socially constructed by scientists, policymakers, and technologists
+[24, 63].
+Gender scholars, as well as transgender and queer activists, have
+also made the distinction between gender identity and gender ex-
+pression. Gender identity typically refers to one’s own internal
+understanding of gender and self-identification. Gender expression
+refers to how one presents one’s own gender and wants to be seen
+by the world. These both can fit into binary notions of gender, but
+can also be expansive and encompass a constellation of different
+identifications and notions of what self-expression can entail. More-
+over, gender expression can be broken up both internally (how one
+is expressing one’s gender and feels about it to themselves) and
+how others perceive that individual’s gender (perceived gender
+expression). In this article, we follow [64] and focus on discussing
+
+Much Ado About Gender
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+gender, given that technological artifacts and systems typically dis-
+cuss social constructions of gender as datafied by informational
+systems. However, it is important to note that many types of infor-
+mation access systems may make claims about having data on sex
+(e.g. through medical imaging or genomics).
+Gender data can be obtained in a plethora of ways, depending
+on the modality. There is robust literature within social science
+research on how to survey for gender, especially when that mea-
+surement moves beyond the male/female gender binary. In survey
+research, much of the focus has centered around ensuring that
+population-level estimates can be inferred from a sample that is
+attentive to the individuals who do not fit into either the category
+of male or female. The Williams Institute has developed tools which
+ask respondents if they identify within the binary and then asks
+about transgender status [72]. This has been criticized as being too
+reductive, however, and may not be applicable for smaller scale
+studies. Others have focused on attempting to obtain a measure
+of how others may perceive their gender expression [41]. More
+recently, many others have addressed how to approach gender as a
+matter of data justice using intersectional feminist and queer theory
+lenses [16, 28].
+Gender data come from many different places in the papers we
+examine, so we do not distinguish between gender identity and
+gender expression. However, it is important to note that these two
+categories are used nearly interchangeably in the computer science
+literature that we surveyed.
+3.3
+Gender in Computational Research
+With the rise in attention to facial recognition as a technology, many
+researchers within HCI and AI have focused on the attribution of
+gender to individual data traces, typically images of people. Keyes
+[35] has written on the dangers of automatic gender recognition
+(AGR), Scheuerman et al. [65] have written on how AGR systems
+perform worse on trans and gender non-conforming people, and
+how these systems cannot legibly recognize non-binary people.
+Gender non-conforming and transgender individuals also feel as
+though these systems produce harm by involuntarily gendering
+them [29]. “Gender” is also necessarily raced; that is, binary genders
+themselves are the endpoint of processes of centuries of European
+colonization [64] and erase other genders which were part of in-
+digenous and non-Western societies. Moreover, gender assessments
+are typically not accorded the same status to non-white women,
+especially Black women, as evidenced by [8].
+Moreover, although there is less academic research in the inter-
+action of gender and text, this is still a strain of research which
+manifests in a few different registers. There is a body of work which
+attempts to predict gender from textual prose (e.g. [51], however
+much of the work in natural language processing focuses on the
+notion of gender bias in text and text representations. One of the
+most major of these interventions [6, 9] suggests that pre-trained
+embedding spaces exhibit sexist biases (e.g. doctors are to males,
+whereas nurses are to females). Recent work has suggested that, al-
+though there is significant work in gender bias in NLP, few of these
+papers engage with gender theory, consider non-binary genders, or
+consider the intersectional, already-racialized notion of gender [14].
+At the intersection of computer vision and natural language pro-
+cessing, gender and racialized-gender bias persist in multi-modal
+domains, such as image search [49], text-image benchmarks [15],
+and multi-modal models such as SCAN and CLIP [74].
+4
+REVIEW OF CURRENT PRACTICES
+In order to better understand the landscape of the use of gender in
+information access systems, we conducted a survey of all papers
+which mentioned sex or gender in key information retrieval and
+recommendation systems publication venues. We desired to assess
+what, in particular, this academic community was doing with the
+concept of gender in academic outputs.
+4.1
+Methods
+To collect a set of papers to analyze, we searched for all papers that
+mentioned gender-related words in SIGIR, CHIIR, RecSys, UMAP,
+and TOIS papers in 2017-2021 using the ACM Digital Library search.
+We selected these venues to furnish examples representative of
+multiple perspectives in, particularly from a computer science per-
+spective; papers in these venues are influential across both research
+and practice. We selected these years because we wanted to take a
+snapshot of relatively current research within this field rather than
+attempt to make any larger claims about changes over time, partic-
+ularly extending to earlier days of information access research.
+We constructed a codebook based on a sample of articles match-
+ing our criteria. The codebook was constructed at the guidance of
+the third author, a sociologist who focuses on the intersections of
+technology, race, and gender, and the final author, a senior computer
+scientist focusing on information access systems. New questions
+were added as needed. For instance, we began the study focusing
+online on whether there was a gender variable and the goals of
+using gender, with the assumption that most articles would address
+user gender. However, we then came to understand that gender
+may have different referents (e.g. the data instance), and that there
+may be multiple referents. Moreover, we began to find that many
+of the uses of gender were part of an audit process to detect bias,
+so we added another question regarding those explicitly.
+The lead author then coded for each of the variables in our
+codebook across all the articles. All authors met weekly to discuss
+the coding process and resolve ambiguities, and to work through
+exemplar cases with the lead author. Because a single person coded
+all the articles, we do not report interrater reliability metrics. The
+full coding process, the codebook, and the dataset are available in
+citation [52].
+4.1.1
+Variables. For each paper, we coded for several different
+variables. Table 1 provides a summary at a glance.
+What is the primary referent? The referent is the group of people
+who gender is being attributed to. This may be users of a recom-
+mender system, subjects of particular data instances (such as cloth-
+ing or musical artists), or annotators who are labeling data. In cases
+in which the paper conducted a user study using a crowdworking
+platform, we coded study participants as “users.” While we began
+this study anticipating only “users”, “subjects”, and “providers” be-
+ing our referent, we added annotators as we continued to code.
+
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Pinney et al.
+Variable
+Possible values
+Primary referent
+User/Subject/Provider/Annotator
+Gender variable?
+Yes/No
+Gender categories
+Binary/Binary+Other
+Gender determination
+Self-identification/Annotator/Inferred
+Bias/fairness?
+Yes/No
+Goals
+User study/survey
+Gender personalization
+Audit system behavior
+Gender prediction
+Protect gender variable
+Persona generation
+Table 1: Summary of variables
+Is there a gender variable? We determined if there was any kind
+of gender variable in the article text at all. If there is no gender
+variable, then this disqualifies answering other questions about the
+paper. We coded a paper as “applied” when the model or experiment
+in the paper did not use gender, but the authors suggest that gender
+could be used with their method.
+What are the gender categories? This variable outlined which
+values the gender variable will take. Sometimes these were explicitly
+mentioned, but often they will be obscured in a table or implicit in
+a statistical model. Moreover, we also noted if the authors coded
+for a third gender, such as “other” or “non-binary.” We also coded
+for whether the authors verbally acknowledged that gender was
+non-binary, but did not operationalize this in any way. We did so
+because we hypothesized that some authors would make a textual
+note that gender was non-binary, but then continue using binary
+values for gender.
+How is gender determined? We coded how the authors are ob-
+taining the gender label. The gender label itself may come from
+self-identification by the user, or from an inference being made
+by the authors, third-party annotators (such as crowdworkers),
+or an automated system. We began from two expected categories
+(self-identification and machine-inferred) but added crowdworker
+inference as we noticed this in the data.
+Is this paper about bias and/or fairness? Many papers will be about
+assessing the bias with a particular system or dataset, attempting
+to debias a dataset, or create a fair dataset or method. This would
+be more akin to the auditing example noted above.
+Goals of using gender. Lastly, we coded for the “goal” of the use of
+the gender variable. Instead of defining a set of discrete goals which
+gender was used for, this was an inductive category, in which we
+added different goals progressively. This included some goals which
+we expected at the start of the research project, such as “Personalize
+based on gender“ or “Gender prediction“ (both used in the KFC
+China example above), but also encompassed some surprising uses.
+We discuss these inductively coded goals below in the findings.
+4.2
+Overview of Data and Univariate Findings
+We collected 801 papers from 4 conferences (CHIIR, SIGIR, RecSys,
+and UMAP) and one journal (TOIS); of these, we coded 598 papers
+and excluded 203 workshop summary papers that didn’t have suffi-
+cient peer review to code. Of the 598 coded papers, we found that 73
+papers had a gender variable of interest, 442 did not have a gender
+variable, and 57 had a gender variable that was “applied.”
+4.2.1
+Gender Referent. In each paper, the authors attribute gender
+to a specific object — the person or thing that the authors are
+referring to when discussing gender. If authors attributed gender
+to multiple entities, one entity was labeled as the primary referent
+and the paper was coded as having multiple referents. We identified
+4 types of referents with which authors associated gender.
+User Referent (52 papers). This set of papers considers gender
+association of users who interact with systems [12, 32, 43, 55, 71].
+This user interaction may be direct where gender identity is self-
+declared (user study or survey), or it may be indirect where gender
+identity is annotated or inferred (annotation of user-generated
+profile, facial inference). For example, Rozen et al. [59] used user-
+stated gender information to evaluate their proposed system in
+predicting user demographic attributes, namely gender, from user
+browsing data and generated comments on news articles.
+Subject Referent (15 papers). In this group of papers, gender is
+associated with subjects or items. Gender of items can be inferred
+from item content, for example, song lyrics, documents, and dataset
+labels [4, 48, 69, 77]. For instance, Rekabsaz and Schedl [56] use gen-
+dered keywords to identify female/male magnitude of retrieved doc-
+uments and provide metrics for measuring gender bias in retrieval
+sets. They use an annotated dataset of gendered and non-gendered
+queries to demonstrate the use of these metrics in measuring gender
+bias of a result set.
+Provider Referent (5 papers). Items can be associated with the
+gender of item providers or content creators (music artists, book au-
+thors), so the gender of the providers or creators is often assigned to
+the items [1, 20, 47]. For example, Ferraro et al. [25] identify gender
+bias of artists in music recommendations and propose a progres-
+sive re-ranking method that achieves improved gender balance of
+musical creators in recommendation systems.
+Annotator Referent (1 paper). This type of paper refers to the gen-
+der of the annotators where their act of annotation is significant
+(compared to if they serve as test users). In the single paper in this
+category [79], the authors collected annotators’ gender informa-
+tion to develop noise-aware sentiment classification models and
+illustrate the possible effect that demographic attributes may have
+on an annotator’s response.
+4.2.2
+Gender Determination. During the coding process, we iden-
+tified several ways with which authors determined the gender of
+the referent(s). The majority of papers (68) involved one method of
+gender determination, but five papers used two.
+Self-identification (53 papers). In these papers, gender is deter-
+mined with self-declarations of gender identity. In some cases, users
+declare their own gender (among other demographic attributes)
+while participating in a study or while using a system [7, 37, 79]; in
+others, authors use publicly available datasets that provide demo-
+graphic data where it can be assumed that gender was self-declared
+[53, 62, 73].
+
+Much Ado About Gender
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Annotators (16 papers). In this work, human annotators assign
+gender for users, providers or subjects [3, 30, 70]. In [20], the authors
+use a dataset where the gender of book authors was annotated by
+library professionals.
+Inferred (7 papers). In these papers, gender is interpreted from
+item content, users’ personal information, interaction behavior or
+with the help of annotators. We identified papers that use users or
+providers name, voice, and images for inferring gender [2, 27, 43].
+For example, Mukherjee et al. [47] use a gender identification tool
+that infer users’ gender from their username and country of origin.
+4.2.3
+Categories of Gender.
+Binary (63 papers). This group of papers considered gender as
+a binary variable where they categorized gender into men and
+women. This is regardless of referent or determination type. These
+papers also do not acknowledge that gender is non-binary [2, 7, 25,
+47, 50, 60, 76].
+Acknowledgement of non-binary gender, or the use of a third gen-
+der category (10 papers). The other ten papers consider the concept
+of gender beyond binary categorization. In six of them, the gen-
+der categories were extended to include unisex, mix-gender, and
+non-gendered groups. For instance, in [22], the authors considered
+unisex and mix-gender categories along with men’s and women’s
+categories to predict buyer’s size preference in e-commerce. The re-
+maining four papers acknowledged the limitations of representing
+gender as a binary construct but continued to do so in any case. For
+example, in [20], the authors use a binary gender variable to assess
+the results of collaborative filtering methods in book ratings and
+recommendations with respect to the gender of content creators,
+but include discussion of the negative effects and consequences of
+representing gender as binary.
+Notably, none of these papers provided classifications which
+affirmed non-binary gender identities. This is distinct from papers
+which provide a “non-gendered” categorization, such as “unisex” or
+“other”, as noted from the examples given in the prior paragraph. We
+discuss positive examples of affirming non-binary gender identities
+in the discussion.
+4.2.4
+Bias and Fairness. With the rise in the interest of bias, fair-
+ness, and ethics in machine learning systems, and the development
+of new venues such as FAccT/FATML, a concomitant rise has been
+seen in the interest in the information access space. We coded for
+whether the papers dealt with issues of bias or fairness in IR sys-
+tems. Of the 73 coded papers, nearly one-third (24) were concerned
+with bias or fairness.
+4.2.5
+Purposes and Uses of Gender. We used an inductive coding
+method to assess the goal of using a gender variable. Inductive
+coding is typically used in grounded theory methodology [11] in
+which one does not presume a set of categories on some type of
+text, such as an interview transcript; we wanted to understand the
+types of goals directly from the literature instead of imposing our
+assumptions on it. In this case, we focused on the paper overall,
+rather than doing line-by-line codings.
+By “goal”, we refer to the intention or technical achievement
+attempted by the method with respect to the gender variable. This
+is often, but not always, distinct from the goal of the paper itself.
+As an example, a paper which attempts to develop a state-of-the-
+art collaborative filtering recommender system with demographic
+data as a goal may integrate a gender variable as part of a vector
+of demographic features. In this case, the goal would be Gender
+Personalization.
+There may also be the cases in which the gender variable is
+used towards some other, broader end. For instance, a paper which
+attempts to show how errors of demographic inference get propa-
+gated in a fair ranking system would be characterized as “auditing
+system behavior,” but not “gender prediction.”
+We developed ten distinct purposes of gender. The majority
+of papers (57) were labeled with one code but a handful (16) were
+coded with two or three codes. The ten purposes are outlined below.
+User Study or Survey (31 papers). In this group of papers, users
+are asked to participate in a user study or are respondents in a
+survey where they assess model outcomes and provide feedback
+on a subjective aspect of a system. User responses are analyzed for
+measurements of perceived usability (user perception, user behav-
+ior, user knowledge retention). In this case, gender is often collected
+as a salient feature among other demographic features (age, loca-
+tion). For instance, in [50], the authors provided participants with
+a set of questions pertaining to a gender-biased result set of images
+to measure their perceived bias and search engine objectivity. In
+their assessment, the authors collected demographic information
+including gender, and determined measurements of two types of
+sexism detected in users in order to analyze the effect of a user’s
+sexist biases on user perception of gender bias in image retrieval.
+Gender Personalization (21 papers). In this group of papers, the
+authors use gender as part of a user profile to personalize recom-
+mendations. For instance, in [12], the authors utilized user-specific
+information (gender, age, social status) to improve musical artist
+recommendations and to assess long-term music interests of users.
+Audit System Behavior (20 papers). In this genre of papers, the
+authors evaluate the behavior and outcomes of an existing model
+or framework and offer recommendations regarding functionality
+and/or fairness based on analysis results. Gender is highlighted
+among other demographic features both in the datasets used and
+when assessing results for fairness. For instance, in [56] the authors
+generated a dataset of non-gendered queries as input for several
+neural ranking models and measured the resulting gender bias.
+Gender Prediction (7 papers). In these papers, the authors infer a
+gender variable from existing data instances and typically use them
+towards some other system end, such as improving the personalized
+recommendations. For instance, in [68], the authors utilized a deep-
+learning collaborative filtering approach to better predict size and
+fit of users within an e-commerce platform. To address the issue of
+data sparsity on user-item interactions, their model learned latent
+representations and implicit features of users (age, gender).
+Protect Gender Variable (3 papers). In this group of papers, the
+main focus is privacy protection around a set of demographic vari-
+ables, of which gender is highlighted. The authors often first sim-
+ulated the system or model’s behavior to illustrate privacy vio-
+lations and/or data leakage. To counteract the issue, the authors
+then proposed and demonstrated an adversarial method designed
+
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Pinney et al.
+to mitigate privacy leakage and provide better protection for users’
+sensitive attributes, namely gender. For instance, in [39], the au-
+thors demonstrated the relative ease with which user behavioral
+data can be unobtrusively retrieved during web browsing via mouse
+cursor movements and subsequently used to predict demographic
+attributes (age, gender). They then provided a web browser ex-
+tension that implements their proposed mitigation technique to
+obfuscate user demographics.
+Persona Generation (3 papers). This genre of papers specifically
+analyzes user perceptions of profile representations derived from
+user data. The authors collected demographic data (age, gender)
+from participants and assessed the design of automatically-generated
+personas with respect to participant responses. In this way, gender
+is highlighted as a demographic point of interest in both users and
+user perceptions of gendered personas. In [61], for instance, the
+authors conducted a survey measuring user perceptions of pseudo-
+personas, specifically in response to pairs of identical profiles where
+the profile features a smiling picture versus a non-smiling picture.
+They found gender to be an influential attribute of generated per-
+sonas, wherein variation in the gender of participants resulted in
+perceptual variation of the gendered personas.
+Indexing Clinical Trials (2 papers). In this genre of papers, the au-
+thors evaluate query expansion and reduction techniques and work
+to determine optimal feature configurations to improve informa-
+tion retrieval within the medical field. The authors utilize a gender
+variable (among other demographics) to improve query results. In
+[1], for instance, the authors evaluated a precision medicine search
+engine and its functionality in retrieving scientific literature and
+clinical trials in which they employ four steps: an indexing step, a
+query reformulation step, a retrieval step, and a filtering step. In
+the indexing step, the authors included a gender field (among other
+demographic fields) to index clinical trials and used these fields to
+determine eligibility in the filtering step.
+Gender Diversity & Inclusion (1 paper). In this body of papers,
+the methods involve using gender, amongst other demographic
+attributes, to algorithmically determine diversity and inclusion
+in model outputs or a UX surface. In the single example in our
+dataset [47], the authors offered an unsupervised summarization
+framework that provides a user with control over the shape and
+content (e.g., the gender of reviewers) of aspect-based summaries
+of tourist reviews on TripAdvisor.
+Linguistic Gender (1 paper). This set of papers deal with how to
+negotiate gendered aspects of language, including pronouns, nouns,
+and other gendered components. In our single example [77], the
+authors morphologically annotated Amharic (a gendered language)
+for the purpose of extending the application of lexical analysis to
+include more languages.
+Gender Interest Personalization (1 paper). In this last group of
+papers, they deal with dyadic gender preferences, rather than the
+gender of the referent themselves, which would fall under the
+concept of Gender Personalization. In our sole example [42], the
+authors focused on a dating app context where “match” suggestions
+depend upon the user’s specific gender preferences of prospective
+companions.
+Figure 1: Breakdown of whether the paper had a gender vari-
+able by year. “N/A” is used when papers refer to phrases such
+as “sexuality” and not biological sex.
+Figure 2: Goals across time
+4.3
+Bivariate Analysis
+The prior section provided an overview of our data findings for each
+of the respective variables we coded for in our review of papers. In
+this section, we dig into some of the trends of data across time and
+variables.
+4.3.1
+Time Trends. Figure 1 shows the breakdown of our dataset
+by year. There has not been more of a focus on gender across time.
+There is a slight increase in the number of papers which mention
+a gender term, but about the same proportion of papers contain a
+gender variable from year to year. However, there are some notable
+changes across the goals of the use of a gender variable across time.
+The goals of using a gender variable have changed across time.
+The top two goals (“user study or survey” and “gender personaliza-
+tion”) are somewhat persistent across the study period, with the
+prior category peaking in 2018 and the latter in 2020. However, our
+third most prevalent category (“audit system behavior”) has been
+steadily climbing since the beginning of the study period, with its
+peak in 2021.
+Similarly, the use of a gender variable with the intent of assessing
+or testing for some kind of bias or fairness issue has risen across
+time, from two papers in 2017 to eight papers in 2021. In fact, in
+2021, the majority of papers (8 of 15) dealt with fairness issues.
+
+1.0
+N/A
+applied
+no
+yes
+0.8
+0.6
+tio
+Ra
+0.4
+0.2
+0.0
+?
+18
+9
+2
+2
+2
+Year1.0
+audit system behavior
+gender personalization
+gender prediction
+user study or survey
+0.8
+gender diversity & inclusion
+persona generation
+protect gender variable
+0.6
+linguistic gender
+Ratio
+indexing clinical trials
+gender interest personalization
+0.4
+0.2
+0.0
+?
+9
+2
+2
+YearMuch Ado About Gender
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Figure 3: Breakdown of bias and fairness by goal.
+Figure 4: Gender determination by different goals of the gen-
+der variable.
+4.3.2
+Bias and Fairness. When looking at the evaluation of bias
+and fairness as it pertains to each individual goal (Figure 3), we
+have found papers which audit system behavior address this topic
+significantly more often than papers which use gender variables
+towards any other end. User studies and surveys address bias at
+the second highest rate. None of our coded papers with the goal of
+“gender prediction” address bias or fairness in their discussion, and
+only two of those papers with the goal of “gender personalization”
+make note of this topic. The one paper which addresses gender
+diversity and inclusion deals with fairness issues.
+4.3.3
+Gender Determination and Goals. Figure 4 shows the bivari-
+ate relationship between gender determination and paper goal.
+Most of the papers used “self-identification” as a gender determina-
+tion. This is overwhelmingly the case for user studies (27), gender
+personalization (19), and auditing of system behavior (12). How-
+ever, only two papers with the goal of “gender prediction” use
+“self-identification” as a gender determination, whereas all but two
+papers regarding “gender personalization” use “self-identification”
+over both inference and annotation. Significantly, papers which
+do gender prediction mostly use an inferred gender, which is not
+surprising, given the method. However, three papers which audit a
+system’s behavior use inferred gender, and one uses it in the case
+of user studies.
+4.4
+Discussion
+From our analysis, there are several areas worth noting with regards
+to the use of a gender variable. Most notably, we found no positive
+incorporation of non-binary genders within the papers we reviewed:
+that is, no papers successfully affirmed or accounted for non-binary
+gender identities. Although there a small portion of papers provided
+additional categories of gender beyond the binary male and female
+labels, it is important to note that the absence or neutrality of
+gender (as implied by “unisex” and “non-gendered” classifications)
+is not synonymous with non-binary gender identities. Over time, it
+appears that discussion, or, at the very least, acknowledgement of
+gender as non-binary has increased, but the successful utilization
+of a non-binary gender variable has yet to be made.
+Secondly, there has been more awareness in fairness-oriented
+uses of gender variables in this research community, and it has
+gone up over time. Although there appears to be more of an effort
+on this front with goals like “audit system behavior”, it remains
+that papers with the goal of “gender personalization” and “gender
+prediction” fail to properly analyze the implications of their findings
+or model behavior in reference to gender bias and fairness. However,
+it may be the case that these two types of goals are antagonistic
+or fundamentally at odds with fairness and ethics, as suggested by
+Keyes [35] and Scheuerman et al. [65].
+Third, the most frequent goal of using a gender variable is as
+input to an analysis in a user study or survey. This suggests that
+these authors are studying how differently gendered individuals
+respond to particular systems, which may be an encouraging result.
+More troubling, however, is the frequency at which systems attempt
+to personalize results based on gender. This itself makes major
+assumptions about what individuals may prefer, based on a gender
+variable, rather than on user preferences. We discuss alternative
+practices of personalization below. A more heartening development,
+however, is that auditing of system behavior has increased over the
+past five years, and that most of these studies do this with some
+kind of fairness evaluation in mind.
+Lastly, across all papers, gender self-identification is the norm,
+rather than the exception. Self-identification is the most ethical
+manner of collecting gender data, although the exact method of
+doing so is still an area of discussion and research, as noted in
+our literature review above. In a small number of cases, however,
+gender is inferred or labeled by third-party annotators. Third-party
+evaluations, either by crowdworkers, paper authors, or machines,
+may perpetuate gender stereotypes or be another vector of misgen-
+dering. When users self-declare their own gender identities within a
+dataset, they are less likely to be misgendered by a system or model
+using that data than when human annotators or systems infer gen-
+der identities from data traces, such as product selection, names,
+face images, or texts that the individual writes. Self-declaration of
+gender, however, does not foreclose the possibility of misgendering,
+because much self-identification data are collected with only binary
+gender categories built into the systems which collect these data in
+the first place.
+5
+RECOMMENDATIONS
+Researchers and practitioners need to proceed with care in dealing
+with gender in computational research. Depending on the goal, use,
+
+user study or survey
+gender personalization
+audit system behavior
+gender prediction
+protect gender variable
+persona generation
+indexing clinical trials
+gender interest personalization
+linguistic gender
+About Bias/Fairness?
+no
+gender diversity & inclusion
+yes
+0
+5
+10
+15
+20
+25
+30user study or survey
+gender personalization
+audit system behavior
+gender prediction
+protect gender variable
+persona generation
+indexing clinical trials
+linguistic gender
+gender determination
+gender interest personalization
+annotators
+inferred
+gender diversity & inclusion
+self-identification
+0
+5
+10
+15
+20
+25
+30CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Pinney et al.
+and determination of gender, both the research process and findings
+of such research may be harmful. This harm may be direct, as when
+a system misgenders a person, or it may be indirect by handling
+gender in a reasonable way on its own but when combined with
+other downstream components causes harm. In this section, we
+provide some high-level recommendations and guidelines about us-
+ing gender information in research on information access systems.
+We are not providing definite rules of using gender in computa-
+tional research; rather, we are providing recommendations that
+researchers and practitioners can consider to avoid inappropriate
+use of gender in their work. We also expect future work to build on
+these guidelines as both understanding and technical possibilities
+evolve.
+5.1
+When to Use Gender?
+Researchers should first determine whether it is appropriate to use
+gender in the first place. For some applications, contexts, or goals,
+using gender in some way may be beneficial; for others, it may just
+not be useful; and in a number of cases it is likely actually harmful.
+Auditing system performance, particularly for fairness and eq-
+uity concerns (the goal of 20 of 73 papers) seems a relatively positive
+use of gender. Its purpose is to identify and mitigate gendered harms
+the system may inflict or reproduce, and the results are usually only
+made visible in aggregate (so errors in gender determination are
+rolled up in statistical aggregates, rather than present in a table of
+genders of individual people, although public datasets to support
+such audits do include individual-level gender annotations). For ex-
+ample, Ramos and Boratto [55] examined systems that rank people
+and may have reputational implications to ensure that the result-
+ing reputation is independent of gender. Care is needed, though,
+in order not to undermine the fairness or equity goal: work that
+aims to improve fairness but only does so within a binary gen-
+der construct, for example, may reinforce discrimination against
+non-binary people. Moreover, audits of system behavior that infers
+gender on individuals may reproduce harm by guaranteeing that a
+system works only for individuals who conform to stereotypical
+gender presentations or expressions. Lastly, this work may be used
+to diversify information access systems (e.g. [46]), but the same
+caveats for doing so via gender inferrence remains.
+Overall, we advise against personalization based on gender as a
+goal or component of a system (the goal of 21 papers). Such person-
+alization inherently depends on stereotypes about peoples’ interests
+and capabilities, either existing stereotypes derived from societal
+assumptions or new ones derived from data. This contradicts the
+premise of online personalization based on extensive user profiles,
+as implemented in collaborative filtering, that we can personalize
+to a user’s particular needs and tastes rather than relying on un-
+personalized or group-based assumptions. As Riedl and Konstan
+argued [58], recommender systems should “box products, not peo-
+ple.” The literature we have surveyed has not made a compelling
+case for gender-based personalization, but rather assumes that it is
+a reasonable thing to do or does it because it has been done before.
+There is also reason to be suspicious of using gender for personal-
+ization even in cold-start scenarios before individual user feedback
+is available: because the feedback from which personalized sys-
+tems learn is not entirely exogenous, but is partly a response to
+the system’s previous outputs [10], the system may learn future
+“data-driven” stereotypes not from organic user interactions but
+from its own initial assumptions. That is, if initial recommendations
+are derived from erroneous gender stereotype assumptions, data
+from the resulting interactions may reinforce those assumptions not
+because they are an accurate model of user interests, but because
+the user would have clicked on any comparable recommendation.
+Further study is needed to identify whether and to what extent this
+is happening, but it is a risk that should be taken seriously.
+Lastly, following critical work on automated gender recognition
+[35, 65], we also advise against gender prediction in information
+access systems (the goal of 7 papers). Many of the papers we find in
+our data focused on gender prediction aim to make that determina-
+tion from user behavior, such as written internet text [59] or more
+esoteric data such as spatial trajectories [69]. However, similar to
+our warning against gender personalization above, these predic-
+tions may perpetuate gender stereotypes and re-entrench them
+by making those determinations based on data instances which
+bear no relationship to gender, and will most likely misrepresent
+individuals who are transgender or gender non-conforming.
+5.2
+How to Use Gender?
+If it is appropriate to consider using gender in some way, actually
+operationalizing and applying it requires additional careful con-
+sideration. In this section, we focus on more ethical goals of using
+gender and ethical strategies of gender determination.
+Our first recommendation is to use an inclusive concept of gender
+to the extent possible. Restricting work to a male/female gender
+binary limits its applicability and reproduces exclusion of gender
+minorities. Data selection is the first obvious application of this
+principle, but it goes beyond simply the data; for example, while
+Ekstrand and Kluver [18] (expanding on [20]) acknowledged non-
+binary gender identities as valid and an important limitation, the
+metric and resulting statistical method they employed cannot be
+applied to non-binary attributes. Even when only binary data is
+available, we advise against methods that cannot be applied outside
+of binary contexts, so that the analysis can be updated if and when
+more inclusive data is located or produced [54].
+Examples of inclusive gender data and analyses are rare, but the
+TREC Fair Ranking track and dataset [19] does use non-binary gen-
+der identities for bibliographic Wikipedia articles where available.
+The appendix of the track description [19] provides full details of
+the gender attribute, but they started with 20+ gender identities
+from Wikidata, collapsed transgender identities (treating trans men
+as men and trans women as women), and folding remaining gender
+identities into a third category; this resulted in “male”, “female”,
+“third” (“nonbinary” in 2022), and “unknown.” This has the benefits
+of reducing combinatorial explosion and the number of groups with
+very few representatives, making the encoding more computation-
+ally practical. One downside of this approach is that it may obscure
+discrimination against binary transgender people specifically.
+Our second recommendation is to document precisely how gen-
+der labels were obtained, whatever schema they use; prior work
+demonstrates that many datasets do not justify where they obtain
+the data nor the schema of data labels [67]. This recommendation
+
+Much Ado About Gender
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+applies to both data obtained from existing sources, including pub-
+lic datasets, and new datasets created for particular projects. Such
+documentation should be reported in relevant publications and
+can also be a part of dataset documentation such as a datasheet
+[26]. This document should document the schema used, the source
+of the data (such as self-identification or expert annotation), the
+construct of gender recorded (e.g. gender identity versus gender
+expression), and the principles used to determine gender when it is
+not self-identification. In specifying the schema, the documentation
+should also describe the options given to respondents, and if various
+instruments or interfaces limited options to the male/female gender
+binary. When working with existing data sets, such information
+may not be immediately obvious, but researchers and practitioners
+alike should perform due diligence to understand how gender was
+collected and recorded before working with the data. Document-
+ing this information can serve as a community benefit for other
+researchers who seek to build on their results and/or work with the
+same data. When data is obtained from an intermediary, both the
+intermediary and the intermediary’s source of gender data should
+be identified. In many of the papers we coded, the paper was not
+explicit about the source of gender data, and we had to infer the
+source from context, background assumptions, or other resources.
+Our third recommendation is to consider greater gender diversity
+in one’s data sample, especially when conducting small-n qualitative
+studies or user studies in which gender may be a significant factor
+for understanding results. We found that only 10 of our 73 papers
+which used a gender variable acknowledged non-binary gender,
+or provided a third option. None, however, positively affirmed a
+non-binary gender option. Therefore, it would be highly advisable
+that non-binary people are explicitly recruited for studies in which
+gender could be a key variable for both the auditing of a system, or
+for user studies which evaluate a system.
+Finally, when constructing new data sets for either research or
+application purposes, we recommend collection and curation that
+is thoughtful and respectful towards different gender identities,
+as well as taking into account that there is a danger in collecting
+demographic information in and of itself, as such information may
+make reductionist assumptions about identity [31], or be used in a
+way that violates privacy [36]. Self-identification is the best way to
+obtain gender data, as it most fully respects individual autonomy
+and self-determination, and it should be obtained through inclusive
+means. The HCI Gender Guidelines [66] provides guidance for how
+to design gender-inclusive survey fields to obtain gender informa-
+tion from respondents. Expert annotation can be legitimate, but
+should be done in a way that respects peoples’ right to self-identify,
+along with their right to be excluded entirely. The Program for
+Cooperative Cataloging established a task force to produce recom-
+mendations for how to record the gender identities of book authors
+in library name authority records [5], whose report provides ex-
+plicit guidance about the type of inferences that should or should
+not be used when recording author information (when an author
+does not state their gender identity, the recommendations allow
+inference from clear indications in sources close to the author, such
+as the choice of gendered pronouns in an author’s own biography,
+but not from names or photographs). The relevant data field is also
+explicitly defined as recording an author’s gender identity [40].
+5.3
+Research Needed
+Our systematic review and the recommendations we draw from it
+and relevant literature and guidance in adjacent fields are by no
+means the last word on the use and misuse of gender in information
+access. Further research is needed to identify and assess the various
+impacts of use-of-gender decisions. There are also open practical
+challenges: for example, while there is important work on measur-
+ing fairness beyond binaries [54, 78], it is not easy to deal computa-
+tionally with rich notions of gender that may be multidimensional,
+combinatorially large, and have categories with relatively few mem-
+bers. When it is appropriate to use gender — for example, in audits
+for discrimination — the details of how to ethically, respectfully,
+and practically collect, store, document, analyze, and present rich
+notions of gender remain to be worked out.
+There is also space to carry out similar analyses to understand
+how gender is being used in other fields such as natural language
+processing or data mining, and to document the use of gender in
+deployed industrial systems that are not yet described in the public
+research literature.
+6
+CONCLUSION
+Gender is a complex and multifaceted construct that is often con-
+nected with important aspects of a person’s identity. A review of
+published literature reveals a variety of goals for which gender is
+employed. Pursuing gender equity in the effects of information
+access systems is an important goal, but this needs to be done
+thoughtfully and in a manner that respects the rights and identities
+of the people involved. Sometimes, gender should not be used; in
+other cases, it should be used but with due care and attention to the
+complexity of gender. This also needs to be accompanied with clear
+discussions of what, precisely, has been done, why, and limitations
+that arise from the chosen approach.
+Our aim with this paper has been to provide an understanding
+of the current state of research practice and pointers to further
+reading to understand gender as it is currently understood, to serve
+as a foundation for robust, rigorous, and respectful investigations
+of how information access systems can avoid reproducing gender-
+related harms and can effectively serve users, content creators, and
+information subjects of all genders.
+ACKNOWLEDGMENTS
+This work was supported by the National Science Foundation under
+Grant No. 17-51278.
+REFERENCES
+[1] Maristella Agosti, Giorgio Maria Di Nunzio, and Stefano Marchesin. 2019. An
+Analysis of Query Reformulation Techniques for Precision Medicine. In Proceed-
+ings of the 42nd International ACM SIGIR Conference on Research and Development
+in Information Retrieval (Paris, France) (SIGIR’19). Association for Computing
+Machinery, 973–976. https://doi.org/10.1145/3331184.3331289
+[2] Ali Ahmadvand, Harshita Sahijwani, and Eugene Agichtein. 2020. Would You
+Like to Talk About Sports Now? Towards Contextual Topic Suggestion for Open-
+Domain Conversational Agents. In Proceedings of the 2020 Conference on Human
+Information Interaction and Retrieval (Vancouver BC, Canada) (CHIIR ’20). Associ-
+ation for Computing Machinery, 83–92. https://doi.org/10.1145/3343413.3377974
+[3] Pinar Barlas, Styliani Kleanthous, Kyriakos Kyriakou, and Jahna Otterbacher. 2019.
+What Makes an Image Tagger Fair?. In Proceedings of the 27th ACM Conference
+on User Modeling, Adaptation and Personalization (Larnaca, Cyprus) (UMAP ’19).
+Association for Computing Machinery, 95–103. https://doi.org/10.1145/3320435.
+3320442
+
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+Pinney et al.
+[4] Manash Pratim Barman, Amit Awekar, and Sambhav Kothari. 2019. Decoding
+The Style And Bias of Song Lyrics. In Proceedings of the 42nd International ACM
+SIGIR Conference on Research and Development in Information Retrieval (Paris,
+France) (SIGIR’19). Association for Computing Machinery, 1165–1168.
+https:
+//doi.org/10.1145/3331184.3331363
+[5] Amber Billey, Matthew Haugen, John Hostage, Nancy Sack, and Adam L Schiff.
+2016. Report of the PCC Ad Hoc Task Group on Gender in Name Authority Records.
+Technical Report. Program for Cooperative Cataloging. https://www.loc.gov/
+aba/pcc/documents/Gender_375%20field_RecommendationReport.pdf
+[6] Tolga Bolukbasi, Kai-Wei Chang, James Zou, Venkatesh Saligrama, and Adam
+Kalai. 2016. Man is to Computer Programmer as Woman is to Homemaker?
+Debiasing Word Embeddings. (July 2016). arXiv:1607.06520 [cs.CL] https:
+//proceedings.neurips.cc/paper/2016/file/a486cd07e4ac3d270571622f4f316ec5-
+Paper.pdf
+[7] Pavel Braslavski, Vladislav Blinov, Valeria Bolotova, and Katya Pertsova. 2018.
+How to Evaluate Humorous Response Generation, Seriously?. In Proceedings of the
+2018 Conference on Human Information Interaction & Retrieval (New Brunswick,
+NJ, USA) (CHIIR ’18). Association for Computing Machinery, 225–228.
+https:
+//doi.org/10.1145/3176349.3176879
+[8] Joy Buolamwini and Timnit Gebru. 2018. Gender Shades: Intersectional Accuracy
+Disparities in Commercial Gender Classification. Proceedings of Machine Learning
+Research 81 (2018), 77–91. http://proceedings.mlr.press/v81/buolamwini18a.html?
+mod=article_inline
+[9] Aylin Caliskan, Joanna J Bryson, and Arvind Narayanan. 2017. Semantics Derived
+Automatically From Language Corpora Contain Human-Like Biases. Science 356,
+6334 (April 2017), 183–186. https://doi.org/10.1126/science.aal4230
+[10] Allison J B Chaney, Brandon M Stewart, and Barbara E Engelhardt. 2018. How
+Algorithmic Confounding in Recommendation Systems Increases Homogeneity
+and Decreases Utility. In Proceedings of the 12th ACM Conference on Recommender
+Systems (Vancouver, British Columbia, Canada) (RecSys ’18). Association for
+Computing Machinery, 224–232. https://doi.org/10.1145/3240323.3240370
+[11] Kathy Charmaz. 2006. Constructing Grounded Theory: A Practical Guide through
+Qualitative Analysis. SAGE.
+[12] Zhiyong Cheng, Jialie Shen, Liqiang Nie, Tat-Seng Chua, and Mohan Kankanhalli.
+2017. Exploring User-Specific Information in Music Retrieval. In Proceedings
+of the 40th International ACM SIGIR Conference on Research and Development
+in Information Retrieval (Shinjuku, Tokyo, Japan) (SIGIR ’17). Association for
+Computing Machinery, 655–664. https://doi.org/10.1145/3077136.3080772
+[13] Matthew Crain. 2018. The Limits of Transparency: Data Brokers and Commodi-
+fication. New Media & Society 20, 1 (Jan. 2018), 88–104. https://doi.org/10.1177/
+1461444816657096
+[14] Hannah Devinney, Jenny Björklund, and Henrik Björklund. 2022. Theories of
+“Gender” in NLP Bias Research. In 2022 ACM Conference on Fairness, Account-
+ability, and Transparency (Seoul, Republic of Korea) (FAccT ’22). Association for
+Computing Machinery, 2083–2102. https://doi.org/10.1145/3531146.3534627
+[15] Mark Diaz and Emily Denton. 2021. A Dataset Exploration Case Study with
+Know Your Data. https://ai.googleblog.com/2021/08/a-dataset-exploration-case-
+study-with.html. https://ai.googleblog.com/2021/08/a-dataset-exploration-case-
+study-with.html Accessed: 2022-10-18.
+[16] Catherine D’Ignazio and Lauren F Klein. 2020. Data Feminism. MIT press.
+[17] Michael D Ekstrand, Anubrata Das, Robin Burke, and Fernando Diaz. 2022. Fair-
+ness in Information Access Systems. Foundations and Trends® in Information
+Retrieval 16, 1-2 (2022), 1–177. https://doi.org/10.1561/1500000079
+[18] Michael D Ekstrand and Daniel Kluver. 2021. Exploring Author Gender in Book
+Rating and Recommendation. User Modeling and User-Adapted Interaction 31, 3
+(2021), 377–420. https://doi.org/10.1007/s11257-020-09284-2
+[19] Michael D Ekstrand, Graham McDonald, Amifa Raj, and Isaac Johnson. 2022.
+Overview of the TREC 2021 Fair Ranking Track. In The Thirtieth Text Retrieval
+Conference (TREC 2021) Proceedings. https://trec.nist.gov/pubs/trec30/papers/
+Overview-F.pdf
+[20] Michael D Ekstrand, Mucun Tian, Mohammed R Imran Kazi, Hoda Mehrpouyan,
+and Daniel Kluver. 2018. Exploring Author Gender in Book Rating and Recom-
+mendation. In Proceedings of the 12th ACM Conference on Recommender Systems
+(Vancouver British Columbia Canada). Association for Computing Machinery,
+242–250. https://doi.org/10.1145/3240323.3240373
+[21] Avriel Epps-Darling, Romain Takeo Bouyer, and Henriette Cramer. 2020. Artist
+Gender Representation in Music Streaming. In Proceedings of the 21st International
+Society for Music Information Retrieval Conference. ISMIR, 248–254.
+https://
+program.ismir2020.net/poster_2-11.html
+[22] Yotam Eshel, Or Levi, Haggai Roitman, and Alexander Nus. 2021. PreSizE: Predict-
+ing Size in E-Commerce Using Transformers. (May 2021). arXiv:2105.01564 [cs.IR]
+http://arxiv.org/abs/2105.01564
+[23] Darrell Etherington. 2016.
+Baidu and KFC’s New Smart Restaurant
+Suggests What to Order Based on Your Face.
+TechCrunch (Dec. 2016).
+https://techcrunch.com/2016/12/23/baidu-and-kfcs-new-smart-restaurant-
+suggests-what-to-order-based-on-your-face/
+[24] Anne Fausto-Sterling. 2000. Sexing the Body: Gender Politics and the Construction
+of Sexuality. Basic Books.
+[25] Andres Ferraro, Xavier Serra, and Christine Bauer. 2021. Break the Loop: Gender
+Imbalance in Music Recommenders. In Proceedings of the 2021 Conference on
+Human Information Interaction and Retrieval (Canberra ACT, Australia) (CHIIR
+’21). Association for Computing Machinery, 249–254. https://doi.org/10.1145/
+3406522.3446033
+[26] Timnit Gebru, Jamie Morgenstern, Briana Vecchione, Jennifer Wortman Vaughan,
+Hanna Wallach, Hal Daumé, III, and Kate Crawford. 2018. Datasheets for Datasets.
+(March 2018). arXiv:1803.09010 [cs.DB] http://arxiv.org/abs/1803.09010
+[27] Avijit Ghosh, Ritam Dutt, and Christo Wilson. 2021. When Fair Ranking Meets
+Uncertain Inference. In Proceedings of the 44th International ACM SIGIR Conference
+on Research and Development in Information Retrieval (Virtual Event, Canada)
+(SIGIR ’21). Association for Computing Machinery, 1033–1043. https://doi.org/
+10.1145/3404835.3462850
+[28] Kevin Guyan. 2022. Queer Data: Using Gender, Sex and Sexuality Data for Action.
+Bloomsbury Academic.
+[29] Foad Hamidi, Morgan Klaus Scheuerman, and Stacy M Branham. 2018. Gender
+Recognition or Gender Reductionism?: The Social Implications of Embedded
+Gender Recognition Systems. In Proceedings of the 2018 CHI Conference on Human
+Factors in Computing Systems (CHI ’18). Association for Computing Machinery, 8.
+https://doi.org/10.1145/3173574.3173582
+[30] Kyungsik Han, Yonggeol Jo, Youngseung Jeon, Bogoan Kim, Junho Song, and
+Sang-Wook Kim. 2018. Photos Don’t Have Me, But How Do You Know Me?
+Analyzing and Predicting Users on Instagram. In Adjunct Publication of the
+26th Conference on User Modeling, Adaptation and Personalization (Singapore,
+Singapore) (UMAP ’18). Association for Computing Machinery, 251–256. https:
+//doi.org/10.1145/3213586.3225232
+[31] Alex Hanna, Emily Denton, Andrew Smart, and Jamila Smith-Loud. 2020. Towards
+a Critical Race Methodology in Algorithmic Fairness. In Proceedings of the 2020
+Conference on Fairness, Accountability, and Transparency (FAccT 2020). Association
+for Computing Machinery, 501–512. https://doi.org/10.1145/3351095.3372826
+[32] Seyyed Hadi Hashemi and Jaap Kamps. 2017. Skip or Stay. In Proceedings of
+the 2017 Conference on Conference Human Information Interaction and Retrieval -
+CHIIR ’17 (Oslo, Norway). ACM Press. https://doi.org/10.1145/3020165.3022160
+[33] Amy Hawkins. 2017.
+KFC China is Using Facial Recognition Tech
+to Serve Customers - But Are They Buying It?
+The Guardian (Jan.
+2017).
+https://www.theguardian.com/technology/2017/jan/11/china-beijing-
+first-smart-restaurant-kfc-facial-recognition
+[34] Chen Karako and Putra Manggala. 2018. Using Image Fairness Representations
+in Diversity-Based Re-ranking for Recommendations. In Adjunct Publication of
+the 26th Conference on User Modeling, Adaptation and Personalization (Singapore,
+Singapore) (UMAP ’18). Association for Computing Machinery, 23–28. https:
+//doi.org/10.1145/3213586.3226206
+[35] Os Keyes. 2018. The Misgendering Machines: Trans/HCI Implications of Auto-
+matic Gender Recognition. Proceedings of the ACM on Human-Computer Interac-
+tion 2, CSCW (Nov. 2018), 1–22. https://doi.org/10.1145/3274357
+[36] Os Keyes and Abraham D Flaxman. 2022. How Census Data Put Trans Children
+at Risk. Scientific American (2022). https://www.scientificamerican.com/article/
+how-census-data-put-trans-children-at-risk/
+[37] Akiva Kleinerman, Ariel Rosenfeld, and Sarit Kraus. 2018. Providing Explanations
+for Recommendations in Reciprocal Environments. In Proceedings of the 12th
+ACM Conference on Recommender Systems (Vancouver, British Columbia, Canada)
+(RecSys ’18). Association for Computing Machinery, 22–30. https://doi.org/10.
+1145/3240323.3240362
+[38] Y Koren, R Bell, and C Volinsky. 2009. Matrix Factorization Techniques for
+Recommender Systems. Computer 42, 8 (Aug. 2009), 30–37. https://doi.org/10.
+1109/MC.2009.263
+[39] Luis A Leiva, Ioannis Arapakis, and Costas Iordanou. 2021. My Mouse, My Rules:
+Privacy Issues of Behavioral User Profiling via Mouse Tracking. In Proceedings of
+the 2021 Conference on Human Information Interaction and Retrieval (Canberra
+ACT, Australia) (CHIIR ’21). Association for Computing Machinery, 51–61. https:
+//doi.org/10.1145/3406522.3446011
+[40] Library of Congress Network Development. 2022. 375 - Gender (R). https://www.
+loc.gov/marc/authority/ad375.html. https://www.loc.gov/marc/authority/ad375.
+html Accessed: 2022-10-17.
+[41] Devon Magliozzi, Aliya Saperstein, and Laurel Westbrook. 2016.
+Scaling
+Up: Representing Gender Diversity in Survey Research. Socius 2 (Jan. 2016),
+2378023116664352. https://doi.org/10.1177/2378023116664352
+[42] Rahul Makhijani, Shreya Chakrabarti, Dale Struble, and Yi Liu. 2019. LORE: A
+Large-Scale Offer Recommendation Engine With Eligibility and Capacity Con-
+straints. In Proceedings of the 13th ACM Conference on Recommender Systems
+(Copenhagen, Denmark) (RecSys ’19). Association for Computing Machinery,
+160–168. https://doi.org/10.1145/3298689.3347027
+[43] Jennifer Marlow and Jason Wiese. 2017. Surveying User Reactions to Recommen-
+dations Based on Inferences Made by Face Detection Technology. In Proceedings of
+the Eleventh ACM Conference on Recommender Systems (Como Italy). Association
+for Computing Machinery. https://doi.org/10.1145/3109859.3109875
+
+Much Ado About Gender
+CHIIR ’23, March 19–23, 2023, Austin, TX, USA
+[44] Rishabh Mehrotra, Ashton Anderson, Fernando Diaz, Amit Sharma, Hanna Wal-
+lach, and Emine Yilmaz. 2017. Auditing Search Engines for Differential Satisfac-
+tion Across Demographics. In Proceedings of the 26th International Conference on
+World Wide Web Companion (Perth, Australia) (WWW ’17 Companion). Interna-
+tional World Wide Web Conferences Steering Committee, Republic and Canton
+of Geneva, Switzerland, 626–633. https://doi.org/10.1145/3041021.3054197
+[45] Danaë Metaxa, Michelle A Gan, Su Goh, Jeff Hancock, and James A Landay. 2021.
+An Image of Society: Gender and Racial Representation and Impact in Image
+Search Results for Occupations. Proceedings of the ACM on Human-Computer
+Interaction 5, CSCW1 (April 2021), 1–23. https://doi.org/10.1145/3449100
+[46] Margaret Mitchell, Dylan Baker, Nyalleng Moorosi, Emily Denton, Ben Hutchin-
+son, Alex Hanna, Timnit Gebru, and Jamie Morgenstern. 2020. Diversity and
+Inclusion Metrics in Subset Selection. In Proceedings of the AAAI/ACM Confer-
+ence on AI, Ethics, and Society (New York, NY, USA) (AIES ’20). Association for
+Computing Machinery, 117–123. https://doi.org/10.1145/3375627.3375832
+[47] Rajdeep Mukherjee, Hari Chandana Peruri, Uppada Vishnu, Pawan Goyal,
+Sourangshu Bhattacharya, and Niloy Ganguly. 2020. Read What You Need: Con-
+trollable Aspect-Based Opinion Summarization of Tourist Reviews. In Proceedings
+of the 43rd International ACM SIGIR Conference on Research and Development in In-
+formation Retrieval (Virtual Event, China) (SIGIR ’20). Association for Computing
+Machinery, 1825–1828. https://doi.org/10.1145/3397271.3401269
+[48] Reza Nasirigerdeh, Reihaneh Torkzadehmahani, Jan Baumbach, and David B
+Blumenthal. 2021. On the Privacy of Federated Pipelines. In Proceedings of the
+44th International ACM SIGIR Conference on Research and Development in Infor-
+mation Retrieval (Virtual Event, Canada) (SIGIR ’21). Association for Computing
+Machinery, 1975–1979. https://doi.org/10.1145/3404835.3462996
+[49] Safiya Umoja Noble. 2018. Algorithms of Oppression. New York University Press.
+https://doi.org/10.18574/nyu/9781479833641.001.0001
+[50] Jahna Otterbacher, Alessandro Checco, Gianluca Demartini, and Paul Clough.
+2018. Investigating User Perception of Gender Bias in Image Search: The Role of
+Sexism. In The 41st International ACM SIGIR Conference on Research & Develop-
+ment in Information Retrieval (Ann Arbor, MI, USA) (SIGIR ’18). Association for
+Computing Machinery, 933–936. https://doi.org/10.1145/3209978.3210094
+[51] Claudia Peersman, Walter Daelemans, and Leona Van Vaerenbergh. 2011. Pre-
+dicting Age and Gender in Online Social Networks. In Proceedings of the 3rd
+International Workshop on Search and Mining User-Generated Contents (Glas-
+gow, Scotland, UK) (SMUC ’11). Association for Computing Machinery, 37–44.
+https://doi.org/10.1145/2065023.2065035
+[52] Christine Pinney, Amifa Raj, Alex Hanna, and Michael D. Ekstrand. 2023. Much
+Ado About Gender (CHIIR 2023) Codebook and Data. https://doi.org/10.5281/
+zenodo.7521838
+[53] Yanru Qu, Bohui Fang, Weinan Zhang, Ruiming Tang, Minzhe Niu, Huifeng
+Guo, Yong Yu, and Xiuqiang He. 2018. Product-Based Neural Networks for User
+Response Prediction Over Multi-Field Categorical Data. ACM Transactions on
+Information and System Security 37, 1 (Oct. 2018), 1–35. https://doi.org/10.1145/
+3233770
+[54] Amifa Raj and Michael D Ekstrand. 2022. Measuring Fairness in Ranked Results:
+An Analytical and Empirical Comparison. In Proceedings of the 45th International
+ACM SIGIR Conference on Research and Development in Information Retrieval.
+ACM Press. https://doi.org/10.1145/3477495.3532018
+[55] Guilherme Ramos and Ludovico Boratto. 2020. Reputation (In)dependence in
+Ranking Systems: Demographics Influence Over Output Disparities. In Proceed-
+ings of the 43rd International ACM SIGIR Conference on Research and Development
+in Information Retrieval (Virtual Event, China) (SIGIR ’20). Association for Com-
+puting Machinery, 2061–2064. https://doi.org/10.1145/3397271.3401278
+[56] Navid Rekabsaz and Markus Schedl. 2020. Do Neural Ranking Models Intensify
+Gender Bias?. In Proceedings of the 43rd International ACM SIGIR Conference on
+Research and Development in Information Retrieval (Virtual Event, China) (SIGIR
+’20). Association for Computing Machinery, 2065–2068. https://doi.org/10.1145/
+3397271.3401280
+[57] Elaine Rich. 1979. User Modeling via Stereotypes. Cognitive Science 3, 4 (Oct. 1979),
+329–354. http://www.sciencedirect.com/science/article/B6W48-4FWF9GC-9/2/
+f924f793eb153d455893e8d39982ef45
+[58] John Riedl and Joseph Konstan. 2002. Word of Mouse. Warner Books.
+[59] Ohad Rozen, Joel Oren, and Ariel Raviv. 2021. Predicting User Demography
+and Device from News Comments. In Proceedings of the 44th International ACM
+SIGIR Conference on Research and Development in Information Retrieval (Virtual
+Event, Canada) (SIGIR ’21). Association for Computing Machinery, 1995–1999.
+https://doi.org/10.1145/3404835.3463024
+[60] Joni Salminen, Bernard J Jansen, Jisun An, Soon-Gyo Jung, Lene Nielsen, and
+Haewoon Kwak. 2018.
+Fixation and Confusion: Investigating Eye-tracking
+Participants’ Exposure to Information in Personas. In Proceedings of the 2018
+Conference on Human Information Interaction & Retrieval (New Brunswick, NJ,
+USA) (CHIIR ’18). Association for Computing Machinery, 110–119.
+https:
+//doi.org/10.1145/3176349.3176391
+[61] Joni Salminen, Soon-Gyo Jung, João M Santos, and Bernard J Jansen. 2019. The
+Effect of Smiling Pictures on Perceptions of Personas. In Adjunct Publication of
+the 27th Conference on User Modeling, Adaptation and Personalization (Larnaca,
+Cyprus) (UMAP’19 Adjunct). Association for Computing Machinery, 75–79. https:
+//doi.org/10.1145/3314183.3324973
+[62] Pablo Sánchez and Alejandro Bellogín. 2019. Attribute-Based Evaluation for
+Recommender Systems: Incorporating User and Item Attributes in Evaluation
+Metrics. In Proceedings of the 13th ACM Conference on Recommender Systems
+(Copenhagen, Denmark) (RecSys ’19). Association for Computing Machinery,
+378–382. https://doi.org/10.1145/3298689.3347049
+[63] Veronica Sanz. 2017. No Way Out of the Binary: A Critical History of the Scientific
+Production of Sex. Signs: Journal of Women in Culture and Society 43, 1 (Sept.
+2017), 1–27. https://doi.org/10.1086/692517
+[64] Morgan Klaus Scheuerman, Madeleine Pape, and Alex Hanna. 2021.
+Auto-
+Essentialization: Gender in Automated Facial Analysis as Extended Colonial
+Project.
+Big Data & Society 8, 2 (July 2021), 20539517211053712.
+https:
+//doi.org/10.1177/20539517211053712
+[65] Morgan Klaus Scheuerman, Jacob M Paul, and Jed R Brubaker. 2019.
+How
+Computers See Gender: An Evaluation of Gender Classification in Commercial
+Facial Analysis Services. Proceedings of the ACM on Human-Computer Interaction
+3, CSCW (Nov. 2019), 1–33. https://doi.org/10.1145/3359246
+[66] Morgan Klaus Scheuerman, Katta Spiel, Oliver L Haimson, Foad Hamidi, and
+Stacy M Branham. 2020.
+HCI Gender Guidelines.
+https://www.morgan-
+klaus.com/gender-guidelines.html.
+https://www.morgan-klaus.com/gender-
+guidelines.html Accessed: 2020-5-21.
+[67] Morgan Klaus Scheuerman, Kandrea Wade, Caitlin Lustig, and Jed R Brubaker.
+2020. How We’ve Taught Algorithms to See Identity: Constructing Race and
+Gender in Image Databases for Facial Analysis. Proceedings of the ACM on Human-
+Computer Interaction 4, CSCW1 (May 2020), 1–35. https://doi.org/10.1145/3392866
+[68] Abdul-Saboor Sheikh, Romain Guigoures, Evgenii Koriagin, Yuen King Ho,
+Reza Shirvany, Roland Vollgraf, and Urs Bergmann. 2019.
+A Deep Learn-
+ing System for Predicting Size and Fit in Fashion E-Commerce. (July 2019).
+arXiv:1907.09844 [cs.LG] http://arxiv.org/abs/1907.09844
+[69] Adir Solomon, Ariel Bar, Chen Yanai, Bracha Shapira, and Lior Rokach. 2018.
+Predict Demographic Information Using Word2vec on Spatial Trajectories. In
+Proceedings of the 26th Conference on User Modeling, Adaptation and Personaliza-
+tion (Singapore, Singapore) (UMAP ’18). Association for Computing Machinery,
+331–339. https://doi.org/10.1145/3209219.3209224
+[70] Xuemeng Song, Xiang Wang, Liqiang Nie, Xiangnan He, Zhumin Chen, and Wei
+Liu. 2018. A Personal Privacy Preserving Framework: I Let You Know Who Can
+See What. In The 41st International ACM SIGIR Conference on Research & Develop-
+ment in Information Retrieval (Ann Arbor, MI, USA) (SIGIR ’18). Association for
+Computing Machinery, 295–304. https://doi.org/10.1145/3209978.3209995
+[71] Maryam Tavakol. 2020. Fair Classification with Counterfactual Learning. In
+Proceedings of the 43rd International ACM SIGIR Conference on Research and De-
+velopment in Information Retrieval (Virtual Event, China) (SIGIR ’20). Association
+for Computing Machinery, 2073–2076. https://doi.org/10.1145/3397271.3401291
+[72] The GenIUSS Group. 2014. Best Practices for Asking Questions to Identify Transgen-
+der and Other Gender Minority Respondents on Population-based Surveys. Williams
+Institute, UCLA School of Law.
+[73] Yuan Tian, Ke Zhou, Mounia Lalmas, Yiqun Liu, and Dan Pelleg. 2020. Cohort
+Modeling Based App Category Usage Prediction. In Proceedings of the 28th ACM
+Conference on User Modeling, Adaptation and Personalization (Genoa, Italy) (UMAP
+’20). Association for Computing Machinery, 248–256. https://doi.org/10.1145/
+3340631.3394849
+[74] Jialu Wang, Yang Liu, and Xin Eric Wang. 2021.
+Are Gender-Neutral
+Queries Really Gender-Neutral? Mitigating Gender Bias in Image Search.
+arXiv:2109.05433 [cs.CV] http://arxiv.org/abs/2109.05433
+[75] Laurel Westbrook and Aliya Saperstein. 2015. New Categories Are Not Enough:
+Rethinking the Measurement of Sex and Gender in Social Surveys. Gender &
+Society 29, 4 (2015), 534–560. https://doi.org/10.1177/0891243215584758
+[76] Le Wu, Yonghui Yang, Kun Zhang, Richang Hong, Yanjie Fu, and Meng Wang.
+2020. Joint Item Recommendation and Attribute Inference: An Adaptive Graph
+Convolutional Network Approach. In Proceedings of the 43rd International ACM
+SIGIR Conference on Research and Development in Information Retrieval (Virtual
+Event, China) (SIGIR ’20). Association for Computing Machinery, 679–688. https:
+//doi.org/10.1145/3397271.3401144
+[77] Tilahun Yeshambel, Josiane Mothe, and Yaregal Assabie. 2021. Morphologically
+Annotated Amharic Text Corpora. In Proceedings of the 44th International ACM
+SIGIR Conference on Research and Development in Information Retrieval (Virtual
+Event, Canada) (SIGIR ’21). Association for Computing Machinery, 2349–2355.
+https://doi.org/10.1145/3404835.3463237
+[78] Meike Zehlike, Tom Sühr, Ricardo Baeza-Yates, Francesco Bonchi, Carlos Castillo,
+and Sara Hajian. 2022. Fair Top-k Ranking with Multiple Protected Groups.
+Information processing & management 59, 1 (Jan. 2022), 102707. https://doi.org/
+10.1016/j.ipm.2021.102707
+[79] Xueying Zhan, Yaowei Wang, Yanghui Rao, and Qing Li. 2019. Learning from
+Multi-annotator Data: A Noise-Aware Classification Framework. ACM Trans-
+actions on Information and System Security 37, 2 (Feb. 2019), 1–28.
+https:
+//doi.org/10.1145/3309543
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf,len=1064
+page_content='Much Ado About Gender  Current Practices and Future Recommendations for Appropriate Gender-Aware Information Access  Christine Pinney  Amifa Raj  christinepinney@u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='boisestate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='edu  amifaraj@u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='boisestate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='edu  People & Information Research Team  Boise State University  Boise, Idaho, USA  Alex Hanna  alex@dair-institute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org  DAIR Institute  USA  Michael D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Ekstrand  ekstrand@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org  People & Information Research Team  Boise State University  Boise, Idaho, USA  ABSTRACT  Information access research (and development) sometimes makes  use of gender, whether to report on the demographics of partici-  pants in a user study, as inputs to personalized results or recommen-  dations, or to make systems gender-fair, amongst other purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  This work makes a variety of assumptions about gender, however,  that are not necessarily aligned with current understandings of  what gender is, how it should be encoded, and how a gender vari-  able should be ethically used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this work, we present a systematic  review of papers on information retrieval and recommender sys-  tems that mention gender in order to document how gender is  currently being used in this field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We find that most papers men-  tioning gender do not use an explicit gender variable, but most  of those that do either focus on contextualizing results of model  performance, personalizing a system based on assumptions of user  gender, or auditing a model’s behavior for fairness or other privacy-  related issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, most of the papers we review rely on  a binary notion of gender, even if they acknowledge that gender  cannot be split into two categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We connect these findings with  scholarship on gender theory and recent work on gender in human-  computer interaction and natural language processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We conclude  by making recommendations for ethical and well-grounded use of  gender in building and researching information access systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  CCS CONCEPTS  Social and professional topics → Gender;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' • Information sys-  tems → Information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  KEYWORDS  information access, gender, auditing, systematic review  ACM Reference Format:  Christine Pinney, Amifa Raj, Alex Hanna, and Michael D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Ekstrand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Much Ado About Gender: Current Practices and Future Recommenda-  tions for Appropriate Gender-Aware Information Access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In ACM SIGIR  Conference on Human Information Interaction and Retrieval (CHIIR ’23),  March 19–23, 2023, Austin, TX, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' ACM, New York, NY, USA, 11 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3576840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3578316  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  © 2023 Copyright held by the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Publication rights licensed to ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  This is the author’s version of the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' It is posted here for your personal use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Not for  redistribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The definitive Version of Record was published in ACM SIGIR Conference  on Human Information Interaction and Retrieval (CHIIR ’23), March 19–23, 2023, Austin,  TX, USA, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3576840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3578316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  1  INTRODUCTION  Research and development of information access systems (IAS) —  search engines, recommender systems, and similar systems that  facilitate access to information, often studied in conferences on in-  formation retrieval (IR) and related topics such as recommendation  and user modeling — often engage with gender in some way or  another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' These uses vary, from reporting the demographic distribu-  tion of participants in a user study to using gender as a feature in  personalized results to seeking to ensure the system treats users or  content providers of various genders fairly, among other objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  There has been little explicit consideration in this literature, how-  ever, about how gender should be used in information access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Most  work takes gender as a categorical feature that can be obtained from  users or inferred from the underlying data set and uses it as any  other feature in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' There are several important questions  about the use of gender in information access research, including:  When should gender be used, and when is it inappropriate,  unhelpful, or harmful to use gender in research or practice?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  When it is appropriate to use gender, how should gender be  defined and operationalized?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Where and how should gender data be obtained?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Are there  methods that are best avoided?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Our goal in this paper is to document the current state of research  practice with respect to these questions and provide a foundation  for discussion, further research, and well-grounded practice among  information access researchers, practitioners, affected parties, and  others that moves the community towards thoughtful, principled  use and non-use of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We agree that it is indeed crucial for  search engines, recommender systems (RS), and other information  access systems to provide effective, appropriate, and useful results  to users of all genders and other demographic affiliations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We argue  that this is best done through careful attention to the meaning of  gender and how its use and operationalization affects the people the  system is aiming to assist, particularly people with marginalized  gender identities and adverse experiences with computational and  datafied representations of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  To that end, we organize this paper in two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' First, we pro-  vide a systematic review and analysis of the use of gender in recent  publications in key information access research venues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We then  identify goals for which gender is used, ways it is encoded, and the  data sources used to obtain gender information for users, content  providers, and other affected people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Finally, we build on this survey  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='04780v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='IR]  12 Jan 2023  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Pinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  and relevant literature from other domains to provide recommenda-  tions for improving research and implementation practices around  gender in information access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  We are certainly not the first to question how gender is used  in computing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Hamidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [29] and Scheuerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  [66] have done crucial work on the (mis)use of gender in human-  computer interaction, and [14] have looked at how it is used in  natural language processing (NLP) research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This highlights how  this issue is not unique to IAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' indeed, this is a common issue in  quantitative social sciences writ large [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We complement their  work by specifically investigating information access applications,  including search and recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  2  MOTIVATING VIGNETTES  The use of gender as a variable in information access systems may  be becoming more ubiquitous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender may be used as an input to  a recommender system or information retrieval model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Some of  the uses of gender may present themselves as more insidious than  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' To motivate our interest in understanding the use of gender,  we present two vignettes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  In China, Kentucky Fried Chicken partnered with Baidu to offer  a product which provided food recommendations based on details  inferred from a customer’s face at 300 stores in Beijing [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  addition to inferring gender, the facial analysis product also inferred  age and “beauty” [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The tool recommends different meals which  are seemingly based on these factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, the author of the  Guardian article was read as a woman in her 30s, and the system  recommended a chicken hamburger meal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' A press release from  Baidu suggested that “‘a male customer in his early 20s’ would be  offered ‘a set meal of crispy chicken hamburger, roasted chicken  wings and coke’, while ‘a female customer in her 50s’ would get a  recommendation of ‘porridge and soybean milk for breakfast’.”  Gender itself is inferred in this system from gender expression,  which has been criticized in the literature which we discuss be-  low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, strong assumptions are made about the role gender  should play in product recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' It’s not clear how, prima  facie, how these meals correlate with these inferred features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  what way does it make sense for features such as inferred gender,  beauty, or age to serve as a suggestion for meal items?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Are those  features indicative of purchasing behavior or desired products?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' To  us, these features, inferred from personal appearance, make spuri-  ous product recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, what we do know is that  the system presents a new avenue for massive collection of facial  images and purchasing patterns, which could be used by Baidu to  monetize other aspects of social and economic life in China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Another, more positive, use of gender can be found in an audit  conducted by Spotify to assess how female artists are represented  and made visible to listeners through the platform’s discovery tools  [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The authors of this study found that recommendations had  a slightly higher proportion of female artists than users’ “organic”  behavior (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' behavior which was not recommendation-driven),  and further, that recommending more female artists correlated with  increases in later user-initiated streaming of music by female artists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  In this case, gender as a variable is used as an identifying fea-  ture of a recommended product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Such work can be valuable in  understanding how information access technologies interact with  societal discrimination, when they propagate such biases, and how  they may be deployed as interventions to promote more equitable  information economies [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  3  BACKGROUND  Gender has been discussed in various ways in information access  research throughout the history of the relevant fields, and there is  also a rich literature on the construct of gender and its interaction  with data and computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' To set the stage for our formal review  in Section 4, we first briefly outline some of that background here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  The Uses of Demographics in IAS  As noted in the introduction and explored much more thoroughly  in our systematic review, there are a variety of ways that gender  appears in information access research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' One of the earliest recom-  mender systems, Grundy [57], explicitly used a user’s gender as  a component of its model of their preferences and incorporated  gender stereotypes into its initial recommendations (which the  user could refine through subsequent conversational interaction);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  in modern personalization, gender is one of the many attributes  data brokers routinely collect and sell to companies to use for a  variety of purposes [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Early work on matrix factorization for  collaborative filtering used a gender affinity axis (“geared toward  females” vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' “males”) to illustrate the idea of embedding movies  [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' A more recent line of work seeks to understand information  access systems’ differential impacts to see if they are treating people  of different genders “fairly” as users [20, 44], as producers of the  information being retrieved [18, 21, 25], or as the subjects of that  information [19, 34, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Aside from discussions in limitations sections of some of these  papers, there is little work on when, why, and how gender is and  should be used in information access research, or putting this work  in the context of discussions about gender in social science or other  computing fields such as human-computer interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This is the  gap we seek to fill in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  Gender as a Category  Much of the literature within sociology and gender studies has  focused on the differences between gender and sex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Typically, “sex”  is used to refer to biological characteristics while “gender” is re-  lated to internal perceptions of self and how external society sees  individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, gender and sex are entangled, and sex itself is  socially constructed by scientists, policymakers, and technologists  [24, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender scholars, as well as transgender and queer activists, have  also made the distinction between gender identity and gender ex-  pression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender identity typically refers to one’s own internal  understanding of gender and self-identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender expression  refers to how one presents one’s own gender and wants to be seen  by the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' These both can fit into binary notions of gender, but  can also be expansive and encompass a constellation of different  identifications and notions of what self-expression can entail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' More-  over, gender expression can be broken up both internally (how one  is expressing one’s gender and feels about it to themselves) and  how others perceive that individual’s gender (perceived gender  expression).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this article, we follow [64] and focus on discussing  Much Ado About Gender  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  gender, given that technological artifacts and systems typically dis-  cuss social constructions of gender as datafied by informational  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, it is important to note that many types of infor-  mation access systems may make claims about having data on sex  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' through medical imaging or genomics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender data can be obtained in a plethora of ways, depending  on the modality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' There is robust literature within social science  research on how to survey for gender, especially when that mea-  surement moves beyond the male/female gender binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In survey  research, much of the focus has centered around ensuring that  population-level estimates can be inferred from a sample that is  attentive to the individuals who do not fit into either the category  of male or female.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The Williams Institute has developed tools which  ask respondents if they identify within the binary and then asks  about transgender status [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This has been criticized as being too  reductive, however, and may not be applicable for smaller scale  studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Others have focused on attempting to obtain a measure  of how others may perceive their gender expression [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' More  recently, many others have addressed how to approach gender as a  matter of data justice using intersectional feminist and queer theory  lenses [16, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender data come from many different places in the papers we  examine, so we do not distinguish between gender identity and  gender expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, it is important to note that these two  categories are used nearly interchangeably in the computer science  literature that we surveyed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3  Gender in Computational Research  With the rise in attention to facial recognition as a technology, many  researchers within HCI and AI have focused on the attribution of  gender to individual data traces, typically images of people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Keyes  [35] has written on the dangers of automatic gender recognition  (AGR), Scheuerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [65] have written on how AGR systems  perform worse on trans and gender non-conforming people, and  how these systems cannot legibly recognize non-binary people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender non-conforming and transgender individuals also feel as  though these systems produce harm by involuntarily gendering  them [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' “Gender” is also necessarily raced;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' that is, binary genders  themselves are the endpoint of processes of centuries of European  colonization [64] and erase other genders which were part of in-  digenous and non-Western societies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, gender assessments  are typically not accorded the same status to non-white women,  especially Black women, as evidenced by [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Moreover, although there is less academic research in the inter-  action of gender and text, this is still a strain of research which  manifests in a few different registers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' There is a body of work which  attempts to predict gender from textual prose (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [51], however  much of the work in natural language processing focuses on the  notion of gender bias in text and text representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' One of the  most major of these interventions [6, 9] suggests that pre-trained  embedding spaces exhibit sexist biases (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' doctors are to males,  whereas nurses are to females).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Recent work has suggested that, al-  though there is significant work in gender bias in NLP, few of these  papers engage with gender theory, consider non-binary genders, or  consider the intersectional, already-racialized notion of gender [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  At the intersection of computer vision and natural language pro-  cessing, gender and racialized-gender bias persist in multi-modal  domains, such as image search [49], text-image benchmarks [15],  and multi-modal models such as SCAN and CLIP [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4  REVIEW OF CURRENT PRACTICES  In order to better understand the landscape of the use of gender in  information access systems, we conducted a survey of all papers  which mentioned sex or gender in key information retrieval and  recommendation systems publication venues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We desired to assess  what, in particular, this academic community was doing with the  concept of gender in academic outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  Methods  To collect a set of papers to analyze, we searched for all papers that  mentioned gender-related words in SIGIR, CHIIR, RecSys, UMAP,  and TOIS papers in 2017-2021 using the ACM Digital Library search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  We selected these venues to furnish examples representative of  multiple perspectives in, particularly from a computer science per-  spective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' papers in these venues are influential across both research  and practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We selected these years because we wanted to take a  snapshot of relatively current research within this field rather than  attempt to make any larger claims about changes over time, partic-  ularly extending to earlier days of information access research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  We constructed a codebook based on a sample of articles match-  ing our criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The codebook was constructed at the guidance of  the third author, a sociologist who focuses on the intersections of  technology, race, and gender, and the final author, a senior computer  scientist focusing on information access systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' New questions  were added as needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, we began the study focusing  online on whether there was a gender variable and the goals of  using gender, with the assumption that most articles would address  user gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, we then came to understand that gender  may have different referents (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' the data instance), and that there  may be multiple referents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, we began to find that many  of the uses of gender were part of an audit process to detect bias,  so we added another question regarding those explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  The lead author then coded for each of the variables in our  codebook across all the articles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' All authors met weekly to discuss  the coding process and resolve ambiguities, and to work through  exemplar cases with the lead author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Because a single person coded  all the articles, we do not report interrater reliability metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The  full coding process, the codebook, and the dataset are available in  citation [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  Variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For each paper, we coded for several different  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Table 1 provides a summary at a glance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  What is the primary referent?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The referent is the group of people  who gender is being attributed to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This may be users of a recom-  mender system, subjects of particular data instances (such as cloth-  ing or musical artists), or annotators who are labeling data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In cases  in which the paper conducted a user study using a crowdworking  platform, we coded study participants as “users.” While we began  this study anticipating only “users”, “subjects”, and “providers” be-  ing our referent, we added annotators as we continued to code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Pinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Variable  Possible values  Primary referent  User/Subject/Provider/Annotator  Gender variable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Yes/No  Gender categories  Binary/Binary+Other  Gender determination  Self-identification/Annotator/Inferred  Bias/fairness?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Yes/No  Goals  User study/survey  Gender personalization  Audit system behavior  Gender prediction  Protect gender variable  Persona generation  Table 1: Summary of variables  Is there a gender variable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We determined if there was any kind  of gender variable in the article text at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' If there is no gender  variable, then this disqualifies answering other questions about the  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We coded a paper as “applied” when the model or experiment  in the paper did not use gender, but the authors suggest that gender  could be used with their method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  What are the gender categories?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This variable outlined which  values the gender variable will take.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Sometimes these were explicitly  mentioned, but often they will be obscured in a table or implicit in  a statistical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, we also noted if the authors coded  for a third gender, such as “other” or “non-binary.” We also coded  for whether the authors verbally acknowledged that gender was  non-binary, but did not operationalize this in any way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We did so  because we hypothesized that some authors would make a textual  note that gender was non-binary, but then continue using binary  values for gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  How is gender determined?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We coded how the authors are ob-  taining the gender label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The gender label itself may come from  self-identification by the user, or from an inference being made  by the authors, third-party annotators (such as crowdworkers),  or an automated system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We began from two expected categories  (self-identification and machine-inferred) but added crowdworker  inference as we noticed this in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Is this paper about bias and/or fairness?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Many papers will be about  assessing the bias with a particular system or dataset, attempting  to debias a dataset, or create a fair dataset or method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This would  be more akin to the auditing example noted above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Goals of using gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Lastly, we coded for the “goal” of the use of  the gender variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Instead of defining a set of discrete goals which  gender was used for, this was an inductive category, in which we  added different goals progressively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This included some goals which  we expected at the start of the research project, such as “Personalize  based on gender“ or “Gender prediction“ (both used in the KFC  China example above), but also encompassed some surprising uses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  We discuss these inductively coded goals below in the findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  Overview of Data and Univariate Findings  We collected 801 papers from 4 conferences (CHIIR, SIGIR, RecSys,  and UMAP) and one journal (TOIS);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' of these, we coded 598 papers  and excluded 203 workshop summary papers that didn’t have suffi-  cient peer review to code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Of the 598 coded papers, we found that 73  papers had a gender variable of interest, 442 did not have a gender  variable, and 57 had a gender variable that was “applied.”  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  Gender Referent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In each paper, the authors attribute gender  to a specific object — the person or thing that the authors are  referring to when discussing gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' If authors attributed gender  to multiple entities, one entity was labeled as the primary referent  and the paper was coded as having multiple referents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We identified  4 types of referents with which authors associated gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  User Referent (52 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This set of papers considers gender  association of users who interact with systems [12, 32, 43, 55, 71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  This user interaction may be direct where gender identity is self-  declared (user study or survey), or it may be indirect where gender  identity is annotated or inferred (annotation of user-generated  profile, facial inference).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For example, Rozen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [59] used user-  stated gender information to evaluate their proposed system in  predicting user demographic attributes, namely gender, from user  browsing data and generated comments on news articles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Subject Referent (15 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this group of papers, gender is  associated with subjects or items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender of items can be inferred  from item content, for example, song lyrics, documents, and dataset  labels [4, 48, 69, 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, Rekabsaz and Schedl [56] use gen-  dered keywords to identify female/male magnitude of retrieved doc-  uments and provide metrics for measuring gender bias in retrieval  sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' They use an annotated dataset of gendered and non-gendered  queries to demonstrate the use of these metrics in measuring gender  bias of a result set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Provider Referent (5 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Items can be associated with the  gender of item providers or content creators (music artists, book au-  thors), so the gender of the providers or creators is often assigned to  the items [1, 20, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For example, Ferraro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [25] identify gender  bias of artists in music recommendations and propose a progres-  sive re-ranking method that achieves improved gender balance of  musical creators in recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Annotator Referent (1 paper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This type of paper refers to the gen-  der of the annotators where their act of annotation is significant  (compared to if they serve as test users).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In the single paper in this  category [79], the authors collected annotators’ gender informa-  tion to develop noise-aware sentiment classification models and  illustrate the possible effect that demographic attributes may have  on an annotator’s response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  Gender Determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' During the coding process, we iden-  tified several ways with which authors determined the gender of  the referent(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The majority of papers (68) involved one method of  gender determination, but five papers used two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Self-identification (53 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In these papers, gender is deter-  mined with self-declarations of gender identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In some cases, users  declare their own gender (among other demographic attributes)  while participating in a study or while using a system [7, 37, 79];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' in  others, authors use publicly available datasets that provide demo-  graphic data where it can be assumed that gender was self-declared  [53, 62, 73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Much Ado About Gender  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Annotators (16 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this work, human annotators assign  gender for users, providers or subjects [3, 30, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In [20], the authors  use a dataset where the gender of book authors was annotated by  library professionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Inferred (7 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In these papers, gender is interpreted from  item content, users’ personal information, interaction behavior or  with the help of annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We identified papers that use users or  providers name, voice, and images for inferring gender [2, 27, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  For example, Mukherjee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [47] use a gender identification tool  that infer users’ gender from their username and country of origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3  Categories of Gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Binary (63 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This group of papers considered gender as  a binary variable where they categorized gender into men and  women.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This is regardless of referent or determination type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' These  papers also do not acknowledge that gender is non-binary [2, 7, 25,  47, 50, 60, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Acknowledgement of non-binary gender, or the use of a third gen-  der category (10 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The other ten papers consider the concept  of gender beyond binary categorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In six of them, the gen-  der categories were extended to include unisex, mix-gender, and  non-gendered groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [22], the authors considered  unisex and mix-gender categories along with men’s and women’s  categories to predict buyer’s size preference in e-commerce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The re-  maining four papers acknowledged the limitations of representing  gender as a binary construct but continued to do so in any case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For  example, in [20], the authors use a binary gender variable to assess  the results of collaborative filtering methods in book ratings and  recommendations with respect to the gender of content creators,  but include discussion of the negative effects and consequences of  representing gender as binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Notably, none of these papers provided classifications which  affirmed non-binary gender identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This is distinct from papers  which provide a “non-gendered” categorization, such as “unisex” or  “other”, as noted from the examples given in the prior paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We  discuss positive examples of affirming non-binary gender identities  in the discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='4  Bias and Fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' With the rise in the interest of bias, fair-  ness, and ethics in machine learning systems, and the development  of new venues such as FAccT/FATML, a concomitant rise has been  seen in the interest in the information access space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We coded for  whether the papers dealt with issues of bias or fairness in IR sys-  tems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Of the 73 coded papers, nearly one-third (24) were concerned  with bias or fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='5  Purposes and Uses of Gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We used an inductive coding  method to assess the goal of using a gender variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Inductive  coding is typically used in grounded theory methodology [11] in  which one does not presume a set of categories on some type of  text, such as an interview transcript;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' we wanted to understand the  types of goals directly from the literature instead of imposing our  assumptions on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this case, we focused on the paper overall,  rather than doing line-by-line codings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  By “goal”, we refer to the intention or technical achievement  attempted by the method with respect to the gender variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This  is often, but not always, distinct from the goal of the paper itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  As an example, a paper which attempts to develop a state-of-the-  art collaborative filtering recommender system with demographic  data as a goal may integrate a gender variable as part of a vector  of demographic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this case, the goal would be Gender  Personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  There may also be the cases in which the gender variable is  used towards some other, broader end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, a paper which  attempts to show how errors of demographic inference get propa-  gated in a fair ranking system would be characterized as “auditing  system behavior,” but not “gender prediction.”  We developed ten distinct purposes of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The majority  of papers (57) were labeled with one code but a handful (16) were  coded with two or three codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The ten purposes are outlined below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  User Study or Survey (31 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this group of papers, users  are asked to participate in a user study or are respondents in a  survey where they assess model outcomes and provide feedback  on a subjective aspect of a system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' User responses are analyzed for  measurements of perceived usability (user perception, user behav-  ior, user knowledge retention).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this case, gender is often collected  as a salient feature among other demographic features (age, loca-  tion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [50], the authors provided participants with  a set of questions pertaining to a gender-biased result set of images  to measure their perceived bias and search engine objectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  their assessment, the authors collected demographic information  including gender, and determined measurements of two types of  sexism detected in users in order to analyze the effect of a user’s  sexist biases on user perception of gender bias in image retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender Personalization (21 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this group of papers, the  authors use gender as part of a user profile to personalize recom-  mendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [12], the authors utilized user-specific  information (gender, age, social status) to improve musical artist  recommendations and to assess long-term music interests of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Audit System Behavior (20 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this genre of papers, the  authors evaluate the behavior and outcomes of an existing model  or framework and offer recommendations regarding functionality  and/or fairness based on analysis results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender is highlighted  among other demographic features both in the datasets used and  when assessing results for fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [56] the authors  generated a dataset of non-gendered queries as input for several  neural ranking models and measured the resulting gender bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender Prediction (7 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In these papers, the authors infer a  gender variable from existing data instances and typically use them  towards some other system end, such as improving the personalized  recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [68], the authors utilized a deep-  learning collaborative filtering approach to better predict size and  fit of users within an e-commerce platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' To address the issue of  data sparsity on user-item interactions, their model learned latent  representations and implicit features of users (age, gender).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Protect Gender Variable (3 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this group of papers, the  main focus is privacy protection around a set of demographic vari-  ables, of which gender is highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The authors often first sim-  ulated the system or model’s behavior to illustrate privacy vio-  lations and/or data leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' To counteract the issue, the authors  then proposed and demonstrated an adversarial method designed  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Pinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  to mitigate privacy leakage and provide better protection for users’  sensitive attributes, namely gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For instance, in [39], the au-  thors demonstrated the relative ease with which user behavioral  data can be unobtrusively retrieved during web browsing via mouse  cursor movements and subsequently used to predict demographic  attributes (age, gender).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' They then provided a web browser ex-  tension that implements their proposed mitigation technique to  obfuscate user demographics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Persona Generation (3 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This genre of papers specifically  analyzes user perceptions of profile representations derived from  user data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The authors collected demographic data (age, gender)  from participants and assessed the design of automatically-generated  personas with respect to participant responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this way, gender  is highlighted as a demographic point of interest in both users and  user perceptions of gendered personas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In [61], for instance, the  authors conducted a survey measuring user perceptions of pseudo-  personas, specifically in response to pairs of identical profiles where  the profile features a smiling picture versus a non-smiling picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  They found gender to be an influential attribute of generated per-  sonas, wherein variation in the gender of participants resulted in  perceptual variation of the gendered personas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Indexing Clinical Trials (2 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this genre of papers, the au-  thors evaluate query expansion and reduction techniques and work  to determine optimal feature configurations to improve informa-  tion retrieval within the medical field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The authors utilize a gender  variable (among other demographics) to improve query results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  [1], for instance, the authors evaluated a precision medicine search  engine and its functionality in retrieving scientific literature and  clinical trials in which they employ four steps: an indexing step, a  query reformulation step, a retrieval step, and a filtering step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  the indexing step, the authors included a gender field (among other  demographic fields) to index clinical trials and used these fields to  determine eligibility in the filtering step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender Diversity & Inclusion (1 paper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this body of papers,  the methods involve using gender, amongst other demographic  attributes, to algorithmically determine diversity and inclusion  in model outputs or a UX surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In the single example in our  dataset [47], the authors offered an unsupervised summarization  framework that provides a user with control over the shape and  content (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=', the gender of reviewers) of aspect-based summaries  of tourist reviews on TripAdvisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Linguistic Gender (1 paper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This set of papers deal with how to  negotiate gendered aspects of language, including pronouns, nouns,  and other gendered components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In our single example [77], the  authors morphologically annotated Amharic (a gendered language)  for the purpose of extending the application of lexical analysis to  include more languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Gender Interest Personalization (1 paper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this last group of  papers, they deal with dyadic gender preferences, rather than the  gender of the referent themselves, which would fall under the  concept of Gender Personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In our sole example [42], the  authors focused on a dating app context where “match” suggestions  depend upon the user’s specific gender preferences of prospective  companions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Figure 1: Breakdown of whether the paper had a gender vari-  able by year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' “N/A” is used when papers refer to phrases such  as “sexuality” and not biological sex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Figure 2: Goals across time  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3  Bivariate Analysis  The prior section provided an overview of our data findings for each  of the respective variables we coded for in our review of papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  this section, we dig into some of the trends of data across time and  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  Time Trends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Figure 1 shows the breakdown of our dataset  by year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' There has not been more of a focus on gender across time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  There is a slight increase in the number of papers which mention  a gender term, but about the same proportion of papers contain a  gender variable from year to year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, there are some notable  changes across the goals of the use of a gender variable across time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  The goals of using a gender variable have changed across time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  The top two goals (“user study or survey” and “gender personaliza-  tion”) are somewhat persistent across the study period, with the  prior category peaking in 2018 and the latter in 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, our  third most prevalent category (“audit system behavior”) has been  steadily climbing since the beginning of the study period, with its  peak in 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Similarly, the use of a gender variable with the intent of assessing  or testing for some kind of bias or fairness issue has risen across  time, from two papers in 2017 to eight papers in 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In fact, in  2021, the majority of papers (8 of 15) dealt with fairness issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='0  N/A  applied  no  yes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='6  tio  Ra  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='0  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  18  9  2  2  2  Year1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='0  audit system behavior  gender personalization  gender prediction  user study or survey  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='8  gender diversity & inclusion  persona generation  protect gender variable  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='6  linguistic gender  Ratio  indexing clinical trials  gender interest personalization  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='0  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  9  2  2  YearMuch Ado About Gender  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Figure 3: Breakdown of bias and fairness by goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Figure 4: Gender determination by different goals of the gen-  der variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  Bias and Fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' When looking at the evaluation of bias  and fairness as it pertains to each individual goal (Figure 3), we  have found papers which audit system behavior address this topic  significantly more often than papers which use gender variables  towards any other end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' User studies and surveys address bias at  the second highest rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' None of our coded papers with the goal of  “gender prediction” address bias or fairness in their discussion, and  only two of those papers with the goal of “gender personalization”  make note of this topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The one paper which addresses gender  diversity and inclusion deals with fairness issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3  Gender Determination and Goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Figure 4 shows the bivari-  ate relationship between gender determination and paper goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Most of the papers used “self-identification” as a gender determina-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This is overwhelmingly the case for user studies (27), gender  personalization (19), and auditing of system behavior (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' How-  ever, only two papers with the goal of “gender prediction” use  “self-identification” as a gender determination, whereas all but two  papers regarding “gender personalization” use “self-identification”  over both inference and annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Significantly, papers which  do gender prediction mostly use an inferred gender, which is not  surprising, given the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, three papers which audit a  system’s behavior use inferred gender, and one uses it in the case  of user studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='4  Discussion  From our analysis, there are several areas worth noting with regards  to the use of a gender variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Most notably, we found no positive  incorporation of non-binary genders within the papers we reviewed:  that is, no papers successfully affirmed or accounted for non-binary  gender identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Although there a small portion of papers provided  additional categories of gender beyond the binary male and female  labels, it is important to note that the absence or neutrality of  gender (as implied by “unisex” and “non-gendered” classifications)  is not synonymous with non-binary gender identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Over time, it  appears that discussion, or, at the very least, acknowledgement of  gender as non-binary has increased, but the successful utilization  of a non-binary gender variable has yet to be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Secondly, there has been more awareness in fairness-oriented  uses of gender variables in this research community, and it has  gone up over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Although there appears to be more of an effort  on this front with goals like “audit system behavior”, it remains  that papers with the goal of “gender personalization” and “gender  prediction” fail to properly analyze the implications of their findings  or model behavior in reference to gender bias and fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However,  it may be the case that these two types of goals are antagonistic  or fundamentally at odds with fairness and ethics, as suggested by  Keyes [35] and Scheuerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Third, the most frequent goal of using a gender variable is as  input to an analysis in a user study or survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This suggests that  these authors are studying how differently gendered individuals  respond to particular systems, which may be an encouraging result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  More troubling, however, is the frequency at which systems attempt  to personalize results based on gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This itself makes major  assumptions about what individuals may prefer, based on a gender  variable, rather than on user preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We discuss alternative  practices of personalization below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' A more heartening development,  however, is that auditing of system behavior has increased over the  past five years, and that most of these studies do this with some  kind of fairness evaluation in mind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Lastly, across all papers, gender self-identification is the norm,  rather than the exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Self-identification is the most ethical  manner of collecting gender data, although the exact method of  doing so is still an area of discussion and research, as noted in  our literature review above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In a small number of cases, however,  gender is inferred or labeled by third-party annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Third-party  evaluations, either by crowdworkers, paper authors, or machines,  may perpetuate gender stereotypes or be another vector of misgen-  dering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' When users self-declare their own gender identities within a  dataset, they are less likely to be misgendered by a system or model  using that data than when human annotators or systems infer gen-  der identities from data traces, such as product selection, names,  face images, or texts that the individual writes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Self-declaration of  gender, however, does not foreclose the possibility of misgendering,  because much self-identification data are collected with only binary  gender categories built into the systems which collect these data in  the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  5  RECOMMENDATIONS  Researchers and practitioners need to proceed with care in dealing  with gender in computational research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Depending on the goal, use,  user study or survey  gender personalization  audit system behavior  gender prediction  protect gender variable  persona generation  indexing clinical trials  gender interest personalization  linguistic gender  About Bias/Fairness?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  no  gender diversity & inclusion  yes  0  5  10  15  20  25  30user study or survey  gender personalization  audit system behavior  gender prediction  protect gender variable  persona generation  indexing clinical trials  linguistic gender  gender determination  gender interest personalization  annotators  inferred  gender diversity & inclusion  self-identification  0  5  10  15  20  25  30CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Pinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  and determination of gender, both the research process and findings  of such research may be harmful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This harm may be direct, as when  a system misgenders a person, or it may be indirect by handling  gender in a reasonable way on its own but when combined with  other downstream components causes harm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this section, we  provide some high-level recommendations and guidelines about us-  ing gender information in research on information access systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  We are not providing definite rules of using gender in computa-  tional research;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' rather, we are providing recommendations that  researchers and practitioners can consider to avoid inappropriate  use of gender in their work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We also expect future work to build on  these guidelines as both understanding and technical possibilities  evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1  When to Use Gender?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Researchers should first determine whether it is appropriate to use  gender in the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For some applications, contexts, or goals,  using gender in some way may be beneficial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' for others, it may just  not be useful;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' and in a number of cases it is likely actually harmful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Auditing system performance, particularly for fairness and eq-  uity concerns (the goal of 20 of 73 papers) seems a relatively positive  use of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Its purpose is to identify and mitigate gendered harms  the system may inflict or reproduce, and the results are usually only  made visible in aggregate (so errors in gender determination are  rolled up in statistical aggregates, rather than present in a table of  genders of individual people, although public datasets to support  such audits do include individual-level gender annotations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' For ex-  ample, Ramos and Boratto [55] examined systems that rank people  and may have reputational implications to ensure that the result-  ing reputation is independent of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Care is needed, though,  in order not to undermine the fairness or equity goal: work that  aims to improve fairness but only does so within a binary gen-  der construct, for example, may reinforce discrimination against  non-binary people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Moreover, audits of system behavior that infers  gender on individuals may reproduce harm by guaranteeing that a  system works only for individuals who conform to stereotypical  gender presentations or expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Lastly, this work may be used  to diversify information access systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' [46]), but the same  caveats for doing so via gender inferrence remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Overall, we advise against personalization based on gender as a  goal or component of a system (the goal of 21 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Such person-  alization inherently depends on stereotypes about peoples’ interests  and capabilities, either existing stereotypes derived from societal  assumptions or new ones derived from data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This contradicts the  premise of online personalization based on extensive user profiles,  as implemented in collaborative filtering, that we can personalize  to a user’s particular needs and tastes rather than relying on un-  personalized or group-based assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' As Riedl and Konstan  argued [58], recommender systems should “box products, not peo-  ple.” The literature we have surveyed has not made a compelling  case for gender-based personalization, but rather assumes that it is  a reasonable thing to do or does it because it has been done before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  There is also reason to be suspicious of using gender for personal-  ization even in cold-start scenarios before individual user feedback  is available: because the feedback from which personalized sys-  tems learn is not entirely exogenous, but is partly a response to  the system’s previous outputs [10], the system may learn future  “data-driven” stereotypes not from organic user interactions but  from its own initial assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' That is, if initial recommendations  are derived from erroneous gender stereotype assumptions, data  from the resulting interactions may reinforce those assumptions not  because they are an accurate model of user interests, but because  the user would have clicked on any comparable recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Further study is needed to identify whether and to what extent this  is happening, but it is a risk that should be taken seriously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Lastly, following critical work on automated gender recognition  [35, 65], we also advise against gender prediction in information  access systems (the goal of 7 papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Many of the papers we find in  our data focused on gender prediction aim to make that determina-  tion from user behavior, such as written internet text [59] or more  esoteric data such as spatial trajectories [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' However, similar to  our warning against gender personalization above, these predic-  tions may perpetuate gender stereotypes and re-entrench them  by making those determinations based on data instances which  bear no relationship to gender, and will most likely misrepresent  individuals who are transgender or gender non-conforming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2  How to Use Gender?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  If it is appropriate to consider using gender in some way, actually  operationalizing and applying it requires additional careful con-  sideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In this section, we focus on more ethical goals of using  gender and ethical strategies of gender determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Our first recommendation is to use an inclusive concept of gender  to the extent possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Restricting work to a male/female gender  binary limits its applicability and reproduces exclusion of gender  minorities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Data selection is the first obvious application of this  principle, but it goes beyond simply the data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' for example, while  Ekstrand and Kluver [18] (expanding on [20]) acknowledged non-  binary gender identities as valid and an important limitation, the  metric and resulting statistical method they employed cannot be  applied to non-binary attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Even when only binary data is  available, we advise against methods that cannot be applied outside  of binary contexts, so that the analysis can be updated if and when  more inclusive data is located or produced [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Examples of inclusive gender data and analyses are rare, but the  TREC Fair Ranking track and dataset [19] does use non-binary gen-  der identities for bibliographic Wikipedia articles where available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  The appendix of the track description [19] provides full details of  the gender attribute, but they started with 20+ gender identities  from Wikidata, collapsed transgender identities (treating trans men  as men and trans women as women), and folding remaining gender  identities into a third category;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' this resulted in “male”, “female”,  “third” (“nonbinary” in 2022), and “unknown.” This has the benefits  of reducing combinatorial explosion and the number of groups with  very few representatives, making the encoding more computation-  ally practical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' One downside of this approach is that it may obscure  discrimination against binary transgender people specifically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Our second recommendation is to document precisely how gen-  der labels were obtained, whatever schema they use;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' prior work  demonstrates that many datasets do not justify where they obtain  the data nor the schema of data labels [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This recommendation  Much Ado About Gender  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  applies to both data obtained from existing sources, including pub-  lic datasets, and new datasets created for particular projects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Such  documentation should be reported in relevant publications and  can also be a part of dataset documentation such as a datasheet  [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This document should document the schema used, the source  of the data (such as self-identification or expert annotation), the  construct of gender recorded (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' gender identity versus gender  expression), and the principles used to determine gender when it is  not self-identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In specifying the schema, the documentation  should also describe the options given to respondents, and if various  instruments or interfaces limited options to the male/female gender  binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' When working with existing data sets, such information  may not be immediately obvious, but researchers and practitioners  alike should perform due diligence to understand how gender was  collected and recorded before working with the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Document-  ing this information can serve as a community benefit for other  researchers who seek to build on their results and/or work with the  same data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' When data is obtained from an intermediary, both the  intermediary and the intermediary’s source of gender data should  be identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In many of the papers we coded, the paper was not  explicit about the source of gender data, and we had to infer the  source from context, background assumptions, or other resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Our third recommendation is to consider greater gender diversity  in one’s data sample, especially when conducting small-n qualitative  studies or user studies in which gender may be a significant factor  for understanding results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' We found that only 10 of our 73 papers  which used a gender variable acknowledged non-binary gender,  or provided a third option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' None, however, positively affirmed a  non-binary gender option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Therefore, it would be highly advisable  that non-binary people are explicitly recruited for studies in which  gender could be a key variable for both the auditing of a system, or  for user studies which evaluate a system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Finally, when constructing new data sets for either research or  application purposes, we recommend collection and curation that  is thoughtful and respectful towards different gender identities,  as well as taking into account that there is a danger in collecting  demographic information in and of itself, as such information may  make reductionist assumptions about identity [31], or be used in a  way that violates privacy [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Self-identification is the best way to  obtain gender data, as it most fully respects individual autonomy  and self-determination, and it should be obtained through inclusive  means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The HCI Gender Guidelines [66] provides guidance for how  to design gender-inclusive survey fields to obtain gender informa-  tion from respondents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Expert annotation can be legitimate, but  should be done in a way that respects peoples’ right to self-identify,  along with their right to be excluded entirely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The Program for  Cooperative Cataloging established a task force to produce recom-  mendations for how to record the gender identities of book authors  in library name authority records [5],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' whose report provides ex-  plicit guidance about the type of inferences that should or should  not be used when recording author information (when an author  does not state their gender identity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' the recommendations allow  inference from clear indications in sources close to the author,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' such  as the choice of gendered pronouns in an author’s own biography,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  but not from names or photographs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' The relevant data field is also  explicitly defined as recording an author’s gender identity [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3  Research Needed  Our systematic review and the recommendations we draw from it  and relevant literature and guidance in adjacent fields are by no  means the last word on the use and misuse of gender in information  access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Further research is needed to identify and assess the various  impacts of use-of-gender decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' There are also open practical  challenges: for example, while there is important work on measur-  ing fairness beyond binaries [54, 78], it is not easy to deal computa-  tionally with rich notions of gender that may be multidimensional,  combinatorially large, and have categories with relatively few mem-  bers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' When it is appropriate to use gender — for example, in audits  for discrimination — the details of how to ethically, respectfully,  and practically collect, store, document, analyze, and present rich  notions of gender remain to be worked out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  There is also space to carry out similar analyses to understand  how gender is being used in other fields such as natural language  processing or data mining, and to document the use of gender in  deployed industrial systems that are not yet described in the public  research literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  6  CONCLUSION  Gender is a complex and multifaceted construct that is often con-  nected with important aspects of a person’s identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' A review of  published literature reveals a variety of goals for which gender is  employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Pursuing gender equity in the effects of information  access systems is an important goal, but this needs to be done  thoughtfully and in a manner that respects the rights and identities  of the people involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Sometimes, gender should not be used;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' in  other cases, it should be used but with due care and attention to the  complexity of gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' This also needs to be accompanied with clear  discussions of what, precisely, has been done, why, and limitations  that arise from the chosen approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Our aim with this paper has been to provide an understanding  of the current state of research practice and pointers to further  reading to understand gender as it is currently understood, to serve  as a foundation for robust, rigorous, and respectful investigations  of how information access systems can avoid reproducing gender-  related harms and can effectively serve users, content creators, and  information subjects of all genders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work was supported by the National Science Foundation under  Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 17-51278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  REFERENCES  [1] Maristella Agosti, Giorgio Maria Di Nunzio, and Stefano Marchesin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' An  Analysis of Query Reformulation Techniques for Precision Medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceed-  ings of the 42nd International ACM SIGIR Conference on Research and Development  in Information Retrieval (Paris, France) (SIGIR’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing  Machinery, 973–976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3331184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3331289  [2] Ali Ahmadvand, Harshita Sahijwani, and Eugene Agichtein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Would You  Like to Talk About Sports Now?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Towards Contextual Topic Suggestion for Open-  Domain Conversational Agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 2020 Conference on Human  Information Interaction and Retrieval (Vancouver BC, Canada) (CHIIR ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Associ-  ation for Computing Machinery, 83–92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3343413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3377974  [3] Pinar Barlas, Styliani Kleanthous, Kyriakos Kyriakou, and Jahna Otterbacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  What Makes an Image Tagger Fair?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='. In Proceedings of the 27th ACM Conference  on User Modeling, Adaptation and Personalization (Larnaca, Cyprus) (UMAP ’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Association for Computing Machinery, 95–103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3320435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  3320442  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  Pinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  [4] Manash Pratim Barman, Amit Awekar, and Sambhav Kothari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Decoding  The Style And Bias of Song Lyrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 42nd International ACM  SIGIR Conference on Research and Development in Information Retrieval (Paris,  France) (SIGIR’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 1165–1168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3331184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3331363  [5] Amber Billey, Matthew Haugen, John Hostage, Nancy Sack, and Adam L Schiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Report of the PCC Ad Hoc Task Group on Gender in Name Authority Records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Technical Report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Program for Cooperative Cataloging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='gov/  aba/pcc/documents/Gender_375%20field_RecommendationReport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='pdf  [6] Tolga Bolukbasi, Kai-Wei Chang, James Zou, Venkatesh Saligrama, and Adam  Kalai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Man is to Computer Programmer as Woman is to Homemaker?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Debiasing Word Embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' (July 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='06520 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='CL] https:  //proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='cc/paper/2016/file/a486cd07e4ac3d270571622f4f316ec5-  Paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='pdf  [7] Pavel Braslavski, Vladislav Blinov, Valeria Bolotova, and Katya Pertsova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  How to Evaluate Humorous Response Generation, Seriously?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='. In Proceedings of the  2018 Conference on Human Information Interaction & Retrieval (New Brunswick,  NJ, USA) (CHIIR ’18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 225–228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3176349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3176879  [8] Joy Buolamwini and Timnit Gebru.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender Shades: Intersectional Accuracy  Disparities in Commercial Gender Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Proceedings of Machine Learning  Research 81 (2018), 77–91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' http://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='press/v81/buolamwini18a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='  mod=article_inline  [9] Aylin Caliskan, Joanna J Bryson, and Arvind Narayanan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Semantics Derived  Automatically From Language Corpora Contain Human-Like Biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Science 356,  6334 (April 2017), 183–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='aal4230  [10] Allison J B Chaney, Brandon M Stewart, and Barbara E Engelhardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' How  Algorithmic Confounding in Recommendation Systems Increases Homogeneity  and Decreases Utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='01564  [23] Darrell Etherington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='  [25] Andres Ferraro, Xavier Serra, and Christine Bauer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' In Proceedings of the 2021 Conference on  Human Information Interaction and Retrieval (Canberra ACT, Australia) (CHIIR  ’21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 249–254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='1145/  3406522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3446033  [26] Timnit Gebru, Jamie Morgenstern, Briana Vecchione, Jennifer Wortman Vaughan,  Hanna Wallach, Hal Daumé, III, and Kate Crawford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' Providing Explanations  for Recommendations in Reciprocal Environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 12th  ACM Conference on Recommender Systems (Vancouver, British Columbia, Canada)  (RecSys ’18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3240362  [38] Y Koren, R Bell, and C Volinsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Matrix Factorization Techniques for  Recommender Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='263  [39] Luis A Leiva, Ioannis Arapakis, and Costas Iordanou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='  [41] Devon Magliozzi, Aliya Saperstein, and Laurel Westbrook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' 2016),  2378023116664352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='1177/2378023116664352  [42] Rahul Makhijani, Shreya Chakrabarti, Dale Struble, and Yi Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' In Proceedings of the 13th ACM Conference on Recommender Systems  (Copenhagen, Denmark) (RecSys ’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='1145/3298689.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3347027  [43] Jennifer Marlow and Jason Wiese.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Surveying User Reactions to Recommen-  dations Based on Inferences Made by Face Detection Technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of  the Eleventh ACM Conference on Recommender Systems (Como Italy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3109875  Much Ado About Gender  CHIIR ’23, March 19–23, 2023, Austin, TX, USA  [44] Rishabh Mehrotra, Ashton Anderson, Fernando Diaz, Amit Sharma, Hanna Wal-  lach, and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' Interna-  tional World Wide Web Conferences Steering Committee, Republic and Canton  of Geneva, Switzerland, 626–633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='1145/3041021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3054197  [45] Danaë Metaxa, Michelle A Gan, Su Goh, Jeff Hancock, and James A Landay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  An Image of Society: Gender and Racial Representation and Impact in Image  Search Results for Occupations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Proceedings of the ACM on Human-Computer  Interaction 5, CSCW1 (April 2021), 1–23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3449100  [46] Margaret Mitchell, Dylan Baker, Nyalleng Moorosi, Emily Denton, Ben Hutchin-  son, Alex Hanna, Timnit Gebru, and Jamie Morgenstern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Diversity and  Inclusion Metrics in Subset Selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the AAAI/ACM Confer-  ence on AI, Ethics, and Society (New York, NY, USA) (AIES ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for  Computing Machinery, 117–123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3375627.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3375832  [47] Rajdeep Mukherjee, Hari Chandana Peruri, Uppada Vishnu, Pawan Goyal,  Sourangshu Bhattacharya, and Niloy Ganguly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Read What You Need: Con-  trollable Aspect-Based Opinion Summarization of Tourist Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings  of the 43rd International ACM SIGIR Conference on Research and Development in In-  formation Retrieval (Virtual Event, China) (SIGIR ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing  Machinery, 1825–1828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3397271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3401269  [48] Reza Nasirigerdeh, Reihaneh Torkzadehmahani, Jan Baumbach, and David B  Blumenthal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' On the Privacy of Federated Pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the  44th International ACM SIGIR Conference on Research and Development in Infor-  mation Retrieval (Virtual Event, Canada) (SIGIR ’21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing  Machinery, 1975–1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3404835.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3462996  [49] Safiya Umoja Noble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Algorithms of Oppression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' New York University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='18574/nyu/9781479833641.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='0001  [50] Jahna Otterbacher, Alessandro Checco, Gianluca Demartini, and Paul Clough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Investigating User Perception of Gender Bias in Image Search: The Role of  Sexism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In The 41st International ACM SIGIR Conference on Research & Develop-  ment in Information Retrieval (Ann Arbor, MI, USA) (SIGIR ’18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for  Computing Machinery, 933–936.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3209978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3210094  [51] Claudia Peersman, Walter Daelemans, and Leona Van Vaerenbergh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Pre-  dicting Age and Gender in Online Social Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 3rd  International Workshop on Search and Mining User-Generated Contents (Glas-  gow, Scotland, UK) (SMUC ’11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 37–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/2065023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='2065035  [52] Christine Pinney, Amifa Raj, Alex Hanna, and Michael D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Ekstrand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Much  Ado About Gender (CHIIR 2023) Codebook and Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='5281/  zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='7521838  [53] Yanru Qu, Bohui Fang, Weinan Zhang, Ruiming Tang, Minzhe Niu, Huifeng  Guo, Yong Yu, and Xiuqiang He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Product-Based Neural Networks for User  Response Prediction Over Multi-Field Categorical Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' ACM Transactions on  Information and System Security 37, 1 (Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018), 1–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/  3233770  [54] Amifa Raj and Michael D Ekstrand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Measuring Fairness in Ranked Results:  An Analytical and Empirical Comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 45th International  ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='. In Proceedings of the 43rd International ACM SIGIR Conference on  Research and Development in Information Retrieval (Virtual Event, China) (SIGIR  ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' 1979),  329–354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='  [59] Ohad Rozen, Joel Oren, and Ariel Raviv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3463024  [60] Joni Salminen, Bernard J Jansen, Jisun An, Soon-Gyo Jung, Lene Nielsen, and  Haewoon Kwak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3176391  [61] Joni Salminen, Soon-Gyo Jung, João M Santos, and Bernard J Jansen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' In Adjunct Publication of  the 27th Conference on User Modeling, Adaptation and Personalization (Larnaca,  Cyprus) (UMAP’19 Adjunct).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' No Way Out of the Binary: A Critical History of the Scientific  Production of Sex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='1145/3359246  [66] Morgan Klaus Scheuerman, Katta Spiel, Oliver L Haimson, Foad Hamidi, and  Stacy M Branham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='  [67] Morgan Klaus Scheuerman, Kandrea Wade, Caitlin Lustig, and Jed R Brubaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' How We’ve Taught Algorithms to See Identity: Constructing Race and  Gender in Image Databases for Facial Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Proceedings of the ACM on Human-  Computer Interaction 4, CSCW1 (May 2020), 1–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3392866  [68] Abdul-Saboor Sheikh, Romain Guigoures, Evgenii Koriagin, Yuen King Ho,  Reza Shirvany, Roland Vollgraf, and Urs Bergmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='09844  [69] Adir Solomon, Ariel Bar, Chen Yanai, Bracha Shapira, and Lior Rokach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Predict Demographic Information Using Word2vec on Spatial Trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  Proceedings of the 26th Conference on User Modeling, Adaptation and Personaliza-  tion (Singapore, Singapore) (UMAP ’18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery,  331–339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3209219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3209224  [70] Xuemeng Song, Xiang Wang, Liqiang Nie, Xiangnan He, Zhumin Chen, and Wei  Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' A Personal Privacy Preserving Framework: I Let You Know Who Can  See What.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In The 41st International ACM SIGIR Conference on Research & Develop-  ment in Information Retrieval (Ann Arbor, MI, USA) (SIGIR ’18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for  Computing Machinery, 295–304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3209978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3209995  [71] Maryam Tavakol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Fair Classification with Counterfactual Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In  Proceedings of the 43rd International ACM SIGIR Conference on Research and De-  velopment in Information Retrieval (Virtual Event, China) (SIGIR ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association  for Computing Machinery, 2073–2076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/3397271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3401291  [72] The GenIUSS Group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Best Practices for Asking Questions to Identify Transgen-  der and Other Gender Minority Respondents on Population-based Surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Williams  Institute, UCLA School of Law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  [73] Yuan Tian, Ke Zhou, Mounia Lalmas, Yiqun Liu, and Dan Pelleg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Cohort  Modeling Based App Category Usage Prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 28th ACM  Conference on User Modeling, Adaptation and Personalization (Genoa, Italy) (UMAP  ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 248–256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1145/  3340631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='3394849  [74] Jialu Wang, Yang Liu, and Xin Eric Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Are Gender-Neutral  Queries Really Gender-Neutral?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Mitigating Gender Bias in Image Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='05433 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='CV] http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='05433  [75] Laurel Westbrook and Aliya Saperstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' New Categories Are Not Enough:  Rethinking the Measurement of Sex and Gender in Social Surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Gender &  Society 29, 4 (2015), 534–560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='1177/0891243215584758  [76] Le Wu, Yonghui Yang, Kun Zhang, Richang Hong, Yanjie Fu, and Meng Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Joint Item Recommendation and Attribute Inference: An Adaptive Graph  Convolutional Network Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 43rd International ACM  SIGIR Conference on Research and Development in Information Retrieval (Virtual  Event, China) (SIGIR ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 679–688.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3401144  [77] Tilahun Yeshambel, Josiane Mothe, and Yaregal Assabie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Morphologically  Annotated Amharic Text Corpora.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' In Proceedings of the 44th International ACM  SIGIR Conference on Research and Development in Information Retrieval (Virtual  Event, Canada) (SIGIR ’21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Association for Computing Machinery, 2349–2355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='3463237  [78] Meike Zehlike, Tom Sühr, Ricardo Baeza-Yates, Francesco Bonchi, Carlos Castillo,  and Sara Hajian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content=' Fair Top-k Ranking with Multiple Protected Groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  Information processing & management 59, 1 (Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2022), 102707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+page_content='102707  [79] Xueying Zhan, Yaowei Wang, Yanghui Rao, and Qing Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' Learning from  Multi-annotator Data: A Noise-Aware Classification Framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' ACM Trans-  actions on Information and System Security 37, 2 (Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content=' 2019), 1–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
+page_content='  https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9E3T4oBgHgl3EQf5Quy/content/2301.04780v1.pdf'}
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+REVIEW OF METHODS FOR AUTOMATIC CEREBRAL
+MICROBLEEDS DETECTION
+A PREPRINT
+Maria Ferlin
+Gda´nsk University of Technology
+Gda´nsk, Poland
+maria.ferlin@pg.edu.pl
+Zuzanna Klawikowska
+Gda´nsk University of Technology
+Gda´nsk, Poland
+zuzanna.klawikowska@pg.edu.pl
+Michał Grochowski
+Gda´nsk University of Technology
+Gda´nsk, Poland
+michal.grochowski@pg.edu.pl
+Małgorzata Grzywi´nska
+Medical University of Gda´nsk
+Gda´nsk, Poland
+malgorzata.grzywinska@gumed.edu.pl
+Edyta Szurowska
+Medical University of Gda´nsk
+Gda´nsk, Poland
+eszurowska@gumed.edu.pl
+February 1, 2023
+ABSTRACT
+Cerebral microbleeds detection is an important and challenging task. With the gaining popularity
+of the MRI, the ability to detect cerebral microbleeds also raises. Unfortunately, for radiologists,
+it is a time-consuming and laborious procedure. For this reason, various solutions to automate
+this process have been proposed for several years, but none of them is currently used in medical
+practice. In this context, the need to systematize the existing knowledge and best practices has been
+recognized as a factor facilitating the imminent synthesis of a real CMBs detection system practically
+applicable in medicine. To the best of our knowledge, all available publications regarding automatic
+cerebral microbleeds detection have been gathered, described, and assessed in this paper in order to
+distinguish the current research state and provide a starting point for future studies.
+1
+Introduction
+Cerebral microbleeds (CMBs) are defined as small, homogeneous, hypointense foci well seen on T2*-weighted MRI
+sequences with the associated so-called ‘blooming effect’. They are collections of blood degradation products (mainly
+hemosiderin) that can remain in macrophages for years, following a microhemorrhage[119, 120, 121, 106]. The
+‘blooming effect’ takes place when the MRI overestimates the diameter of the microbleed [12]. CMBs may occur in
+every region of the brain and can be categorized relative to that area [160, 7, 69], (Fig. 1). They may appear due to
+a range of pathological processes in the cerebral vessels [121, 9, 8]. Around 5% of population have microbleeds and
+they are completely healthy [10, 106]. However, the increased number of CMBs in the patient’s brain may indicate the
+existence of some medical condition [7]. Additionally, they are sometimes accidentally found in association with other
+pathologies [164]. Undeniably, however, high prevalence of cerebral microbleeds is closely associated with cognitive
+disfunction [11].
+CMBs detection is a challenging task due to small size of the lesion compared to the whole image (Fig. 2). Moreover,
+there are many lesions that mimic the CMBs. The main CMB mimics include calcifications, flow voids in pial blood
+vessels, iron deposits, and deoxyhemoglobin [12]. Both calcium and iron deposits may appear as small foci of low
+signal intensity on a T2*-weighted MRI. Flow voids caught in the cross-sections of cortical sulci can be distinguished
+from CMBs by their sulcal location, equal visibility on T2-weighted SE and GRE sequences, and linear structure
+when examined over contiguous slices, particularly evident at smaller slice thickness. The presence of paramagnetic
+deoxyhemoglobin in cerebral venules produces its own blooming effect, which requires the rater to rely on their
+tubular structure for differentiating them from CMBs. Metastatic melanoma in the brain can appear hypointense on
+arXiv:2301.13549v1  [cs.CV]  31 Jan 2023
+
+Review of methods for automatic cerebral microbleeds detection
+T2*-weighted MRI and may mimic CMB. Other mimics, such as mineralization of the basal ganglia or diffuse axonal
+injury, for instance, can be excluded based on the appearance or clinical history.
+CMBs detection is very important considering proper diagnosis and treatment, as they may indicate some major and
+more complicated issues. From the medical perspective, the crucial information is the number of detected cerebral
+microbleeds [174, 113, 12, 148]. Another useful information is their location [161, 162, 7, 69, 163]. Therefore, there
+is no need to perform segmentation which is a complex computational algorithm, it is enough to detect them.
+With gaining popularity of the MRI as a good imaging tool, the ability to detect cerebral microbleeds also raises. Un-
+fortunately, for radiologists, it is a time-consuming and laborious process. Technology and automatic image processing
+can come to the rescue in this case.
+Different solutions have been proposed for last years. However, the problem is complex and there is no unification
+and consistency between the researches. According to our best knowledge, the results achieved so far are still not
+used in medical practice. In this context, the authors recognized the need to systematize the existing knowledge and
+best practices as a factor which will facilitate imminent synthesis of a real CMBs detection system, which would be
+practically applicable in medicine.
+The existing research results are in fact difficult to compare due to various, unavailable publicly datasets and the lack
+of system evaluation metrics. The guidelines included in this paper are expected to present new research in a more
+beneficial way. Probably, the prevalence of a few publicly available datasets will result in evaluation of new approaches
+on these datasets.
+Figure 1: Brain anatomy in the sagittal plane. In addition to the presented structures, the temporal lobe, the insula, and
+the external and internal capsules, which are not visible in this plane, are also important in the context of scales used
+to rate CMB. CMBs can be found in all structures indicated in the figure as well as in those mentioned above.
+1.1
+Review criteria
+The aim of this research was to gather all previous works and achievements in the field of cerebral microbleeds
+detection. Regarding the lack of order in existing research and comparison ability we decided to collate different
+approaches and methods, in order to distinguish the current research state and provide a starting point for future
+studies. It is noteworthy that the key word in this matter is automatic as a guide for a radiologist to detect microbleeds
+on the MRI existed well beyond [107, 109, 108, 106, 105, 104].
+Firstly, a comprehensive literature review regarding automatic cerebral microbleeds detection have been done. In order
+to do that, careful search was performed for all papers connected with this topic in Google Scholar, IEEE Xplore, and
+2
+
+parietal lobe
+gray matter
+corpus callosum
+cortex
+occipital lobe
+white matter
+frontal lobe
+basal ganglia
+thalumus
+cerebellum
+brain stemReview of methods for automatic cerebral microbleeds detection
+Figure 2: Example of CMB. Upper images present the same microbleed in three planes, while bottom ones present
+sequence of adjacent slices fragments, in which the microbleed is visible (marked by red frame). Images acquired
+using ImFusion software.
+Elsevier platforms, using key phrases: automatic cerebral microbleeds detection, automatic CMB detection, cerebral
+microbleeds detection.
+The next step was the search for related papers in the references of all gathered works. The literature review dates back
+to year 2011, in which, to the best of our knowledge, first papers about automatic CMB detection were published.
+The main information gathered from each paper referred to: database, pre-processing, methods used, proposed ap-
+proach with the best or the most significant results, conclusions, and challenges.
+For the majority of modern methods, the key issue is the availability of datasets, therefore we decided to collate the
+information about all datasets used in this type of research in Section 2, which also introduces the issues of MRI and
+CMB characteristics and CMB rating.
+To maintain clarity of the paper, descriptions of particular algorithms are given in Section 3, while the exact approach
+leveraging from those algorithms is presented in Table 3. The algorithms described in Section 3 are divided into
+two main groups referring to detection and verification of CMB candidates. Subsection 3.1 also presents different
+pre-processing algorithms that were used to prepare a dataset for training and testing. Eventually, all methods and
+algorithms that were used to solve this task are presented. It turned out during the reported research that the evaluation
+of results is a challenging problem due to the lack of a standard for the metrics used. It is not only problematic for
+existing approaches comparison, but also makes it impossible to assess a specific method itself. To address this, a
+range of metrics is presented in Subsection 3.4, along with their features and dependencies.
+Section 4 provides a comprehensive assessment of all the presented research, followed by conclusions and challenges,
+both gathered during literature review and emerging from this analysis.
+3
+
+MR: (0) - 2019.08.30 19:03:13
+5cm
+4#1 xoq 6upu
+A
+AL
+5cm
+.
+2cmReview of methods for automatic cerebral microbleeds detection
+2
+Data sources
+In order to understand the task of cerebral microbleeds detection it is essential to understand the magnetic resonance
+imaging, acquisition process and rating procedure. Therefore, we decided to introduce the process of MR images
+formation. Further, the relevant sequences and rating scales are described. Finally, we present datasets used for
+cerebral microbleeds detection.
+2.1
+Magnetic Resonance Imaging Sequences
+Among the types of brain imaging they are CT (computed tomography) and MRI (magnetic resonance imaging). This
+paper focuses on MRI because it is the most commonly used technique to study CMB. The main reason is the fact that
+the CT density of the hemorrhage in CMBs rapidly decreases over days as CMBs become indistinguishable with brain
+tissue after around 7–10 days [174]. Consequently, the sensitivity of CT in imaging CMBs is the highest within the
+first few days of their appearance. On MR images, CMBs remain visible much longer than on CT.
+MRI is the imaging technique in which each sequence is a combination of radiofrequency pulses and gradients. There
+are over a hundred different sequence types, the acronyms of which depend on the manufacturer. Regardless of the
+type of sequence, the goal is to obtain the signal of a particular tissue - contrast, as quickly as possible - speed, while
+limiting the artifacts and without altering the signal to noise ratio [122].
+Figure 3: Transverse brain plane. Sequences in first row [118]: T1W (a), T2W (b), FLAIR (c); in second row [117]:
+Magnitude (d), Phase (e), SWI (f).
+There are three essential components for any imaging sequence. The first is the radio frequency (RF) excitation pulse
+which is required for the phenomenon of magnetic resonance. The second are the gradients for spatial encoding
+whose arrangement will determine how the k-space is filled. The third component is signal reading, which combines
+echo types determining the type of contrast - varying influence of relaxation times: T1, T2 and T2*. Additionally,
+more sequence parameters, such as repetition time or flip angle, must be chosen to find a balance between contrast,
+resolution, and speed [147].
+There are three types of relaxation times: T1, T2, and T2* [123]. The term relaxation means that, once the RF pulse
+is turned off, the spins are relaxing back into their lowest energy state or to the equilibrium state, realigning with
+the axis of the magnetic field. T1 is called the longitudinal relaxation time, as it refers to the time needed for the
+spins to realign along the longitudinal (z)-axis. T2 is defined as the predicted time constant for the decay of transverse
+magnetization arising from natural interactions at the atomic or molecular level. However, in a real MR experiment, the
+transverse magnetization decays much faster than would be predicted by natural atomic and molecular mechanisms.
+This accelerated decay rate is denoted as T2*.
+There are two main sequence families, depending on the type of echo recorded. The first family comprises Spin
+Echo (SE) sequences, which have two essential parameters: TR and TE. They consist of a series of events: 90°pulse;
+180°rephasing pulse at half of echo time (TE) and signal reading at TE, repeated at each time interval TR (Repetition
+Time). During each repetition, the line of k-space is filled due to different phase encoding. The example of such se-
+quence is FLuid Attenuation Inversion Recovery (FLAIR). The second family includes Gradient Echo (GE) sequences,
+4
+
+a)
+b)
+c)
+(p
+OReview of methods for automatic cerebral microbleeds detection
+Figure 4: Overview of data processing steps in SWI.
+during which the flip angle (FA) is usually below 90°, which decreases the amount of magnetization tipped into the
+transverse plane. In this case, there is no 180°RF rephasing pulse. The example of this sequence is Susceptibility
+Weighted Imaging (SWI). Numerous variations have been developed within each of these families, mainly to increase
+the acquisition speed.
+A T1-weighted (T1W) sequence demonstrates differences in the T1 relaxation times of tissues. The T1-weighted
+image is consistent with the anatomy: gray matter is dark and white matter bright. Anatomical gray-white inversion is
+observed in T2-weighted (T2W) images, in which gray matter is bright and white matter dark. It highlights differences
+in the T2 relaxation time of tissues. Another sequence is FLAIR, which removes signal from the cerebrospinal fluid
+(CSF) in the resulting image. Brain tissue in the FLAIR image appears similar to that in the T2W image with gray
+matter brighter than white matter, but in this case, CSF is dark instead of bright. SWI is a 3D high-spatial-resolution
+fully velocity corrected gradient-echo MRI sequence which takes advantage of the effect of both phase and magnitude.
+Fig. 3 shows the described sequences and the data processing steps in SWI are shown in Fig. 4.
+Susceptibility weighted sequences are named differently depending on the MRI vendor [170]. For example, the term
+SWI is owned by Siemens, GE Healthcare offers a sequence called SWAN , and Philips Healthcare has proposed
+the name SWIp. Obtaining these sequences differs, due to licensing and patent issues [172]. The differences lie
+in the use of different ways of combining the sequences, e.g. SWI uses phase and magnitude, while SWAN uses
+a weighted sum of longer TEs, which preserves T2* dephasing effects, but also increases the signal-to-noise ratio
+[170, 171]. However, regardless of the vendor SWI-like sequences are most commonly used in CMB detection, as
+they have greater sensitivity to this lesion than other sequences [111, 39, 34, 40, 112, 113]. It is not only used in
+terms of automatic detection but also in everyday clinical practice. Another factor that improves the detectability of
+microbleeds is the strength of the magnetic field [114, 115, 116, 34].
+Clinical image data is typically stored in the DICOM format. For scientific analysis, the alternative format is NIFTY.
+2.2
+CMB rating
+Technology that automates clinicians’ work should be developed in accordance with clinical practice. It is important
+to know the ways of assessing a disease, so that the results provided by the proposed tools fit into these guidelines.
+Two ways used by clinicians to assess CMB are Brain Observer Microbleed Scale (BOMBS) [7] and Microbleed
+Anatomical Rating Scale (MARS) [69], proposed in 2009. The evaluation categories are presented in Table 1. Stan-
+dardized CMB rating scales provide a uniform assessment methodology and enable easy and reliable quantification
+and categorization of CMBs even when the scales are used by observers with different backgrounds or experience, and
+thus increase the reliability of the measurement.
+Measurement reliability refers to the consistency or repeatability of the measurement. Low reliability indicates large
+differences in measurement while retesting. It precludes reproduction or interpretation of the results, and finally makes
+5
+
+MAGNITUDE
+SWI
+mIP of SWI
+Minimum
+PHASE
+intensity
+projection
+Background
+removal, weighting
+mask generationReview of methods for automatic cerebral microbleeds detection
+Table 1: CMBs evaluation categories according to rating scales
+BOMBS
+MARS
+• certainty:
+1. certain,
+2. uncertain,
+• size:
+1. <5 mm,
+2. 5-10 mm,
+• side of brain:
+1. left,
+2. right,
+• location (Fig. 1):
+1. lobar:
+(a) cortex/gray–white junction,
+(b) subcortical white matter,
+2. deep:
+(a) basal ganglia,
+(b) internal and external capsules,
+(c) thalamus,
+3. posterior fossa:
+(a) brain stem,
+(b) cerebellum.
+• appearance of the lesion:
+1. definite,
+2. possible,
+• side of brain:
+1. left,
+2. right,
+• location (Fig. 1):
+1. lobar:
+(a) frontal,
+(b) parietal,
+(c) temporal,
+(d) occipital,
+(e) insula,
+2. deep:
+(a) basal ganglia,
+(b) internal capsule,
+(c) external capsule,
+(d) thalumus,
+(e) corpus callosum,
+(f) deep and
+periventricular
+white
+matter,
+3. infratentorial:
+(a) brain stem,
+(b) cerebellum.
+distinguishing between participants with and without specific medical conditions impossible due to significant mea-
+surement error. In clinical evaluation, a measurement error can be introduced by the observer. Therefore, determining
+observer (clinician) reliability is important for making full comparison of measurement reliability between studies.
+There are two ways of doing it – inter- and intra-observer agreement.
+Intra-observer agreement determines the degree of agreement between the two studies that use the same technique, in
+the same patient, obtained by the one observer [110]. Inter-observer agreement determines the degree of agreement
+between the two studies that use the same technique, in the same patient, obtained by the two observers [110].
+The reliable rating of CMBs presence, number, and location is the important factor for further diagnosis of various
+diseases. However, many research institutions use their own methods to rate CMBs. Although their reliability based
+on intra- and inter-observer agreement is reported, details of the methods used are usually not described [109].
+6
+
+Review of methods for automatic cerebral microbleeds detection
+Table 2: Comparison of dataset acquisition parameters used in the reviewed approaches.
+ref.
+# of
+subject
+/# of CMB
+RES [mm2]
+ST [mm]
+TR [ms]
+TE [ms]
+FA [°]
+BW
+[Hz/px]
+IMS
+[vox-
+els]
+FOV
+[ mm3\mm2\mm ]
+Sequences
+β [T]
+Rating
+Avail.
+[32]
+2 / 4
+0.35x0.35
+0.3
+20
+2.5/15
+-
+-
+-
+-
+T2*W
+7
+MARS
+on
+request
+[25]
+6 / 26
+0.5x1
+2
+57
+40
+20
+-
+512x320x48
+-
+Fully Flow-
+Compensated
+3 DGRE
+1.5
+[173]
+-
+[14,
+77, 23]
+10 / -
+0.5x0.5
+2
+-
+20
+15
+120
+364x448x48
+-
+SWI
+3
+MARS
+-
+[26,
+51]
+15 / 420
+0.5x0.5
+2
+56
+28
+20
+-
+u x u 40
+240
+T2*W
+3
+similar to
+BOMBS/
+MARS
+10
+subjects
+[33]
+18 / 54
+0.35x0.35 T2*W,
+0.66x0.66 T1W
+0.3 T2*W,
+0.7 T1W
+20 T2*W,
+7 T1W
+2.5/15 T2*W,
+3 T1W
+-
+-
+-
+-
+T2*W,
+T1W turbo
+field echo
+7
+MARS
+on
+request
+[75, 49],
+[46, 47, 48],
+[4, 53]
+20 / -
+0.5x0.5
+2
+28
+20
+15
+120
+364x448×48
+-
+SWI
+3
+MARS
+-
+[138]
+20 / -
+0.45x0.45
+2
+17
+24
+-
+-
+-
+-
+SWI
+3
+-
+-
+[42, 24],
+[18, 76]
+[43]
+[3]
+20 / 117,
+44 / 615,
+320 / 1149
+0.45x0.45
+2
+17
+24
+-
+-
+512x512x150
+230x230
+SWI
+3
+-,
+MARS,
+MARS
+20
+subjects
+[6]
+24 / >157
+1x1
+1
+T1WMP & T2W
+1.5 SWI
+1900
+T1W MPRAGE
+(T1WMP),
+3200 T2W,
+35 SWI
+2.93
+T1WMP,
+408 T2W,
+7.5/
+15/
+22.5/
+30
+SWI
+9
+T1WMP,
+120 T2W,
+15 SWI
+170
+T1WMP,
+750 T2W,
+200 SWI
+256x256x176
+T1WMP & T2W,
+256x192x96 SWI
+-
+T1WMP,
+T2W,
+SWI
+3
+Inspired
+by
+BOMBS
+on
+request
+[126]
+26 / -
+-
+3
+-
+-
+-
+-
+u x u x 40-
+60
+-
+SWI
+-
+-
+-
+[44]
+26 / 404
+0.45x0.45 SWI,
+1x1 T1W-MPRAGE
+(magnetization
+prepared
+rapid
+gradient
+echo)
+2 SWI,
+1 T1W-MPRAGE
+-
+25
+-
+-
+-
+-
+SWI,
+T1W-MPRAGE
+3
+-
+-
+[41]
+[28]
+[27]
+30 / 64,
+41 / 103,
+66 / 231
+0.93x0.93 SWI,
+1x1 T1W
+1.75 SWI,
+1.2 T1W
+27 SWI,
+2.3 T1W
+20 SWI,
+2.98 T1W
+20 SWI,
+9 T1W
+-
+-
+240x256 T1W,
+SWI, T1W
+3
+-,
+MARS,
+MARS
+on
+request
+[29,
+45]
+51 / 627
+0.98x0.98 SWI,
+1x1 T1 MP-RAGE
+(T1MPR)
+-
+27 SWI,
+2300 T1MPR
+20 SWI,
+2.98 T1MPR
+15 SWI,
+9 T1MPR
+120 SWI,
+240T1 MPR
+-
+-
+SWI,
+T1-MPRAGE
+3
+MARS
+-
+7
+
+Review of methods for automatic cerebral microbleeds detection
+Table 2: Continued: Datasets acquisition parameters comparison
+[19]
+58 / 1301
+-
+5
+T2F & T2WF,
+2 SWAN-W
+5727
+T2 FRFSE (T2F),
+77.3 SWAN-W,
+8400
+T2W FLAIR (T2WF)
+93 T2F,
+45 SWAN-W,
+145 T2WF
+15
+SWAN-W,
+145
+T2WF
+833
+T2F & T2WF,
+625
+SWAN-W
+512x512 x
+u
+240
+T2F,
+SWAN-W,
+T2WF
+3
+-
+-
+[2]
+72 / 64
+0.43×0.43
+T2*W SWI,
+0.43×0.43
+T2*W GRE
+1 T1W,
+2 T2*W SWI,
+1 T2*W GRE
+6.6 T1W,
+17 T2*W SWI,
+15 T2*W GRE
+3 T1W,
+24 T2*W SWI,
+22 T2*W GRE
+-
+-
+-
+256x200 T1W,
+244x197 T2*W SWI,
+220x181 T2*W GRE
+T1W,
+T2*W SWI,
+T2*W
+GRE
+3
+[12]
+on
+request
+[35]
+72 / 148
+0.96x0.96
+T2*W & FLAIR,
+1x1 T1W
+3 T2*W &
+FLAIR,
+1 T1W
+1653 T2*W,
+11000 FLAIR,
+7.9 T1W
+20 T2*W,
+125 FLAIR,
+4.5 T1W
+-
+-
+-
+-
+T2*W,
+FLAIR,
+T1W turbo
+field echo
+3
+MARS
+on
+request
+[1, 30],
+[18]
+72 / 188
+HR,
+107 / 572
+LR
+0.50×0.50
+HR,
+0.80x0.80
+LR
+2
+27 HR,
+40 LR
+20 HR,
+13.7 LR
+15
+120
+512x448x72 HR,
+288x252x72 LR
+256x224 HR,
+201×229 LR
+SWI,
+Phase,
+Magnitude
+3
+[12]
+no
+[17]
+73 / 2835
+0.5x0.5
+1 SWI,
+2
+3DSPGR
+40 SWI,
+50
+3DSPGR
+2.4/12/14.3/20.3
+SWI,
+16
+3DSPGR
+25
+-
+512x512 x
+u
+-
+4-echo
+3D TOF-SWI,
+3DSPGR
+(3D Spoiled
+Gradient
+Recalled)
+7
+computer-
+aided
+detection
+developed
+by [26]
+with rater
+-
+[73]
+74 / -
+0.938x0.938
+5
+6000
+T2W Fast Spin Echo
+(T2WFSE),
+300 T2*GRE
+105 T2WFSE,
+40 T2*GRE
+20
+T2*GRE
+-
+256x224x u
+T2WFSE
+240x180
+T2WFSE,
+T2* GRE
+1.5
+MARS
+on
+request
+[13]
+186 / 1716
+0.63x0.63
+2
+1050
+20
+21
+-
+-
+220x198
+3D
+Fast
+Field-Echo
+3
+-
+-
+[74]
+214 / 235
+0.93×0.93 SWI,
+1x1 T1W
+1.75 SWI,
+1.2 T1W
+27 SWI,
+2.3 T1W
+20 SWI,
+2.98 T1W
+20 SWI,
+9 T1W
+-
+u x u x 160
+T1W
+240x256 T1W
+SWI, T1W
+3
+MARS
+on
+request
+[5]
+220 / 1011
+0.45-0.53x
+0.57-1.05 1.5T,
+0.50-0.54x
+0.50-1.07 3T
+2-2.65 1.5T,
+2/2.3 3T
+49/50 1.5T,
+27-34 3T
+40 1.5T,
+17.5-20 3T
+15 1.5T,
+12/15 3T
+80 1.5T,
+100-425 3T
+512x
+304-448x
+56/60 1.5T,
+448-512x
+322-416x
+56/128 3T
+-
+-
+1.5/3
+-
+on
+request
+[21]
+237 / 631
+0.5x0.5
+1.6 T2*W,
+0.8 GRE PDW
+-
+-
+-
+-
+-
+-
+3D T2*W,
+GRE
+Proton-
+Density
+Weighted
+1.5
+-
+-
+[20]
+270 / >505
+0.9x0x8
+T2*-GRE,
+0.8x0.8
+SWI
+5 T2*-GRE,
+3 SWI
+504 T2*-GRE,
+27 SWI
+15 T*2-GRE,
+9.4/20 SWI
+-
+-
+640x640x28
+T2*-GRE,
+256x288x48 SWI
+-
+T2*-GRE,
+SWI
+-/3
+MARS
+on
+request
+[72]
+320 / 114
+SWI,
+179 / 760
+SVS
+0.45x0.45
+SWI
+2
+17 SWI,
+27/40 SVS
+24 SWI,
+20/14 SVS
+15
+SVS
+120 SVS
+512x512x150
+SWI
+230x230 SWI
+SWI
+3
+MARS
+SWI /
+[12]
+SVS
+-
+8
+
+Review of methods for automatic cerebral microbleeds detection
+Figure 5: Pipeline of a typical CMB detection approach.
+2.3
+Datasets
+Studies on the tools that automatically detect microbleeds can be divided into three categories based on the source of
+the data used. The first category includes researches that use data from specific, existing studies: [25, 2, 41, 28, 27, 21,
+78, 32, 33, 35, 5, 74, 34, 6, 20]. The second category refers to studies that collected data specifically to develop this
+tools: [1, 30, 26, 51, 17, 42, 43, 3, 80, 79, 24, 18, 14, 77, 23, 35, 19, 31, 76, 22, 75, 49, 73, 72, 46, 47, 48], whereas
+the third category contains studies that do not specify the sources of data used: [52, 45, 29, 13, 44, 53, 4, 50, 126,
+124, 125, 138, 137, 140, 139]. The researches focused on diagnosing several medical conditions: Alzheimer’s and
+elderly diseases (AD) [25, 2, 41, 28, 27, 21, 78, 35, 74], Cerebral Autosomal Dominant Arteriopathy with Subcortical
+Infarcts and Leukoencephalopathy (CADASIL) [52, 14, 77, 23, 75, 49, 53, 4, 50, 46, 47, 48, 124, 125, 139], Second
+Manifestation of Arterial Disease (SMART) [32, 33], Traumatic Brain Injury (TBI) [45, 29, 5, 44, 140], stroke [31, 5,
+73, 20], Intracerebral Haemorrhages (ICH) [34, 20], gliomas [26, 51, 17], hemodialysis cases [5], Cerebral Amyloid
+Angiopathy (CAA) [34], atherosclerosis [6], or did not distinguish any particular disease besides the appearance of
+CMBs [1, 30, 42, 43, 3, 80, 79, 24, 18, 19, 76, 22, 13, 72, 20, 126, 138, 137]. Datasets used in the first category of
+researches focused on AD [81, 82, 83, 36, 84, 85], SMART [37], TBI [86], stroke [86, 89], ICH [87, 90, 91], gliomas
+[70], hemodialysis cases [86], CAA [88], atherosclerosis [38], or CMBs [92].
+Clinicians rated the CMBs present in the images from these datasets according to the MARS scale, the BOMBS scale,
+or an unspecified standard. Details related to the number of patients, image acquisition parameters, types of sequences,
+strength of magnetic field and data availability are given in Table 2. The abbreviations used in the table stand for: RES
+– resolution, TR – repetition time, TE – echo time, FA – flip angle, BW – bandwidth, IMS – image matrix size, ST –
+slice thickness, FOV – field of view, u - unknown dimension.
+Datasets that were not included in the table due to insufficient information are [137, 140, 124, 125, 52, 139, 22, 78].
+They contained only information about, for example, the number of patients or the type of sequence.
+3
+Methodology
+A comprehensive analysis of the past works regarding cerebral microbleeds detection has led to the proposition of a
+generalized pipeline of such a system. The majority of works can be divided into three stages: Pre-processing, CMB
+Candidates Detection and CMB Candidates Verification. Therefore, we decided to describe the methodology having
+regard to such division. The overall idea is presented in Fig. 5. All the methods and algorithms available within each
+stage are firstly described as single transform, that can be applied. Their further synthesis into a complete approach
+along with the paper in which it was used are in Table 3.
+3.1
+Pre-processing
+Data pre-processing is an important step in system synthesis. Proper preparation of data has a significant impact on
+further system performance.
+It is important to understand that phrase raw data does not always mean that data were not pre-processed by MRI
+software. From the system’s perspective, raw data are those provided by the MRI. However, there is a variety of MRI
+9
+
+Stage 1
+Stage 2
+Stage 3
+CMB candidates
+Preprocessing
+CMB candidates
+Report
+detection
+verification
+Raw data
+三
+Bias field correction
+FRST
+Geometrical features
+performance report
+DICOM
+Normalization
+Intensity threshold
+Rodon Transform
+nameplate
+NIFTY
+Skull stripping
+CNN
+Region growing
+trustworthiness
+assessment
+etc.
+etc.
+etc.
+etc.Review of methods for automatic cerebral microbleeds detection
+device suppliers, who design an operating system of their own, which performs different operations on a particular
+scan before the image delivery. Therefore, it is crucial to know how the data has already been processed and what else
+can be improved to meet system needs.
+Below the most popular types of operations performed on raw data are presented and few examples illustrated in Fig.
+6. Firstly, there are operations for removing artifacts and unnecessary information.
+Bias field correction is the operation that reduces negative influence of the bias field, which is an undesired artifact
+in most MRI images, especially old ones. It can also be called intensity inhomogeneity correction. The most
+commonly known techniques include N3 Bias Correction [60] and its successor N4ITK/N4 [59], FSL FAST [65] or
+reconstruction Syngo MR B17 provided by the manufacturer. Nevertheless, there are also other methods for bias field
+correction [93, 16]. This operation was applied by [21, 28, 27, 44, 45, 46, 29, 5, 125, 6, 74, 20]. Skull stripping also
+known as brain extraction is an operation of removing skull and background from the image, leaving only the brain.
+There are plenty of algorithms for performing this task: Brain Extraction Tool (BET) [56], BrainSuite [57], and others
+[98, 97]. Brain extraction was applied in [32, 25, 21, 26, 28, 44, 45, 29, 24, 51, 17, 1, 30, 2, 13, 138, 20].
+Normalization is a typical operation of rescaling the pixel values into range (0,1) or (-1,1). This enables bias reduction
+in the next stages of system creation. It was applied by [32, 73, 25, 33, 35, 26, 41, 28, 27, 42, 43, 45, 5, 6, 18, 72].
+Standardization is an equally common operation as normalization and involves subtraction of mean value of pixels
+and division by the standard deviation of them. It was claimed to be used in [32, 33, 35, 18].
+Mask generation is a wide term as different types of masks might be generated. The most common is binary mask that
+might be generated using Statistical Parametric Mapping Toolbox [95] or morphological operations [100, 99]. Further,
+there are typically neurological masks such as cerebrovascular fluid (CSF) mask, gray-white matter (GWM) mask and
+white-matter (WM) mask. Masks were generated in [32, 73, 33, 35, 26, 41, 28, 27, 45, 29, 78, 17, 126, 23, 76, 2, 72].
+Further image generation involves using images provided by the MRI device to make a new image consisting more
+information. For instance, a SWI sequence is generated from the Magnitude and Phase sequences. These days, it
+is the standard sequence generated by the scanner. Further, the SWI data might be processed using [103] for phase
+enhancement, like in [44] Similarly, T2*-weighted images are nowadays provided by the MRI scanner, but in the past
+they had to be obtained from PD-weighted images using, for example, Elastix Tool [61]. It was performed for example
+in [21, 5, 17]. A QSM image can be generated using Morphology Enabled Dipol Inversion (MEDI) [64], like in [6].
+Slice merging can also be considered as a new image creation, which involves concatenation of adjacent slices to
+provide 3D information. Generally, MRI images are one-channel. It enables putting three adjacent slices into one
+image using RGB channels. The concatenation of different sequences of corresponding slices might be done as well.
+However, in this case it may be necessary to align the slices with each other, if there were different parameters of
+acquisition. This kind of operation was performed in [3, 1, 30, 18].
+Useful software to perform these operations is Neuroimaging Core [94] involving Advanced Normalization Tools
+(ANT), FMRIB Software Library (FSL) [55, 66, 67, 127] and Statistical Parametric Mapping (SPM). The last software
+is also implemented in [95] based on [96].
+There are also some typical transforms performed in standard image pre-processing. It is noteworthy that medical data
+are highly sensitive to any transformation, after which significant information can be accidentally lost.
+DICOM to JPG conversion is an excellent example of lossy data conversion technique, which might influence further
+processing stages. It was done by [19]. Although DICOM or NIFTY formats might be considered not developer–
+friendly, working on original image matrices should be a standard.
+Resize is a common operation of changing image size. It is usually performed to obtain equal sizes of all images, or
+to enlarge images so that the objects were more visible. It can also be forced by requirements of a method used in the
+CMB Candidates Detection stage. The images were resized in [25, 5, 2, 18].
+Padding is performing an artificial size change by addition of a black frame to obtain a desired image size without
+applying resize. It was utilized by [6, 18, 72].
+Image cut is a common operation performed to simplify the detection task. It involves image partitioning into smaller
+parts and then feeding them into the classifier. It might be performed using the sliding neighborhood processing (SNP)
+technique to produce smaller fragments of the original image. A lot of works utilized this method: [46, 22, 53, 48, 47,
+52, 139, 4, 14, 77, 23, 124, 125, 75, 49].
+Rotation is a simple operation of changing image orientation. However, it can be a loss operation, and therefore a
+rotation with original intensity should be considered, like in [20], for instance by using - fslreorient2std tool [127].
+10
+
+Review of methods for automatic cerebral microbleeds detection
+Figure 6: Example of pre-processing operations: a) sliding neighborhood processing [23], b) Canny edge detection
+[2], c) CSF mask [13] d) brain extraction using BrainSuite software.
+Inversion is the operation which consists of swapping intensity values in relation to the center of the intensity interval
+and it was performed by [27].
+Finally, there is data augmentation, which is not always considered as a pre-processing technique, but rather a
+regularization one. However, it is sometimes performed at this stage and consists of image transformations, therefore
+it is placed in this section. It enhances a dataset, especially in case of small amount of data by creating new, slightly
+modified, artificial images. There is a wide range of transformations, including those described above, along with blur,
+crop, etc. [135, 101, 102]. Augmentation was used in [140, 78, 124, 6, 13, 19, 18, 74, 138].
+3.2
+Algorithms for CMB candidates detection
+Over the years, a wide range of algorithms were used to detect cerebral microbleeds, starting from the simplest methods
+based on traditional image transformations, up to complicated deep learning models.
+3.2.1
+Classical methods
+In early works regarding CMBs detection the candidates were extracted using predetermined features such as: inten-
+sity threshold and area size [25, 21, 42, 43, 24]. In the SWI sequence CMBs occur as low-intensity spheres, therefore
+applying a proper intensity threshold allows for binary mask generation. Sometimes the authors also applied morpho-
+logical operations such as filtering, hole filling, etc. [73, 24, 138]. However, this kind of operations were used at all
+the stages described in this paper, as they were also useful for CMB candidates verification. Next, the detecting proce-
+dures evolved to include more complicated voxel features, such as: eigenvalues in [20] – scalars associated with the
+given linear transformation, line detection in [41] – defining the line where edge points are located, Gaussian filter
+in [20] and Laplacian of Gaussian operator in[28, 27, 20], which highlight the rapid change of the image intensity,
+Hough transform in [2] that enables shape detection by finding objects - local maxima, Canny filter in [2] which
+enables edge detection watershed transform in [137] - transforming images to grayscale topographic like map, and
+distinguishing objects on the basis of its intensity value or Frangi filters in [20] - a dedicated filter enabling vessel
+distinction, or 3D gradient co-occurrence matrix (3D GCM) in [72], which indicates the differences between intensity
+of two adjacent pixels.
+Simultaneously, the researchers began to use the Radial Symmetry Transform (RST), and its successor Fast Radial
+Symmetry Transform (FRST) [54]. This algorithm deserves special attention since it is successfully used to this
+day [32, 33, 35, 26, 51, 5, 17, 20]. In this transform, a gradient of the image is computed, then the orientation and
+magnitude of each pixel is established. Next, using the above values, points of interest can be selected according to the
+given formula. This algorithm was later developed so that it could be used in 3D space. However, despite its common
+use, when applied to candidates detection, FRST generates a lot of false positives, which forces introducing the third
+stage to the whole detection procedure.
+11
+
+a)
+b)
+C
+dReview of methods for automatic cerebral microbleeds detection
+Another algorithm used in the CMB Candidates Detection stage by [44] was the region growing that inspects the
+homogeneity of the considered pixel - or voxel in case of 3D [165].
+3.2.2
+Neural networks-based methods
+Then, with the development of neural networks (NN), algorithms based on these networks gained more attention.
+Generally, two approaches for neural networks usage may be distinguished: custom or general purpose pretrained
+neural network In the first case, in the domain of CMBs detection various approaches were used, such as: simple
+artificial neural networks (ANN) [155] used in [48, 74], which is basically a sum of inputs multiplied by weights
+assigned in the training process, back-propagation neural networks (BPNN) [166] utilized in [139] that are ANNs
+extended with the information about the error, sparse auto-encoder (SAE) [167] used in [46, 47] that is a neural
+network consisted of encoder and decoder with the additional sparsity penalty algorithm.
+The Random Forest algorithm [68] was used as well in [45, 29]. It is a black-box algorithm that consists of an
+ensemble of classifiers that predict an output value based on a part of a dataset and then these predictions are averaged
+into one.
+Finally, there are convolutional neural networks (CNN) [168], which are the most popular solution [22, 53, 78, 77,
+23, 124, 75, 49, 72].
+Basically, CNN consists of a number of feed-forward convolutional layers, where the features are extracted by perform-
+ing a convolution with predefined filters on every image and then further modified during training. Each convolution
+layer is followed by a non-linear activation function. Consecutive convolution layers are interspersed by pooling layers
+that extract the most important features. Then, mostly, there is a fully connected layer or other classifier that assigns a
+predicted class based on the previously extracted features. An interesting approach is replacement of a fully-connected
+layer by Extreme Learning Machine [128], which is much more efficient [49].
+In the second approach, one takes advantage of a deep neural network architecture that has already been trained
+on a vast dataset – transfer-learning – often very different from terminal one and just adjusts it to the considered
+problem. These networks usually consist of millions of parameters and are hard to train on the CPU due to hardware
+limitations. Additionally, it is a good method for dealing with small dataset problem. The transfer-learning idea is
+to use a pre-trained network that has already learned some image features and fine-tune it on the particular dataset.
+Several networks were used for this purpose, including: AlexNet [131] in [126], ResNet50 [15] in [14], Faster-RCNN
+[129] in [18], VGG [132] in [125], U-Net [63] in [6], YOLOv2 [130] in [1, 30], DenseNet 201 [133] in [4] or SSD
+[62] in [19] with the modification of feature enhancement. Sometimes, especially in case of SNP algorithm usage
+the detection task was substituted by classification of small fragments of image using either CNN or ResNet50 for
+instance in [14, 77]. Considering the main aim of this paper, the description of each network is omitted, as they are
+explained in detail in the mentioned papers. Nevertheless, the reader is strongly encouraged to get familiar with these
+architectures.
+Relatively new and still not fully explored architectures are 3D convolutional neural networks (3D CNN). The idea
+is the same as in 2D CNNs, but instead of performing convolution on 2D matrices, it is performed on 3D patches.
+They were applied in [3, 140].
+3.3
+Algorithms for CMB candidates verification
+Due to the nature of the considered problem, most of the presented approaches involved the CMB Candidates Verifi-
+cation stage. In spite of this, some solutions still have not managed to acquire satisfying quality.
+In some cases, the process of false positive candidates elimination was performed manually by a radiologist [32, 25,
+33, 35, 51, 17, 2]. Although this kind of approach significantly reduced the time needed for one scan rating, it is a
+semi-automated one.
+A large part of the research involved at this stage establishing a batch of predefined features of CMB : from simple
+ones as intensity or size, to very complicated parameters of a single voxel, calculated in 2D or 3D spaces. There were
+also other methods for defining the feature vectors, for instance 2D CNN in [42, 138], 3D ISA network [152] in [43],
+3D Radon Transform [153] in [28, 27] or feed-forward feature selection (FFFS) [154] in [21].
+In some cases, thresholds of geometric features were set, and on this ground the classification was performed [26, 44,
+70, 2, 20].
+In others, these features together with the previously prepared fragments of images were passed to the classifier. A
+lot of classifiers have already been tested: Supported Vector Machine (SVM) [58] in [25, 42, 43, 24], linear criterion
+12
+
+Review of methods for automatic cerebral microbleeds detection
+classifier (LDC) [134], quadratic discriminant classifier (QDC) [151], Parzen classifier [150] in [21] and Random
+Forrest Classifier (RFC) [68] in [28, 27].
+A common approach at this point was also using a previously generated CSF mask to distinguish a real CMB from
+vessels, and a WM mask to include the information about the location of potential microbleed [26, 2, 13].
+Another approach utilized the advantage of a 3D CNN. It was usually performed for 3D information inclusion, result-
+ing with FP reduction, after the 2D algorithm used in the Candidates detection stage [169] [3, 5, 17, 1, 30].
+Some works present also usage of region growing algorithm for CMB verfication [26, 29, 70].
+There was also an algorithm investigating the overlap between predictions from adjacent slices [18]. It not only enabled
+removal of false positive predictions that were in fact a ground truth, although labeled in the adjacent slice, but also
+helped finding a real CMB that was detected in the adjacent slice in spite of the previous false negative prediction.
+3.4
+System output and evaluation
+To comprehensively validate the quality and robustness of the system, one should take advantage of a number of
+commonly accepted metrics that provide complementary insight into various aspects of system performance.
+A common oversight is to not include metrics that are complementary and provide a view of the system as a whole,
+not just a part of it. For instance, the sensitivity metric is useless alone, as it can be artificially inflated. It is necessary
+to provide the precision or F1 score value to properly interpret the sensitivity. In addition, the lack of a uniform way
+of result evaluation makes it impossible to compare approaches and effectively assess their usefulness.
+The evaluation should be performed on a separate dataset or at least separate subjects, using, for instance, cross-
+validation to avoid randomness.
+There are different metrics regarding the type of solved problem. For classification evaluation, the most popular
+metrics are accuracy (1), precision (4), sensitivity/recall (2), and F1 score (5) that combines precision and sensitivity.
+In the case of detection and segmentation, more detailed metrics are required as not only a proper class is important,
+but also the overlapped area of ground truth label and prediction. In that case, the average precision (7) metric is used,
+and it is calculated for different values of IoU (6).
+The CMBs detection task is known to produce large number of false positive predictions. Therefore two additional
+metrics were provided particularly for this problem, namely it is FPavg (8) and FPcmb (9).
+The mentioned metrics are calculated as follows:
+accuracy =
+TP + TN
+TP + TN + FP + FN
+(1)
+sensitivity =
+TP
+TP + FN
+(2)
+specificity =
+TN
+TN + FP
+(3)
+precision =
+TP
+TP + FP
+(4)
+F1 score = 2 × sensitivity × precision
+sensitivity + precision
+(5)
+IoU = Overlaparea
+Unionarea
+(6)
+AP =
+� 1
+0
+p(r) dr
+(7)
+FPavg = FP
+n
+(8)
+FPcmb = FP
+m
+(9)
+where:
+13
+
+Review of methods for automatic cerebral microbleeds detection
+• TP—true positive – the number of actual CMBs detected;
+• FP—false positive – the number of predicted CMBs that were not marked as CMB in ground truth;
+• FN—false negative – the number of actual CMBs not detected;
+• IoU—intersection over union;
+• r—recall (sensitivity);
+• p(r)—precision as function of recall;
+• n— number of subjects (patients) in the test set;
+• m— number of CMBs in the test set.
+Accuracy (ACC) (1) shows how the system deals with the classification in general. A high score means that almost all
+labels have been properly assigned.
+Sensitivity/recall (2), also known as true positive rate (TPR), shows how the system deals with the ground truth
+detection or classification. A high score means that almost all ground-true samples have been determined.
+Specificity, also known as true negative rate (TNR) (3), discloses the system ability to recognize the negative class.
+Precision (4), or positive predictive value (PPV), informs whether the prediction matches ground truth. A high score
+means that the system generates a small number of false positives.
+F1 score (5) helps to check whether there is a balance between sensitivity and precision.
+IoU (6) stands for Intersection over Union and shows the common area between prediction and ground truth. It is
+actually a special case of geometrically oriented Jaccard Index [71]. The average precision (7) AP@0.5 represents
+the area under the precision-recall curve with IoU of 0.5 and it is used in detection and segmentation. There is also
+an AUC - area under curve - metric. In case of classification it refers to the ROC curve - sensitivity as a function of
+1-specificity.
+FPavg (8) shows the average number of false positive predictions per subject, while FPcmb (9) is the number of false
+positive predictions per one ground truth sample. For example, when we have one subject with 5 ground truth CMBs
+and 1 false positive prediction. The FPavg will equal 1 and FPcmb will equal 0.2.
+14
+
+Review of methods for automatic cerebral microbleeds detection
+Table 3: Comparison of existing approaches 1 The most promising ones are marked with bold.
+Reference
+Pre-processing
+First stage
+Second stage
+TPR
+PPV
+F1
+FPavg
+FP/CMB
+TNR
+ACC
+Kuijf et al.,
+SPM8, BET,
+3D RST
+manual
+-
+-
+-
+5*
+-
+-
+-
+2011, [32]
+normalization,
+inspection
+standardization
+Seghier et al.,
+SPM8,
+CSF, GWM, CMBs,
+morphological
+Authors did not provide any metric, only the table
+2011, [73]
+normalization
+skull scalp,
+operations
+of results for each case.
+background img
+(2 iterations)
+Barnes et al.,
+brain extraction,
+intensity histogram
+SVM, manual
+81.7
+-
+-
+107.5*
+5.4*
+100
+-
+2011, [25]
+resize,
+threshold
+review
+normalization
+Ghafaryasl et al.,
+N3, Elastix,
+intensity and
+FFFS →LDC,
+90.9
+-
+-
+4.1
+1.8*
+-
+-
+2012, [21]
+BET
+area threshold
+QDC, SVC,
+Parzen
+Kuijf et al.,
+SPM8,
+3D RST
+manual
+71.2
+-
+-
+17.17
+4.68*
+-
+-
+2012, [33]
+normalization,
+inspection
+standardization
+Kuijf et al.,
+SPM8,
+3D RST
+manual
+87
+-
+-
+45
+-
+-
+-
+2013, [35]
+normalization,
+inspection
+standardization
+Bian et al.,
+BET, ARC, mIP,
+FRST
+vessel mask
+86.5
+-
+-
+44.9
+1.5*
+-
+-
+2013, [26]
+normalization
+screening,
+3D region
+growing,
+geometric
+features
+Fazlollahi et al.,
+CSF,
+multi-scale 1D
+center
+100
+-
+-
+158.93*
+-
+99.9
+-
+2013, [41]
+invertion,
+line detection
+detection →
+normalization,
+Hessian
+Gaussian blur
+matrix
+Fazlollahi et al.,
+N4, CSF,
+multi-scale
+3D Rodon
+92.04
+-
+-
+16.84
+6.7*
+-
+-
+2014, [28]
+skull-stripping,
+Laplacian
+Transform →
+normalization,
+of Gaussian
+Hessian
+equalization,
+matrix,
+anisotropic
+RFC
+diffusion
+Fazlollahi et al.,
+N4, CSF,
+Laplacian
+3D Rodon
+87
+-
+-
+27.1
+-
+-
+-
+2015, [27]
+inversion,
+of Gaussian
+Transform →
+normalization,
+Hessian
+equalization,
+matrix,
+anisotropic
+RFC
+15
+
+Review of methods for automatic cerebral microbleeds detection
+diffusion
+Roy et al.,
+N4,
+3D region
+RST,
+85.7
+-
+-
+-
+-
+99.5
+-
+2015, [44]
+skull stripping,
+growing
+WM mask,
+phase
+geometric
+enhancement
+features
+Chen et al.,
+normalization
+intensity
+CNN,
+89.13
+56.16
+68.91
+6.4
+-
+-
+-
+2015, [42]
+threshold
+3D concatenation,
+SVM
+Dou et al.,
+normalization
+intensity
+ISA
+89.44
+-
+-
+7.7
+0.9
+-
+-
+2015, [43]
+threshold
+SVM
+van den
+FSL FLIRT,
+voxel based
+-
+90
+-
+-
+-
+1.3
+-
+-
+Heuvel et al.,
+FSL FAST,
+features →
+2015, [45]
+N3, SPM12b,
+RFC
+normalization
+Dou et al.,
+slices
+hierarchical
+3D CNN
+93.16
+44.31
+60.06
+2.74
+-
+-
+2016, [3]
+merging
+3D CNN
+Zhang et al.,
+reconstruction
+SAE
+-
+93.20
+-
+-
+-
+-
+93.25
+93.22
+2016, [46]
+Syngo MR B17,
+SNP
+van den
+FSL FLIRT,
+voxel based
+object
+93
+-
+-
+25.9
+0.29
+-
+-
+Heuvel et al.,
+FSL FAST,
+features →
+classifier,
+2016, [29]
+N3, SPM12b
+RFC
+growing-based
+algorithm
+Lu et al.,
+square
+CNN
+-
+97.29
+-
+-
+-
+-
+92.23
+96.05
+2017, [22]
+window size
+Wang et al.,
+SNP,
+CNN+RAP
+-
+96.94
+-
+-
+-
+-
+97.18
+97.18
+2017, [53]
+discard
+borders,
+cost ratio
+Tajudin et al.,
+-
+watershed
+-
+Authors provided only mean square error MSE = 0.089 and peak
+2017, [137]
+transform,
+signal to noise ratio PSNR = 34.5221
+active contour
+(Chan-Vese)
+Standvoss et al.,
+augmentation,
+3D CNN,
+-
+87
+-
+-
+16.75
+2.5
+-
+-
+2018, [140]
+selective
+connected
+sampling
+component
+analysis
+Zhang et al.,
+SNP,
+ANN
+-
+93.05
+-
+-
+-
+-
+93.06
+93.06
+2018, [47]
+discard
+borders,
+cost ratio
+Zhang et al.,
+SNP,
+SAE-DNN
+-
+95.13
+-
+-
+-
+-
+93.33
+94.23
+16
+
+Review of methods for automatic cerebral microbleeds detection
+2018, [48]
+discard
+borders
+Ateeq et al.,
+BrainSuite
+intensity
+SVM, QDA,
+93.7
+-
+-
+56
+5.3
+-
+-
+2018, [24]
+threshold,
+ensemble
+filtering,
+classifier
+hole filling
+Morrison et al.,
+BET
+FRST
+region
+86.7
+-
+-
+44.9
+1.5*
+-
+-
+2018, [51]
+growing,
+geometric
+features,
+manual
+validation
+Bao et al.,
+SNP
+Bayesian
+-
+74.53
+-
+-
+-
+-
+74.51
+74.52
+2018, [52]
+classifier
+Tao et al.,
+SNP
+GA-BPNN
+-
+72.90
+-
+-
+-
+-
+72.89
+72.90
+2018, [139]
+Gunter et al.,
+intensity
+CNN
+-
+Authors provided only AUC = 98.5
+2018, [78]
+threshold,
+image cut,
+data
+augmentation
+Liu et al.,
+N4,
+3D FRST
+3D CNN
+95.80
+70.90
+81.49*
+1.6
+0.39
+-
+-
+2019, [5]
+SWI generation,
+resize,
+normalization
+Chen et al.,
+ARC, BET,
+FRST
+manual
+94.69
+71.98
+81.79
+11.58
+-
+-
+-
+2019, [17]
+SWI generation,
+validation,
+negative
+3D ResNet
+phase mask
+Wang et al.,
+sliding
+Dense-Net 201
+-
+97.78
+97.65
+-
+-
+-
+97.64
+97.71
+2019, [4]
+window
+Hong et al.,
+SNP
+ResNet50
+-
+95.71
+-
+-
+-
+-
+99.21
+97.46
+2019, [14]
+Hong et al.,
+SNP
+CNN
+-
+98.87
+-
+-
+-
+-
+96.49
+97.68
+2019, [77]
+Sa-ngiem et al.,
+intensity
+AlexNet,
+-
+-
+-
+-
+-
+-
+-
+95.45
+2019, [126]
+enhancement,
+brain area
+binarization,
+extraction
+morphological
+operations,
+geometrical
+features
+17
+
+Review of methods for automatic cerebral microbleeds detection
+Hong et al.,
+SNP, brain area
+CNN
+-
+99.74
+-
+-
+-
+-
+96.89
+98.32
+2020, [23]
+enhancement
+Doke et al.,
+sliding
+CNN
+-
+98.97
+99.66
+-
+-
+-
+98.14
+98.54
+2020, [124]
+window,
+augmentation
+Liu et al.,
+binarization.
+Fourier
+-
+85.2
+3.2
+-
+69.5
+-
+-
+-
+2020, [76]
+noise
+descriptor
+reduction
+Lu et al.,
+reconstruction
+VGG-ELM-BAC
+-
+93.08
+-
+-
+-
+-
+87.12
+90.00
+2020, [125]
+Syngo MR B17,
+SNP
+Al-masni et al.,
+BET,
+YOLOv2
+3D-CNN
+94.32
+61.94
+74.78
+1.42
+-
+-
+-
+2020, [30, 1]
+slices merging
+Rashid et al.,
+N4,
+U-Net
+-
+84
+59
+-
+-
+-
+-
+-
+2020, [6]
+QSM generation,
+padding,
+normalization,
+augmentation
+Chesebro et al.,
+BET,
+Sobel
+CSF filtering,
+95.00
+11.00
+19.72
+9.7
+-
+-
+-
+2021, [2]
+CSF mask,
+filter,
+3D geometric
+resize
+Hough
+filtering,
+transform
+manual
+validation
+Myung et al.,
+BET
+YOLO
+CSF
+66.90
+79.75
+72.76
+2.15
+-
+-
+-
+2021, [13]
+augmentation
+filtering
+Li et al.,
+ANTs,
+SSD + FE
+-
+90
+79.7
+84.54*
+-
+0.23
+-
+-
+2021, [19]
+JPG conversion,
+augmentation
+Ferlin et al.,
+padding,
+Faster RCNN
+overlap
+92.62
+89.74
+90.84
+0.24
+-
+-
+-
+2021, [18]
+resize,
+between
+normalization,
+slices
+standardization,
+slices merging,
+annotations
+modification
+augmentation
+Lu et al.,
+SNP
+CNN+ELM+BA
+-
+92.93
+-
+-
+-
+-
+83.35
+88.56
+2021, [49]
+Lu et al.,
+SNP
+CNN+EN
+-
+98.27
+-
+-
+-
+-
+98.93
+98.60
+2021, [75]
+Momeni et al.,
+N4,
+ANN
+-
+18.6
+9.2
+-
+3.6
+-
+99.4
+96.8
+18
+
+Review of methods for automatic cerebral microbleeds detection
+2021, [74]
+augmentation,
+synthetic
+CMBs
+generation
+Afzal et al.,
+BrainSuite,
+K-means
+Alex-Net
+97.26
+-
+-
+-
+-
+96.5
+96.21
+2022, [138]
+augmentation
+clustering,
+geometrical
+features
+Stanley et al.,
+resize,
+1D CNN+LSTM
+-
+98.76
+-
+98.78
+-
+-
+97.21
+98.24
+2022, [72]
+contrast
+stretching,
+normalization,
+Gaussian Filter,
+histogram
+equalization,
+morphological
+operations,
+Sharr gradient,
+3D GCM
+Sundersan et al.,
+fslreorient2std,
+Frangi filters,
+geometric
+91
+-
+-
+-
+-
+81
+86
+2022, [20]
+FSL FAST,
+FRST, intensity
+features
+BET
+transformations,
+level
+eigenvalues,
+threshold
+Gaussian filter,
+Laplacian
+of Gaussian
+1Data marked with * were not provided in original paper. Instead, they were calculated either by us or the Authors of other papers listed in Table 3, based on data provided in the
+original paper.
+19
+
+Review of methods for automatic cerebral microbleeds detection
+3.5
+Comparison of existing approaches
+Table 3 presents, in chronological order, multiple approaches regarding cerebral microbleed detection that had place in
+recent years. It can be observed that firstly, the prevailing solutions were those based on traditional image processing
+techniques and only later the proposals based on machine learning algorithms have taken the lead. It can be seen, that
+they achieved considerably higher performance, both in terms of sensitivity and low false positive generation. There-
+fore, it can be assumed that this latter path is more promising regarding practically applicable solutions. Alternatively,
+a combination of traditional and ML methods might be considered.
+Regarding the pre-processing stage, there are several operations, such as bias field correction, skull stripping and
+normalization, that should be done before providing data into the system. Other transforms may also be used in
+particular cases, but they are not essential.
+An important issue is related with selecting the type of solved problem: whether it should be classification, detection,
+or segmentation. A large part of solutions is based on cutting images into smaller fragments and their further classifi-
+cation. These approaches are reported to have significantly better ability to distinguish CMB from its mimic. On the
+other hand, in the case of detection, a lot of false positive predictions are generated, which often forces introducing the
+second stage, namely false positive reduction or predictions verification, as high false positive generation is the main
+problem in CMBs detection. Another challenge that can be overcome by using classification instead of detection is
+the size of the lesion. CMBs are small objects, which makes them difficult to find in the original image.
+No significant improvement can be seen for 3D CNN over 2D CNN. Probably, a larger training dataset could enable
+taking benefit from the 3D CNN structure and consequently achieve better results. For now, however, choosing this
+type of solution is discouraging, due to higher computation cost.
+Moreover, it is clearly visible, that the reported research often lack in some metrics. Even if we accept that mentioning
+all of indicators is not necessary, it is crucial to provide a proper evaluation.
+We would like to emphasize that in our opinion, based on the gathered data, it is difficult to state which approach is
+the best and it is still the area that requires development. However, we can draw attention to some most promising
+solutions: in case of classification [72, 4] and [75] with the best ACC=98.60%; while in case of detection [19] and [18]
+with F1=90.84%. The mentioned research distinguish also in terms of balanced results - similar values of all metrics,
+which is an advantage in comparison to for instance [1, 30, 2] that report higher sensitivity, however suffer from a high
+false positive predictions generation - low precision.
+Although [124, 23] also report high accuracy, the datasets used by them were small. Results reported in [72, 18, 19]
+were performed on relatively big, but diverse datasets, therefore are hard to compare. From mentioned proposals only
+[4] and [75] can be compared, as they used the same, but small dataset.
+Nevertheless, the above careful and comprehensive analysis provides an opportunity to formulate some conclusions,
+outline best practices, and point out the key elements of a reliable automatic cerebral microbleeds detection system.
+4
+Discussion
+In this section we discuss the most important aspects for automatic CMBs detection system.
+As previously mentioned, a base for any automatic system, especially machine learning model, is the data. Although
+traditional image processing methods do not require large amount of data for training, just for validation and testing
+purposes, it is still essential for proper system evaluation.
+In Section 2 a range of datasets is listed which were used in all reported approaches. These datasets differ not only in
+terms of acquisition parameters, but also by the origin and medical history of patients. This kind of diversity makes
+any comparison of newly proposed approaches almost impossible. Moreover, some datasets have extremely small
+number of subjects [25, 32]. In that case, the tested subset is not representative enough. The system trained on such
+a narrowed dataset will reveal low generalization ability [29]. Therefore, a big, diversified dataset is needed and
+advanced regularization techniques should be applied [149] to prevent over-fitting.
+An interesting approach to overcome the data shortage problem was proposed by Momeni et al. [74]. It consisted of
+synthetic microbleeds generation based on previously extracted CMB features. Another way to produce huge amounts
+of synthesized data are Generative Adversarial Networks (GANs) [141]. They are able to create new images based
+on the features automatically extracted from the existing, real dataset. However, again, it is a method that requires
+relatively large dataset at the beginning. Despite the risk of biased data generation, both approaches seem promising
+for extending datasets, next to other augmentation methods.
+20
+
+Review of methods for automatic cerebral microbleeds detection
+A good practice regarding a general system evaluation is using a completely unrelated dataset for testing to ensure that
+the obtained results are impartial like in [18, 74]. The term unrelated dataset means the data acquired from a different
+MRI machine, from subjects of different origin and medical history, and ranked by another rater. Examinations
+performed on various MRI machines may differ in parameters. It is important to synthesize system resistant to features
+that do not have a direct impact on prediction. Usage of various datasets ensures insight into the model’s generalization
+ability. This, however, is an ideal situation, not always achievable in practice.
+There are also methods such as k-fold validation that may enable better evaluation within the same dataset. It is
+recommended especially during system development as depending on chosen training, validation and testing sets, the
+obtained results may differ [1, 30, 18]. Another idea is preparation of a system nameplate with detailed description of
+system properties and target data type and it should point out operating conditions of the system and its limitations.
+The unavailability of the used datasets is another limitation in terms of approach comparison. Although there are
+many legal restrictions regarding medical data sharing, establishing a benchmark dataset would significantly trigger
+the development in this domain [146], similarly as it was in case of brain glioma segmentation [156] or determining
+skeletal age [158, 157].
+Another aspect is the pre-processing stage of system synthesis. Subjecting images to any transformations should be
+well–thought and justified. Considering the risk of valuable data loss, precautions should be taken to prevent that.
+A common method of pre-processing is bias field correction as it enables restoring some important information. Using
+dedicated tools for skull stripping seems to be a better approach than simply removing part of the image just as
+in [47, 48, 53]. Although unintentionally, the image passed to the system may still be deformed or partial. Any
+operations that modify the size of the image, should be performed without content loss just as in [20].
+When it comes to system designing, there are several issues that should be considered. Firstly, the MRI data is given in
+the three-dimensional space. Regardless the used algorithms, at some stage it is inevitable to use the information from
+the third dimension. Especially, when detecting cerebral microbleeds is concerned, that kind of data is very important,
+as it enables distinguishing the CMBs from their most common mimics - vessels [26, 28, 42, 3, 5, 17, 1, 2, 18]. While
+vessels can be distinguished based on 3D information, the other CMB mimic - calcification looks similar also in the
+3D space considering its shape. In such case, other MRI sequences, except SWI, may be helpful [1].
+In the majority of reported research, the solution process is divided into three stages: Pre-processing, CMB Candidates
+Detection, and CMB Candidates Verification (Table 3). This approach is caused by similarities between CMBs and
+their mimics, with consequent high production of false positive candidates. All this compels the use of CMB Candi-
+dates verification stage to eliminate FP candidates. It may extend the computation time, but it is necessary to obtain
+satisfying results. Still, keeping the balance between accuracy and efficiency is important, particularly when real-time
+usage is concerned.
+The next, worth considering issue is the nature of cerebral microbleeds. They are small hemorrhages, which are
+sometimes difficult to notice even for an experienced radiologist. Therefore, the system to be designed should be
+sensitive to small objects. For this purpose, automatic systems may turn out even better, as they are able to consider
+the information that is not visible for human eye. It is also important to note that more accurate and sensitive MRI
+machines with properly adjusted parameters increase the chance for finding all microbleeds [34].
+Another problem is related to the possibility of missing some CMBs by an experienced rater. In any research regarding
+detection a ground truth has to be established. However, this is extremely difficult, as the rater agreement may be at
+a relatively low level, for instance - κ = 0.68 [73]. To reduce this problem, preliminary rating should be performed
+by as many raters as possible. Additionally, verification of system results may be helpful, as some missing CMBs
+may be detected by the system and should not be treated as false positive [74]. On the other hand, the radiologist has
+ability to look at the potential CMB from different perspectives and consult it with others, whereas the system does
+not. Therefore, providing additional information about gender, age, injury, angiography scans, etc. might also turn out
+beneficial [35].
+When designing such a system from the clinical application point of view, certain practical aspects must also be
+taken into account. It is important to remember about the end-user’s perspective. In this context, the form of results
+presentation should be designed considering user experience.
+Obviously, the indication by a bounding-box or circle should be provided, but other useful information such as the
+confidence score of the prediction could also be included. This value is rather provided by the machine-learning
+system, but it gives the information to the radiologist about certainty, which can accelerate the rating process.
+Other idea might be the presentation of results based on the existing rating scales such as MARS [69] or BOMBS [7]
+(Section 2.2).
+21
+
+Review of methods for automatic cerebral microbleeds detection
+Moreover, there should be the ability of result acceptance or rejection. As the system to be designed is the computer
+aided system, the user should have the possibility to agree with the proposed result or not, as his decision is final. This
+decision, however, has to be strongly distinguished from involving a human in the loop. The raters have knowledge
+essential for CMBs rating, therefore they may be used during system design, for instance to validate preliminary results
+or to label extracted candidates as CMB and non-CMB, similarly as in [17], but they should not be used as the last stage
+of the process to increase the system performance. The reported 100% precision or specificity of a semi-automated
+system in which a human is part of the FP reduction process is simply misleading [25, 35, 51]. Even if it significantly
+reduces the single scan rating time, this type of evaluation is confusing.
+However, the feedback from the radiologist about the prediction may be used for continual learning [159]. This kind
+of approach may cause improvement of the already working system.
+This smoothly leads to the problem of system evaluation. Section 3.4 presented different metrics and their correlations.
+Depending on the selected task: classification, detection, or segmentation - different metrics are used. However, it is
+crucial to present as many metrics as possible, as they focus on different aspects of the system. The sensitivity of 99%
+may seem an outstanding result, but when it goes with precision of 40% it is not satisfying. The researchers sometimes
+stress out the importance of sensitivity and diminish the number of potential false positives, but it can be harmful in
+terms of reliable system synthesis [25]. All this leads to the conclusion that a properly designed system should be
+balanced and optimized as a whole.
+System evaluation is also important for enabling comparison between different approaches. It is clearly visible in
+Table 3 that the researchers not always provide all necessary metrics, which significantly hinders identifying the state-
+of-the-art.
+Despite the current levels of metrics, there is a general issue of system trustworthiness. While the systems based on
+morphological operations and traditional image transformations are pretty easy to explain, the interpretability of black-
+box machine-learning systems is still a challenging task [142, 143, 144]. This problem is crucial, especially in such
+a life-impacting domain as medicine. The process of decision making should be clear to ensure that the conclusions
+are drawn based on the nature of the examined object and not on the bias. Therefore, there is an urgent need of bias
+reduction [145]. A list of guidelines regarding designing a responsible and trustworthy AI system is given in [136].
+To the best of our knowledge, the paper collates all available research reports regarding automatic cerebral microbleeds
+detection. The challenges of this task and some flaws of existing proposals have been outlined. We believe that this
+paper will serve as a mine of knowledge and ideas for further research within this domain. We hope that it will
+stimulate better practices regarding exchanging knowledge between different research groups.
+References
+[1] Al-masni, M., Kim, W., Kim, E., Noh, Y. & Kim, D. Automated detection of cerebral microbleeds in
+MR images: A two-stage deep learning approach. NeuroImage: Clinical. 28 pp. 102464 (2020), DOI:
+10.1016/j.nicl.2020.102464, ISSN: 2213-1582
+[2] Chesebro, A., Amarante, E., Lao, P., Meier, I., Mayeux, R. & Brickman, A. Automated detection of cerebral
+microbleeds on T2*-weighted MRI. Scientific Reports. 11, 1-13 (2021), DOI: 10.1038/s41598-021-83607-0,
+ISSN: 20452322
+[3] Dou, Q., Chen, H., Yu, L., Zhao, L., Qin, J., Wang, D., Mok, V., Shi, L. & Heng, P. Automatic Detection of
+Cerebral Microbleeds from MR Images via 3D Convolutional Neural Networks. IEEE Transactions On Medical
+Imaging. 35, 1182-1195 (2016), DOI: 10.1109/TMI.2016.2528129, ISSN: 1558254X
+[4] Wang, S., Tang, C., Sun, J. & Zhang, Y. Cerebral micro-bleeding detection based on densely connected neural
+network. Frontiers In Neuroscience. 13, 1-11 (2019), DOI: 10.3389/fnins.2019.00422, ISSN: 1662453X
+[5] Liu, S., Utriainen, D., Chai, C., Chen, Y., Wang, L., Sethi, S., Xia, S. & Haacke, E. Cerebral microbleed
+detection using Susceptibility Weighted Imaging and deep learning. NeuroImage. 198, 271-282 (2019), DOI:
+10.1016/j.neuroimage.2019.05.046, ISSN: 10959572
+[6] Rashid, T., Abdulkadir, A., Nasrallah, I., Ware, J., Liu, H., Spincemaille, P., Romero, J., Bryan, R., Heckbert,
+S. & Habes, M. DEEPMIR: a deep neural network for differential detection of cerebral microbleeds and iron
+deposits in MRI. Scientific Reports. 11, 14124 (2021), DOI: 10.1038/s41598-021-93427-x, ISSN: 2045-2322
+[7] Cordonnier, C., Potter, G., Jackson, C., Doubal, F., Keir, S., Sudlow, C., Wardlaw, J. & Al-Shahi Salman, R.
+Improving interrater agreement about brain microbleeds: Development of the Brain Observer MicroBleed Scale
+(BOMBS). Stroke. 40, 94-99 (2009), DOI: 10.1161/STROKEAHA.108.526996, ISSN: 00392499
+22
+
+Review of methods for automatic cerebral microbleeds detection
+[8] Mazurek, M., Papuc, E. & Rejdak, K. Czynniki wplywajace na wystepowanie mikrokrwawien mozgowych.
+Polski Przeglad Neurologiczny. 14, 151-155 (2018), ISSN: 1734-9745, in polish
+[9] Shams, S., Granberg, T., Martola, J., Li, X., Shams, M., Fereshtehnejad, S., Cavallin, L., Aspelin, P.,
+Kristoffersen-Wiberg, M. & Wahlund, L. Cerebrospinal fluid profiles with increasing number of cerebral mi-
+crobleeds in a continuum of cognitive impairment.. Journal Of Cerebral Blood Flow And Metabolism : Official
+Journal Of The International Society Of Cerebral Blood Flow And Metabolism. 36, 621-628 (2016), DOI:
+10.1177/0271678X15606141, ISSN: 1559-7016 (Electronic)
+[10] Akoudad, S., Portegies, M., Koudstaal, P., Hofman, A., Lugt, A., Ikram, M. & Vernooij, M. Cerebral Mi-
+crobleeds Are Associated With an Increased Risk of Stroke: The Rotterdam Study.. Circulation. 132, 509-516
+(2015), DOI: 10.1161/CIRCULATIONAHA.115.016261, ISSN: 1524-4539 (Electronic)
+[11] Yakushiji, Y., Nishiyama, M., Yakushiji, S., Hirotsu, T., Uchino, A., Nakajima, J., Eriguchi, M., Nanri, Y., Hara,
+M., Horikawa, E. & Kuroda, Y. Brain microbleeds and global cognitive function in adults without neurological
+disorder. Stroke. 39, 3323-3328 (2008), DOI: 10.1161/STROKEAHA.108.516112, ISSN: 00392499
+[12] Greenberg, S., Vernooij, M., Cordonnier, C., Viswanathan, A., Al-Shahi Salman, R., Warach, S., Launer, L.,
+Van Buchem, M. & Breteler, M. Cerebral microbleeds: a guide to detection and interpretation. The Lancet
+Neurology. 8, 165-174 (2009), DOI: 10.1016/S1474-4422(09)70013-4, ISSN: 14744422
+[13] Myung, M., Lee, K., Kim, H., Oh, J., Lee, J., Shin, I., Kim, E. & Lee, J. Novel Approaches to Detection of
+Cerebral Microbleeds: Single Deep Learning Model to Achieve a Balanced Performance. Journal Of Stroke
+And Cerebrovascular Diseases. 30, 105886 (2021), DOI: 10.1016/j.jstrokecerebrovasdis.2021.105886, ISSN:
+1052-3057
+[14] Hong, J., Cheng, H., Zhang, Y. & Liu, J. Detecting cerebral microbleeds with transfer learning. Machine Vision
+And Applications. 30, 1123-1133 (2019), DOI: 10.1007/s00138-019-01029-5, ISSN: 14321769
+[15] He, K., Zhang, X., Ren, S. & Sun, J. Deep Residual Learning for Image Recognition. 2016 IEEE Conference
+On Computer Vision And Pattern Recognition (CVPR). pp. 770-778 (2016), DOI: 10.1109/CVPR.2016.90
+[16] Lupo, J., Banerjee, S., Hammond, K., Kelley, D., Xu, D., Chang, S., Vigneron, D., Majumdar, S. & Nelson,
+S. GRAPPA-based susceptibility-weighted imaging of normal volunteers and patients with brain tumor at 7 T.
+Magnetic Resonance Imaging. 27, 480-488 (2009), DOI: 10.1016/j.mri.2008.08.003, ISSN: 0730-725X
+[17] Chen, Y., Villanueva-Meyer, J., Morrison, M. & Lupo, J. Toward Automatic Detection of Radiation-Induced
+Cerebral Microbleeds Using a 3D Deep Residual Network. Journal Of Digital Imaging. 32, 766-772 (2019),
+DOI: 10.1007/s10278-018-0146-z, ISSN: 1618727X
+[18] Ferlin, M., Grochowski, M., Kwasigroch, A., Mikołajczyk, A., Szurowska, E., Grzywi´nska, M. & Sabisz, A.
+A Comprehensive Analysis of Deep Neural-Based Cerebral Microbleeds Detection System. Electronics. 10
+(2021), DOI: 10.3390/electronics10182208, ISSN: 2079-9292
+[19] Li, T., Zou, Y., Bai, P., Li, S., Wang, H., Chen, X., Meng, Z., Kang, Z. & Zhou, G. Detecting cerebral microb-
+leeds via deep learning with features enhancement by reusing ground truth. Computer Methods And Programs
+In Biomedicine. 204 (2021), DOI: 10.1016/j.cmpb.2021.106051, ISSN: 18727565
+[20] Sundaresan, V., Arthofer, C., Zamboni, G., Dineen, R., Rothwell, P., Sotiropoulos, S., Auer, D., Tozer, D.,
+Markus, H., Miller, K., Dragonu, I., Sprigg, N., Alfaro-Almagro, F., Jenkinson, M. & Griffanti, L. Automated
+Detection of Candidate Subjects With Cerebral Microbleeds Using Machine Learning. Frontiers In Neuroinfor-
+matics. 15 pp. 777828 (2022), DOI: 10.3389/fninf.2021.777828, ISSN: 1662-5196
+[21] Ghafaryasl, B., Lijn, F., Poels, M., Vrooman, H., Ikram, M., Niessen, W., Lugt, A., Vernooij, M. & Bruijne,
+M. A computer aided detection system for cerebral microbleeds in brain MRI. 2012 9th IEEE International
+Symposium On Biomedical Imaging (ISBI). pp. 138-141 (2012), DOI: 10.1109/ISBI.2012.6235503
+[22] Lu, S., Lu, Z., Hou, X., Cheng, H. & Wang, S. Detection of cerebral microbleeding based on deep con-
+volutional neural network. 2016 13th International Computer Conference On Wavelet Active Media Tech-
+nology And Information Processing, ICCWAMTIP 2017. 2018-Febru pp. 93-96 (2017), DOI: 10.1109/IC-
+CWAMTIP.2017.8301456, ISBN: 9781509061259
+[23] Hong, J., Wang, S., Cheng, H. & Liu, J. Classification of cerebral microbleeds based on fully-optimized convo-
+lutional neural network. Multimedia Tools And Applications. 79, 15151-15169 (2020), DOI: 10.1007/s11042-
+018-6862-z, ISSN: 1380-7501, 1573-7721
+[24] Ateeq, T., Majeed, M., Anwar, S., Maqsood, M., Rehman, Z., Lee, J., Muhammad, K., Wang, S., Baik, S.
+& Mehmood, I. Ensemble-classifiers-assisted detection of cerebral microbleeds in brain MRI. Computers &
+Electrical Engineering. 69 pp. 768-781 (2018), DOI: 10.1016/j.compeleceng.2018.02.021, ISSN: 00457906
+23
+
+Review of methods for automatic cerebral microbleeds detection
+[25] Barnes, S., Haacke, E., Ayaz, M., Boikov, A., Kirsch, W. & Kido, D. Semiautomated detection
+of cerebral microbleeds in magnetic resonance images. Magnetic Resonance Imaging. 29, 844-852
+(2011), https://linkinghub.elsevier.com/retrieve/pii/S0730725X1100097X, DOI: 10.1016/j.mri.2011.02.028,
+ISSN: 0730725X
+[26] Bian, W., Hess, C., Chang, S., Nelson, S. & Lupo, J. Computer-aided detection of radiation-induced cere-
+bral microbleeds on susceptibility-weighted MR images. NeuroImage: Clinical. 2 pp. 282-290 (2013), DOI:
+10.1016/j.nicl.2013.01.012, ISSN: 22131582
+[27] Fazlollahi, A., Meriaudeau, F., Giancardo, L., Villemagne, V., Rowe, C., Yates, P., Salvado, O. & Bourgeat, P.
+Computer-aided detection of cerebral microbleeds in susceptibility-weighted imaging. Computerized Medical
+Imaging And Graphics. 46 pp. 269-276 (2015), DOI: 10.1016/j.compmedimag.2015.10.001, ISSN: 08956111
+[28] Fazlollahi, A., Meriaudeau, F., Villemagne, V., Rowe, C., Yates, P., Salvado, O. & Bourgeat, P. Efficient
+machine learning framework for computer-aided detection of cerebral microbleeds using the Radon trans-
+form. 2014 IEEE 11th International Symposium On Biomedical Imaging (ISBI). pp. 113-116 (2014), DOI:
+10.1109/ISBI.2014.6867822, ISBN: 978-1-4673-1961-4
+[29] Heuvel, T., Eerden, A., Manniesing, R., Ghafoorian, M., Tan, T., Andriessen, T., Vande Vyvere, T., Hauwe, L.,
+Haar Romeny, B., Goraj, B. & Platel, B. Automated detection of cerebral microbleeds in patients with traumatic
+brain injury. NeuroImage: Clinical. 12 pp. 241-251 (2016), DOI: 10.1016/j.nicl.2016.07.002, ISSN: 22131582
+[30] Al-masni, M., Kim, W., Kim, E., Noh, Y. & Kim, D. A Two Cascaded Network Integrating Regional-
+based YOLO and 3D-CNN for Cerebral Microbleeds Detection. 2020 42nd Annual International Confer-
+ence Of The IEEE Engineering In Medicine & Biology Society (EMBC). pp. 1055-1058 (2020), DOI:
+10.1109/EMBC44109.2020.9176073, ISBN: 978-1-72811-990-8
+[31] Liu, T., Surapaneni, K., Lou, M., Cheng, L., Spincemaille, P. & Wang, Y. Cerebral Microbleeds: Burden
+Assessment by Using Quantitative Susceptibility Mapping. Radiology. 262, 269-278 (2012), DOI: 10.1148/ra-
+diol.11110251, ISSN: 0033-8419, 1527-1315
+[32] Kuijf, H., Bresser, J., Biessels, G., Viergever, M. & Vincken, K. Detecting cerebral microbleeds in 7.0 T MR
+images using the radial symmetry transform. 2011 IEEE International Symposium On Biomedical Imaging:
+From Nano To Macro. pp. 758-761 (2011), DOI: 10.1109/ISBI.2011.5872516, ISBN: 978-1-4244-4127-3
+[33] Kuijf, H., Bresser, J., Geerlings, M., Conijn, M., Viergever, M., Biessels, G. & Vincken, K. Efficient detection
+of cerebral microbleeds on 7.0T MR images using the radial symmetry transform. NeuroImage. 59, 2266-2273
+(2012), DOI: 10.1016/j.neuroimage.2011.09.061, ISSN: 10538119
+[34] Nandigam, R., Viswanathan, A., Delgado, P., Skehan, M., Smith, E., Rosand, J., Greenberg, S. & Dickerson,
+B. MR imaging detection of cerebral microbleeds: Effect of susceptibility-weighted imaging, section thickness,
+and field strength. American Journal Of Neuroradiology. 30, 338-343 (2009), DOI: 10.3174/ajnr.A1355, ISSN:
+01956108
+[35] Kuijf, H., Brundel, M., Bresser, J., Veluw, S., Heringa, S., Viergever, M., Biessels, G. & Vincken, K. Semi-
+Automated Detection of Cerebral Microbleeds on 3.0 T MR Images. PLoS ONE. 8, e66610 (2013), DOI:
+10.1371/journal.pone.0066610, ISSN: 1932-6203
+[36] Hofman, A., Breteler, M., Duijn, C., Krestin, G., Pols, H., Stricker, B., Tiemeier, H., Uitterlinden, A., Vinger-
+ling, J. & Witteman, J. The Rotterdam Study: objectives and design update. European Journal Of Epidemiology.
+22, 819-829 (2007), DOI: 10.1007/s10654-007-9199-x, ISSN: 0393-2990
+[37] Simons, P., Algra, A., Laak, M., Grobbee, D. & Graaf, Y. Second Manifestations of ARTerial disease
+(SMART) study: Rationale and design. European Journal Of Epidemiology. 15, 773-781 (1999), DOI:
+10.1023/A:1007621514757, ISSN: 1573-7284
+[38] Heckbert, S., Austin, T., Jensen, P., Floyd, J., Psaty, B., Soliman, E. & Kronmal, R. Yield and consistency of
+arrhythmia detection with patch electrocardiographic monitoring: The Multi-Ethnic Study of Atherosclerosis.
+Journal Of Electrocardiology. 51, 997-1002 (2018), DOI: 10.1016/j.jelectrocard.2018.07.027, ISSN: 1532-
+8430
+[39] Akiyama, Y., Miyata, K., Harada, K., Minamida, Y., Nonaka, T., Koyanagi, I., Asai, Y. & Houkin, K.
+Susceptibility-Weighted Magnetic Resonance Imaging for the Detection of Cerebral Microhemorrhage in Pa-
+tients With Traumatic Brain Injury. Neurologia Medico-chirurgica. 49, 97-99 (2009), DOI: 10.2176/nmc.49.97,
+ISSN: 0470-8105, 1349-8029
+[40] Park, J., Park, S., Kang, S., Nam, T., Min, B. & Hwang, S. Detection of Traumatic Cerebral Microbleeds
+by Susceptibility-Weighted Image of MRI. Journal Of Korean Neurosurgical Society. 46, 365 (2009), DOI:
+10.3340/jkns.2009.46.4.365, ISSN: 2005-3711
+24
+
+Review of methods for automatic cerebral microbleeds detection
+[41] Fazlollahi, A., Meriaudeau, F., Villemagne, V., Rowe, C., Desmond, P., Yates, P., Salvado, O. & Bourgeat, P.
+Automatic detection of small spherical lesions using multiscale approach in 3D medical images. 2013 IEEE In-
+ternational Conference On Image Processing. pp. 1158-1162 (2013), DOI: 10.1109/ICIP.2013.6738239, ISBN:
+978-1-4799-2341-0
+[42] Chen, H., Yu, L., Dou, Q., Shi, L., Mok, V. & Heng, P. Automatic detection of cerebral microbleeds via deep
+learning based 3D feature representation. 2015 IEEE 12th International Symposium On Biomedical Imaging
+(ISBI). pp. 764-767 (2015), DOI: 10.1109/ISBI.2015.7163984, ISBN: 978-1-4799-2374-8
+[43] Qi Dou, Hao Chen, Lequan Yu, Lin Shi, Defeng Wang, Mok, V. & Pheng Ann Heng Automatic cerebral
+microbleeds detection from MR images via Independent Subspace Analysis based hierarchical features. 2015
+37th Annual International Conference Of The IEEE Engineering In Medicine And Biology Society (EMBC). pp.
+7933-7936 (2015), DOI: 10.1109/EMBC.2015.7320232, ISBN: 978-1-4244-9271-8
+[44] Roy, S., Jog, A., Magrath, E., Butman, J. & Pham, D. Cerebral microbleed segmentation from suscep-
+tibility weighted images. Medical Imaging 2015: Image Processing. 9413 pp. 364 - 370 (2015), DOI:
+10.1117/12.2082237
+[45] T. L. A. van den Heuvel, M. Ghafoorian, A. W. van der Eerden M.D., B. M. Goraj, T. M. J. C. Andriessen,
+B. M. ter Haar Romeny & B. Platel Computer aided detection of brain micro-bleeds in traumatic brain injury.
+Medical Imaging 2015: Computer-Aided Diagnosis. 9414 pp. 94142F (2015), DOI: 10.1117/12.2075353
+[46] Zhang, Y., Hou, X., Lv, Y., Chen, H., Zhang, Y. & Wang, S. Sparse Autoencoder Based Deep Neural Network
+for Voxelwise Detection of Cerebral Microbleed. 2016 IEEE 22nd International Conference On Parallel And
+Distributed Systems (ICPADS). pp. 1229-1232 (2016), DOI: 10.1109/ICPADS.2016.0166, ISBN: 978-1-5090-
+4457-3
+[47] Zhang, Y., Hou, X., Chen, Y., Chen, H., Yang, M., Yang, J. & Wang, S. Voxelwise detection of cerebral microb-
+leed in CADASIL patients by leaky rectified linear unit and early stopping. Multimedia Tools And Applications.
+77, 21825-21845 (2018), DOI: 10.1007/s11042-017-4383-9, ISSN: 1380-7501, 1573-7721
+[48] Zhang, Y., Zhang, Y., Hou, X., Chen, H. & Wang, S. Seven-layer deep neural network based on sparse autoen-
+coder for voxelwise detection of cerebral microbleed. Multimedia Tools And Applications. 77, 10521-10538
+(2018), DOI: 10.1007/s11042-017-4554-8, ISSN: 1380-7501, 1573-7721
+[49] Lu, S., Liu, S., Wang, S. & Zhang, Y. Cerebral Microbleed Detection via Convolutional Neural Network and
+Extreme Learning Machine. Frontiers In Computational Neuroscience. 15 pp. 738885 (2021), DOI: 10.3389/fn-
+com.2021.738885, ISSN: 1662-5188
+[50] Wang, S., Sun, J., Mehmood, I., Pan, C., Chen, Y. & Zhang, Y. Cerebral micro-bleeding identification based
+on a nine-layer convolutional neural network with stochastic pooling. Concurrency And Computation: Practice
+And Experience. 32 (2020), DOI: 10.1002/cpe.5130, ISSN: 1532-0626, 1532-0634
+[51] Morrison, M., Payabvash, S., Chen, Y., Avadiappan, S., Shah, M., Zou, X., Hess, C. & Lupo, J. A user-guided
+tool for semi-automated cerebral microbleed detection and volume segmentation_ Evaluating vascular injury
+and data labelling for machine learning. Neuroimage: Clinical. pp. 8 (2018), DOI: 10.1016/j.nicl.2018.08.002
+[52] Bao, F., Shi, M. & Macdonald, F. Voxelwise Detection of Cerebral Microbleed in CADASIL Patients by Naive
+Bayesian Classifier. Proceedings Of The 2018 International Conference On Information Technology And Man-
+agement Engineering (ICITME 2018). (2018), DOI: 10.2991/icitme-18.2018.35, ISBN: 978-94-6252-607-5
+[53] Wang, S., Jiang, Y., Hou, X., Cheng, H. & Du, S. Cerebral Micro-Bleed Detection Based on the Convo-
+lution Neural Network With Rank Based Average Pooling. IEEE Access. 5 pp. 16576-16583 (2017), DOI:
+10.1109/ACCESS.2017.2736558, ISSN: 2169-3536
+[54] Loy, G. & Zelinsky, A. Fast radial symmetry for detecting points of interest. IEEE Transactions On Pattern
+Analysis And Machine Intelligence. 25, 959-973 (2003), DOI: 10.1109/TPAMI.2003.1217601, ISSN: 0162-
+8828
+[55] Ashburner,
+J.
+&
+Friston,
+K.
+Unified
+segmentation.
+NeuroImage.
+26,
+839-851
+(2005),
+DOI:
+10.1016/j.neuroimage.2005.02.018, ISSN: 10538119
+[56] Smith, S. Fast robust automated brain extraction. Human Brain Mapping. 17, 143-155 (2002), DOI:
+10.1002/hbm.10062, ISSN: 1065-9471, 1097-0193
+[57] Shattuck, D. & Leahy, R. BrainSuite: An automated cortical surface identification tool. Medical Image Analysis.
+pp. 14 (2002)
+[58] Chang, C. & Lin, C. LIBSVM: A library for support vector machines. ACM Transactions On Intelligent Systems
+And Technology. 2, 1-27 (2011), DOI: 10.1145/1961189.1961199, ISSN: 2157-6904, 2157-6912
+25
+
+Review of methods for automatic cerebral microbleeds detection
+[59] Tustison, N., Avants, B., Cook, P., Yuanjie Zheng, Egan, A., Yushkevich, P. & Gee, J. N4ITK: Improved N3 Bias
+Correction. IEEE Transactions On Medical Imaging. 29, 1310-1320 (2010), DOI: 10.1109/TMI.2010.2046908,
+ISSN: 0278-0062, 1558-254X
+[60] Sled, J., Zijdenbos, A. & Evans, A. A nonparametric method for automatic correction of intensity nonuniformity
+in MRI data. IEEE Transactions On Medical Imaging. 17, 87-97 (1998), DOI: 10.1109/42.668698, ISSN:
+02780062
+[61] Klein, S., Staring, M., Murphy, K., Viergever, M. & Pluim, J. elastix:
+A Toolbox for Intensity-
+Based Medical Image Registration. IEEE Transactions On Medical Imaging. 29, 196-205 (2010), DOI:
+10.1109/TMI.2009.2035616, ISSN: 0278-0062, 1558-254X
+[62] Liu, W., Anguelov, D., Erhan, D., Szegedy, C., Reed, S., Fu, C. & Berg, A. SSD: Single Shot MultiBox
+Detector. Computer Vision – ECCV 2016. 9905 pp. 21-37 (2016), DOI: 10.1007/978-3-319-46448-0_2, ISBN:
+978-3-319-46447-3 978-3-319-46448-0
+[63] Ronneberger, O., Fischer, P. & Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation.
+ArXiv. (2015), arXiv: 1505.04597
+[64] Liu, J., Liu, T., Rochefort, L., Ledoux, J., Khalidov, I., Chen, W., Tsiouris, A., Wisnieff, C., Spincemaille,
+P., Prince, M. & Wang, Y. Morphology enabled dipole inversion for quantitative susceptibility mapping using
+structural consistency between the magnitude image and the susceptibility map. NeuroImage. 59, 2560-2568
+(2012), DOI: 10.1016/j.neuroimage.2011.08.082, ISSN: 10538119
+[65] Zhang, Y., Brady, M. & Smith, S. Segmentation of brain MR images through a hidden Markov random field
+model and the expectation-maximization algorithm. IEEE Transactions On Medical Imaging. 20, 45-57 (2001),
+DOI: 10.1109/42.906424, ISSN: 02780062
+[66] Jenkinson, M. & Smith, S. A global optimisation method for robust affine registration of brain images. Medical
+Image Analysis. 5, 143-156 (2001), DOI: 10.1016/S1361-8415(01)00036-6, ISSN: 13618415
+[67] Jenkinson, M., Bannister, P., Brady, M. & Smith, S. Improved Optimization for the Robust and Accu-
+rate Linear Registration and Motion Correction of Brain Images. NeuroImage. 17, 825-841 (2002), DOI:
+10.1006/nimg.2002.1132, ISSN: 10538119
+[68] Breiman, L. Random Forests. Machine Learning. 45, 5-32 (2001), DOI: 10.1023/A:1010933404324, ISSN:
+1573-0565
+[69] Gregoire, S., Chaudhary, U., Brown, M., Yousry, T., Kallis, C., Jäger, H. & Werring, D. The Microbleed
+Anatomical Rating Scale (MARS). Neurology. 73, 1759 (2009), DOI: 10.1212/WNL.0b013e3181c34a7d
+[70] Bian, W., Morrison, M., Zhu, X., Avadiappan, S., Chen, Y., Payabvash, S., Shah, M., Hess, C. & Lupo, J. CMB
+labeler. Github. (2018)
+[71] Real, R. & Vargas, J. The Probabilistic Basis of Jaccard’s Index of Similarity. SYSTEMATIC BIOLOGY. 45 pp.
+6 (1996)
+[72] Stanley, B. & Wilfred Franklin, S. Automated cerebral microbleed detection using selective 3D gradient co-
+occurance matrix and convolutional neural network. Biomedical Signal Processing And Control. 75 pp. 103560
+(2022), DOI: 10.1016/j.bspc.2022.103560, ISSN: 1746-8094
+[73] Seghier, M., Kolanko, M., Leff, A., Jäger, H., Gregoire, S. & Werring, D. Microbleed Detection Using Au-
+tomated Segmentation (MIDAS): A New Method Applicable to Standard Clinical MR Images. PLoS ONE. 6,
+e17547 (2011), DOI: 10.1371/journal.pone.0017547, ISSN: 1932-6203
+[74] Momeni, S., Fazlollahi, A., Yates, P., Rowe, C., Gao, Y., Liew, A. & Salvado, O. Synthetic microbleeds gen-
+eration for classifier training without ground truth. Computer Methods And Programs In Biomedicine. 207 pp.
+106127 (2021), DOI: 10.1016/j.cmpb.2021.106127, ISSN: 0169-2607
+[75] Lu, S., Nayak, D., Wang, S. & Zhang, Y. A cerebral microbleed diagnosis method via FeatureNet
+and ensembled randomized neural networks. Applied Soft Computing. 109 pp. 107567 (2021), DOI:
+10.1016/j.asoc.2021.107567, ISSN: 1568-4946
+[76] Liu, H., Rashid, T. & Habes, M. Cerebral Microbleed Detection Via Fourier Descriptor with Dual Domain
+Distribution Modeling. 2020 IEEE 17th International Symposium On Biomedical Imaging Workshops (ISBI
+Workshops). pp. 1-4 (2020), DOI: 10.1109/ISBIWorkshops50223.2020.9153365
+[77] Hong, J., Cheng, H., Wang, S. & Liu, J. Improvement of Cerebral Microbleeds Detection Based on Discrimi-
+native Feature Learning. Fundamenta Informaticae. 168, 231-248 (2019), DOI: 10.3233/FI-2019-1830, ISSN:
+1875-8681
+26
+
+Review of methods for automatic cerebral microbleeds detection
+[78] Gunter, J., Spychalla, A., Ward, C., Graff-Radford, J., Huston, J., Kantarci, K., Knopman, D., Petersen,
+R. & Jack Jr., C. P4-232: Automating Cerebral Microbleed Detection in Support of Alzheimer’s Disease
+Trials Using a Convolutional Neural Network Ai. Alzheimer’s & Dementia. 14, P1530-P1531 (2018), DOI:
+10.1016/j.jalz.2018.07.053, ISSN: 1552-5279
+[79] Dou, Q., Chen, H., Qin, J. & Heng, P. CHAPTER NINE - Automatic lesion detection with three-dimensional
+convolutional neural networks. Biomedical Information Technology (Second Edition). pp. 265-293 (2020), DOI:
+10.1016/B978-0-12-816034-3.00009-2, ISBN: 978-0-12-816034-3
+[80] Chen, H., Dou, Q., Yu, L., Qin, J., Zhao, L., Mok, V., Wang, D., Shi, L. & Heng, P. Chapter 6 - Deep Cascaded
+Networks for Sparsely Distributed Object Detection from Medical Images. Deep Learning For Medical Image
+Analysis. pp. 133-154 (2017), DOI: 10.1016/B978-0-12-810408-8.00008-0, ISBN: 978-0-12-810408-8
+[81] Kirsch, W., McAuley, G., Holshouser, B., Petersen, F., Ayaz, M., Vinters, H., Dickson, C., Haacke, E., Britt III,
+W., Larsen, J., Kim, I., Mueller, C., Schrag, M. & Kido, D. Serial Susceptibility Weighted MRI Measures Brain
+Iron and Microbleeds in Dementia. Journal Of Alzheimer’s Disease. 17, 599-609 (2009), DOI: 10.3233/JAD-
+2009-1073, ISSN: 1387-2877
+[82] Mayeux, R. Washington Heights-Hamilton Heights-Inwood Columbia Aging Project. (Columbia University
+Irving Medical Center Neurological Institute, The Taub Institute for Research on Alzheimer’s Disease),
+https://cheba.unsw.edu.au/consortia/cosmic/studies/washington-heights-inwood-and-columbia-aging-project-
+whicap, Accessed: 2022-06-01
+[83] Ellis, K., Bush, A., Darby, D., Fazio, D., Foster, J., Hudson, P., Lautenschlager, N., Lenzo, N., Martins, R.,
+Maruff, P., Masters, C., Milner, A., Pike, K., Rowe, C., Savage, G., Szoeke, C., Taddei, K., Villemagne,
+V., Woodward, M., Ames, D. & Group, T. The Australian Imaging, Biomarkers and Lifestyle (AIBL) study
+of aging: methodology and baseline characteristics of 1112 individuals recruited for a longitudinal study of
+Alzheimer’s disease. International Psychogeriatrics. 21, 672-687 (2009), DOI: 10.1017/S1041610209009405,
+ISSN: 1741-203X, 1041-6102
+[84] Medical Education, M. & Research Alzheimer’s Disease Research Center - Data Sharing and Re-
+sources.
+(https://www.mayo.edu/research/centers-programs/alzheimers-disease-research-center/research-
+activities/mayo-clinic-study-aging/for-researchers/data-sharing-resources), Accessed: 2022-04-04
+[85] Initiative, A. ADNI ACCESS DATA. (https://adni.loni.usc.edu/data-samples/access-data/), Accesed: 2022-04-
+04
+[86] Pacurar,
+E.,
+Sethi,
+S.,
+Habib,
+C.,
+Laze,
+M.,
+Martis-Laze,
+R. & Haacke,
+E. Database integra-
+tion of protocol-specific neurological imaging datasets. NeuroImage. 124 pp. 1220-1224 (2016), DOI:
+10.1016/j.neuroimage.2015.04.066, ISSN: 1053-8119
+[87] O’Donnell, H., Rosand, J., Knudsen, K., Furie, K., Segal, A., Chiu, R., Ikeda, D. & Greenberg, S. Apolipopro-
+tein E Genotype and the Risk of Recurrent Lobar Intracerebral Hemorrhage. New England Journal Of Medicine.
+342, 240-245 (2000), DOI: 10.1056/NEJM200001273420403, ISSN: 0028-4793
+[88] Chen, Y., Gurol, M., Rosand, J., Viswanathan, A., Rakich, S., Groover, T., B.Eng., Greenberg, S. & Smith,
+E. Progression of white matter lesions and hemorrhages in cerebral amyloid angiopathy. Neurology. 67, 83-87
+(2006), DOI: 10.1212/01.wnl.0000223613.57229.24, ISSN: 0028-3878
+[89] Rothwell, P., Coull, A., Giles, M., Howard, S., Silver, L., Bull, L., Gutnikov, S., Edwards, P., Mant, D., Sackley,
+C., Farmer, A., Sandercock, P., Dennis, M., Warlow, C., Bamford, J. & Anslow, P. Change in stroke incidence,
+mortality, case-fatality, severity, and risk factors in Oxfordshire, UK from 1981 to 2004 (Oxford Vascular
+Study). The Lancet. 363, 1925-1933 (2004), DOI: 10.1016/S0140-6736(04)16405-2, ISSN: 0140-6736
+[90] Sprigg, N., Flaherty, K., Appleton, J., Salman, R., Bereczki, D., Beridze, M., Christensen, H., Ciccone, A.,
+Collins, R., Czlonkowska, A., Dineen, R., Duley, L., Egea-Guerrero, J., England, T., Krishnan, K., Laska,
+A., Law, Z., Ozturk, S., Pocock, S., Roberts, I., Robinson, T., Roffe, C., Seiffge, D., Scutt, P., Thanabalan,
+J., Werring, D., Whynes, D. & Bath, P. Tranexamic acid for hyperacute primary IntraCerebral Haemorrhage
+(TICH-2): an international randomised, placebo-controlled, phase 3 superiority trial. The Lancet. 391, 2107-
+2115 (2018), DOI: 10.1016/S0140-6736(18)31033-X, ISSN: 0140-6736
+[91] Dineen, R., Pszczolkowski, S., Flaherty, K., Law, Z., Morgan, P., Roberts, I., Werring, D., Salman, R., England,
+T., Bath, P. & Sprigg, N. Does tranexamic acid lead to changes in MRI measures of brain tissue health in
+patients with spontaneous intracerebral haemorrhage? Protocol for a MRI substudy nested within the double-
+blind randomised controlled TICH-2 trial. BMJ Open. 8, e019930 (2018), DOI: 10.1136/bmjopen-2017-019930
+[92] Centre, U. UK Biobank - UK Biobank. (https://www.ukbiobank.ac.uk/), Accessed: 2022-04-04
+27
+
+Review of methods for automatic cerebral microbleeds detection
+[93] Song, S., Zheng, Y. & He, Y. A review of Methods for Bias Correction in Medical Images. Biomedical Engi-
+neering Review. 3 (2017), DOI: 10.18103/bme.v3i1.1550, ISSN: 23759143, 23759151
+[94] Patterson,
+D.
+Neuroimaging
+Core
+Documentation.
+(https://neuroimaging-core-
+docs.readthedocs.io/en/latest/index.html), Accessed: 2022-04-04
+[95] Human Neuroimaging, U. SPM. (https://www.fil.ion.ucl.ac.uk/spm/), Accessed: 2022-04-04
+[96] Penny, W., Friston, K., Ashburner, J., Kiebel, S. & Nicholas, T. Statistical Parametric Mapping: The Analysis
+of Functional. (Academic Press,2006), ISBN: 978-0-12-372560-8
+[97] Carass, A., Wheeler, M., Cuzzocreo, J., Bazin, P., Bassett, S. & Prince, J. A joint registration and segmentation
+approach to skull stripping. 2007 4th IEEE International Symposium On Biomedical Imaging. pp. 656-659
+(2007), DOI: 10.1109/ISBI.2007.356937, ISBN: 1424406722
+[98] Carass,
+A.,
+Cuzzocreo,
+J.,
+Wheeler,
+M.,
+Bazin,
+P.,
+Resnick,
+S. & Prince,
+J. Simple paradigm
+for extra-cerebral tissue removal:
+Algorithm and analysis. NeuroImage. 56, 1982-1992 (2011), DOI:
+10.1016/j.neuroimage.2011.03.045, ISSN: 10538119
+[99] Seghier, M., Ramlackhansingh, A., Crinion, J., Leff, A. & Price, C. Lesion identification using uni-
+fied segmentation-normalisation models and fuzzy clustering. NeuroImage. 41, 1253-1266 (2008), DOI:
+10.1016/j.neuroimage.2008.03.028, ISSN: 10538119
+[100] Soille, P. Morphological Image Analysis. (Springer Berlin Heidelberg,2004), DOI: 10.1007/978-3-662-05088-
+0, ISBN: 978-3-642-07696-1 978-3-662-05088-0
+[101] Buslaev, A., Iglovikov, V., Khvedchenya, E., Parinov, A., Druzhinin, M. & Kalinin, A. Albumentations: Fast
+and Flexible Image Augmentations. Information. 11 (2020), DOI: 10.3390/info11020125, ISSN: 2078-2489
+[102] Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N.,
+Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner,
+B., Fang, L., Bai, J. & Chintala, S. PyTorch: An Imperative Style, High-Performance Deep Learning Library.
+Advances In Neural Information Processing Systems 32. pp. 8024-8035 (2019)
+[103] Li, N., Wang, W., Sati, P., Pham, D. & Butman, J. Quantitative assessment of susceptibility-weighted imag-
+ing processing methods. Journal Of Magnetic Resonance Imaging : JMRI. 40, 1463-1473 (2014), DOI:
+10.1002/jmri.24501, ISSN: 1522-2586
+[104] Tsushima, Y., Tanizaki, Y., Aoki, J. & Endo, K. MR Detection of microhemorrhages in neurologically healthy
+adults. Neuroradiology. 44, 31-36 (2002), DOI: 10.1007/s002340100649, ISSN: 0028-3940, 1432-1920
+[105] Kaaouana, T., Bertrand, A., Ouamer, F., Law-ye, B., Pyatigorskaya, N., Bouyahia, A., Thiery, N., Dufouil, C.,
+Delmaire, C., Dormont, D., Rochefort, L. & Chupin, M. Improved cerebral microbleeds detection using their
+magnetic signature on T2*-phase-contrast: A comparison study in a clinical setting. NeuroImage: Clinical. 15
+pp. 274-283 (2017), DOI: 10.1016/j.nicl.2016.08.005, ISSN: 22131582
+[106] Cordonnier, C., Al-Shahi Salman, R. & Wardlaw, J. Spontaneous brain microbleeds: systematic review,
+subgroup analyses and standards for study design and reporting. Brain. 130, 1988-2003 (2007), DOI:
+10.1093/brain/awl387, ISSN: 0006-8950, 1460-2156
+[107] Charidimou, A. & Werring, D. Cerebral microbleeds: detection, mechanisms and clinical challenges. Future
+Neurology. 6, 587-611 (2011), DOI: 10.2217/fnl.11.42, ISSN: 1479-6708, 1748-6971
+[108] Charidimou, A., Krishnan, A., Werring, D. & Rolf Jäger, H. Cerebral microbleeds: a guide to detection and
+clinical relevance in different disease settings. Neuroradiology. 55, 655-674 (2013), DOI: 10.1007/s00234-013-
+1175-4, ISSN: 0028-3940, 1432-1920
+[109] Charidimou, A., Jäger, H. & Werring, D. Cerebral microbleed detection and mapping: Principles, method-
+ological aspects and rationale in vascular dementia. Experimental Gerontology. 47, 843-852 (2012), DOI:
+10.1016/j.exger.2012.06.008, ISSN: 05315565
+[110] Filippi, M., Horsfield, M., Bressi, S., Martinelli, V., Baratti, C., Reganati, P., Campi, A., Miller, D. & Comi,
+G. Intra- and inter-observer agreement of brain MRI lesion volume measurements in multiple sclerosis: A
+comparison of techniques. Brain. 118, 1593-1600 (1995), DOI: 10.1093/brain/118.6.1593, ISSN: 0006-8950
+[111] Cheng, A., Batool, S., McCreary, C., Lauzon, M., Frayne, R., Goyal, M. & Smith, E. Susceptibility-Weighted
+Imaging is More Reliable Than T2*-Weighted Gradient-Recalled Echo MRI for Detecting Microbleeds. Stroke.
+44, 2782-2786 (2013), DOI: 10.1161/STROKEAHA.113.002267, ISSN: 0039-2499, 1524-4628
+[112] Vernooij, M., Ikram, M., Wielopolski, P., Krestin, G., Breteler, M. & Lugt, A. Cerebral Microbleeds: Ac-
+celerated 3D T2*-weighted GRE MR Imaging versus Conventional 2D T2*-weighted GRE MR Imaging for
+Detection. Radiology. 248, 272-277 (2008), DOI: 10.1148/radiol.2481071158, ISSN: 0033-8419
+28
+
+Review of methods for automatic cerebral microbleeds detection
+[113] Shams, S., Martola, J., Cavallin, L., Granberg, T., Shams, M., Aspelin, P., Wahlund, L. & Kristoffersen-Wiberg,
+M. SWI or T2*: Which MRI Sequence to Use in the Detection of Cerebral Microbleeds? The Karolinska Imag-
+ing Dementia Study. American Journal Of Neuroradiology. 36, 1089-1095 (2015), DOI: 10.3174/ajnr.A4248,
+ISSN 0195-6108, 1936-959X
+[114] Scheid, R., Ott, D., Roth, H., Schroeter, M. & Cramon, D. Comparative Magnetic Resonance Imaging at 1.5
+and 3 Tesla for the Evaluation of Traumatic Microbleeds. Journal Of Neurotrauma. 24, 1811-1816 (2007), DOI:
+10.1089/neu.2007.0382, ISSN: 0897-7151
+[115] Conijn, M., Geerlings, M., Biessels, G., Takahara, T., Witkamp, T., Zwanenburg, J., Luijten, P. & Hendrikse, J.
+Cerebral Microbleeds on MR Imaging: Comparison between 1.5 and 7T. American Journal Of Neuroradiology.
+32, 1043-1049 (2011), DOI: 10.3174/ajnr.A2450, ISSN: 0195-6108, 1936-959X
+[116] Bresser, J., Brundel, M., Conijn, M., Dillen, J., Geerlings, M., Viergever, M., Luijten, P. & Biessels, G. Visual
+Cerebral Microbleed Detection on 7T MR Imaging: Reliability and Effects of Image Processing. American
+Journal Of Neuroradiology. 34, E61-E64 (2013), DOI: 10.3174/ajnr.A2960, ISSN: 0195-6108, 1936-959X
+[117] Liu, S., Buch, S., Chen, Y., Choi, H., Dai, Y., Habib, C., Hu, J., Jung, J., Luo, Y., Utriainen, D., Wang, M.,
+Wu, D., Xia, S. & Haacke, E. Susceptibility Weighted Imaging: Current Status and Future Directions. NMR In
+Biomedicine. 30, 10.1002/nbm.3552 (2017), DOI: 10.1002/nbm.3552, ISSN: 0952-3480
+[118] Reserve, C. MRI Basics. (https://case.edu/med/neurology/NR/MRI
+[119] Werring, D. Cerebral Microbleeds: Clinical and Pathophysiological Significance. Journal Of Neuroimaging.
+17, 193-203 (2007), DOI: 10.1111/j.1552-6569.2006.00070.x, ISSN: 10512284, 15526569
+[120] Shoamanesh, A., Kwok, C. & Benavente, O. Cerebral Microbleeds: Histopathological Correlation of Neu-
+roimaging. Cerebrovascular Diseases. 32, 528-534 (2011), DOI: 10.1159/000331466, ISSN: 1421-9786, 1015-
+9770
+[121] Martinez-Ramirez, S., Greenberg, S. & Viswanathan, A. Cerebral microbleeds: overview and implications in
+cognitive impairment. Alzheimer’s Research & Therapy. 6, 33 (2014), DOI: 10.1186/alzrt263, ISSN: 1758-9193
+[122] Imaios Introduction to MRI sequences. (https://www.imaios.com/en/e-Courses/e-MRI/MRI-Sequences/MRI-
+sequences), ISBN 978-1847537768, Accessed: 2022-04-29
+[123] Lipton, M. Image Contrast: T1, T2, T2, and Proton Density. Totally Accessible MRI: A User’s Guide To Princi-
+ples, Technology, And Applications. pp. 38-46 (2008), DOI: 10.1007/978-0-387-48896-7_4, ISBN: 978-0-387-
+48896-7
+[124] Doke, P., Shrivastava, D., Pan, C., Zhou, Q. & Zhang, Y. Using CNN with Bayesian optimization to identify
+cerebral micro-bleeds. Machine Vision And Applications. 31, 36 (2020), DOI: 10.1007/s00138-020-01087-0,
+ISSN: 0932-8092, 1432-1769
+[125] Lu, S., Xia, K. & Wang, S. Diagnosis of cerebral microbleed via VGG and extreme learning machine trained
+by Gaussian map bat algorithm. Journal Of Ambient Intelligence And Humanized Computing. (2020), DOI:
+10.1007/s12652-020-01789-3, ISSN: 1868-5137, 1868-5145
+[126] Sa-ngiem, S., Dittakan, K., Temkiatvises, K., Yaisoongnern, S. & Kespechara, K. Cerebral Microbleed Detec-
+tion by Extracting Area and Number from Susceptibility Weighted Imagery Using Convolutional Neural Net-
+work. Journal Of Physics: Conference Series. 1229, 012038 (2019), DOI: 10.1088/1742-6596/1229/1/012038,
+ISSN: 1742-6588, 1742-6596
+[127] Jenkinson, M., Beckmann, C., Behrens, T., Woolrich, M. & Smith, S. FSL. Neuroimage. 62, 782-790 (2012),
+DOI: 10.1016/j.neuroimage.2011.09.015
+[128] Huang, G., Zhu, Q. & Siew, C. Extreme learning machine: Theory and applications. Neurocomputing. 70,
+489-501 (2006), DOI: 10.1016/j.neucom.2005.12.126, ISSN: 09252312
+[129] Ren, S., He, K., Girshick, R. & Sun, J. Faster R-CNN: Towards Real-Time Object Detection with Region Pro-
+posal Networks. Proceedings Of The 28th International Conference On Neural Information Processing Systems
+- Volume 1. pp. 91-99 (2015)
+[130] Redmon, J. & Farhadi, A. YOLO9000: Better, Faster, Stronger. Proceedings Of The IEEE Conference On
+Computer Vision And Pattern Recognition (CVPR). (2017)
+[131] Krizhevsky, A., Sutskever, I. & Hinton, G. ImageNet Classification with Deep Convolutional Neural Networks.
+Advances In Neural Information Processing Systems. 25 (2012)
+[132] Simonyan, K. & Zisserman, A. Very Deep Convolutional Networks for Large-Scale Image Recognition. (2015),
+arXiv:1409.1556
+29
+
+Review of methods for automatic cerebral microbleeds detection
+[133] Huang, G., Liu, Z., Maaten, L. & Weinberger, K. Densely Connected Convolutional Networks. (2018),
+arXiv:1608.06993
+[134] Barnard, E. & Casasent, D. A comparison between criterion functions for linear classifiers, with an appli-
+cation to neural nets. IEEE Transactions On Systems, Man, And Cybernetics. 19, 1030-1041 (1989), DOI:
+10.1109/21.44018
+[135] Mikolajczyk, A. & Grochowski, M. Data augmentation for improving deep learning in image classifica-
+tion problem. 2018 International Interdisciplinary PhD Workshop (IIPhDW). pp. 117-122 (2018), DOI:
+10.1109/IIPHDW.2018.8388338, ISBN: 978-1-5386-6143-7
+[136] GoogleAI
+Responsible
+AI
+practices.
+(https://ai.google/responsibilities/responsible-ai-
+practices?category=general), Accessed: 2022-05-14
+[137] Tajudin, A., Sulaiman, S., Isa, I., Soh, Z., Karim, N. & Shuaib, I. Microbleeds detection using watershed-
+driven active contour. 2017 7th IEEE International Conference On Control System, Computing And Engineering
+(ICCSCE). pp. 320-324 (2017), DOI: 10.1109/ICCSCE.2017.8284427, ISBN: 978-1-5386-3897-2
+[138] Afzal, S., Khan, I. & Lee, J. A Transfer Learning-Based Approach to Detect Cerebral Microbleeds. Computers,
+Materials & Continua. 71, 1903 (2022), DOI: 10.32604/cmc.2022.021930, ISSN: 1546-2218
+[139] Tao, Y. & Cloutie, R. Voxelwise Detection of Cerebral Microbleed in CADASIL Patients by Genetic Algorithm
+and Back Propagation Neural Network. Proceedings Of The 2018 3rd International Conference On Communica-
+tions, Information Management And Network Security (CIMNS 2018). (2018), DOI: 10.2991/cimns-18.2018.23,
+ISBN: 978-94-6252-620-4
+[140] Standvoss, K., Crijns, T., Goerke, L., Janssen, D., Kern, S., Niedek, T., Vugt, J., Burgos, N., Gerritse, E., Mol,
+J., Vooren, D., Ghafoorian, M., Heuvel, T. & Manniesing, R. Cerebral microbleed detection in traumatic brain
+injury patients using 3D convolutional neural networks. Medical Imaging 2018: Computer-Aided Diagnosis.
+10575 pp. 314 - 321 (2018), DOI: 10.1117/12.2294016
+[141] Creswell, A.,
+White, T., Dumoulin,
+V.,
+Arulkumaran,
+K.,
+Sengupta,
+B. & Bharath,
+A. Genera-
+tive Adversarial Networks:
+An Overview. IEEE Signal Processing Magazine. 35, 53-65 (2018), DOI:
+10.1109/MSP.2017.2765202, ISSN: 1053-5888
+[142] The Precise4Q consortium, Amann, J., Blasimme, A., Vayena, E., Frey, D. & Madai, V. Explainability for
+artificial intelligence in healthcare: a multidisciplinary perspective. BMC Medical Informatics And Decision
+Making. 20, 310 (2020), DOI: 10.1186/s12911-020-01332-6, ISSN: 1472-6947
+[143] Barredo Arrieta, A., Díaz-Rodríguez, N., Del Ser, J., Bennetot, A., Tabik, S., Barbado, A., Garcia, S., Gil-Lopez,
+S., Molina, D., Benjamins, R., Chatila, R. & Herrera, F. Explainable Artificial Intelligence (XAI): Concepts,
+taxonomies, opportunities and challenges toward responsible AI. Information Fusion. 58 pp. 82-115 (2020),
+DOI: 10.1016/j.inffus.2019.12.012, ISSN: 1566-2535
+[144] Angelov, P., Soares, E., Jiang, R., Arnold, N. & Atkinson, P. Explainable artificial intelligence: an analytical
+review. WIREs Data Mining And Knowledge Discovery. 11 (2021), DOI: 10.1002/widm.1424, ISSN: 1942-
+4787, 1942-4795
+[145] Mikołajczyk, A., Grochowski, M. & Kwasigroch, A. Towards Explainable Classifiers Using the Counterfac-
+tual Approach - Global Explanations for Discovering Bias in Data. Journal Of Artificial Intelligence And Soft
+Computing Research. 11, 51-67 (2021), DOI: 10.2478/jaiscr-2021-0004, ISSN: 2083-2567
+[146] Leming, M., Das, S. & Im, H. Construction of a confounder-free clinical MRI dataset in the Mass General
+Brigham system for classification of Alzheimer’s disease. Artificial Intelligence In Medicine. 129 pp. 102309
+(2022), DOI: 10.1016/j.artmed.2022.102309, ISSN: 09333657
+[147] Currie, S., Hoggard, N., Craven, I., Hadjivassiliou, M. & Wilkinson, I. Understanding MRI: basic MR physics
+for physicians. Postgraduate Medical Journal. 89, 209-223 (2013), DOI: 10.1136/postgradmedj-2012-131342,
+ISSN: 0032-5473, 1469-0756
+[148] Poels, M., Ikram, M., Lugt, A., Hofman, A., Krestin, G., Breteler, M. & Vernooij, M. Incidence of Cerebral
+Microbleeds in the General Population. Stroke. 42, 656-661 (2011), DOI: 10.1161/STROKEAHA.110.607184
+[149] Nusrat, I. & Jang, S. A Comparison of Regularization Techniques in Deep Neural Networks. Symmetry. 10, 648
+(2018), DOI:10.3390/sym10110648 , ISSN:2073-8994
+[150] Jain, A. & Ramaswami, M. Classifier Design with Parzen Windows. Pattern Recognition And Artificial Intelli-
+gence. 7 pp. 211-228 (1988), DOI:10.1016/B978-0-444-87137-4.50021-7, ISSN: 0923-0459
+[151] Tharwat, A. Linear vs. quadratic discriminant analysis classifier: a tutorial. International Journal Of Applied
+Pattern Recognition. 3, 145 (2016), DOI:10.1504/IJAPR.2016.079050, ISSN: 2049-887X, 2049-8888
+30
+
+Review of methods for automatic cerebral microbleeds detection
+[152] Comon, P. Supervised classification: a probabilistic approach. ESANN95-European Symposium On Artificial
+Neural Networks. pp. 111-128 (1995)
+[153] Averbuch, A. & Shkolnisky, Y. 3D Fourier based discrete Radon transform. Applied And Computational Har-
+monic Analysis. 15, 33-69 (2003), DOI:10.1016/S1063-5203(03)00030-7, ISSN: 1063-5203
+[154] Luo, L., Ye, L., Luo, M., Huang, D., Peng, H. & Yang, F. Methods of forward feature selection based on
+the aggregation of classifiers generated by single attribute. Computers In Biology And Medicine. 41, 435-441
+(2011), DOI:10.1016/j.compbiomed.2011.04.005, ISSN: 00104825
+[155] Wang, S. Artificial Neural Network. Interdisciplinary Computing In Java Programming. pp. 81-100 (2003),
+DOI: 10.1007/978-1-4615-0377-4_5, ISBN: 978-1-4615-0377-4
+[156] Al., U. The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic
+Classification. ArXiv. (2021), Number: arXiv:2107.02314, arXiv:2107.02314 [cs]
+[157] Siegel, E. What Can We Learn from the RSNA Pediatric Bone Age Machine Learning Challenge?. Radiology.
+290, 504-505 (2019), DOI: 10.1148/radiol.2018182657, ISSN: 0033-8419, 1527-1315
+[158] Halabi, S., Prevedello, L., Kalpathy-Cramer, J., Mamonov, A., Bilbily, A., Cicero, M., Pan, I., Pereira, L.,
+Sousa, R., Abdala, N., Kitamura, F., Thodberg, H., Chen, L., Shih, G., Andriole, K., Kohli, M., Erickson, B.
+& Flanders, A. The RSNA Pediatric Bone Age Machine Learning Challenge. Radiology. 290, 498-503 (2019),
+DOI: 10.1148/radiol.2018180736, ISSN: 0033-8419, 1527-1315
+[159] Pianykh, O., Langs, G., Dewey, M., Enzmann, D., Herold, C., Schoenberg, S. & Brink, J. Continuous Learn-
+ing AI in Radiology: Implementation Principles and Early Applications. Radiology. 297, 6-14 (2020), DOI:
+10.1148/radiol.2020200038, ISSN:0033-8419, 1527-1315
+[160] Sveinbjornsdottir, S., Sigurdsson, S., Aspelund, T., Kjartansson, O., Eiriksdottir, G., Valtysdottir, B., Lopez,
+O., Buchem, M., Jonsson, P., Gudnason, V. & Launer, L. Cerebral microbleeds in the population based
+AGES–Reykjavik study: prevalence and location. Journal Of Neurology, Neurosurgery & Psychiatry. 79, 1002
+(2008)
+[161] Werring, D. Cognitive dysfunction in patients with cerebral microbleeds on T2*-weighted gradient-echo MRI.
+Brain. 127, 2265-2275 (2004), DOI: 10.1093/brain/awh253, ISSN: 1460-2156
+[162] Poels, M., Ikram, M., Lugt, A., Hofman, A., Niessen, W., Krestin, G., Breteler, M. & Vernooij, M.
+Cerebral microbleeds are associated with worse cognitive function. Neurology. 78, 326 (2012), DOI:
+10.1212/WNL.0b013e3182452928
+[163] Cordonnier, C. & Flier, W. Brain microbleeds and Alzheimer’s disease: innocent observation or key player?.
+Brain. 134, 335-344 (2011), DOI: 10.1093/brain/awq321, ISSN: 1460-2156, 0006-8950
+[164] Bian, W., Hess, C., Chang, S., Nelson, S. & Lupo, J. Susceptibility-weighted MR imaging of radiation therapy-
+induced cerebral microbleeds in patients with glioma: a comparison between 3T and 7T. Neuroradiology. 56,
+91-96 (2014), DOI: 10.1007/s00234-013-1297-8, ISSN: 0028-3940, 1432-1920
+[165] Revol-Muller, C., Peyrin, F., Carrillon, Y. & Odet, C. Automated 3D region growing algorithm based on an
+assessment function. Pattern Recognition Letters. 23, 137-150 (2002), DOI: 10.1016/S0167-8655(01)00116-7,
+ISSN: 01678655
+[166] Buscema, M. Back Propagation Neural Networks. Substance Use & Misuse. 33, 233-270 (1998,1), DOI:
+10.3109/10826089809115863, ISSN: 1082-6084, 1532-2491
+[167] Lee, H., Battle, A., Raina, R. & Ng, A. Efficient sparse coding algorithms. Advances In Neural Information
+Processing Systems 19. pp. 8 (2006)
+[168] O’Shea, K. & Nash, R. An Introduction to Convolutional Neural Networks. (arXiv,2015), Number:
+arXiv:1511.08458 [cs]
+[169] Singh, S., Wang, L., Gupta, S., Goli, H., Padmanabhan, P. & Gulyás, B. 3D Deep Learning on Medical Images:
+A Review. Sensors. 20, 5097 (2020), DOI: 10.3390/s20185097, ISSN: 1424-8220
+[170] Haller, S., Haacke, E., Thurnher, M. & Barkhof, F. Susceptibility-weighted Imaging: Technical Essentials
+and Clinical Neurologic Applications. Radiology. 299, 3-26 (2021,4), ISSN: 0033-8419, 1527-1315, DOI:
+10.1148/radiol.2021203071
+[171] Hodel, J., Rodallec, M., Gerber, S., Blanc, R., Maraval, A., Caron, S., Tyvaert, L., Zuber, M. & Zins, M.
+Séquences IRM SWAN, SWI et VenoBOLD exploitant le phénomène de susceptibilité magnétique : principes
+techniques et applications cliniques. Journal Of Neuroradiology. 39, 71-86 (2012,5,1), ISSN: 0150-9861, DOI:
+10.1016/j.neurad.2011.11.006, language: French
+31
+
+Review of methods for automatic cerebral microbleeds detection
+[172] Nandigam, K. & Scully, M. SWAN MRI revealing multiple microhemorrhages secondary to septic emboli
+from mucormycosisAuthor Response. Neurology. 81, 199-200 (2013,7,9), ISSN: 0028-3878, 1526-632X, DOI:
+10.1212/01.wnl.0000432237.13307.12
+[173] Ayaz, M., Boikov, A., Haacke, E., Kido, D. & Kirsch, W. Imaging cerebral microbleeds using susceptibility
+weighted imaging: one step toward detecting vascular dementia. Journal Of Magnetic Resonance Imaging:
+JMRI. 31, 142-148 (2010), ISSN: 1522-2586, DOI: 10.1002/jmri.22001
+[174] Haller, S., Vernooij, M., Kuijer, J., Larsson, E., Jäger, H. & Barkhof, F. Cerebral Microbleeds: Imaging and
+Clinical Significance. Radiology. 287, 11-28 (2018), DOI: 10.1148/radiol.2018170803, ISSN: 0033-8419
+32
+
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+page_content='REVIEW OF METHODS FOR AUTOMATIC CEREBRAL  MICROBLEEDS DETECTION  A PREPRINT  Maria Ferlin  Gda´nsk University of Technology  Gda´nsk, Poland  maria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='pl  Zuzanna Klawikowska  Gda´nsk University of Technology  Gda´nsk, Poland  zuzanna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='pl  Michał Grochowski  Gda´nsk University of Technology  Gda´nsk, Poland  michal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='pl  Małgorzata Grzywi´nska  Medical University of Gda´nsk  Gda´nsk, Poland  malgorzata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='grzywinska@gumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='pl  Edyta Szurowska  Medical University of Gda´nsk  Gda´nsk, Poland  eszurowska@gumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='pl  February 1, 2023  ABSTRACT  Cerebral microbleeds detection is an important and challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' With the gaining popularity  of the MRI, the ability to detect cerebral microbleeds also raises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Unfortunately, for radiologists,  it is a time-consuming and laborious procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For this reason, various solutions to automate  this process have been proposed for several years, but none of them is currently used in medical  practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In this context, the need to systematize the existing knowledge and best practices has been  recognized as a factor facilitating the imminent synthesis of a real CMBs detection system practically  applicable in medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' To the best of our knowledge, all available publications regarding automatic  cerebral microbleeds detection have been gathered, described, and assessed in this paper in order to  distinguish the current research state and provide a starting point for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  1  Introduction  Cerebral microbleeds (CMBs) are defined as small, homogeneous, hypointense foci well seen on T2*-weighted MRI  sequences with the associated so-called ‘blooming effect’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' They are collections of blood degradation products (mainly  hemosiderin) that can remain in macrophages for years, following a microhemorrhage[119, 120, 121, 106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The  ‘blooming effect’ takes place when the MRI overestimates the diameter of the microbleed [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' CMBs may occur in  every region of the brain and can be categorized relative to that area [160, 7, 69], (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' They may appear due to  a range of pathological processes in the cerebral vessels [121, 9, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Around 5% of population have microbleeds and  they are completely healthy [10, 106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, the increased number of CMBs in the patient’s brain may indicate the  existence of some medical condition [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Additionally, they are sometimes accidentally found in association with other  pathologies [164].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Undeniably, however, high prevalence of cerebral microbleeds is closely associated with cognitive  disfunction [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  CMBs detection is a challenging task due to small size of the lesion compared to the whole image (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Moreover,  there are many lesions that mimic the CMBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The main CMB mimics include calcifications, flow voids in pial blood  vessels, iron deposits, and deoxyhemoglobin [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Both calcium and iron deposits may appear as small foci of low  signal intensity on a T2*-weighted MRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Flow voids caught in the cross-sections of cortical sulci can be distinguished  from CMBs by their sulcal location, equal visibility on T2-weighted SE and GRE sequences, and linear structure  when examined over contiguous slices, particularly evident at smaller slice thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The presence of paramagnetic  deoxyhemoglobin in cerebral venules produces its own blooming effect, which requires the rater to rely on their  tubular structure for differentiating them from CMBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Metastatic melanoma in the brain can appear hypointense on  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='13549v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='CV]  31 Jan 2023  Review of methods for automatic cerebral microbleeds detection  T2*-weighted MRI and may mimic CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Other mimics, such as mineralization of the basal ganglia or diffuse axonal  injury, for instance, can be excluded based on the appearance or clinical history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  CMBs detection is very important considering proper diagnosis and treatment, as they may indicate some major and  more complicated issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' From the medical perspective, the crucial information is the number of detected cerebral  microbleeds [174, 113, 12, 148].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another useful information is their location [161, 162, 7, 69, 163].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, there  is no need to perform segmentation which is a complex computational algorithm, it is enough to detect them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  With gaining popularity of the MRI as a good imaging tool, the ability to detect cerebral microbleeds also raises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Un-  fortunately, for radiologists, it is a time-consuming and laborious process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Technology and automatic image processing  can come to the rescue in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Different solutions have been proposed for last years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, the problem is complex and there is no unification  and consistency between the researches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' According to our best knowledge, the results achieved so far are still not  used in medical practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In this context, the authors recognized the need to systematize the existing knowledge and  best practices as a factor which will facilitate imminent synthesis of a real CMBs detection system, which would be  practically applicable in medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The existing research results are in fact difficult to compare due to various, unavailable publicly datasets and the lack  of system evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The guidelines included in this paper are expected to present new research in a more  beneficial way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Probably, the prevalence of a few publicly available datasets will result in evaluation of new approaches  on these datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Figure 1: Brain anatomy in the sagittal plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In addition to the presented structures, the temporal lobe, the insula, and  the external and internal capsules, which are not visible in this plane, are also important in the context of scales used  to rate CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' CMBs can be found in all structures indicated in the figure as well as in those mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1  Review criteria  The aim of this research was to gather all previous works and achievements in the field of cerebral microbleeds  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Regarding the lack of order in existing research and comparison ability we decided to collate different  approaches and methods, in order to distinguish the current research state and provide a starting point for future  studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is noteworthy that the key word in this matter is automatic as a guide for a radiologist to detect microbleeds  on the MRI existed well beyond [107, 109, 108, 106, 105, 104].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Firstly, a comprehensive literature review regarding automatic cerebral microbleeds detection have been done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In order  to do that, careful search was performed for all papers connected with this topic in Google Scholar, IEEE Xplore, and  2  parietal lobe  gray matter  corpus callosum  cortex  occipital lobe  white matter  frontal lobe  basal ganglia  thalumus  cerebellum  brain stemReview of methods for automatic cerebral microbleeds detection  Figure 2: Example of CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Upper images present the same microbleed in three planes, while bottom ones present  sequence of adjacent slices fragments, in which the microbleed is visible (marked by red frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Images acquired  using ImFusion software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Elsevier platforms, using key phrases: automatic cerebral microbleeds detection, automatic CMB detection, cerebral  microbleeds detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The next step was the search for related papers in the references of all gathered works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The literature review dates back  to year 2011, in which, to the best of our knowledge, first papers about automatic CMB detection were published.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The main information gathered from each paper referred to: database, pre-processing, methods used, proposed ap-  proach with the best or the most significant results, conclusions, and challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  For the majority of modern methods, the key issue is the availability of datasets, therefore we decided to collate the  information about all datasets used in this type of research in Section 2, which also introduces the issues of MRI and  CMB characteristics and CMB rating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  To maintain clarity of the paper, descriptions of particular algorithms are given in Section 3, while the exact approach  leveraging from those algorithms is presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The algorithms described in Section 3 are divided into  two main groups referring to detection and verification of CMB candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1 also presents different  pre-processing algorithms that were used to prepare a dataset for training and testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Eventually, all methods and  algorithms that were used to solve this task are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It turned out during the reported research that the evaluation  of results is a challenging problem due to the lack of a standard for the metrics used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is not only problematic for  existing approaches comparison, but also makes it impossible to assess a specific method itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' To address this, a  range of metrics is presented in Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='4, along with their features and dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Section 4 provides a comprehensive assessment of all the presented research, followed by conclusions and challenges,  both gathered during literature review and emerging from this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3  MR: (0) - 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='30 19:03:13  5cm  4#1 xoq 6upu  A  AL  5cm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  2cmReview of methods for automatic cerebral microbleeds detection  2  Data sources  In order to understand the task of cerebral microbleeds detection it is essential to understand the magnetic resonance  imaging, acquisition process and rating procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, we decided to introduce the process of MR images  formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Further, the relevant sequences and rating scales are described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Finally, we present datasets used for  cerebral microbleeds detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1  Magnetic Resonance Imaging Sequences  Among the types of brain imaging they are CT (computed tomography) and MRI (magnetic resonance imaging).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This  paper focuses on MRI because it is the most commonly used technique to study CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The main reason is the fact that  the CT density of the hemorrhage in CMBs rapidly decreases over days as CMBs become indistinguishable with brain  tissue after around 7–10 days [174].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Consequently, the sensitivity of CT in imaging CMBs is the highest within the  first few days of their appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' On MR images, CMBs remain visible much longer than on CT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  MRI is the imaging technique in which each sequence is a combination of radiofrequency pulses and gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' There  are over a hundred different sequence types, the acronyms of which depend on the manufacturer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Regardless of the  type of sequence, the goal is to obtain the signal of a particular tissue - contrast, as quickly as possible - speed, while  limiting the artifacts and without altering the signal to noise ratio [122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Figure 3: Transverse brain plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Sequences in first row [118]: T1W (a), T2W (b), FLAIR (c);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' in second row [117]:  Magnitude (d), Phase (e), SWI (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are three essential components for any imaging sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The first is the radio frequency (RF) excitation pulse  which is required for the phenomenon of magnetic resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The second are the gradients for spatial encoding  whose arrangement will determine how the k-space is filled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The third component is signal reading, which combines  echo types determining the type of contrast - varying influence of relaxation times: T1, T2 and T2*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Additionally,  more sequence parameters, such as repetition time or flip angle, must be chosen to find a balance between contrast,  resolution, and speed [147].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are three types of relaxation times: T1, T2, and T2* [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The term relaxation means that, once the RF pulse  is turned off, the spins are relaxing back into their lowest energy state or to the equilibrium state, realigning with  the axis of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' T1 is called the longitudinal relaxation time, as it refers to the time needed for the  spins to realign along the longitudinal (z)-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' T2 is defined as the predicted time constant for the decay of transverse  magnetization arising from natural interactions at the atomic or molecular level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, in a real MR experiment, the  transverse magnetization decays much faster than would be predicted by natural atomic and molecular mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  This accelerated decay rate is denoted as T2*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are two main sequence families, depending on the type of echo recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The first family comprises Spin  Echo (SE) sequences, which have two essential parameters: TR and TE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' They consist of a series of events: 90°pulse;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  180°rephasing pulse at half of echo time (TE) and signal reading at TE, repeated at each time interval TR (Repetition  Time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' During each repetition, the line of k-space is filled due to different phase encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The example of such se-  quence is FLuid Attenuation Inversion Recovery (FLAIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The second family includes Gradient Echo (GE) sequences,  4  a)  b)  c)  (p  OReview of methods for automatic cerebral microbleeds detection  Figure 4: Overview of data processing steps in SWI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  during which the flip angle (FA) is usually below 90°, which decreases the amount of magnetization tipped into the  transverse plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In this case, there is no 180°RF rephasing pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The example of this sequence is Susceptibility  Weighted Imaging (SWI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Numerous variations have been developed within each of these families, mainly to increase  the acquisition speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  A T1-weighted (T1W) sequence demonstrates differences in the T1 relaxation times of tissues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The T1-weighted  image is consistent with the anatomy: gray matter is dark and white matter bright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Anatomical gray-white inversion is  observed in T2-weighted (T2W) images, in which gray matter is bright and white matter dark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It highlights differences  in the T2 relaxation time of tissues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another sequence is FLAIR, which removes signal from the cerebrospinal fluid  (CSF) in the resulting image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Brain tissue in the FLAIR image appears similar to that in the T2W image with gray  matter brighter than white matter, but in this case, CSF is dark instead of bright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' SWI is a 3D high-spatial-resolution  fully velocity corrected gradient-echo MRI sequence which takes advantage of the effect of both phase and magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 3 shows the described sequences and the data processing steps in SWI are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Susceptibility weighted sequences are named differently depending on the MRI vendor [170].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For example, the term  SWI is owned by Siemens, GE Healthcare offers a sequence called SWAN , and Philips Healthcare has proposed  the name SWIp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Obtaining these sequences differs, due to licensing and patent issues [172].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The differences lie  in the use of different ways of combining the sequences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' SWI uses phase and magnitude, while SWAN uses  a weighted sum of longer TEs, which preserves T2* dephasing effects, but also increases the signal-to-noise ratio  [170, 171].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, regardless of the vendor SWI-like sequences are most commonly used in CMB detection, as  they have greater sensitivity to this lesion than other sequences [111, 39, 34, 40, 112, 113].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is not only used in  terms of automatic detection but also in everyday clinical practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another factor that improves the detectability of  microbleeds is the strength of the magnetic field [114, 115, 116, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Clinical image data is typically stored in the DICOM format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For scientific analysis, the alternative format is NIFTY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2  CMB rating  Technology that automates clinicians’ work should be developed in accordance with clinical practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is important  to know the ways of assessing a disease, so that the results provided by the proposed tools fit into these guidelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Two ways used by clinicians to assess CMB are Brain Observer Microbleed Scale (BOMBS) [7] and Microbleed  Anatomical Rating Scale (MARS) [69], proposed in 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The evaluation categories are presented in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Stan-  dardized CMB rating scales provide a uniform assessment methodology and enable easy and reliable quantification  and categorization of CMBs even when the scales are used by observers with different backgrounds or experience, and  thus increase the reliability of the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Measurement reliability refers to the consistency or repeatability of the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Low reliability indicates large  differences in measurement while retesting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It precludes reproduction or interpretation of the results, and finally makes  5  MAGNITUDE  SWI  mIP of SWI  Minimum  PHASE  intensity  projection  Background  removal, weighting  mask generationReview of methods for automatic cerebral microbleeds detection  Table 1: CMBs evaluation categories according to rating scales  BOMBS  MARS  certainty:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' certain,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' uncertain,  size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' <5 mm,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 5-10 mm,  side of brain:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' left,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' right,  location (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 1):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' lobar:  (a) cortex/gray–white junction,  (b) subcortical white matter,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' deep:  (a) basal ganglia,  (b) internal and external capsules,  (c) thalamus,  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' posterior fossa:  (a) brain stem,  (b) cerebellum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  appearance of the lesion:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' definite,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' possible,  side of brain:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' left,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' right,  location (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 1):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' lobar:  (a) frontal,  (b) parietal,  (c) temporal,  (d) occipital,  (e) insula,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' deep:  (a) basal ganglia,  (b) internal capsule,  (c) external capsule,  (d) thalumus,  (e) corpus callosum,  (f) deep and  periventricular  white  matter,  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' infratentorial:  (a) brain stem,  (b) cerebellum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  distinguishing between participants with and without specific medical conditions impossible due to significant mea-  surement error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In clinical evaluation, a measurement error can be introduced by the observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, determining  observer (clinician) reliability is important for making full comparison of measurement reliability between studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are two ways of doing it – inter- and intra-observer agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Intra-observer agreement determines the degree of agreement between the two studies that use the same technique, in  the same patient, obtained by the one observer [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Inter-observer agreement determines the degree of agreement  between the two studies that use the same technique, in the same patient, obtained by the two observers [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The reliable rating of CMBs presence, number, and location is the important factor for further diagnosis of various  diseases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, many research institutions use their own methods to rate CMBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although their reliability based  on intra- and inter-observer agreement is reported, details of the methods used are usually not described [109].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  6  Review of methods for automatic cerebral microbleeds detection  Table 2: Comparison of dataset acquisition parameters used in the reviewed approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  # of  subject  /# of CMB  RES [mm2]  ST [mm]  TR [ms]  TE [ms]  FA [°]  BW  [Hz/px]  IMS  [vox-  els]  FOV  [ mm3\\mm2\\mm ]  Sequences  β [T]  Rating  Avail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  [32]  2 / 4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='35x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3  20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5/15 T2*W  7  MARS  on  request  [25]  6 / 26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5x1  2  57  40  20 512x320x48 Fully Flow-  Compensated  3 DGRE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5  [173] [14,  77, 23]  10 / -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5  2 20  15  120  364x448x48 SWI  3  MARS [26,  51]  15 / 420  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5  2  56  28  20 u x u 40  240  T2*W  3  similar to  BOMBS/  MARS  10  subjects  [33]  18 / 54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='35x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='35 T2*W,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='66x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='66 T1W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3 T2*W,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='7 T1W  20 T2*W,  7 T1W  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5/15 T2*W,  3 T1W T2*W,  T1W turbo  field echo  7  MARS  on  request  [75, 49],  [46, 47, 48],  [4, 53]  20 / -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5  2  28  20  15  120  364x448×48 SWI  3  MARS [138]  20 / -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45  2  17  24 SWI  3 [42, 24],  [18, 76]  [43]  [3]  20 / 117,  44 / 615,  320 / 1149  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45  2  17  24 512x512x150  230x230  SWI  3  ,  MARS,  MARS  20  subjects  [6]  24 / >157  1x1  1  T1WMP & T2W  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5 SWI  1900  T1W MPRAGE  (T1WMP),  3200 T2W,  35 SWI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='93  T1WMP,  408 T2W,  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5/  15/  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5/  30  SWI  9  T1WMP,  120 T2W,  15 SWI  170  T1WMP,  750 T2W,  200 SWI  256x256x176  T1WMP & T2W,  256x192x96 SWI T1WMP,  T2W,  SWI  3  Inspired  by  BOMBS  on  request  [126]  26 / - 3 u x u x 40-  60 SWI [44]  26 / 404  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='45 SWI,  1x1 T1W-MPRAGE  (magnetization  prepared  rapid  gradient  echo)  2 SWI,  1 T1W-MPRAGE 25 SWI,  T1W-MPRAGE  3 [41]  [28]  [27]  30 / 64,  41 / 103,  66 / 231  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='93x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='93 SWI,  1x1 T1W  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='75 SWI,  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2 T1W  27 SWI,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3 T1W  20 SWI,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='98 T1W  20 SWI,  9 T1W 240x256 T1W,  SWI, T1W  3  ,  MARS,  MARS  on  request  [29,  45]  51 / 627  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' Intracerebral Haemorrhages (ICH) [34,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 20],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' gliomas [26,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 51,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 17],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' hemodialysis cases [5],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Amyloid  Angiopathy (CAA) [34],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' atherosclerosis [6],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' or did not distinguish any particular disease besides the appearance of  CMBs [1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 30,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 42,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 43,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 80,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 79,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 76,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 72,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 126,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 138,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Datasets used in the first category of  researches focused on AD [81, 82, 83, 36, 84, 85], SMART [37], TBI [86], stroke [86, 89], ICH [87, 90, 91], gliomas  [70], hemodialysis cases [86], CAA [88], atherosclerosis [38], or CMBs [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Clinicians rated the CMBs present in the images from these datasets according to the MARS scale, the BOMBS scale,  or an unspecified standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Details related to the number of patients, image acquisition parameters, types of sequences,  strength of magnetic field and data availability are given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The abbreviations used in the table stand for: RES  – resolution, TR – repetition time, TE – echo time, FA – flip angle, BW – bandwidth, IMS – image matrix size, ST –  slice thickness, FOV – field of view, u - unknown dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Datasets that were not included in the table due to insufficient information are [137, 140, 124, 125, 52, 139, 22, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  They contained only information about, for example, the number of patients or the type of sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3  Methodology  A comprehensive analysis of the past works regarding cerebral microbleeds detection has led to the proposition of a  generalized pipeline of such a system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The majority of works can be divided into three stages: Pre-processing, CMB  Candidates Detection and CMB Candidates Verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, we decided to describe the methodology having  regard to such division.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The overall idea is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' All the methods and algorithms available within each  stage are firstly described as single transform, that can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Their further synthesis into a complete approach  along with the paper in which it was used are in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1  Pre-processing  Data pre-processing is an important step in system synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Proper preparation of data has a significant impact on  further system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  It is important to understand that phrase raw data does not always mean that data were not pre-processed by MRI  software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' From the system’s perspective, raw data are those provided by the MRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, there is a variety of MRI  9  Stage 1  Stage 2  Stage 3  CMB candidates  Preprocessing  CMB candidates  Report  detection  verification  Raw data  三  Bias field correction  FRST  Geometrical features  performance report  DICOM  Normalization  Intensity threshold  Rodon Transform  nameplate  NIFTY  Skull stripping  CNN  Region growing  trustworthiness  assessment  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='Review of methods for automatic cerebral microbleeds detection  device suppliers, who design an operating system of their own, which performs different operations on a particular  scan before the image delivery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, it is crucial to know how the data has already been processed and what else  can be improved to meet system needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Below the most popular types of operations performed on raw data are presented and few examples illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Firstly, there are operations for removing artifacts and unnecessary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Bias field correction is the operation that reduces negative influence of the bias field, which is an undesired artifact  in most MRI images, especially old ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It can also be called intensity inhomogeneity correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The most  commonly known techniques include N3 Bias Correction [60] and its successor N4ITK/N4 [59], FSL FAST [65] or  reconstruction Syngo MR B17 provided by the manufacturer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Nevertheless, there are also other methods for bias field  correction [93, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This operation was applied by [21, 28, 27, 44, 45, 46, 29, 5, 125, 6, 74, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Skull stripping also  known as brain extraction is an operation of removing skull and background from the image, leaving only the brain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are plenty of algorithms for performing this task: Brain Extraction Tool (BET) [56], BrainSuite [57], and others  [98, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Brain extraction was applied in [32, 25, 21, 26, 28, 44, 45, 29, 24, 51, 17, 1, 30, 2, 13, 138, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Normalization is a typical operation of rescaling the pixel values into range (0,1) or (-1,1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This enables bias reduction  in the next stages of system creation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was applied by [32, 73, 25, 33, 35, 26, 41, 28, 27, 42, 43, 45, 5, 6, 18, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Standardization is an equally common operation as normalization and involves subtraction of mean value of pixels  and division by the standard deviation of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was claimed to be used in [32, 33, 35, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Mask generation is a wide term as different types of masks might be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The most common is binary mask that  might be generated using Statistical Parametric Mapping Toolbox [95] or morphological operations [100, 99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Further,  there are typically neurological masks such as cerebrovascular fluid (CSF) mask, gray-white matter (GWM) mask and  white-matter (WM) mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Masks were generated in [32, 73, 33, 35, 26, 41, 28, 27, 45, 29, 78, 17, 126, 23, 76, 2, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Further image generation involves using images provided by the MRI device to make a new image consisting more  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For instance, a SWI sequence is generated from the Magnitude and Phase sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' These days, it  is the standard sequence generated by the scanner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Further, the SWI data might be processed using [103] for phase  enhancement, like in [44] Similarly, T2*-weighted images are nowadays provided by the MRI scanner, but in the past  they had to be obtained from PD-weighted images using, for example, Elastix Tool [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was performed for example  in [21, 5, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A QSM image can be generated using Morphology Enabled Dipol Inversion (MEDI) [64], like in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Slice merging can also be considered as a new image creation, which involves concatenation of adjacent slices to  provide 3D information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Generally, MRI images are one-channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It enables putting three adjacent slices into one  image using RGB channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The concatenation of different sequences of corresponding slices might be done as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  However, in this case it may be necessary to align the slices with each other, if there were different parameters of  acquisition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This kind of operation was performed in [3, 1, 30, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Useful software to perform these operations is Neuroimaging Core [94] involving Advanced Normalization Tools  (ANT), FMRIB Software Library (FSL) [55, 66, 67, 127] and Statistical Parametric Mapping (SPM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The last software  is also implemented in [95] based on [96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are also some typical transforms performed in standard image pre-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is noteworthy that medical data  are highly sensitive to any transformation, after which significant information can be accidentally lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  DICOM to JPG conversion is an excellent example of lossy data conversion technique, which might influence further  processing stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was done by [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although DICOM or NIFTY formats might be considered not developer–  friendly, working on original image matrices should be a standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Resize is a common operation of changing image size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is usually performed to obtain equal sizes of all images, or  to enlarge images so that the objects were more visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It can also be forced by requirements of a method used in the  CMB Candidates Detection stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The images were resized in [25, 5, 2, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Padding is performing an artificial size change by addition of a black frame to obtain a desired image size without  applying resize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was utilized by [6, 18, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Image cut is a common operation performed to simplify the detection task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It involves image partitioning into smaller  parts and then feeding them into the classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It might be performed using the sliding neighborhood processing (SNP)  technique to produce smaller fragments of the original image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A lot of works utilized this method: [46, 22, 53, 48, 47,  52, 139, 4, 14, 77, 23, 124, 125, 75, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Rotation is a simple operation of changing image orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, it can be a loss operation, and therefore a  rotation with original intensity should be considered, like in [20], for instance by using - fslreorient2std tool [127].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  10  Review of methods for automatic cerebral microbleeds detection  Figure 6: Example of pre-processing operations: a) sliding neighborhood processing [23], b) Canny edge detection  [2], c) CSF mask [13] d) brain extraction using BrainSuite software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Inversion is the operation which consists of swapping intensity values in relation to the center of the intensity interval  and it was performed by [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Finally, there is data augmentation, which is not always considered as a pre-processing technique, but rather a  regularization one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, it is sometimes performed at this stage and consists of image transformations, therefore  it is placed in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It enhances a dataset, especially in case of small amount of data by creating new, slightly  modified, artificial images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' There is a wide range of transformations, including those described above, along with blur,  crop, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' [135, 101, 102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Augmentation was used in [140, 78, 124, 6, 13, 19, 18, 74, 138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2  Algorithms for CMB candidates detection  Over the years, a wide range of algorithms were used to detect cerebral microbleeds, starting from the simplest methods  based on traditional image transformations, up to complicated deep learning models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1  Classical methods  In early works regarding CMBs detection the candidates were extracted using predetermined features such as: inten-  sity threshold and area size [25, 21, 42, 43, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In the SWI sequence CMBs occur as low-intensity spheres, therefore  applying a proper intensity threshold allows for binary mask generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Sometimes the authors also applied morpho-  logical operations such as filtering, hole filling, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' [73, 24, 138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, this kind of operations were used at all  the stages described in this paper, as they were also useful for CMB candidates verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Next,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' the detecting proce-  dures evolved to include more complicated voxel features,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' such as: eigenvalues in [20] – scalars associated with the  given linear transformation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' line detection in [41] – defining the line where edge points are located,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Gaussian filter  in [20] and Laplacian of Gaussian operator in[28,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 20],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' which highlight the rapid change of the image intensity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Hough transform in [2] that enables shape detection by finding objects - local maxima,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Canny filter in [2] which  enables edge detection watershed transform in [137] - transforming images to grayscale topographic like map,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' and  distinguishing objects on the basis of its intensity value or Frangi filters in [20] - a dedicated filter enabling vessel  distinction,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' or 3D gradient co-occurrence matrix (3D GCM) in [72],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' which indicates the differences between intensity  of two adjacent pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Simultaneously, the researchers began to use the Radial Symmetry Transform (RST), and its successor Fast Radial  Symmetry Transform (FRST) [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This algorithm deserves special attention since it is successfully used to this  day [32, 33, 35, 26, 51, 5, 17, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In this transform, a gradient of the image is computed, then the orientation and  magnitude of each pixel is established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Next, using the above values, points of interest can be selected according to the  given formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This algorithm was later developed so that it could be used in 3D space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, despite its common  use, when applied to candidates detection, FRST generates a lot of false positives, which forces introducing the third  stage to the whole detection procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  11  a)  b)  C  dReview of methods for automatic cerebral microbleeds detection  Another algorithm used in the CMB Candidates Detection stage by [44] was the region growing that inspects the  homogeneity of the considered pixel - or voxel in case of 3D [165].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2  Neural networks-based methods  Then, with the development of neural networks (NN), algorithms based on these networks gained more attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Generally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' two approaches for neural networks usage may be distinguished: custom or general purpose pretrained  neural network In the first case,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' in the domain of CMBs detection various approaches were used,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' such as: simple  artificial neural networks (ANN) [155] used in [48,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 74],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' which is basically a sum of inputs multiplied by weights  assigned in the training process,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' back-propagation neural networks (BPNN) [166] utilized in [139] that are ANNs  extended with the information about the error,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' sparse auto-encoder (SAE) [167] used in [46,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 47] that is a neural  network consisted of encoder and decoder with the additional sparsity penalty algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The Random Forest algorithm [68] was used as well in [45, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is a black-box algorithm that consists of an  ensemble of classifiers that predict an output value based on a part of a dataset and then these predictions are averaged  into one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Finally, there are convolutional neural networks (CNN) [168], which are the most popular solution [22, 53, 78, 77,  23, 124, 75, 49, 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Basically, CNN consists of a number of feed-forward convolutional layers, where the features are extracted by perform-  ing a convolution with predefined filters on every image and then further modified during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Each convolution  layer is followed by a non-linear activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Consecutive convolution layers are interspersed by pooling layers  that extract the most important features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Then, mostly, there is a fully connected layer or other classifier that assigns a  predicted class based on the previously extracted features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' An interesting approach is replacement of a fully-connected  layer by Extreme Learning Machine [128], which is much more efficient [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In the second approach, one takes advantage of a deep neural network architecture that has already been trained  on a vast dataset – transfer-learning – often very different from terminal one and just adjusts it to the considered  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' These networks usually consist of millions of parameters and are hard to train on the CPU due to hardware  limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Additionally, it is a good method for dealing with small dataset problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The transfer-learning idea is  to use a pre-trained network that has already learned some image features and fine-tune it on the particular dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Several networks were used for this purpose, including: AlexNet [131] in [126], ResNet50 [15] in [14], Faster-RCNN  [129] in [18], VGG [132] in [125], U-Net [63] in [6], YOLOv2 [130] in [1, 30], DenseNet 201 [133] in [4] or SSD  [62] in [19] with the modification of feature enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Sometimes, especially in case of SNP algorithm usage  the detection task was substituted by classification of small fragments of image using either CNN or ResNet50 for  instance in [14, 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Considering the main aim of this paper, the description of each network is omitted, as they are  explained in detail in the mentioned papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Nevertheless, the reader is strongly encouraged to get familiar with these  architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Relatively new and still not fully explored architectures are 3D convolutional neural networks (3D CNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The idea  is the same as in 2D CNNs, but instead of performing convolution on 2D matrices, it is performed on 3D patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  They were applied in [3, 140].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3  Algorithms for CMB candidates verification  Due to the nature of the considered problem, most of the presented approaches involved the CMB Candidates Verifi-  cation stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In spite of this, some solutions still have not managed to acquire satisfying quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In some cases, the process of false positive candidates elimination was performed manually by a radiologist [32, 25,  33, 35, 51, 17, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although this kind of approach significantly reduced the time needed for one scan rating, it is a  semi-automated one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  A large part of the research involved at this stage establishing a batch of predefined features of CMB : from simple  ones as intensity or size, to very complicated parameters of a single voxel, calculated in 2D or 3D spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' There were  also other methods for defining the feature vectors, for instance 2D CNN in [42, 138], 3D ISA network [152] in [43],  3D Radon Transform [153] in [28, 27] or feed-forward feature selection (FFFS) [154] in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In some cases, thresholds of geometric features were set, and on this ground the classification was performed [26, 44,  70, 2, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In others, these features together with the previously prepared fragments of images were passed to the classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A  lot of classifiers have already been tested: Supported Vector Machine (SVM) [58] in [25, 42, 43, 24], linear criterion  12  Review of methods for automatic cerebral microbleeds detection  classifier (LDC) [134], quadratic discriminant classifier (QDC) [151], Parzen classifier [150] in [21] and Random  Forrest Classifier (RFC) [68] in [28, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  A common approach at this point was also using a previously generated CSF mask to distinguish a real CMB from  vessels, and a WM mask to include the information about the location of potential microbleed [26, 2, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Another approach utilized the advantage of a 3D CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It was usually performed for 3D information inclusion, result-  ing with FP reduction, after the 2D algorithm used in the Candidates detection stage [169] [3, 5, 17, 1, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Some works present also usage of region growing algorithm for CMB verfication [26, 29, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There was also an algorithm investigating the overlap between predictions from adjacent slices [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It not only enabled  removal of false positive predictions that were in fact a ground truth, although labeled in the adjacent slice, but also  helped finding a real CMB that was detected in the adjacent slice in spite of the previous false negative prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='4  System output and evaluation  To comprehensively validate the quality and robustness of the system, one should take advantage of a number of  commonly accepted metrics that provide complementary insight into various aspects of system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  A common oversight is to not include metrics that are complementary and provide a view of the system as a whole,  not just a part of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For instance, the sensitivity metric is useless alone, as it can be artificially inflated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is necessary  to provide the precision or F1 score value to properly interpret the sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In addition, the lack of a uniform way  of result evaluation makes it impossible to compare approaches and effectively assess their usefulness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The evaluation should be performed on a separate dataset or at least separate subjects, using, for instance, cross-  validation to avoid randomness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are different metrics regarding the type of solved problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For classification evaluation, the most popular  metrics are accuracy (1), precision (4), sensitivity/recall (2), and F1 score (5) that combines precision and sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In the case of detection and segmentation, more detailed metrics are required as not only a proper class is important,  but also the overlapped area of ground truth label and prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In that case, the average precision (7) metric is used,  and it is calculated for different values of IoU (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The CMBs detection task is known to produce large number of false positive predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore two additional  metrics were provided particularly for this problem, namely it is FPavg (8) and FPcmb (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The mentioned metrics are calculated as follows:  accuracy =  TP + TN  TP + TN + FP + FN  (1)  sensitivity =  TP  TP + FN  (2)  specificity =  TN  TN + FP  (3)  precision =  TP  TP + FP  (4)  F1 score = 2 × sensitivity × precision  sensitivity + precision  (5)  IoU = Overlaparea  Unionarea  (6)  AP =  � 1  0  p(r) dr  (7)  FPavg = FP  n  (8)  FPcmb = FP  m  (9)  where:  13  Review of methods for automatic cerebral microbleeds detection  TP—true positive – the number of actual CMBs detected;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  FP—false positive – the number of predicted CMBs that were not marked as CMB in ground truth;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  FN—false negative – the number of actual CMBs not detected;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  IoU—intersection over union;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  r—recall (sensitivity);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  p(r)—precision as function of recall;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  n— number of subjects (patients) in the test set;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  m— number of CMBs in the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Accuracy (ACC) (1) shows how the system deals with the classification in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A high score means that almost all  labels have been properly assigned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Sensitivity/recall (2), also known as true positive rate (TPR), shows how the system deals with the ground truth  detection or classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A high score means that almost all ground-true samples have been determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Specificity, also known as true negative rate (TNR) (3), discloses the system ability to recognize the negative class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Precision (4), or positive predictive value (PPV), informs whether the prediction matches ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A high score  means that the system generates a small number of false positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  F1 score (5) helps to check whether there is a balance between sensitivity and precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  IoU (6) stands for Intersection over Union and shows the common area between prediction and ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is  actually a special case of geometrically oriented Jaccard Index [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The average precision (7) AP@0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5 represents  the area under the precision-recall curve with IoU of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5 and it is used in detection and segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' There is also  an AUC - area under curve - metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In case of classification it refers to the ROC curve - sensitivity as a function of  1-specificity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  FPavg (8) shows the average number of false positive predictions per subject, while FPcmb (9) is the number of false  positive predictions per one ground truth sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For example, when we have one subject with 5 ground truth CMBs  and 1 false positive prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The FPavg will equal 1 and FPcmb will equal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  14  Review of methods for automatic cerebral microbleeds detection  Table 3: Comparison of existing approaches 1 The most promising ones are marked with bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Reference  Pre-processing  First stage  Second stage  TPR  PPV  F1  FPavg  FP/CMB  TNR  ACC  Kuijf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  SPM8, BET,  3D RST  manual 5* 2011, [32]  normalization,  inspection  standardization  Seghier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  SPM8,  CSF, GWM, CMBs,  morphological  Authors did not provide any metric, only the table  2011, [73]  normalization  skull scalp,  operations  of results for each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  background img  (2 iterations)  Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  brain extraction,  intensity histogram  SVM, manual  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='7 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5*  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='4*  100 2011, [25]  resize,  threshold  review  normalization  Ghafaryasl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  N3, Elastix,  intensity and  FFFS →LDC,  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='8* 2012, [21]  BET  area threshold  QDC, SVC,  Parzen  Kuijf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  SPM8,  3D RST  manual  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='17  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='68* 2012, [33]  normalization,  inspection  standardization  Kuijf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  SPM8,  3D RST  manual  87 45 2013, [35]  normalization,  inspection  standardization  Bian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  BET, ARC, mIP,  FRST  vessel mask  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5* 2013, [26]  normalization  screening,  3D region  growing,  geometric  features  Fazlollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  CSF,  multi-scale 1D  center  100 158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='93* 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='9 2013, [41]  invertion,  line detection  detection →  normalization,  Hessian  Gaussian blur  matrix  Fazlollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  N4, CSF,  multi-scale  3D Rodon  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='04 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='84  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='7* 2014, [28]  skull-stripping,  Laplacian  Transform →  normalization,  of Gaussian  Hessian  equalization,  matrix,  anisotropic  RFC  diffusion  Fazlollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  N4, CSF,  Laplacian  3D Rodon  87 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1 2015, [27]  inversion,  of Gaussian  Transform →  normalization,  Hessian  equalization,  matrix,  anisotropic  RFC  15  Review of methods for automatic cerebral microbleeds detection  diffusion  Roy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  N4,  3D region  RST,  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='7 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5 2015, [44]  skull stripping,  growing  WM mask,  phase  geometric  enhancement  features  Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  normalization  intensity  CNN,  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='13  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='16  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='91  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='4 2015, [42]  threshold  3D concatenation,  SVM  Dou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  normalization  intensity  ISA  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='44 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='9 2015, [43]  threshold  SVM  van den  FSL FLIRT,  voxel based 90 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3 Heuvel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  FSL FAST,  features →  2015, [45]  N3, SPM12b,  RFC  normalization  Dou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  slices  hierarchical  3D CNN  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='16  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='31  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='74 2016, [3]  merging  3D CNN  Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  reconstruction  SAE 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='20 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='25  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='22  2016, [46]  Syngo MR B17,  SNP  van den  FSL FLIRT,  voxel based  object  93 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='29 Heuvel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  FSL FAST,  features →  classifier,  2016, [29]  N3, SPM12b  RFC  growing-based  algorithm  Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  square  CNN 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='29 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='23  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='05  2017, [22]  window size  Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  SNP,  CNN+RAP 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='94 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='18  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='18  2017, [53]  discard  borders,  cost ratio  Tajudin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', watershed Authors provided only mean square error MSE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='089 and peak  2017, [137]  transform,  signal to noise ratio PSNR = 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5221  active contour  (Chan-Vese)  Standvoss et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='5  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='21  2022, [138]  augmentation  clustering,  geometrical  features  Stanley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  resize,  1D CNN+LSTM 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='76 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='78 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='21  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='24  2022, [72]  contrast  stretching,  normalization,  Gaussian Filter,  histogram  equalization,  morphological  operations,  Sharr gradient,  3D GCM  Sundersan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  fslreorient2std,  Frangi filters,  geometric  91 81  86  2022, [20]  FSL FAST,  FRST, intensity  features  BET  transformations,  level  eigenvalues,  threshold  Gaussian filter,  Laplacian  of Gaussian  1Data marked with * were not provided in original paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Instead, they were calculated either by us or the Authors of other papers listed in Table 3, based on data provided in the  original paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  19  Review of methods for automatic cerebral microbleeds detection  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='5  Comparison of existing approaches  Table 3 presents, in chronological order, multiple approaches regarding cerebral microbleed detection that had place in  recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It can be observed that firstly, the prevailing solutions were those based on traditional image processing  techniques and only later the proposals based on machine learning algorithms have taken the lead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It can be seen, that  they achieved considerably higher performance, both in terms of sensitivity and low false positive generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' There-  fore, it can be assumed that this latter path is more promising regarding practically applicable solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Alternatively,  a combination of traditional and ML methods might be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Regarding the pre-processing stage, there are several operations, such as bias field correction, skull stripping and  normalization, that should be done before providing data into the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Other transforms may also be used in  particular cases, but they are not essential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  An important issue is related with selecting the type of solved problem: whether it should be classification, detection,  or segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A large part of solutions is based on cutting images into smaller fragments and their further classifi-  cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' These approaches are reported to have significantly better ability to distinguish CMB from its mimic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' On the  other hand, in the case of detection, a lot of false positive predictions are generated, which often forces introducing the  second stage, namely false positive reduction or predictions verification, as high false positive generation is the main  problem in CMBs detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another challenge that can be overcome by using classification instead of detection is  the size of the lesion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' CMBs are small objects, which makes them difficult to find in the original image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  No significant improvement can be seen for 3D CNN over 2D CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Probably, a larger training dataset could enable  taking benefit from the 3D CNN structure and consequently achieve better results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For now, however, choosing this  type of solution is discouraging, due to higher computation cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Moreover, it is clearly visible, that the reported research often lack in some metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Even if we accept that mentioning  all of indicators is not necessary, it is crucial to provide a proper evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  We would like to emphasize that in our opinion, based on the gathered data, it is difficult to state which approach is  the best and it is still the area that requires development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, we can draw attention to some most promising  solutions: in case of classification [72, 4] and [75] with the best ACC=98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='60%;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' while in case of detection [19] and [18]  with F1=90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='84%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The mentioned research distinguish also in terms of balanced results - similar values of all metrics,  which is an advantage in comparison to for instance [1, 30, 2] that report higher sensitivity, however suffer from a high  false positive predictions generation - low precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Although [124, 23] also report high accuracy, the datasets used by them were small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Results reported in [72, 18, 19]  were performed on relatively big, but diverse datasets, therefore are hard to compare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' From mentioned proposals only  [4] and [75] can be compared, as they used the same, but small dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Nevertheless, the above careful and comprehensive analysis provides an opportunity to formulate some conclusions,  outline best practices, and point out the key elements of a reliable automatic cerebral microbleeds detection system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  4  Discussion  In this section we discuss the most important aspects for automatic CMBs detection system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  As previously mentioned, a base for any automatic system, especially machine learning model, is the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although  traditional image processing methods do not require large amount of data for training, just for validation and testing  purposes, it is still essential for proper system evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In Section 2 a range of datasets is listed which were used in all reported approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' These datasets differ not only in  terms of acquisition parameters, but also by the origin and medical history of patients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This kind of diversity makes  any comparison of newly proposed approaches almost impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Moreover, some datasets have extremely small  number of subjects [25, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In that case, the tested subset is not representative enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The system trained on such  a narrowed dataset will reveal low generalization ability [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, a big, diversified dataset is needed and  advanced regularization techniques should be applied [149] to prevent over-fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  An interesting approach to overcome the data shortage problem was proposed by Momeni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It consisted of  synthetic microbleeds generation based on previously extracted CMB features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another way to produce huge amounts  of synthesized data are Generative Adversarial Networks (GANs) [141].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' They are able to create new images based  on the features automatically extracted from the existing, real dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, again, it is a method that requires  relatively large dataset at the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Despite the risk of biased data generation, both approaches seem promising  for extending datasets, next to other augmentation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  20  Review of methods for automatic cerebral microbleeds detection  A good practice regarding a general system evaluation is using a completely unrelated dataset for testing to ensure that  the obtained results are impartial like in [18, 74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The term unrelated dataset means the data acquired from a different  MRI machine, from subjects of different origin and medical history, and ranked by another rater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Examinations  performed on various MRI machines may differ in parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is important to synthesize system resistant to features  that do not have a direct impact on prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Usage of various datasets ensures insight into the model’s generalization  ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This, however, is an ideal situation, not always achievable in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  There are also methods such as k-fold validation that may enable better evaluation within the same dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is  recommended especially during system development as depending on chosen training, validation and testing sets, the  obtained results may differ [1, 30, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Another idea is preparation of a system nameplate with detailed description of  system properties and target data type and it should point out operating conditions of the system and its limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The unavailability of the used datasets is another limitation in terms of approach comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although there are  many legal restrictions regarding medical data sharing, establishing a benchmark dataset would significantly trigger  the development in this domain [146], similarly as it was in case of brain glioma segmentation [156] or determining  skeletal age [158, 157].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Another aspect is the pre-processing stage of system synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Subjecting images to any transformations should be  well–thought and justified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Considering the risk of valuable data loss, precautions should be taken to prevent that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  A common method of pre-processing is bias field correction as it enables restoring some important information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Using  dedicated tools for skull stripping seems to be a better approach than simply removing part of the image just as  in [47, 48, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Although unintentionally, the image passed to the system may still be deformed or partial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Any  operations that modify the size of the image, should be performed without content loss just as in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  When it comes to system designing, there are several issues that should be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Firstly, the MRI data is given in  the three-dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Regardless the used algorithms, at some stage it is inevitable to use the information from  the third dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Especially, when detecting cerebral microbleeds is concerned, that kind of data is very important,  as it enables distinguishing the CMBs from their most common mimics - vessels [26, 28, 42, 3, 5, 17, 1, 2, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' While  vessels can be distinguished based on 3D information, the other CMB mimic - calcification looks similar also in the  3D space considering its shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In such case, other MRI sequences, except SWI, may be helpful [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  In the majority of reported research, the solution process is divided into three stages: Pre-processing, CMB Candidates  Detection, and CMB Candidates Verification (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This approach is caused by similarities between CMBs and  their mimics, with consequent high production of false positive candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' All this compels the use of CMB Candi-  dates verification stage to eliminate FP candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It may extend the computation time, but it is necessary to obtain  satisfying results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Still, keeping the balance between accuracy and efficiency is important, particularly when real-time  usage is concerned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  The next, worth considering issue is the nature of cerebral microbleeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' They are small hemorrhages, which are  sometimes difficult to notice even for an experienced radiologist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, the system to be designed should be  sensitive to small objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' For this purpose, automatic systems may turn out even better, as they are able to consider  the information that is not visible for human eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is also important to note that more accurate and sensitive MRI  machines with properly adjusted parameters increase the chance for finding all microbleeds [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Another problem is related to the possibility of missing some CMBs by an experienced rater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In any research regarding  detection a ground truth has to be established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, this is extremely difficult, as the rater agreement may be at  a relatively low level, for instance - κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='68 [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' To reduce this problem, preliminary rating should be performed  by as many raters as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Additionally, verification of system results may be helpful, as some missing CMBs  may be detected by the system and should not be treated as false positive [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' On the other hand, the radiologist has  ability to look at the potential CMB from different perspectives and consult it with others, whereas the system does  not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, providing additional information about gender, age, injury, angiography scans, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' might also turn out  beneficial [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  When designing such a system from the clinical application point of view, certain practical aspects must also be  taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is important to remember about the end-user’s perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' In this context, the form of results  presentation should be designed considering user experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Obviously, the indication by a bounding-box or circle should be provided, but other useful information such as the  confidence score of the prediction could also be included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This value is rather provided by the machine-learning  system, but it gives the information to the radiologist about certainty, which can accelerate the rating process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Other idea might be the presentation of results based on the existing rating scales such as MARS [69] or BOMBS [7]  (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  21  Review of methods for automatic cerebral microbleeds detection  Moreover, there should be the ability of result acceptance or rejection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' As the system to be designed is the computer  aided system, the user should have the possibility to agree with the proposed result or not, as his decision is final.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This  decision, however, has to be strongly distinguished from involving a human in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The raters have knowledge  essential for CMBs rating, therefore they may be used during system design, for instance to validate preliminary results  or to label extracted candidates as CMB and non-CMB, similarly as in [17], but they should not be used as the last stage  of the process to increase the system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The reported 100% precision or specificity of a semi-automated  system in which a human is part of the FP reduction process is simply misleading [25, 35, 51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Even if it significantly  reduces the single scan rating time, this type of evaluation is confusing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  However, the feedback from the radiologist about the prediction may be used for continual learning [159].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This kind  of approach may cause improvement of the already working system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  This smoothly leads to the problem of system evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='4 presented different metrics and their correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Depending on the selected task: classification, detection, or segmentation - different metrics are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' However, it is  crucial to present as many metrics as possible, as they focus on different aspects of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The sensitivity of 99%  may seem an outstanding result, but when it goes with precision of 40% it is not satisfying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The researchers sometimes  stress out the importance of sensitivity and diminish the number of potential false positives, but it can be harmful in  terms of reliable system synthesis [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' All this leads to the conclusion that a properly designed system should be  balanced and optimized as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  System evaluation is also important for enabling comparison between different approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' It is clearly visible in  Table 3 that the researchers not always provide all necessary metrics, which significantly hinders identifying the state-  of-the-art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Despite the current levels of metrics, there is a general issue of system trustworthiness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' While the systems based on  morphological operations and traditional image transformations are pretty easy to explain, the interpretability of black-  box machine-learning systems is still a challenging task [142, 143, 144].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' This problem is crucial, especially in such  a life-impacting domain as medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The process of decision making should be clear to ensure that the conclusions  are drawn based on the nature of the examined object and not on the bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Therefore, there is an urgent need of bias  reduction [145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A list of guidelines regarding designing a responsible and trustworthy AI system is given in [136].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  To the best of our knowledge, the paper collates all available research reports regarding automatic cerebral microbleeds  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The challenges of this task and some flaws of existing proposals have been outlined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' We believe that this  paper will serve as a mine of knowledge and ideas for further research within this domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' We hope that it will  stimulate better practices regarding exchanging knowledge between different research groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  References  [1] Al-masni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kim, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Noh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Automated detection of cerebral microbleeds in  MR images: A two-stage deep learning approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' NeuroImage: Clinical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 28 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 102464 (2020), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='nicl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='102464, ISSN: 2213-1582  [2] Chesebro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Amarante, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Meier, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Mayeux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Brickman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Automated detection of cerebral  microbleeds on T2*-weighted MRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Scientific Reports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 11, 1-13 (2021), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1038/s41598-021-83607-0,  ISSN: 20452322  [3] Dou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Mok, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Heng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Automatic Detection of  Cerebral Microbleeds from MR Images via 3D Convolutional Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' IEEE Transactions On Medical  Imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 35, 1182-1195 (2016), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1109/TMI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2528129, ISSN: 1558254X  [4] Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Tang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral micro-bleeding detection based on densely connected neural  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Frontiers In Neuroscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 13, 1-11 (2019), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3389/fnins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='00422, ISSN: 1662453X  [5] Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Utriainen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Sethi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Xia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Haacke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral microbleed  detection using Susceptibility Weighted Imaging and deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' NeuroImage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 198, 271-282 (2019), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='neuroimage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='046, ISSN: 10959572  [6] Rashid, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Abdulkadir, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nasrallah, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ware, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Spincemaille, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Romero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Bryan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Heckbert,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Habes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' DEEPMIR: a deep neural network for differential detection of cerebral microbleeds and iron  deposits in MRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Scientific Reports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 11, 14124 (2021), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1038/s41598-021-93427-x, ISSN: 2045-2322  [7] Cordonnier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Potter, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Jackson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Doubal, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Keir, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Sudlow, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wardlaw, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Al-Shahi Salman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Improving interrater agreement about brain microbleeds: Development of the Brain Observer MicroBleed Scale  (BOMBS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Stroke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 40, 94-99 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1161/STROKEAHA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='526996, ISSN: 00392499  22  Review of methods for automatic cerebral microbleeds detection  [8] Mazurek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Papuc, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Rejdak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Czynniki wplywajace na wystepowanie mikrokrwawien mozgowych.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Polski Przeglad Neurologiczny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 14, 151-155 (2018), ISSN: 1734-9745, in polish  [9] Shams, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Granberg, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Martola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shams, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Fereshtehnejad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cavallin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Aspelin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Kristoffersen-Wiberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Wahlund, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebrospinal fluid profiles with increasing number of cerebral mi-  crobleeds in a continuum of cognitive impairment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='. Journal Of Cerebral Blood Flow And Metabolism : Official  Journal Of The International Society Of Cerebral Blood Flow And Metabolism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 36, 621-628 (2016), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1177/0271678X15606141, ISSN: 1559-7016 (Electronic)  [10] Akoudad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Portegies, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Koudstaal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hofman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lugt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ikram, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Vernooij, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Mi-  crobleeds Are Associated With an Increased Risk of Stroke: The Rotterdam Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='. Circulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 132, 509-516  (2015), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1161/CIRCULATIONAHA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='016261, ISSN: 1524-4539 (Electronic)  [11] Yakushiji, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nishiyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Yakushiji, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hirotsu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Uchino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nakajima, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Eriguchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nanri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hara,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Horikawa, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Kuroda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Brain microbleeds and global cognitive function in adults without neurological  disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Stroke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 39, 3323-3328 (2008), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1161/STROKEAHA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='516112, ISSN: 00392499  [12] Greenberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Vernooij, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cordonnier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Viswanathan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Al-Shahi Salman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Warach, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Launer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Van Buchem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Breteler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral microbleeds: a guide to detection and interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The Lancet  Neurology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 8, 165-174 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/S1474-4422(09)70013-4, ISSN: 14744422  [13] Myung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Oh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Novel Approaches to Detection of  Cerebral Microbleeds: Single Deep Learning Model to Achieve a Balanced Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 30, 105886 (2021), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='jstrokecerebrovasdis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='105886, ISSN:  1052-3057  [14] Hong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Detecting cerebral microbleeds with transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Machine Vision  And Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 30, 1123-1133 (2019), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/s00138-019-01029-5, ISSN: 14321769  [15] He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Deep Residual Learning for Image Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 2016 IEEE Conference  On Computer Vision And Pattern Recognition (CVPR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 770-778 (2016), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='90  [16] Lupo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hammond, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kelley, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Vigneron, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Majumdar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Nelson,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' GRAPPA-based susceptibility-weighted imaging of normal volunteers and patients with brain tumor at 7 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Magnetic Resonance Imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 27, 480-488 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Smith, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rosand, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Greenberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 30, 338-343 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Brundel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Bresser, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Veluw, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Heringa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Viergever, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Biessels, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 8, e66610 (2013), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='0066610, ISSN: 1932-6203  [36] Hofman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Pols, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Stricker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Tiemeier, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Uitterlinden, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Vinger-  ling, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Witteman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The Rotterdam Study: objectives and design update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='  22, 819-829 (2007), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/s10654-007-9199-x, ISSN: 0393-2990  [37] Simons, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Algra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Laak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='1023/A:1007621514757, ISSN: 1573-7284  [38] Heckbert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Austin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Jensen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Floyd, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Minamida, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nonaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Asai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nam, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Min, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Hwang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' Journal Of Korean Neurosurgical Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 46, 365 (2009), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Rowe, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Desmond, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Yates, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Mok, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='1007/s11042-017-4383-9, ISSN: 1380-7501, 1573-7721  [48] Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 738885 (2021), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Mehmood, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Pan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 32 (2020), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Payabvash, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Avadiappan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shah, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hess, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Lupo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A user-guided  tool for semi-automated cerebral microbleed detection and volume segmentation_ Evaluating vascular injury  and data labelling for machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 8 (2018), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='nicl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='002  [52] Bao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Macdonald, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' (2018), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='35, ISBN: 978-94-6252-607-5  [53] Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Micro-Bleed Detection Based on the Convo-  lution Neural Network With Rank Based Average Pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' IEEE Access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 14 (2002)  [58] Chang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='2046908,  ISSN: 0278-0062, 1558-254X  [60] Sled, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zijdenbos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='1109/42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Staring, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Pluim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='2035616, ISSN: 0278-0062, 1558-254X  [62] Liu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Erhan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Reed, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Brox, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' (2015), arXiv: 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='04597  [64] Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Ledoux, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Khalidov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Tsiouris, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wisnieff, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 20, 45-57 (2001),  DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1109/42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='906424, ISSN: 02780062  [66] Jenkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Smith, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Bannister, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 6,  e17547 (2011), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='0017547, ISSN: 1932-6203  [74] Momeni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Fazlollahi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Nayak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Rashid, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Habes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 1-4 (2020), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='9153365  [77] Hong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='3233/FI-2019-1830, ISSN:  1875-8681  26  Review of methods for automatic cerebral microbleeds detection  [78] Gunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Spychalla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ward, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Graff-Radford, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Huston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kantarci, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Knopman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Petersen,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Jack Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' P4-232: Automating Cerebral Microbleed Detection in Support of Alzheimer’s Disease  Trials Using a Convolutional Neural Network Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 14, P1530-P1531 (2018), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='053, ISSN: 1552-5279  [79] Dou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Heng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' CHAPTER NINE - Automatic lesion detection with three-dimensional  convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Biomedical Information Technology (Second Edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 265-293 (2020), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/B978-0-12-816034-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='00009-2, ISBN: 978-0-12-816034-3  [80] Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Dou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Mok, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Heng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Chapter 6 - Deep Cascaded  Networks for Sparsely Distributed Object Detection from Medical Images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Deep Learning For Medical Image  Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 133-154 (2017), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/B978-0-12-810408-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='00008-0, ISBN: 978-0-12-810408-8  [81] Kirsch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', McAuley, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Holshouser, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Petersen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ayaz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Vinters, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Dickson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Haacke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Britt III,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Larsen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kim, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Mueller, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Schrag, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Kido, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Serial Susceptibility Weighted MRI Measures Brain  Iron and Microbleeds in Dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Journal Of Alzheimer’s Disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 17, 599-609 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3233/JAD-  2009-1073, ISSN: 1387-2877  [82] Mayeux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Washington Heights-Hamilton Heights-Inwood Columbia Aging Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (Columbia University  Irving Medical Center Neurological Institute, The Taub Institute for Research on Alzheimer’s Disease),  https://cheba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='au/consortia/cosmic/studies/washington-heights-inwood-and-columbia-aging-project-  whicap, Accessed: 2022-06-01  [83] Ellis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Bush, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Darby, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Fazio, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Foster, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hudson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lautenschlager, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lenzo, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Martins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Maruff, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Masters, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Milner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Pike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rowe, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Savage, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Szoeke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Taddei, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Villemagne,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Woodward, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ames, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Group, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' The Australian Imaging, Biomarkers and Lifestyle (AIBL) study  of aging: methodology and baseline characteristics of 1112 individuals recruited for a longitudinal study of  Alzheimer’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' International Psychogeriatrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 21, 672-687 (2009), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1017/S1041610209009405,  ISSN: 1741-203X, 1041-6102  [84] Medical Education, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Research Alzheimer’s Disease Research Center - Data Sharing and Re-  sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='edu/research/centers-programs/alzheimers-disease-research-center/research-  activities/mayo-clinic-study-aging/for-researchers/data-sharing-resources), Accessed: 2022-04-04  [85] Initiative, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' ADNI ACCESS DATA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (https://adni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='edu/data-samples/access-data/), Accesed: 2022-04-  04  [86] Pacurar,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Sethi,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Habib,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Laze,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Martis-Laze,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Haacke,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Database integra-  tion of protocol-specific neurological imaging datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' NeuroImage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 124 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 1220-1224 (2016), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='neuroimage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='066, ISSN: 1053-8119  [87] O’Donnell, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rosand, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Knudsen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Furie, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Segal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chiu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ikeda, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Greenberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Apolipopro-  tein E Genotype and the Risk of Recurrent Lobar Intracerebral Hemorrhage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' New England Journal Of Medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  342, 240-245 (2000), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1056/NEJM200001273420403, ISSN: 0028-4793  [88] Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Gurol, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rosand, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Viswanathan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rakich, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Groover, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Greenberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Smith,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Progression of white matter lesions and hemorrhages in cerebral amyloid angiopathy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Neurology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 67, 83-87  (2006), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1212/01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 363, 1925-1933 (2004), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Friston, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ashburner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Nicholas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Wheeler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Cuzzocreo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Bazin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Bassett, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Prince, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='356937, ISBN: 1424406722  [98] Carass,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Cuzzocreo,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Wheeler,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Bazin,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=',  Resnick,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Prince,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Tanizaki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Bertrand, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 30, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' (https://case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='edu/med/neurology/NR/MRI  [119] Werring, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='  17, 193-203 (2007), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='00070.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='x, ISSN: 10512284, 15526569  [120] Shoamanesh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kwok, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Benavente, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Microbleeds: Histopathological Correlation of Neu-  roimaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 32, 528-534 (2011), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1159/000331466, ISSN: 1421-9786, 1015-  9770  [121] Martinez-Ramirez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Greenberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Viswanathan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral microbleeds: overview and implications in  cognitive impairment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='1186/alzrt263, ISSN: 1758-9193  [122] Imaios Introduction to MRI sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='com/en/e-Courses/e-MRI/MRI-Sequences/MRI-  sequences), ISBN 978-1847537768, Accessed: 2022-04-29  [123] Lipton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Image Contrast: T1, T2, T2, and Proton Density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 38-46 (2008), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/978-0-387-48896-7_4, ISBN: 978-0-387-  48896-7  [124] Doke, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Shrivastava, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Pan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' Machine Vision And Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 31, 36 (2020), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/s00138-020-01087-0,  ISSN: 0932-8092, 1432-1769  [125] Lu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Xia, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Diagnosis of cerebral microbleed via VGG and extreme learning machine trained  by Gaussian map bat algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Journal Of Ambient Intelligence And Humanized Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (2020), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/s12652-020-01789-3, ISSN: 1868-5137, 1868-5145  [126] Sa-ngiem, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Dittakan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Temkiatvises, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Yaisoongnern, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Kespechara, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Microbleed Detec-  tion by Extracting Area and Number from Susceptibility Weighted Imagery Using Convolutional Neural Net-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Journal Of Physics: Conference Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 1229, 012038 (2019), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1088/1742-6596/1229/1/012038,  ISSN: 1742-6588, 1742-6596  [127] Jenkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Beckmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Behrens, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Woolrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Smith, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' FSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Neuroimage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 62, 782-790 (2012),  DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='neuroimage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='015  [128] Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zhu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Siew, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Extreme learning machine: Theory and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Neurocomputing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 70,  489-501 (2006), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='neucom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='126, ISSN: 09252312  [129] Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Girshick, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Faster R-CNN: Towards Real-Time Object Detection with Region Pro-  posal Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Proceedings Of The 28th International Conference On Neural Information Processing Systems  Volume 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 91-99 (2015)  [130] Redmon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Farhadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' YOLO9000: Better, Faster, Stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Proceedings Of The IEEE Conference On  Computer Vision And Pattern Recognition (CVPR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (2017)  [131] Krizhevsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Sutskever, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' ImageNet Classification with Deep Convolutional Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Advances In Neural Information Processing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 25 (2012)  [132] Simonyan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Zisserman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Very Deep Convolutional Networks for Large-Scale Image Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (2015),  arXiv:1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1556  29  Review of methods for automatic cerebral microbleeds detection  [133] Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Maaten, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Weinberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Densely Connected Convolutional Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (2018),  arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='06993  [134] Barnard, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Casasent, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' A comparison between criterion functions for linear classifiers, with an appli-  cation to neural nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 19, 1030-1041 (1989), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1109/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='44018  [135] Mikolajczyk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Grochowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 2018 International Interdisciplinary PhD Workshop (IIPhDW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 117-122 (2018), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Díaz-Rodríguez, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=', Jonsson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' & Launer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral microbleeds in the population based  AGES–Reykjavik study: prevalence and location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Journal Of Neurology, Neurosurgery & Psychiatry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 79, 1002  (2008)  [161] Werring, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 127, 2265-2275 (2004), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1093/brain/awh253, ISSN: 1460-2156  [162] Poels, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Ikram, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Lugt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hofman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Niessen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Krestin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Breteler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Vernooij, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Cerebral microbleeds are associated with worse cognitive function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Neurology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 78, 326 (2012), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1212/WNL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='0b013e3182452928  [163] Cordonnier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Flier, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Brain microbleeds and Alzheimer’s disease: innocent observation or key player?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 134, 335-344 (2011), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1093/brain/awq321, ISSN: 1460-2156, 0006-8950  [164] Bian, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Hess, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Chang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Nelson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Lupo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Susceptibility-weighted MR imaging of radiation therapy-  induced cerebral microbleeds in patients with glioma: a comparison between 3T and 7T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 56,  91-96 (2014), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1007/s00234-013-1297-8, ISSN: 0028-3940, 1432-1920  [165] Revol-Muller, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Peyrin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Carrillon, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Odet, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Automated 3D region growing algorithm based on an  assessment function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Pattern Recognition Letters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 23, 137-150 (2002), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1016/S0167-8655(01)00116-7,  ISSN: 01678655  [166] Buscema, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 33, 233-270 (1998,1), DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3109/10826089809115863, ISSN: 1082-6084, 1532-2491  [167] Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Battle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Raina, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Ng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Efficient sparse coding algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Advances In Neural Information  Processing Systems 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 8 (2006)  [168] O’Shea, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Nash, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' An Introduction to Convolutional Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' (arXiv,2015), Number:  arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='08458 [cs]  [169] Singh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Gupta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Goli, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Padmanabhan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Gulyás, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 3D Deep Learning on Medical Images:  A Review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 20, 5097 (2020), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='3390/s20185097, ISSN: 1424-8220  [170] Haller, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Haacke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Thurnher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Barkhof, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 299, 3-26 (2021,4), ISSN: 0033-8419, 1527-1315, DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='2021203071  [171] Hodel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Rodallec, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Gerber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Blanc, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Maraval, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Caron, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Tyvaert, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Zuber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Zins, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='  Séquences IRM SWAN, SWI et VenoBOLD exploitant le phénomène de susceptibilité magnétique : principes  techniques et applications cliniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 39, 71-86 (2012,5,1), ISSN: 0150-9861, DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='neurad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='006, language: French  31  Review of methods for automatic cerebral microbleeds detection  [172] Nandigam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Scully, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content=' 81, 199-200 (2013,7,9), ISSN: 0028-3878, 1526-632X, DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='12  [173] Ayaz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Boikov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Haacke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kido, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Kirsch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+page_content='22001  [174] Haller, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Vernooij, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Kuijer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Larsson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=', Jäger, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' & Barkhof, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Cerebral Microbleeds: Imaging and  Clinical Significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' Radiology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content=' 287, 11-28 (2018), DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='1148/radiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
+page_content='2018170803, ISSN: 0033-8419  32' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FRT4oBgHgl3EQfYTew/content/2301.13549v1.pdf'}
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+Dynamic Regret of Randomized Online Service
+Caching in Edge Computing
+Siqi Fan, I-Hong Hou
+Texas A&M University
+College Station, USA
+{siqifan, ihou}@tamu.edu
+Van Sy Mai
+National Institute of Standards and Technology
+Gaithersburg, USA
+vansy.mai@nist.gov
+Abstract—This paper studies an online service caching prob-
+lem, where an edge server, equipped with a prediction window of
+future service request arrivals, needs to decide which services to
+host locally subject to limited storage capacity. The edge server
+aims to minimize the sum of a request forwarding cost (i.e., the
+cost of forwarding requests to remote data centers to process)
+and a service instantiating cost (i.e., that of retrieving and setting
+up a service). Considering request patterns are usually non-
+stationary in practice, the performance of the edge server is
+measured by dynamic regret, which compares the total cost with
+that of the dynamic optimal offline solution. To solve the problem,
+we propose a randomized online algorithm with low complexity
+and theoretically derive an upper bound on its expected dynamic
+regret. Simulation results show that our algorithm significantly
+outperforms other state-of-the-art policies in terms of the runtime
+and expected total cost.
+I. INTRODUCTION
+Edge computing is a paradigm shift from cloud computing,
+where computation and data storage are brought closer to end
+users instead of offloading to a central cloud. This is done
+through the deployment of edge servers that can host (or
+cache) some popular services and process the corresponding
+computation tasks directly without having to forward them to
+remote clouds. Such close proximity provided by edge com-
+puting not only reduces bandwidth consumption in backhaul
+links, but also is critical for supporting various services and
+applications that require real-time data processing, such as
+augmented reality, virtual reality, and autonomous vehicles.
+To fully realize the potential of edge computing in prac-
+tice, several challenges in designing efficient service caching
+algorithms running on edge servers must be dealt with. First,
+edge servers can often host only a small number of services
+due to their limited storage capacity. Second, user requests
+are typically time-varying, and it is usually infeasible to
+fully predict future requests. Third, reconfiguring edge servers,
+which involves downloading necessary data and setting up
+virtual machines or containers, can incur significant delay and
+communication cost.
+Existing studies for addressing these challenges typically
+design online policies that aim at learning and adopting an
+optimal static offline policy, e.g., Paschos et al. [1] and Zhang
+et al. [2]. Here, a static offline policy is one that knows all
+future requests but only caches the same set of services at all
+times, and the cost difference between an online policy and the
+optimal offline counterpart is known as static regret. Clearly,
+by focusing on learning the optimal static offline policy, these
+studies ignore potential gains from dynamically reconfiguring
+edge servers in response to changes in request arrival patterns.
+As a result, static regret is deemed less applicable when the
+environment is constantly changing. This motivates the notion
+of dynamic regret, where an online algorithm is compared
+against optimal dynamic solutions in hindsight. Few recent
+studies [3], [4] investigate dynamic regret for different applica-
+tions but only design online algorithms that produce fractional
+solutions. Since service caching decisions are required to be
+integers, these algorithm cannot be applied directly.
+In this paper, we propose an online service caching policy
+with provably low dynamic regret by combining the strengths
+of two recently proposed algorithms, one is an online gradient
+algorithm [4] that has low dynamic regret but only produces
+fractional solutions and the other is a randomized algorithm
+[5] that turns fractional solutions into integer ones but has no
+bounds on dynamic regret. We point out that this combination
+is not trivial because simply applying these two algorithms to
+our cost function does not readily lead to low dynamic regret
+due to the accumulated error from the randomization step.
+Thus, in order to bridge the gap between these two algorithms,
+we carefully construct an auxiliary function that not only
+admits fractional solutions but also explicitly incorporates the
+additional costs due to the randomized algorithm. Specifically,
+in each time slot, our algorithm first applies a projected
+gradient descent method to the auxiliary cost function using a
+customized efficient projection step. The output of this step
+is then treated as the probabilities of caching services at
+the edge server. Finally, a randomized algorithm is used to
+determine actual integer caching decisions. We also note that
+both algorithms in [4] and [5] do not provide low complexity
+implementations of their projected gradient steps.
+Our contributions in this paper are as follows. First, we
+develop an online service caching algorithm that yields integer
+solutions with provably low dynamic regret. In particular, we
+establish an upper bound of the regret that is sublinear in time
+when the path length, a measure of how frequently request
+arrival patterns change, is also sublinear in time. We prove
+that this upper bound can be further reduced when a finite
+window of request arrival predictions is available to the edge
+server. In addition, we develop a new algorithm for computing
+arXiv:2301.04128v1  [cs.NI]  10 Jan 2023
+
+exact projection onto a bounded simplex in nearly linear time;
+existing methods either run in quadratic time or only compute
+an approximate. This projection algorithm not only leads to an
+efficient implementation of our online caching algorithm, but
+is also of independent interest in other applications. Finally,
+simulation results show that our policy outperforms other state-
+of-the-art online algorithms under a variety of settings.
+The rest of the paper is organized as follows. Section II
+reviews closely related work. Section III introduces our system
+model and the online caching problem of interest. Section IV
+provides details of our randomized online service caching
+algorithm. Section V analyzes the expected dynamic regret of
+the algorithm. Section VI proposes an efficient projection al-
+gorithm and analyzes the complexity of our randomized online
+algorithm. Some simulation results are given in Section VII.
+Finally, Section VIII concludes the paper.
+II. RELATED WORK
+The majority of studies on the online caching problem are
+focused on static regret, which is evaluated by comparing with
+a static offline policy. For example, Paschos et al. [1], Zhang
+et al. [2], Salem et al. [6] and Tan et al. [7] form caching
+problems into online convex optimization and apply gradient
+method to obtain algorithms with sublinear static regret. Fan
+et al. [5] consider the problem of jointly optimizing service
+caching and routing and show that an online gradient descent
+method can achieve a sublinear static regret. Considering
+competitive ratio, Chen et al. [8] proposes an online algorithm
+based on LASSO, while Lin et al. [9] and Shi et al. [10]
+modify receding horizon control algorithm. All these studies
+focus on comparison with static optimal policy.
+Dynamic regret is first introduced by Zinkevich [11]. Chen
+et al. [3] proposes an adaptive online saddle-point method and
+studies its dynamic regret. By allowing temporary constraint
+violation, Jin et al. [12], [13] proposes different online learning
+models with a dynamic regret bound. However, these studies
+do not consider instantiating costs.
+Some recent studies explore using predictions to improve
+the performance of online algorithms. Considering precise
+request predictions, Chen et al. [14] and Goel et al. [15]
+study an online caching problem with 2-norm instantiating
+costs and propose different algorithms with low competitive
+ratios. In addition, Comden et al. [16] and Li et al. [4]
+propose online caching algorithms and analyze their dynamic
+regret. Furthermore, Chen et al. [17] and Li et al. [18]
+consider noisy predictions and analyze dynamic regret of their
+proposed algorithms. These studies, however, do not guarantee
+to produce integer solutions, and hence are not applicable to
+service caching when the services are indivisible.
+III. SYSTEM MODEL
+We consider a system with multiple clients, an edge server,
+and a remote data center providing N different services. The
+edge server is located near the clients and can cache a small
+subset of services. Any request from clients sent to the server
+can be processed immediately if the corresponding service is
+cached locally, otherwise it is forwarded to the remote center
+for processing.
+Assume that time is slotted, and the total number of time
+slots is T. The edge server can dynamically adjust the set
+of services it caches. However, changing the set of cached
+services involves time-consuming operations such as down-
+loading and setting up new services. Hence, we assume that the
+edge server can only adjust its cached services at the beginning
+of each time slot.
+Let xn,t ∈ {0, 1} denote the caching decision for service
+n at time t. Let Xt := [x1,t, x2,t, . . . , xN,t] be the caching
+decision at time t and Xa:b := [Xa, Xa+1, . . . , Xb]. Since the
+edge server often has limited storage, we assume that at most
+M services can be cached at any time, that is,
+N
+�
+n=1
+xn,t ≤ M,
+∀t.
+(1)
+Whenever the edge server caches a new service, it needs
+to download and install the said service. We model the cost
+of downloading and installing service n by imposing an
+instantiating cost of βn. Thus, the total instantiating cost at
+time t is
+N
+�
+n=1
+βn|xn,t − xn,t−1|+,
+where |x|+ := max{x, 0} for any x ∈ R.
+Next, we discuss the model for request arrivals and pro-
+cessing. Denote the total number of requests for service n
+in time slot t as λn,t. Let Λt = [λ1,t, λ2,t, . . . , λN,t] and
+Λa:b := [Λa, Λa+1, . . . , Λb]. We make the following mild
+assumption about Λt: If service n and service m are both
+among the top M + 1 most popular services at time t, then
+λn,t ̸= λm,t. This mild assumption is to ensure that the
+ordering of the top M services is always unique.
+The edge server can process all requests for its cached
+services locally. For services not cached at the edge, i.e.,
+xn,t = 0, the edge server must forward all associated requests
+to the remote data center for processing, which inevitably leads
+to larger delays. The round-trip time between the edge server
+and the remote data center is determined by the conditions
+of the backbone network and the remote data center, and is
+little impacted by the edge server’s caching decisions. Hence,
+we assume that there is a constant delay for requests that are
+processed by the remote data center, and say that the system
+suffers a constant forwarding cost of α for each forwarded
+request. The total forwarding cost in time slot t is then
+α
+N
+�
+n=1
+λn,t(1 − xn,t).
+Therefore, the total cost in time slot t can be written as
+Ft(Xt, Xt−1) :=
+N
+�
+n=1
+(αλn,t(1 − xn,t) + βn|xn,t − xn,t−1|+).
+
+The goal of the edge server is to solve the problem of
+minimizing the total cost, which is shown below.
+min
+X1:T
+T
+�
+t=1
+Ft(Xt, Xt−1),
+(2)
+s.t.
+xn,t ∈ {0, 1},
+∀n, ∀t,
+(3)
+N
+�
+n=1
+xn,t ≤ M,
+∀t.
+(4)
+Note that solving this problem exactly is already challenging
+in the offline setting (i.e., all request arrivals are known in
+advance) due to the binary constraint in (3). It is even more so
+(if not impossible) in the online setting, where the edge server
+needs to determine caching decision Xt at the beginning of
+each time slot t given limited knowledge about future request
+arrivals. We assume that the edge server employs an online
+algorithm and has exact predictions of request arrivals only
+in next W time slots at any time t. Note that setting W = 0
+would correspond to the case where the edge server has no
+prediction ability; the case of using imprecise predictions is
+left for future work. The concept of an online algorithm is
+formally defined as follows:
+Definition 1. An online service caching algorithm is one that,
+after knowing X1:t−1 and Λ1:t+W −1, determines, possibly at
+random, Xt at time t.
+The expected cost of an online algorithm ξ is denoted by
+C(ξ) := E[�T
+t=1 Ft(Xt, Xt−1)|ξ], where E[·] denotes the
+expectation function over all possible randomness.
+To measure the performance of ξ, we compare the total cost
+of algorithm ξ to that of an optimal dynamic offline policy,
+which is formally defined as follows.
+Definition 2 (Optimal Dynamic Offline Policy (OPT)). An
+optimal dynamic offline policy is one that produces optimal
+solution X∗
+1:T for the problem in (2)–(4).
+Note that we allow any offline algorithm to cache different
+services in different time slots. This feature makes our work
+different from most existing studies on service caching that
+only consider optimal static offline policies, where the same
+set of services is cached in all time slots.
+The difference between the expected cost of ξ and the cost
+of optimal dynamic offline policy, denoted by C(OPT), is
+called expected dynamic regret, i.e.,
+Reg(ξ) := C(ξ) − C(OPT).
+(5)
+Obviously, the expected dynamic regret of any online policy
+depends on the request arrivals Λ1:T . We characterize Λ1:T by
+its path length. Specifically, let θn,t be the indicator function
+that service n is among the top M services with the most
+requests in time slot t. Then, the path length of Λ1:T is defined
+as �T
+t=1
+�N
+n=1 |θn,t −θn,t−1|. Let Θt := [θ1,t, θ2,t, . . . , θN,t].
+Loosely speaking, the path length measures the variation of the
+request distribution over time. We assume that the path length
+of Λ1:T is upper-bounded by HT , i.e., �T
+t=1 ∥Θt −Θt−1∥1 ≤
+HT , and the edge server knows the value of HT .
+The goal of this work is to develop an online service caching
+algorithm whose expected dynamic regret is o(T) whenever
+HT = o(T).
+IV. RANDOMIZED ONLINE SERVICE CACHING
+ALGORITHM
+In this section, we propose a randomized online service
+caching algorithm. Our algorithm mainly consists of two
+components. The first component determines the probability
+of caching a service n at time t with the goal of minimizing an
+auxiliary cost function. The second component is a randomized
+algorithm that determines which service to be cached at the
+edge based on the result of the first component while limiting
+the resulting instantiating cost. As we will show in the next
+section, combining these two components gives rise to an
+upper bound on the expected dynamic regret.
+To express the probability distribution of Xt, we construct
+K sample paths, each representing a probability mass of
+1
+K .
+At the beginning of the whole process, the edge server chooses
+a number k∗ uniformly at random from {1, 2, . . . , K}. Then,
+it uses the sample path k∗ at time t as the caching decision
+in time t.
+For sample paths designed above, the portion of sample
+paths that cache a service is the same as the probability
+we cache this service. Let pn,t be the probability that the
+edge server caches service n at time slot t, and let Pt :=
+[p1,t, p2,t, . . . , pN,t] and Pa:b := [Pa, Pa+1, . . . , Pb]. Due to
+(1), Pt is restricted to be in the following feasible set
+D :=
+�
+[p1, . . . , pN] | 0 ≤ pn ≤ 1, ∀n,
+N
+�
+n=1
+pn ≤ M
+�
+.
+(6)
+For decisions in sample paths, we use sk,n,t ∈ {0, 1} to de-
+note the indicator function that service n is cached on sample
+path k at time t, and let Sk,t := [sk,1,t, sk,2,t, . . . ]. Then, the
+edge server sets Xt = Sk∗,t in each time slot t as caching de-
+cisions. Thus, a randomized online service caching algorithm
+is effectively one that determines S1,t, S2,t, . . . , SK,t, in each
+time slot t.
+As described above, our algorithm consists of two parts
+in each time slot t. In particular, we first determine caching
+probability Pt based on previous probabilities and request
+arrivals Λt−1:t+W −1. Then, we use Pt and sample paths at
+t − 1, i.e., [S1,t−1, S2,t−1, . . . , SK,t−1], to determine sample
+paths at t. The overall algorithm is shown in Algorithm 1
+and detailed steps are given in the next subsections. Here, to
+simplify notation, we let our algorithm start from t = −W +1
+with Λt, Sk,t, Pt set to zero for all t ≤ 0.
+A. Caching Probability Update
+Let us now discuss in detail our approach for determining Pt
+in the first part of our algorithm. Define the following auxiliary
+
+Algorithm 1 Randomized Online Service Caching (ROSC)
+Parameter: K
+1: Choose k∗ uniformly at random from {1, 2, . . . , K}
+2: ¯P−W +1:T ← 0
+3: for t = −W + 1 to T do
+4:
+Obtain parameter Λt+W −1
+5:
+Apply HeapSort on Λt+W −1 to calculate Θt+W −1
+6:
+Pt+W ← Θt+W −1
+7:
+if W > 0 then
+8:
+Pt:t+W −1, ¯Pt:t+W −1←Algo. 2(Λt:t+W −1, Pt−1:t+W ,
+¯Pt:t+W −1, t)
+9:
+if t ≥ 1 then
+10:
+[S1,t, . . . , SK,t] ← Algo. 3(Pt, S1,t−1, . . . , SK,t−1)
+11:
+Xt ← Sk∗,t
+cost function ˆFt, which will be used as our surrogate objective
+function.
+ˆFt(Pt, Pt−1) :=
+�
+j : 0≤pj,t−pj,t−1≤γ
+3βj
+γ (pj,t − pj,t−1)2+
+�
+i : pi,t−pi,t−1>γ
+3βi(pi,t − pi,t−1) + α
+�
+1≤n≤N
+λn,t(1 − pn,t),
+(7)
+where γ > 0 is a parameter whose value will be discussed
+in the next section. By comparing ˆFt with Ft, one can see
+that the only difference is in the instantiating cost component.
+Here, the quadratic term is to ensure that ˆFt is differentiable
+everywhere, and a factor of 3 is added in order to bound
+the expected dynamic regret introduced by the randomized
+algorithm that will be discussed in the next section.
+At each time t, after obtaining the prediction Λt+W −1, the
+edge server first sets Pt+W = Θt+W −1, i.e., pn,t+W = 1
+if service n is among the top M most requested services
+in time slot t + W − 1, and pn,t+W
+= 0, otherwise. If
+W > 0, we will further update Pt:t+W −1 so as to reduce
+�t+W −1
+τ=t
+ˆFτ(Pτ, Pτ−1) through projected gradient descent
+with step size η.
+Note that each Pτ only appears in ˆFτ and ˆFτ+1. Thus, we
+obtain the gradient of �t+W −1
+τ=t
+ˆFτ(Pτ, Pτ−1) with respect to
+Pτ, denoted as ∇Pτ ( ˆFτ(Pτ, Pτ−1)+ ˆFτ+1(Pτ+1, Pτ)), where
+∂
+∂pn,τ
+� ˆFτ(Pτ, Pτ−1) + ˆFτ+1(Pτ+1, Pτ)
+�
+(8)
+=
+�
+gn(pn,τ−1, pn,τ) − αλn,τ − gn(pn,τ, pn,τ+1)
+if τ < T
+gn(pn,τ−1, pn,τ) − αλn,τ
+if τ = T
+and the value of gn(a, b) is set to be 0 if b − a < 0, set to be
+6βn
+γ (b − a) if 0 ≤ b − a ≤ γ, and set to be 3βn if b − a > γ.
+Then, we update Pτ from τ = t+W −1 down to τ = t. To
+ensure the gradient of �t+W −1
+τ=t
+ˆFτ(Pτ, Pτ−1) with respect to
+Pτ is obtained based on Pτ−1, Pτ, and Pτ+1 with the same
+update times, we use the updated Pτ+1, the original Pτ and
+the Pτ−1 in the previous iteration before its update, which is
+denoted as ¯Pτ−1, to calculate the gradient. Thus, we update
+Pτ by
+Pτ = ΠD(Pτ − η∇Pτ ( ˆFτ(Pτ, ¯Pτ−1) + ˆFτ+1(Pτ+1, Pτ)),
+where ΠD(·) is the projection operator onto set D given in (6).
+This distinction is important for establishing an expected
+dynamic regret bound, as will be discussed in Section V.
+Algorithm 2 shows the detail of updating Pt:t+W −1.
+Algorithm 2 Projected Gradient Descent
+Input: Λt:t+W −1, Pt−1:t+W , ¯Pt−1:t+W , t
+Parameter: γ, η
+1: for τ = t + W − 1 to max{1, t} do
+2:
+Calculate ∇Pτ ( ˆFτ(Pτ, ¯Pτ−1) + ˆFτ(Pτ+1, Pτ)) by (8)
+3:
+¯Pτ ← Pτ
+4:
+Pτ ← ΠD(Pτ −η∇Pτ ( ˆFτ(Pτ, ¯Pτ−1)+ ˆFτ+1(Pτ+1, Pτ))
+Output: Pt:t+W −1, ¯Pt:t+W −1
+B. Sample Path Update
+Our algorithm for determining [Sk,t] employs that in Fan
+et al. [5], which studies online randomized algorithm for a
+different setting without establishing expected dynamic regret
+bound. The first step is to quantize every pn,t in Pt into a
+multiple of
+1
+K , denoted as pQ
+n,t. Let P Q
+t
+:= [pQ
+1,t, . . . , pQ
+N,t].
+Note that each service n in [Sk,t] needs to be cached in exactly
+KpQ
+n,t sample paths. Set sample path Sk,t = Sk,t−1 for all
+k at time t. Then, for each n, randomly choose K(pQ
+n,t −
+pQ
+n,t−1) sample paths without service n to cache service n if
+pQ
+n,t > pQ
+n,t−1, and delete service n from K(pQ
+n,t−1 − pQ
+n,t)
+randomly chosen sample paths with service n if the pQ
+n,t <
+pQ
+n,t−1. Finally, for each sample path k that caches more than
+M services, find another sample path k′ with less than M
+cached services, and randomly choose a service n that k caches
+and k′ does not. Delete service n from k and cache it in the
+k′. Detailed steps are shown in Algorithm 3. This algorithm
+is designed so that the number of changes, which corresponds
+to the instantiating cost at time t, can be bounded.
+V. EXPECTED DYNAMIC REGRET
+In this section, we analyze the regret of ROSC. The main
+result is the following.
+Theorem 1. Let γ =
+�
+HT
+T
+and η =
+γ
+12β∗ with β∗ :=
+maxn βn. If the number of requests in each time slot is upper-
+bounded by U, that is, �N
+n=1 λn,t ≤ U, ∀t, then
+Reg(ROSC) ≤
+�6
+√
+2Mβ∗(α + 3β∗)
+αW
++ 3β∗N
+��
+HT T
++ (αU + 6β∗N)T
+K
++ 2β∗HT .
+(9)
+In particular, Reg(ROSC) = o(T) if HT = o(T) and K =
+√
+T.
+We will prove this result in two steps. First, let P
+′
+1:T
+be the final value of P1:T in Algorithm 1 and let P ∗
+1:T be
+
+Algorithm 3 Randomized Caching
+Input: Pt, S1,t−1, S2,t−1, . . . , SK,t−1
+1: P Q
+t ← quantize every pn,t in Pt into a multiple of
+1
+K
+2: P Q
+t−1 ← 1
+K
+�K
+k=1 Sk,t−1
+3: ∆t := [δ1,t, . . . , δN,t] ← P Q
+t − P Q
+t−1
+4: S1,t, S2,t, . . . , SK,t ← S1,t−1, S2,t−1, . . . , SK,t−1
+5: for n = 1, 2, . . . , N do
+6:
+if δn,t > 0 then
+7:
+Find the set {sk,n,t|sk,n,t = 0}, randomly pick Kδn,t
+elements in it and set to 1
+8:
+else if δn,t < 0 then
+9:
+Find the set {sk,n,t|sk,n,t = 1}, randomly pick
+|Kδn,t| elements in it and set to 0
+10: while ∃ �N
+n=1 sk,n,t > M do
+11:
+Find k′ that �N
+n=1 sk′,n,t < M
+12:
+Randomly choose a service n′ from the set {n|sk′,n,t =
+0, sk,n,t = 1}
+13:
+sk′,n′,t ← 1, sk,n′,t ← 0
+Output: S1,t, S2,t, . . . , SK,t
+the optimal vector for minimizing the auxiliary cost function
+�T
+t=1 ˆFt(Pt, Pt−1) under the constraint (4). We will derive
+an upper bound on �T
+t=1 ˆFt(P
+′
+t , P
+′
+t−1)−�T
+t=1 ˆFt(P ∗
+t , P ∗
+t−1).
+Second, we will show that Reg(ROSC), which is defined with
+respect to Ft(·) instead of ˆFt(·), can actually be bounded by
+a function of �T
+t=1 ˆFt(P
+′
+t , P
+′
+t−1) − �T
+t=1 ˆFt(P ∗
+t , P ∗
+t−1).
+A. Bounding �T
+t=1 ˆFt(P
+′
+t , P
+′
+t−1) − �T
+t=1 ˆFt(P ∗
+t , P ∗
+t−1)
+We first compare ROSC with an offline policy and then
+bound �T
+t=1 ˆFt(P
+′
+t , P
+′
+t−1)−�T
+t=1 ˆFt(P ∗
+t , P ∗
+t−1). Consider an
+offline policy that knows Λ1:T and employs the projected
+gradient descent algorithm to minimize
+J(Q) :=
+T
+�
+t=1
+ˆFt(Qt, Qt−1)
+subject to the constraint Q = [Q1, . . . , QT ] ∈ H, where
+Qt := [q1,t, q2,t, . . . , qN,t] and H := {Q | 0 ≤ qn,t ≤
+1, ∀n, t, �N
+n=1 qn,t ≤ M, ∀t}. Following a projected gradient
+descent algorithm, the offline policy first initializes Q0
+t = Λt−1
+and then updates its caching decisions Q in each iteration
+w = 1, . . . , W as follows
+Qw ← ΠH
+�
+Qw−1 − η∇J(Qw−1)
+�
+.
+(10)
+Note that the following has been shown in Li et al. [4].
+Lemma 1. For update (10), we have QW
+t
+= P
+′
+t , ∀t.
+Using this result, we can prove the following.
+Lemma 2. Consider ROSC with step size η =
+γ
+12β∗ . Then
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1)
+≤ 6β∗
+γW
+T
+�
+t=1
+∥Θt−1 − P ∗
+t ∥2
+2.
+Proof: First, it can be seen that J(·) is 12β∗
+γ
+smooth. Then
+the result follows by simply applying [19, Theorem 10.21] to
+the offline policy (10) and then using Lemma 1.
+Next, we bound the term �T
+t=1 ∥Θt−1 − P ∗
+t ∥2
+2. In fact,
+Lemma 3. We have
+T
+�
+t=1
+∥Θt−1 − P ∗
+t ∥2
+2 ≤
+√
+2M(α + 3β∗)
+α
+HT .
+(11)
+Proof: First, note that if 0 ≤ pj,t − pj,t−1 ≤ γ, then
+3βj
+γ (pj,t − pj,t−1)2 ≤ 3βj(pj,t − pj,t−1). Using this and the
+definitions of ˆFt, we have ˆFt(Θt, Θt−1) ≤ α �N
+n=1 λn,t(1 −
+θn,t) + 3 �N
+n=1 βn|θn,t − θn,t−1|+.
+Since
+P ∗
+1:T
+minimizes
+�T
+t=1 ˆFt(Pt, Pt−1),
+we
+have
+�T
+t=1 ˆFt(P ∗
+t , P ∗
+t−1)
+≤
+�T
+t=1 ˆFt(Θt, Θt−1)
+≤
+�T
+t=1
+�N
+n=1
+�
+αλn,t(1 − θn,t) + 3βn|θn,t − θn,t−1|+)
+�
+.
+Plugging
+in
+the
+definition
+of
+ˆFt(P ∗
+t , P ∗
+t−1)
+and
+then
+rearranging this relation yields α �T
+t=1
+�N
+n−1 λn,t(θn,t −
+p∗
+n,t) ≤ 3 �T
+t=1
+�T
+n=1 βn|θn,t − θn,t−1|+ ≤ 3β∗HT .
+Without loss of generality, we can assume that λ1,t ≥ λ2,t ≥
+· · · ≥ λN,t for a given t. Then, λn,t ≥ λn+1,t + 1 for 1 ≤
+n ≤ M. Combining this with the fact that θ1,t = θ2,t =
+· · · = θM,t = 1 and θM+1,t = θM+2,t = · · · = θN,t = 0, we
+have �N
+n=1 λn,tθn,t − �N
+n=1 λn,tp∗
+n,t ≥ �N
+n=1 |θn,t − p∗
+n,t|.
+Therefore,
+T
+�
+t=1
+N
+�
+n=1
+|θn,t − p∗
+n,t| ≤
+T
+�
+t=1
+N
+�
+n=1
+λn,t(θn,t − p∗
+t ) ≤ 3β∗HT
+α
+.
+Next, using the triangle inequality, we have
+T
+�
+t=1
+||Θt−1 − P ∗
+t ||2 ≤
+T
+�
+t=1
+||Θt−1 − Θt||2 +
+T
+�
+t=1
+||Θt − P ∗
+t ||2
+≤
+T
+�
+t=1
+||Θt−1 − Θt||1 +
+T
+�
+t=1
+||Θt − P ∗
+t ||1
+≤ HT + 3β∗HT
+α
+= α + 3β∗
+α
+HT .
+Since the caching limit is M, it follows that ∥Θt−1 −P ∗
+t ∥2 ≤
+√
+2M. As a result,
+T
+�
+t=1
+||Θt−1 − P ∗
+t ||2
+2 ≤
+√
+2M
+T
+�
+t=1
+||Θt−1 − P ∗
+t ||2
+≤
+√
+2M(α + 3β∗)
+α
+HT .
+
+This completes the proof of the lemma.
+Now, by combining Lemma 3 and Lemma 2, we obtain
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1)
+≤ 6
+√
+2Mβ∗(α + 3β∗)
+αγW
+HT .
+(12)
+B. Bounding Reg(ROSC)
+We now analyze the cost introduced by the auxiliary objec-
+tive function and the randomized algorithm, and then bound
+Reg(ROSC).
+Considering the structure of the auxiliary cost function and
+the analysis of the randomized algorithm in [5], we can show
+the following.
+Lemma 4. By choosing 0 < γ < 1,
+Reg(ROSC) ≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1)
++ 3γβ∗NT + (αU + 6β∗N)T
+K
++ 2β∗HT .
+(13)
+Proof: It has been shown in [5] that, under ROSC,
+E[xn,t] = pQ
+n,t and E
+� �T
+t=1
+�N
+n=1 |xn,t − xn,t−1|+
+�
+≤
+3 �T
+t=1
+�N
+n=1 |pQ
+n,t − pQ
+n,t−1|+, where pQ
+n,t is the quantized
+version of p
+′
+n,t. Hence, we have
+E[
+T
+�
+t=1
+Ft(Xt, Xt−1)] ≤
+T
+�
+t=1
+N
+�
+n=1
+αλn,t(1 − pQ
+n,t)
++ 3
+T
+�
+t=1
+N
+�
+n=1
+βn|pQ
+n,t − pQ
+n,t−1|+.
+Since the difference between pQ
+n,t and p
+′
+n,t is at most
+1
+K
+according to the design of Algorithm 3, we have
+E[
+T
+�
+t=1
+Ft(Xt, Xt−1)] ≤
+T
+�
+t=1
+N
+�
+n=1
+αλn,t(1 − p
+′
+n,t) + αUT
+K
++ 3
+T
+�
+t=1
+N
+�
+n=1
+βn|p
+′
+n,t − p
+′
+n,t−1|+ + 6β∗NT
+K
+≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) + 3β∗γNT + (αU + 6β∗N)T
+K
+.
+Then, by comparing ˆFt(·) and Ft(·), we have
+C(OPT) =
+T
+�
+t=1
+Ft(X∗
+t , X∗
+t−1)
+≥
+T
+�
+t=1
+ˆFt(X∗
+t , X∗
+t−1) − 2
+T
+�
+t=1
+N
+�
+n=1
+βn|x∗
+n,t − x∗
+n,t−1|.
+Thus,
+Reg(ROSC) = E[
+T
+�
+t=1
+Ft(Xt, Xt−1)] − C(OPT)
+≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) + 3γβ∗NT + (αU + 6β∗N)T
+K
+− C(OPT)
+≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(X∗
+t , X∗
+t−1) + 3γβ∗NT
++ 2
+T
+�
+t=1
+N
+�
+n=1
+βn|x∗
+n,t − x∗
+n,t−1| + (αU + 6β∗N)T
+K
+≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1) + 3γβ∗NT
++ 2
+T
+�
+t=1
+N
+�
+n=1
+βn|x∗
+n,t − x∗
+n,t−1| + (αU + 6β∗N)T
+K
+.
+Note from the definitions of Θt and X∗
+1:T that
+T
+�
+t=1
+N
+�
+n=t
+(x∗
+n,t − x∗
+n,t−1) ≤
+T
+�
+t=1
+N
+�
+n=t
+(θn,t − θn,t−1).
+Therefore,
+Reg(ROSC) ≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1)
++ 3γβ∗NT + (αU + 6β∗)NT
+K
++ 2
+T
+�
+t=1
+βn∥Θn,t − Θn,t−1∥1
+≤
+T
+�
+t=1
+ˆFt(P
+′
+t , P
+′
+t−1) −
+T
+�
+t=1
+ˆFt(P ∗
+t , P ∗
+t−1) + 3γβ∗NT
++ (αU + 6β∗N)T
+K
++ 2β∗HT .
+This completes the proof of the lemma.
+We are now ready to prove Theorem 1.
+Proof of Theorem 1: By combining Lemma 4 and (12),
+the expected dynamic regret is bounded by
+Reg(ROSC) ≤6
+√
+2Mβ∗(α + 3β∗)
+αγW
+HT + 3γβ∗NT
++ (αU + 6β∗N)T
+K
++ 2β∗HT .
+By taking γ =
+�
+HT
+T , we obtain (9) as desired.
+VI. AN EFFICIENT IMPLEMENTATION FOR ROSC
+In this section, we propose a projection algorithm to effi-
+ciently implement ROSC and then analyze the complexity of
+ROSC. The main result is shown below.
+Theorem 2. Using Algorithm 5 below for projection, the
+complexity of ROSC is O(max{WN log(N), KMN}) per
+time slot.
+
+An important bottleneck of the complexity when imple-
+menting ROSC is the projection step in step 4 of Algorithm 2.
+In previous works, Wang [20] proposes an O(N 2) algorithm
+for computing exact projections, and Beck et al. [19, p. 150]
+demonstrates an algorithm based on a bisection method for
+computing an approximate projection onto a bounded simplex.
+Based on these ideas, we develop an efficient O(N log(N))
+projection algorithm for computing exact projection onto the
+set D in Algorithm 2. That is, given Z ∈ RN, find Y =
+ΠD(Z). The idea of our projection algorithm is based on the
+following lemma.
+Lemma 5. If Z is sorted in a descending order and Y =
+ΠD(Z), then Y
+is also sorted in the same fashion, and
+there exists an index i∗ ∈ [0, N] such that Y1:i∗ = 1 and
+Y(i∗+1):N < 1 is the projection of Z(i∗+1):N onto the simplex
+Si∗ = {V ∈ [0, ∞)N−i∗ | �N−i∗
+j=1
+vj = M − i∗}.
+Proof: First, it is clear that yi = 0 if zi ≤ 0. Thus,
+Y = ΠD([Z]+) where [Z]+ = max{Z, 0}. Moreover, if the
+projection of Z onto [0, 1]N, denoted by Y
+′ = Π[0,1]N (Z), is
+such that ⟨1, Y
+′⟩ ≤ M, then Y = Y
+′. Thus, w.l.o.g., we will
+consider
+Z ≥ 0,
+⟨1, Π[0,1]N (Z)⟩ ≥ M.
+(14)
+A consequence of (14) is that ⟨1, Z⟩ ≥ M and ⟨1, Y ⟩ = M.
+Thus, we instead consider the following problem:
+Y = arg min
+Y ∈[0,1]N
+�1
+2∥Z − Y ∥2
+2 | ⟨1, Y ⟩ = M
+�
+(15)
+Let us introduce a Lagrangian of (15)
+L(Y, µ, ν, ρ) = 1
+2∥Z − Y ∥2
+2 + ⟨ν, Y − 1⟩ − ⟨µ, Y ⟩
++ ρ(⟨1, Y ⟩ − M),
+where µ, ν, ρ are the corresponding Lagrange multipliers.
+Since the problem is convex, the KKT conditions are necessary
+and sufficient for optimality, i.e.,
+yi − zi − µi + νi + ρ = 0, ∀i
+(16)
+µiyi = 0,
+νi(yi − 1) = 0, ∀i
+(17)
+0 ≤ yi ≤ 1,
+�N
+i=1 yi = M
+(18)
+µ ≥ 0,
+ν ≥ 0,
+ρ ∈ R.
+(19)
+Clearly, if 0 ≤ yi ≤ 1, then it must hold that yi = zi − ρ.
+As a result, the optimal solution can be partitioned as:
+I1 = {i|yi = 1}, I2 = {i|yi = zi − ρ}, I3 = {i|yi = 0}.
+Since M = �N
+i=1 yi = |I1| + �
+I2(xi − ρ), we have
+ρ|I2| =
+�
+i∈I2
+zi − (M − |I1|).
+Next, observe that
+• On I1: µi = 0 and zi = µi + ρ + 1 ≥ ρ + 1.
+• On I2: µi = νi = 0 and ρ < zi < ρ + 1.
+• On I3: νi = 0 and zi = ρ − yi ≤ ρ.
+The above facts imply that if Z is sorted decreasing, then
+Y is also sorted decreasing and can be expressed as
+Y = [11:i∗, ¯Y ]
+where i∗ = |I1| and
+¯Y = [z(i∗+1):(i∗+|I2|) − ρ, 0(i∗+|I2|+1):N] < 1.
+(20)
+Assume Z is sorted decreasing and ˆZ := [zi∗+1, . . . , zN].
+Then, the projection of ˆZ onto the simplex Si∗ is given by
+˜Y = arg min
+˜Y ∈S
+�1
+2∥ ˆZ − ˜Y ∥2
+2 | ⟨1, ˜Y ⟩ = M − i∗�
+.
+(21)
+It is easy to verify that by using (Y, µ, ν, ρ) satisfying (16)-
+(19), ( ¯Y , {νi}i≥i∗, ρ) satisfy the KKT conditions of problem
+(21), and hence ¯Y is the projection of ˆZ onto simplex Si∗.
+By using this lemma, we can further show that i∗ is indeed
+the smallest index i ∈ [0, N] such that the projection of
+Z(i+1):N onto the simplex Si is strictly less than 1; the proof is
+straightforward and thus skipped for brevity. As a result, when
+Z is sorted in a descending order, we can use a binary search to
+find the index i∗. Note that in each step of the search, we need
+to find the projection onto a simplex, which can be computed
+efficiently, e.g., using the algorithm in [21]. We recall this
+algorithm below.
+Algorithm 4 Πsimplex(A, c): Projection onto a Simplex
+Input: A ∈ Rm, c > 0 s.t. a1 ≥ a2 ≥ · · · ≥ am
+1: I ← maxi≥1{i | (�m
+j=1 aj − c)/i < ai
+2: τ ← (�m
+j=1 aj − c)/I
+3: for j = 1 to m do
+4:
+a∗
+j ← max{aj − τ, 0}
+Output: A∗
+The runtime of Algorithm 4 is linear in the input size.
+Therefore, by using a binary search and applying Algorithm 4
+repeatedly, we can find index i∗ in nearly linear time; the
+details are given in Algorithm 5 below.
+We now show that Algorithm 5 has low complexity.
+Lemma 6. By using HeapSort as the sorting method, the time
+complexity of Algorithm 5 is O(N log N).
+Proof: We analyze the time complexity of Algorithm 5
+line by line. First, the complexity of lines 1–4 is O(N). Then,
+the sorting operation in line 6 can be finished in O(N log N)
+using HeapSort. Finally, the loop in binary search runs at most
+log M times, each of which calls Algorithm 4 once and thus
+takes only O(N). Therefore, the overall time complexity of
+Algorithm 5 is O(N log N).
+We are ready to prove Theorem 2.
+Proof of Theorem 2:
+In each time slot, ROSC’s pro-
+cedures include a single run of initialization, Algorithm 2,
+Algorithm 3 and assignment of Xt.
+We first analyze the time complexity of Algorithm 2.
+According to (8) and Lemma 6, line 2, 3 and 4 in Algorithm 2
+
+Algorithm 5 ΠD(Z): Projection onto a Bounded Simplex
+Input: Z ∈ RN, M > 0
+1: Z ← max{Z, 0}
+2: V ← min{Z, 1}
+3: if ⟨V, 1⟩ ≤ M then
+4:
+Y ← V
+5: else
+6:
+[Z, Id] ← sort(Z, ′descend′)
+7:
+V ← 0, l ← 0, r ← M
+8:
+for n = 0 to ⌈log2(M)⌉ do
+9:
+i∗ ← ⌊(r + l)/2⌋
+10:
+Y
+′ ← Πsimplex(Z(i∗+1):N, M − i∗)
+11:
+if i∗ == l then
+12:
+if any y
+′
+i ≥ 1 then
+13:
+V ← [11:r, Πsimplex(Z(r+1):N, M − r)]
+14:
+else
+15:
+V = [11:l, Y
+′]
+16:
+break
+17:
+if any y
+′
+i ≥ 1 then
+18:
+l ← i∗
+19:
+else
+20:
+r ← i∗
+21:
+Y (Id) ← V
+Output: Y
+run in O(N), O(N) and O(N log N), respectively. Since the
+for-loop in Algorithm 2 runs at most W times, the complexity
+of Algorithm 2 is O(WN log(N)).
+Next, Fan et al. [5] shows that the complexity of Algo-
+rithm 3 is O(KMN). For initialization and assignment in
+ROSC, it is easy to verify that the complexity is O(N).
+Therefore, the total complexity of ROSC per time slot is
+O(max{WN log(N), KMN}).
+VII. EVALUATION
+In this section, we evaluate the performance of ROSC
+through various simulations and compare it to that of other
+state-of-the-art policies. We also evaluate the case when the
+prediction of future arrivals can be inaccurate.
+A. Setup
+Data. We conduct experiments on two different data sets.
+The first data set is based on a random replacement model
+presented by Elayoubi et al. [22]. The requests in this data
+set follow a Zipf distribution, while the ranking of services
+changes frequently according to real-world measured statistics.
+We call this the Replacement data set. The second data set
+follows the model introduced by Traverso et al. [23]. Services
+are divided into 5 groups in which services share the same
+lifetime in the same group. The beginnings of the services
+follow a Poisson process determined by their group. We
+call this the Poisson data set. Table I summarizes important
+parameters of data sets.
+Default parameters. Throughout the evaluation, we set
+K = 100 for ROSC and assume β1 = β2 = · · · = βN = β∗.
+TABLE I
+REQUEST MODEL PARAMETERS
+Model
+N
+T
+U
+Ranking Lifetime∗
+Replacement
+103
+104
+200
+Follow Table 2 in [22]
+Poisson
+103
+104
+Follow Trace 1 in [23]
+∗ Represent how often the popularity of each service changes
+Since the forwarding cost and instantiating cost per service
+vary for different edge servers, we fix α = 0.05 and then
+evaluate the total cost using different
+β∗
+α . For the auxiliary
+function, we set γ = 0.05 as T and HT are not available to
+the online algorithm. We also set the step size to be η =
+γ
+12β∗
+as suggested in Theorem 1.
+Comparison schemes. We compare ROSC with four other
+algorithms:
+• Receding Horizon Control (RHC): RHC is introduced
+in [16], [24], [25]. In each time slot t, it chooses
+to cache Xt
+by solving the optimization problem
+arg minXt:t+W −1
+�t+W −1
+τ=t
+Fτ(Xτ, Xτ−1).
+• Committed Horizon Control (CHC): CHC is generalized
+RHC and has been proposed in [16], [17]. It’s caching
+decision in time slot t is the average of RHC solutions
+Xt in the previous W time slots.
+• Static Optimal Offline Algorithm (SOPT): This is an
+offline policy that has knowledge of all future requests
+and caches the same services in all time slots that
+minimize �T
+t=1 Ft(Xt, Xt−1). Specifically, it caches the
+same M services with the largest total requests with
+�T
+t=1 λn,t ≥ β∗
+α in all time slots.
+• ROSC, W=300: Lemma. 1 has proven that results of
+ROSC with W prediction window size are the same as
+the results of applying offline projected gradient descent
+algorithm with W update times. Hence, we can approx-
+imate the optimal dynamic offline algorithm by using
+ROSC with a large W = 300.
+Noisy prediction model Considering predictions are im-
+perfect in practice, we use the the prediction error model in
+Chen et al. [17] to simulate predictions with noisy errors. In
+detail, the error at time τ for the prediction of service n at
+time t is calculated by λn,t
+�t
+s=τ Ren(s), where R is a noise
+weight and en(s) is per-step noise for service n at time s.
+In the simulations, we let en(s), ∀n, s follow standard normal
+distribution and simulate on various R.
+B. Evaluation Results
+We present results of our simulations in Table. II, Fig. 1
+and Fig. 2. Throughout the simulations, parameters are set as
+β∗
+α = 200, M = 10, W = 10 and R = 0 if they are not
+specified. We run 10 independent simulations for each setting
+and report the average.
+Table. II evaluates the runtimes of algorithms. It can be seen
+that ROSC runs much faster than RHC and CHC, and it is less
+influenced by the increment of the prediction window size W.
+Both RHC and CHC require solving a complex finite-horizon
+optimization problem with size O(NW), which is why their
+
+0
+100
+200
+300
+400
+*/
+16
+18
+20
+22
+24
+26
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(a) Variable cost ratio
+0
+5
+10
+15
+20
+M
+16
+18
+20
+22
+24
+26
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(b) Variable caching limit
+0
+5
+10
+15
+20
+W
+16
+18
+20
+22
+24
+26
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(c) Variable prediction window size
+0
+0.005
+0.01
+0.015
+0.02
+0.025
+0.03
+R
+16
+18
+20
+22
+24
+26
+Cost per time slot
+ROSC, W=1
+ROSC, W=5
+ROSC, W=10
+ROSC, W=20
+(d) Variable prediction error weight
+Fig. 1. Simulation results of cost per time slot on the Replacement data set.
+0
+100
+200
+300
+400
+*/
+0
+2
+4
+6
+8
+10
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(a) Variable cost ratio
+0
+5
+10
+15
+20
+M
+0
+2
+4
+6
+8
+10
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(b) Variable caching limit
+0
+5
+10
+15
+20
+W
+0
+2
+4
+6
+8
+10
+Cost per time slot
+ROSC
+SOPT
+RHC
+CHC
+ROSC, W=300
+(c) Variable prediction window size
+0
+0.005
+0.01
+0.015
+0.02
+0.025
+0.03
+R
+0
+2
+4
+6
+8
+10
+Cost per time slot
+ROSC, W=1
+ROSC, W=5
+ROSC, W=10
+ROSC, W=20
+(d) Variable prediction error weight
+Fig. 2. Simulation results of cost per time slot on the Poisson data set.
+runtimes increase nearly exponentially as W increases. In
+contrast, under our ROSC, the runtime is linear in W.
+TABLE II
+AVERAGE RUNTIME OF ALGORITHMS
+Algorithm
+W = 1
+5
+10
+15
+20
+RHC
+426∗
+739
+1499
+2585
+4036
+CHC
+855
+1463
+2979
+5100
+8072
+ROSC
+124
+130
+137
+144
+150
+∗ Results are measured in seconds.
+Figs. 1a – 1d and 2a – 2c compare the costs incurred under
+different algorithms over various settings. It can be observed
+that RHC and CHC both perform much worse than our ROSC
+in most cases, especially when W is small. Based on the
+algorithm design, RHC and CHC will only change their caches
+to host a service n at time t if �t+W −1
+τ=t
+λn,τ > β∗
+α . Hence,
+when W is small, RHC and CHC are not responsive to gradual
+changes in long-term trends. It can also be observed that ROSC
+performs better than the static optimal offline algorithm in the
+Poisson data set, and has a close performance to SOPT in the
+replacement data set. In the Poisson data set, the popularity of
+services changes over time, and no service is always popular.
+The offline algorithm performs worse than ROSC as it cannot
+catch the changes in popularity.
+Finally, Fig. 1d and Fig. 2d show the result of ROSC
+with different W under different R. It should be noticed that
+the standard deviation of the prediction error at time t is
+WRλn,t, which increases with both W and R. Simulation
+results show that ROSC is very robust against prediction
+errors. For example, even when W = 10 and R = 0.03, under
+which case the prediction error is 30% of the arrival rate,
+ROSC still outperforms RHC and CHC without prediction
+error in both data sets.
+VIII. CONCLUSION
+This paper studies an online service caching problem with
+predictions and analyzes the performance of the proposed
+algorithm with expected dynamic regret and complexity. In
+detail, we introduce an auxiliary cost function and then pro-
+pose a randomized online algorithm, ROSC. ROSC applies
+an online projected gradient descent step with respect to the
+auxiliary cost function and uses a randomized algorithm to
+obtain integer solutions. We show that the expected dynamic
+regret of ROSC is bounded by the total time horizon and
+the path length of the requests, which represents changes
+in requests over time. We further prove that this bound is
+sublinear with the length of time horizon when the path length
+is sublinear and parameters are properly chosen. Simulations
+with two different data sets have shown that ROSC has much
+better performance than two state-of-the-art algorithms, RHC
+and CHC, under various parameter settings.
+ACKNOWLEDGMENT
+This material is based upon work supported in part by
+NSF under Award Number ECCS-2127721, in part by the
+U.S. Army Research Laboratory and the U.S. Army Research
+Office under Grant Number W911NF-22-1-0151, and in part
+by Office of Naval Research under Contract N00014-21-1-
+2385.
+
+REFERENCES
+[1] G. S. Paschos, A. Destounis, L. Vigneri, and G. Iosifidis, “Learning to
+cache with no regrets,” in IEEE INFOCOM 2019-IEEE Conference on
+Computer Communications, pp. 235–243, IEEE, 2019.
+[2] X. Zhang, C. Wu, Z. Li, and F. C. Lau, “Proactive vnf provisioning
+with multi-timescale cloud resources: Fusing online learning and online
+optimization,” in IEEE INFOCOM 2017-IEEE Conference on Computer
+Communications, pp. 1–9, IEEE, 2017.
+[3] T. Chen, Y. Shen, Q. Ling, and G. B. Giannakis, “Online learning
+for “thing-adaptive” fog computing in iot,” in 2017 51st Asilomar
+Conference on Signals, Systems, and Computers, pp. 664–668, IEEE,
+2017.
+[4] Y. Li, G. Qu, and N. Li, “Online optimization with predictions and
+switching costs: Fast algorithms and the fundamental limit,” IEEE
+Transactions on Automatic Control, 2020.
+[5] S. Fan, I.-H. Hou, V. S. Mai, and L. Benmohamed, “Online service
+caching and routing at the edge with unknown arrivals,” in ICC 2022 -
+IEEE International Conference on Communications, pp. 383–388, 2022.
+[6] T. S. Salem, G. Neglia, and S. Ioannidis, “No-regret caching via
+online mirror descent,” in ICC 2021-IEEE International Conference on
+Communications, pp. 1–6, IEEE, 2021.
+[7] Y. Tan and C. H. Xia, “An adaptive learning approach for efficient
+resource provisioning in cloud services,” ACM Sigmetrics Performance
+Evaluation Review, vol. 42, no. 4, pp. 3–11, 2015.
+[8] N. Chen, A. Agarwal, A. Wierman, S. Barman, and L. L. Andrew,
+“Online convex optimization using predictions,” in Proceedings of the
+2015 ACM SIGMETRICS International Conference on Measurement and
+Modeling of Computer Systems, pp. 191–204, 2015.
+[9] M. Lin, Z. Liu, A. Wierman, and L. L. Andrew, “Online algorithms for
+geographical load balancing,” in 2012 international green computing
+conference (IGCC), pp. 1–10, IEEE, 2012.
+[10] M. Shi, X. Lin, and L. Jiao, “On the value of look-ahead in competitive
+online convex optimization,” Proceedings of the ACM on Measurement
+and Analysis of Computing Systems, vol. 3, no. 2, pp. 1–42, 2019.
+[11] M. Zinkevich, “Online convex programming and generalized infinitesi-
+mal gradient ascent,” in Proceedings of the 20th international conference
+on machine learning (icml-03), pp. 928–936, 2003.
+[12] Y. Jin, L. Jiao, Z. Qian, S. Zhang, N. Chen, S. Lu, and X. Wang, “Pro-
+visioning edge inference as a service via online learning,” in 2020 17th
+Annual IEEE International Conference on Sensing, Communication, and
+Networking (SECON), pp. 1–9, IEEE, 2020.
+[13] Y. Jin, L. Jiao, Z. Qian, S. Zhang, S. Lu, and X. Wang, “Resource-
+efficient and convergence-preserving online participant selection in
+federated learning,” in 2020 IEEE 40th International Conference on
+Distributed Computing Systems (ICDCS), pp. 606–616, IEEE, 2020.
+[14] N. Chen, G. Goel, and A. Wierman, “Smoothed online convex optimiza-
+tion in high dimensions via online balanced descent,” in Conference On
+Learning Theory, pp. 1574–1594, PMLR, 2018.
+[15] G. Goel and A. Wierman, “An online algorithm for smoothed regression
+and lqr control,” in The 22nd International Conference on Artificial
+Intelligence and Statistics, pp. 2504–2513, PMLR, 2019.
+[16] J. Comden, S. Yao, N. Chen, H. Xing, and Z. Liu, “Online optimization
+in cloud resource provisioning: Predictions, regrets, and algorithms,”
+Proceedings of the ACM on Measurement and Analysis of Computing
+Systems, vol. 3, no. 1, pp. 1–30, 2019.
+[17] N. Chen, J. Comden, Z. Liu, A. Gandhi, and A. Wierman, “Using
+predictions in online optimization: Looking forward with an eye on
+the past,” ACM SIGMETRICS Performance Evaluation Review, vol. 44,
+no. 1, pp. 193–206, 2016.
+[18] Y. Li and N. Li, “Leveraging predictions in smoothed online convex
+optimization via gradient-based algorithms,” in Advances in Neural
+Information Processing Systems (H. Larochelle, M. Ranzato, R. Hadsell,
+M. F. Balcan, and H. Lin, eds.), vol. 33, pp. 14520–14531, Curran
+Associates, Inc., 2020.
+[19] A. Beck, First-order methods in optimization. SIAM, 2017.
+[20] W. Wang and C. Lu, “Projection onto the capped simplex,” arXiv
+preprint arXiv:1503.01002, 2015.
+[21] J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra, “Efficient
+projections onto the l 1-ball for learning in high dimensions,” in
+Proceedings of the 25th international conference on Machine learning,
+pp. 272–279, 2008.
+[22] S.-E. Elayoubi and J. Roberts, “Performance and cost effectiveness of
+caching in mobile access networks,” in Proceedings of the 2nd ACM
+Conference on Information-Centric Networking, pp. 79–88, 2015.
+[23] S. Traverso, M. Ahmed, M. Garetto, P. Giaccone, E. Leonardi, and
+S. Niccolini, “Temporal locality in today’s content caching: Why it mat-
+ters and how to model it,” ACM SIGCOMM Computer Communication
+Review, vol. 43, no. 5, pp. 5–12, 2013.
+[24] E. F. Camacho and C. B. Alba, Model predictive control.
+Springer
+science & business media, 2013.
+[25] C. E. Garcia, D. M. Prett, and M. Morari, “Model predictive control:
+Theory and practice—a survey,” Automatica, vol. 25, no. 3, pp. 335–348,
+1989.
+
diff --git a/mtE2T4oBgHgl3EQfzQgZ/content/tmp_files/load_file.txt b/mtE2T4oBgHgl3EQfzQgZ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bd00682dc88e539e1182e88d19b66ad056789498
--- /dev/null
+++ b/mtE2T4oBgHgl3EQfzQgZ/content/tmp_files/load_file.txt
@@ -0,0 +1,688 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf,len=687
+page_content='Dynamic Regret of Randomized Online Service  Caching in Edge Computing  Siqi Fan, I-Hong Hou  Texas A&M University  College Station, USA  {siqifan, ihou}@tamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='edu  Van Sy Mai  National Institute of Standards and Technology  Gaithersburg, USA  vansy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='mai@nist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='gov  Abstract—This paper studies an online service caching prob-  lem, where an edge server, equipped with a prediction window of  future service request arrivals, needs to decide which services to  host locally subject to limited storage capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The edge server  aims to minimize the sum of a request forwarding cost (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', the  cost of forwarding requests to remote data centers to process)  and a service instantiating cost (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', that of retrieving and setting  up a service).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Considering request patterns are usually non-  stationary in practice, the performance of the edge server is  measured by dynamic regret, which compares the total cost with  that of the dynamic optimal offline solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' To solve the problem,  we propose a randomized online algorithm with low complexity  and theoretically derive an upper bound on its expected dynamic  regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Simulation results show that our algorithm significantly  outperforms other state-of-the-art policies in terms of the runtime  and expected total cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' INTRODUCTION  Edge computing is a paradigm shift from cloud computing,  where computation and data storage are brought closer to end  users instead of offloading to a central cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This is done  through the deployment of edge servers that can host (or  cache) some popular services and process the corresponding  computation tasks directly without having to forward them to  remote clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Such close proximity provided by edge com-  puting not only reduces bandwidth consumption in backhaul  links, but also is critical for supporting various services and  applications that require real-time data processing, such as  augmented reality, virtual reality, and autonomous vehicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  To fully realize the potential of edge computing in prac-  tice, several challenges in designing efficient service caching  algorithms running on edge servers must be dealt with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' First,  edge servers can often host only a small number of services  due to their limited storage capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Second, user requests  are typically time-varying, and it is usually infeasible to  fully predict future requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Third, reconfiguring edge servers,  which involves downloading necessary data and setting up  virtual machines or containers, can incur significant delay and  communication cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Existing studies for addressing these challenges typically  design online policies that aim at learning and adopting an  optimal static offline policy, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', Paschos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [1] and Zhang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Here, a static offline policy is one that knows all  future requests but only caches the same set of services at all  times, and the cost difference between an online policy and the  optimal offline counterpart is known as static regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Clearly,  by focusing on learning the optimal static offline policy, these  studies ignore potential gains from dynamically reconfiguring  edge servers in response to changes in request arrival patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  As a result, static regret is deemed less applicable when the  environment is constantly changing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This motivates the notion  of dynamic regret, where an online algorithm is compared  against optimal dynamic solutions in hindsight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Few recent  studies [3], [4] investigate dynamic regret for different applica-  tions but only design online algorithms that produce fractional  solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Since service caching decisions are required to be  integers, these algorithm cannot be applied directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  In this paper, we propose an online service caching policy  with provably low dynamic regret by combining the strengths  of two recently proposed algorithms, one is an online gradient  algorithm [4] that has low dynamic regret but only produces  fractional solutions and the other is a randomized algorithm  [5] that turns fractional solutions into integer ones but has no  bounds on dynamic regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We point out that this combination  is not trivial because simply applying these two algorithms to  our cost function does not readily lead to low dynamic regret  due to the accumulated error from the randomization step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Thus, in order to bridge the gap between these two algorithms,  we carefully construct an auxiliary function that not only  admits fractional solutions but also explicitly incorporates the  additional costs due to the randomized algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Specifically,  in each time slot, our algorithm first applies a projected  gradient descent method to the auxiliary cost function using a  customized efficient projection step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The output of this step  is then treated as the probabilities of caching services at  the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Finally, a randomized algorithm is used to  determine actual integer caching decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We also note that  both algorithms in [4] and [5] do not provide low complexity  implementations of their projected gradient steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Our contributions in this paper are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' First, we  develop an online service caching algorithm that yields integer  solutions with provably low dynamic regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In particular, we  establish an upper bound of the regret that is sublinear in time  when the path length, a measure of how frequently request  arrival patterns change, is also sublinear in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We prove  that this upper bound can be further reduced when a finite  window of request arrival predictions is available to the edge  server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In addition, we develop a new algorithm for computing  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='04128v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='NI]  10 Jan 2023  exact projection onto a bounded simplex in nearly linear time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  existing methods either run in quadratic time or only compute  an approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This projection algorithm not only leads to an  efficient implementation of our online caching algorithm, but  is also of independent interest in other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Finally,  simulation results show that our policy outperforms other state-  of-the-art online algorithms under a variety of settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Section II  reviews closely related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Section III introduces our system  model and the online caching problem of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Section IV  provides details of our randomized online service caching  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Section V analyzes the expected dynamic regret of  the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Section VI proposes an efficient projection al-  gorithm and analyzes the complexity of our randomized online  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Some simulation results are given in Section VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Finally, Section VIII concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' RELATED WORK  The majority of studies on the online caching problem are  focused on static regret, which is evaluated by comparing with  a static offline policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For example, Paschos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [1], Zhang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [2], Salem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [6] and Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [7] form caching  problems into online convex optimization and apply gradient  method to obtain algorithms with sublinear static regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Fan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [5] consider the problem of jointly optimizing service  caching and routing and show that an online gradient descent  method can achieve a sublinear static regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Considering  competitive ratio, Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [8] proposes an online algorithm  based on LASSO, while Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [9] and Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [10]  modify receding horizon control algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' All these studies  focus on comparison with static optimal policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Dynamic regret is first introduced by Zinkevich [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [3] proposes an adaptive online saddle-point method and  studies its dynamic regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' By allowing temporary constraint  violation, Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [12], [13] proposes different online learning  models with a dynamic regret bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' However, these studies  do not consider instantiating costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Some recent studies explore using predictions to improve  the performance of online algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Considering precise  request predictions, Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [14] and Goel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [15]  study an online caching problem with 2-norm instantiating  costs and propose different algorithms with low competitive  ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In addition, Comden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [16] and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [4]  propose online caching algorithms and analyze their dynamic  regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Furthermore, Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [17] and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [18]  consider noisy predictions and analyze dynamic regret of their  proposed algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' These studies, however, do not guarantee  to produce integer solutions, and hence are not applicable to  service caching when the services are indivisible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' SYSTEM MODEL  We consider a system with multiple clients, an edge server,  and a remote data center providing N different services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The  edge server is located near the clients and can cache a small  subset of services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Any request from clients sent to the server  can be processed immediately if the corresponding service is  cached locally, otherwise it is forwarded to the remote center  for processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Assume that time is slotted, and the total number of time  slots is T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The edge server can dynamically adjust the set  of services it caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' However, changing the set of cached  services involves time-consuming operations such as down-  loading and setting up new services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hence, we assume that the  edge server can only adjust its cached services at the beginning  of each time slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Let xn,t ∈ {0, 1} denote the caching decision for service  n at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let Xt := [x1,t, x2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , xN,t] be the caching  decision at time t and Xa:b := [Xa, Xa+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , Xb].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Since the  edge server often has limited storage, we assume that at most  M services can be cached at any time, that is,  N  �  n=1  xn,t ≤ M,  ∀t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (1)  Whenever the edge server caches a new service, it needs  to download and install the said service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We model the cost  of downloading and installing service n by imposing an  instantiating cost of βn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus, the total instantiating cost at  time t is  N  �  n=1  βn|xn,t − xn,t−1|+,  where |x|+ := max{x, 0} for any x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Next, we discuss the model for request arrivals and pro-  cessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Denote the total number of requests for service n  in time slot t as λn,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let Λt = [λ1,t, λ2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , λN,t] and  Λa:b := [Λa, Λa+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , Λb].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We make the following mild  assumption about Λt: If service n and service m are both  among the top M + 1 most popular services at time t, then  λn,t ̸= λm,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This mild assumption is to ensure that the  ordering of the top M services is always unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The edge server can process all requests for its cached  services locally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For services not cached at the edge, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=',  xn,t = 0, the edge server must forward all associated requests  to the remote data center for processing, which inevitably leads  to larger delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The round-trip time between the edge server  and the remote data center is determined by the conditions  of the backbone network and the remote data center, and is  little impacted by the edge server’s caching decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hence,  we assume that there is a constant delay for requests that are  processed by the remote data center, and say that the system  suffers a constant forwarding cost of α for each forwarded  request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The total forwarding cost in time slot t is then  α  N  �  n=1  λn,t(1 − xn,t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Therefore, the total cost in time slot t can be written as  Ft(Xt, Xt−1) :=  N  �  n=1  (αλn,t(1 − xn,t) + βn|xn,t − xn,t−1|+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The goal of the edge server is to solve the problem of  minimizing the total cost, which is shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  min  X1:T  T  �  t=1  Ft(Xt, Xt−1),  (2)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  xn,t ∈ {0, 1},  ∀n, ∀t,  (3)  N  �  n=1  xn,t ≤ M,  ∀t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (4)  Note that solving this problem exactly is already challenging  in the offline setting (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', all request arrivals are known in  advance) due to the binary constraint in (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It is even more so  (if not impossible) in the online setting, where the edge server  needs to determine caching decision Xt at the beginning of  each time slot t given limited knowledge about future request  arrivals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We assume that the edge server employs an online  algorithm and has exact predictions of request arrivals only  in next W time slots at any time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Note that setting W = 0  would correspond to the case where the edge server has no  prediction ability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' the case of using imprecise predictions is  left for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The concept of an online algorithm is  formally defined as follows:  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' An online service caching algorithm is one that,  after knowing X1:t−1 and Λ1:t+W −1, determines, possibly at  random, Xt at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The expected cost of an online algorithm ξ is denoted by  C(ξ) := E[�T  t=1 Ft(Xt, Xt−1)|ξ], where E[·] denotes the  expectation function over all possible randomness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  To measure the performance of ξ, we compare the total cost  of algorithm ξ to that of an optimal dynamic offline policy,  which is formally defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Definition 2 (Optimal Dynamic Offline Policy (OPT)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' An  optimal dynamic offline policy is one that produces optimal  solution X∗  1:T for the problem in (2)–(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Note that we allow any offline algorithm to cache different  services in different time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This feature makes our work  different from most existing studies on service caching that  only consider optimal static offline policies, where the same  set of services is cached in all time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The difference between the expected cost of ξ and the cost  of optimal dynamic offline policy, denoted by C(OPT), is  called expected dynamic regret, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=',  Reg(ξ) := C(ξ) − C(OPT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (5)  Obviously, the expected dynamic regret of any online policy  depends on the request arrivals Λ1:T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We characterize Λ1:T by  its path length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Specifically, let θn,t be the indicator function  that service n is among the top M services with the most  requests in time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then, the path length of Λ1:T is defined  as �T  t=1  �N  n=1 |θn,t −θn,t−1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let Θt := [θ1,t, θ2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , θN,t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Loosely speaking, the path length measures the variation of the  request distribution over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We assume that the path length  of Λ1:T is upper-bounded by HT , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', �T  t=1 ∥Θt −Θt−1∥1 ≤  HT , and the edge server knows the value of HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The goal of this work is to develop an online service caching  algorithm whose expected dynamic regret is o(T) whenever  HT = o(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' RANDOMIZED ONLINE SERVICE CACHING  ALGORITHM  In this section, we propose a randomized online service  caching algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Our algorithm mainly consists of two  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The first component determines the probability  of caching a service n at time t with the goal of minimizing an  auxiliary cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The second component is a randomized  algorithm that determines which service to be cached at the  edge based on the result of the first component while limiting  the resulting instantiating cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' As we will show in the next  section, combining these two components gives rise to an  upper bound on the expected dynamic regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  To express the probability distribution of Xt, we construct  K sample paths, each representing a probability mass of  1  K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  At the beginning of the whole process, the edge server chooses  a number k∗ uniformly at random from {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , K}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then,  it uses the sample path k∗ at time t as the caching decision  in time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  For sample paths designed above, the portion of sample  paths that cache a service is the same as the probability  we cache this service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let pn,t be the probability that the  edge server caches service n at time slot t, and let Pt :=  [p1,t, p2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , pN,t] and Pa:b := [Pa, Pa+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , Pb].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Due to  (1), Pt is restricted to be in the following feasible set  D :=  �  [p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , pN] | 0 ≤ pn ≤ 1, ∀n,  N  �  n=1  pn ≤ M  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (6)  For decisions in sample paths, we use sk,n,t ∈ {0, 1} to de-  note the indicator function that service n is cached on sample  path k at time t, and let Sk,t := [sk,1,t, sk,2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then, the  edge server sets Xt = Sk∗,t in each time slot t as caching de-  cisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus, a randomized online service caching algorithm  is effectively one that determines S1,t, S2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t, in each  time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  As described above, our algorithm consists of two parts  in each time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In particular, we first determine caching  probability Pt based on previous probabilities and request  arrivals Λt−1:t+W −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then, we use Pt and sample paths at  t − 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', [S1,t−1, S2,t−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t−1], to determine sample  paths at t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The overall algorithm is shown in Algorithm 1  and detailed steps are given in the next subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Here, to  simplify notation, we let our algorithm start from t = −W +1  with Λt, Sk,t, Pt set to zero for all t ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Caching Probability Update  Let us now discuss in detail our approach for determining Pt  in the first part of our algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Define the following auxiliary  Algorithm 1 Randomized Online Service Caching (ROSC)  Parameter: K  1: Choose k∗ uniformly at random from {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , K}  2: ¯P−W +1:T ← 0  3: for t = −W + 1 to T do  4:  Obtain parameter Λt+W −1  5:  Apply HeapSort on Λt+W −1 to calculate Θt+W −1  6:  Pt+W ← Θt+W −1  7:  if W > 0 then  8:  Pt:t+W −1, ¯Pt:t+W −1←Algo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2(Λt:t+W −1, Pt−1:t+W ,  ¯Pt:t+W −1, t)  9:  if t ≥ 1 then  10:  [S1,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t] ← Algo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3(Pt, S1,t−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t−1)  11:  Xt ← Sk∗,t  cost function ˆFt, which will be used as our surrogate objective  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  ˆFt(Pt, Pt−1) :=  �  j : 0≤pj,t−pj,t−1≤γ  3βj  γ (pj,t − pj,t−1)2+  �  i : pi,t−pi,t−1>γ  3βi(pi,t − pi,t−1) + α  �  1≤n≤N  λn,t(1 − pn,t),  (7)  where γ > 0 is a parameter whose value will be discussed  in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' By comparing ˆFt with Ft, one can see  that the only difference is in the instantiating cost component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Here, the quadratic term is to ensure that ˆFt is differentiable  everywhere, and a factor of 3 is added in order to bound  the expected dynamic regret introduced by the randomized  algorithm that will be discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  At each time t, after obtaining the prediction Λt+W −1, the  edge server first sets Pt+W = Θt+W −1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', pn,t+W = 1  if service n is among the top M most requested services  in time slot t + W − 1, and pn,t+W  = 0, otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' If  W > 0, we will further update Pt:t+W −1 so as to reduce  �t+W −1  τ=t  ˆFτ(Pτ, Pτ−1) through projected gradient descent  with step size η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Note that each Pτ only appears in ˆFτ and ˆFτ+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus, we  obtain the gradient of �t+W −1  τ=t  ˆFτ(Pτ, Pτ−1) with respect to  Pτ, denoted as ∇Pτ ( ˆFτ(Pτ, Pτ−1)+ ˆFτ+1(Pτ+1, Pτ)), where  ∂  ∂pn,τ  � ˆFτ(Pτ, Pτ−1) + ˆFτ+1(Pτ+1, Pτ)  �  (8)  =  �  gn(pn,τ−1, pn,τ) − αλn,τ − gn(pn,τ, pn,τ+1)  if τ < T  gn(pn,τ−1, pn,τ) − αλn,τ  if τ = T  and the value of gn(a, b) is set to be 0 if b − a < 0, set to be  6βn  γ (b − a) if 0 ≤ b − a ≤ γ, and set to be 3βn if b − a > γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Then, we update Pτ from τ = t+W −1 down to τ = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' To  ensure the gradient of �t+W −1  τ=t  ˆFτ(Pτ, Pτ−1) with respect to  Pτ is obtained based on Pτ−1, Pτ, and Pτ+1 with the same  update times, we use the updated Pτ+1, the original Pτ and  the Pτ−1 in the previous iteration before its update, which is  denoted as ¯Pτ−1, to calculate the gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus, we update  Pτ by  Pτ = ΠD(Pτ − η∇Pτ ( ˆFτ(Pτ, ¯Pτ−1) + ˆFτ+1(Pτ+1, Pτ)),  where ΠD(·) is the projection operator onto set D given in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  This distinction is important for establishing an expected  dynamic regret bound, as will be discussed in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Algorithm 2 shows the detail of updating Pt:t+W −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Algorithm 2 Projected Gradient Descent  Input: Λt:t+W −1, Pt−1:t+W , ¯Pt−1:t+W , t  Parameter: γ, η  1: for τ = t + W − 1 to max{1, t} do  2:  Calculate ∇Pτ ( ˆFτ(Pτ, ¯Pτ−1) + ˆFτ(Pτ+1, Pτ)) by (8)  3:  ¯Pτ ← Pτ  4:  Pτ ← ΠD(Pτ −η∇Pτ ( ˆFτ(Pτ, ¯Pτ−1)+ ˆFτ+1(Pτ+1, Pτ))  Output: Pt:t+W −1, ¯Pt:t+W −1  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Sample Path Update  Our algorithm for determining [Sk,t] employs that in Fan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [5], which studies online randomized algorithm for a  different setting without establishing expected dynamic regret  bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The first step is to quantize every pn,t in Pt into a  multiple of  1  K , denoted as pQ  n,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let P Q  t  := [pQ  1,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , pQ  N,t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Note that each service n in [Sk,t] needs to be cached in exactly  KpQ  n,t sample paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Set sample path Sk,t = Sk,t−1 for all  k at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then, for each n, randomly choose K(pQ  n,t −  pQ  n,t−1) sample paths without service n to cache service n if  pQ  n,t > pQ  n,t−1, and delete service n from K(pQ  n,t−1 − pQ  n,t)  randomly chosen sample paths with service n if the pQ  n,t <  pQ  n,t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Finally, for each sample path k that caches more than  M services, find another sample path k′ with less than M  cached services, and randomly choose a service n that k caches  and k′ does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Delete service n from k and cache it in the  k′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Detailed steps are shown in Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' This algorithm  is designed so that the number of changes, which corresponds  to the instantiating cost at time t, can be bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' EXPECTED DYNAMIC REGRET  In this section, we analyze the regret of ROSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The main  result is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Let γ =  �  HT  T  and η =  γ  12β∗ with β∗ :=  maxn βn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' If the number of requests in each time slot is upper-  bounded by U, that is, �N  n=1 λn,t ≤ U, ∀t, then  Reg(ROSC) ≤  �6  √  2Mβ∗(α + 3β∗)  αW  + 3β∗N  ��  HT T  + (αU + 6β∗N)T  K  + 2β∗HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (9)  In particular, Reg(ROSC) = o(T) if HT = o(T) and K =  √  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We will prove this result in two steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' First, let P  ′  1:T  be the final value of P1:T in Algorithm 1 and let P ∗  1:T be  Algorithm 3 Randomized Caching  Input: Pt, S1,t−1, S2,t−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t−1  1: P Q  t ← quantize every pn,t in Pt into a multiple of  1  K  2: P Q  t−1 ← 1  K  �K  k=1 Sk,t−1  3: ∆t := [δ1,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , δN,t] ← P Q  t − P Q  t−1  4: S1,t, S2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t ← S1,t−1, S2,t−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t−1  5: for n = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , N do  6:  if δn,t > 0 then  7:  Find the set {sk,n,t|sk,n,t = 0}, randomly pick Kδn,t  elements in it and set to 1  8:  else if δn,t < 0 then  9:  Find the set {sk,n,t|sk,n,t = 1}, randomly pick  |Kδn,t| elements in it and set to 0  10: while ∃ �N  n=1 sk,n,t > M do  11:  Find k′ that �N  n=1 sk′,n,t < M  12:  Randomly choose a service n′ from the set {n|sk′,n,t =  0, sk,n,t = 1}  13:  sk′,n′,t ← 1, sk,n′,t ← 0  Output: S1,t, S2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , SK,t  the optimal vector for minimizing the auxiliary cost function  �T  t=1 ˆFt(Pt, Pt−1) under the constraint (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We will derive  an upper bound on �T  t=1 ˆFt(P  ′  t , P  ′  t−1)−�T  t=1 ˆFt(P ∗  t , P ∗  t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Second, we will show that Reg(ROSC), which is defined with  respect to Ft(·) instead of ˆFt(·), can actually be bounded by  a function of �T  t=1 ˆFt(P  ′  t , P  ′  t−1) − �T  t=1 ˆFt(P ∗  t , P ∗  t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Bounding �T  t=1 ˆFt(P  ′  t , P  ′  t−1) − �T  t=1 ˆFt(P ∗  t , P ∗  t−1)  We first compare ROSC with an offline policy and then  bound �T  t=1 ˆFt(P  ′  t , P  ′  t−1)−�T  t=1 ˆFt(P ∗  t , P ∗  t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Consider an  offline policy that knows Λ1:T and employs the projected  gradient descent algorithm to minimize  J(Q) :=  T  �  t=1  ˆFt(Qt, Qt−1)  subject to the constraint Q = [Q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , QT ] ∈ H, where  Qt := [q1,t, q2,t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , qN,t] and H := {Q | 0 ≤ qn,t ≤  1, ∀n, t, �N  n=1 qn,t ≤ M, ∀t}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Following a projected gradient  descent algorithm, the offline policy first initializes Q0  t = Λt−1  and then updates its caching decisions Q in each iteration  w = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , W as follows  Qw ← ΠH  �  Qw−1 − η∇J(Qw−1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (10)  Note that the following has been shown in Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For update (10), we have QW  t  = P  ′  t , ∀t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Using this result, we can prove the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Consider ROSC with step size η =  γ  12β∗ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1)  ≤ 6β∗  γW  T  �  t=1  ∥Θt−1 − P ∗  t ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Proof: First, it can be seen that J(·) is 12β∗  γ  smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then  the result follows by simply applying [19, Theorem 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='21] to  the offline policy (10) and then using Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Next, we bound the term �T  t=1 ∥Θt−1 − P ∗  t ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In fact,  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We have  T  �  t=1  ∥Θt−1 − P ∗  t ∥2  2 ≤  √  2M(α + 3β∗)  α  HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (11)  Proof: First, note that if 0 ≤ pj,t − pj,t−1 ≤ γ, then  3βj  γ (pj,t − pj,t−1)2 ≤ 3βj(pj,t − pj,t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Using this and the  definitions of ˆFt, we have ˆFt(Θt, Θt−1) ≤ α �N  n=1 λn,t(1 −  θn,t) + 3 �N  n=1 βn|θn,t − θn,t−1|+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Since  P ∗  1:T  minimizes  �T  t=1 ˆFt(Pt, Pt−1),  we  have  �T  t=1 ˆFt(P ∗  t , P ∗  t−1)  ≤  �T  t=1 ˆFt(Θt, Θt−1)  ≤  �T  t=1  �N  n=1  �  αλn,t(1 − θn,t) + 3βn|θn,t − θn,t−1|+)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Plugging  in  the  definition  of  ˆFt(P ∗  t , P ∗  t−1)  and  then  rearranging this relation yields α �T  t=1  �N  n−1 λn,t(θn,t −  p∗  n,t) ≤ 3 �T  t=1  �T  n=1 βn|θn,t − θn,t−1|+ ≤ 3β∗HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Without loss of generality, we can assume that λ1,t ≥ λ2,t ≥  · · ≥ λN,t for a given t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then, λn,t ≥ λn+1,t + 1 for 1 ≤  n ≤ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Combining this with the fact that θ1,t = θ2,t =  · · = θM,t = 1 and θM+1,t = θM+2,t = · · · = θN,t = 0, we  have �N  n=1 λn,tθn,t − �N  n=1 λn,tp∗  n,t ≥ �N  n=1 |θn,t − p∗  n,t|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Therefore,  T  �  t=1  N  �  n=1  |θn,t − p∗  n,t| ≤  T  �  t=1  N  �  n=1  λn,t(θn,t − p∗  t ) ≤ 3β∗HT  α  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Next, using the triangle inequality, we have  T  �  t=1  ||Θt−1 − P ∗  t ||2 ≤  T  �  t=1  ||Θt−1 − Θt||2 +  T  �  t=1  ||Θt − P ∗  t ||2  ≤  T  �  t=1  ||Θt−1 − Θt||1 +  T  �  t=1  ||Θt − P ∗  t ||1  ≤ HT + 3β∗HT  α  = α + 3β∗  α  HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Since the caching limit is M, it follows that ∥Θt−1 −P ∗  t ∥2 ≤  √  2M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' As a result,  T  �  t=1  ||Θt−1 − P ∗  t ||2  2 ≤  √  2M  T  �  t=1  ||Θt−1 − P ∗  t ||2  ≤  √  2M(α + 3β∗)  α  HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  This completes the proof of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Now, by combining Lemma 3 and Lemma 2, we obtain  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1)  ≤ 6  √  2Mβ∗(α + 3β∗)  αγW  HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (12)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Bounding Reg(ROSC)  We now analyze the cost introduced by the auxiliary objec-  tive function and the randomized algorithm, and then bound  Reg(ROSC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Considering the structure of the auxiliary cost function and  the analysis of the randomized algorithm in [5], we can show  the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' By choosing 0 < γ < 1,  Reg(ROSC) ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1)  + 3γβ∗NT + (αU + 6β∗N)T  K  + 2β∗HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (13)  Proof: It has been shown in [5] that, under ROSC,  E[xn,t] = pQ  n,t and E  � �T  t=1  �N  n=1 |xn,t − xn,t−1|+  �  ≤  3 �T  t=1  �N  n=1 |pQ  n,t − pQ  n,t−1|+, where pQ  n,t is the quantized  version of p  ′  n,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hence, we have  E[  T  �  t=1  Ft(Xt, Xt−1)] ≤  T  �  t=1  N  �  n=1  αλn,t(1 − pQ  n,t)  + 3  T  �  t=1  N  �  n=1  βn|pQ  n,t − pQ  n,t−1|+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Since the difference between pQ  n,t and p  ′  n,t is at most  1  K  according to the design of Algorithm 3, we have  E[  T  �  t=1  Ft(Xt, Xt−1)] ≤  T  �  t=1  N  �  n=1  αλn,t(1 − p  ′  n,t) + αUT  K  + 3  T  �  t=1  N  �  n=1  βn|p  ′  n,t − p  ′  n,t−1|+ + 6β∗NT  K  ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) + 3β∗γNT + (αU + 6β∗N)T  K  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Then, by comparing ˆFt(·) and Ft(·), we have  C(OPT) =  T  �  t=1  Ft(X∗  t , X∗  t−1)  ≥  T  �  t=1  ˆFt(X∗  t , X∗  t−1) − 2  T  �  t=1  N  �  n=1  βn|x∗  n,t − x∗  n,t−1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Thus,  Reg(ROSC) = E[  T  �  t=1  Ft(Xt, Xt−1)] − C(OPT)  ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) + 3γβ∗NT + (αU + 6β∗N)T  K  − C(OPT)  ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(X∗  t , X∗  t−1) + 3γβ∗NT  + 2  T  �  t=1  N  �  n=1  βn|x∗  n,t − x∗  n,t−1| + (αU + 6β∗N)T  K  ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1) + 3γβ∗NT  + 2  T  �  t=1  N  �  n=1  βn|x∗  n,t − x∗  n,t−1| + (αU + 6β∗N)T  K  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Note from the definitions of Θt and X∗  1:T that  T  �  t=1  N  �  n=t  (x∗  n,t − x∗  n,t−1) ≤  T  �  t=1  N  �  n=t  (θn,t − θn,t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Therefore,  Reg(ROSC) ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1)  + 3γβ∗NT + (αU + 6β∗)NT  K  + 2  T  �  t=1  βn∥Θn,t − Θn,t−1∥1  ≤  T  �  t=1  ˆFt(P  ′  t , P  ′  t−1) −  T  �  t=1  ˆFt(P ∗  t , P ∗  t−1) + 3γβ∗NT  + (αU + 6β∗N)T  K  + 2β∗HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  This completes the proof of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We are now ready to prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Proof of Theorem 1: By combining Lemma 4 and (12),  the expected dynamic regret is bounded by  Reg(ROSC) ≤6  √  2Mβ∗(α + 3β∗)  αγW  HT + 3γβ∗NT  + (αU + 6β∗N)T  K  + 2β∗HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  By taking γ =  �  HT  T , we obtain (9) as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' AN EFFICIENT IMPLEMENTATION FOR ROSC  In this section, we propose a projection algorithm to effi-  ciently implement ROSC and then analyze the complexity of  ROSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The main result is shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Using Algorithm 5 below for projection, the  complexity of ROSC is O(max{WN log(N), KMN}) per  time slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  An important bottleneck of the complexity when imple-  menting ROSC is the projection step in step 4 of Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  In previous works, Wang [20] proposes an O(N 2) algorithm  for computing exact projections, and Beck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [19, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 150]  demonstrates an algorithm based on a bisection method for  computing an approximate projection onto a bounded simplex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Based on these ideas, we develop an efficient O(N log(N))  projection algorithm for computing exact projection onto the  set D in Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' That is, given Z ∈ RN, find Y =  ΠD(Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The idea of our projection algorithm is based on the  following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' If Z is sorted in a descending order and Y =  ΠD(Z), then Y  is also sorted in the same fashion, and  there exists an index i∗ ∈ [0, N] such that Y1:i∗ = 1 and  Y(i∗+1):N < 1 is the projection of Z(i∗+1):N onto the simplex  Si∗ = {V ∈ [0, ∞)N−i∗ | �N−i∗  j=1  vj = M − i∗}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Proof: First, it is clear that yi = 0 if zi ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus,  Y = ΠD([Z]+) where [Z]+ = max{Z, 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Moreover, if the  projection of Z onto [0, 1]N, denoted by Y  ′ = Π[0,1]N (Z), is  such that ⟨1, Y  ′⟩ ≤ M, then Y = Y  ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Thus, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', we will  consider  Z ≥ 0,  ⟨1, Π[0,1]N (Z)⟩ ≥ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (14)  A consequence of (14) is that ⟨1, Z⟩ ≥ M and ⟨1, Y ⟩ = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Thus, we instead consider the following problem:  Y = arg min  Y ∈[0,1]N  �1  2∥Z − Y ∥2  2 | ⟨1, Y ⟩ = M  �  (15)  Let us introduce a Lagrangian of (15)  L(Y, µ, ν, ρ) = 1  2∥Z − Y ∥2  2 + ⟨ν, Y − 1⟩ − ⟨µ, Y ⟩  + ρ(⟨1, Y ⟩ − M),  where µ, ν, ρ are the corresponding Lagrange multipliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Since the problem is convex, the KKT conditions are necessary  and sufficient for optimality, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=',  yi − zi − µi + νi + ρ = 0, ∀i  (16)  µiyi = 0,  νi(yi − 1) = 0, ∀i  (17)  0 ≤ yi ≤ 1,  �N  i=1 yi = M  (18)  µ ≥ 0,  ν ≥ 0,  ρ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (19)  Clearly, if 0 ≤ yi ≤ 1, then it must hold that yi = zi − ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  As a result, the optimal solution can be partitioned as:  I1 = {i|yi = 1}, I2 = {i|yi = zi − ρ}, I3 = {i|yi = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Since M = �N  i=1 yi = |I1| + �  I2(xi − ρ), we have  ρ|I2| =  �  i∈I2  zi − (M − |I1|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Next, observe that  On I1: µi = 0 and zi = µi + ρ + 1 ≥ ρ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  On I2: µi = νi = 0 and ρ < zi < ρ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  On I3: νi = 0 and zi = ρ − yi ≤ ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The above facts imply that if Z is sorted decreasing, then  Y is also sorted decreasing and can be expressed as  Y = [11:i∗, ¯Y ]  where i∗ = |I1| and  ¯Y = [z(i∗+1):(i∗+|I2|) − ρ, 0(i∗+|I2|+1):N] < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (20)  Assume Z is sorted decreasing and ˆZ := [zi∗+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' , zN].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Then, the projection of ˆZ onto the simplex Si∗ is given by  ˜Y = arg min  ˜Y ∈S  �1  2∥ ˆZ − ˜Y ∥2  2 | ⟨1, ˜Y ⟩ = M − i∗�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  (21)  It is easy to verify that by using (Y, µ, ν, ρ) satisfying (16)-  (19), ( ¯Y , {νi}i≥i∗, ρ) satisfy the KKT conditions of problem  (21), and hence ¯Y is the projection of ˆZ onto simplex Si∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  By using this lemma, we can further show that i∗ is indeed  the smallest index i ∈ [0, N] such that the projection of  Z(i+1):N onto the simplex Si is strictly less than 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' the proof is  straightforward and thus skipped for brevity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' As a result, when  Z is sorted in a descending order, we can use a binary search to  find the index i∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Note that in each step of the search, we need  to find the projection onto a simplex, which can be computed  efficiently, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', using the algorithm in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We recall this  algorithm below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Algorithm 4 Πsimplex(A, c): Projection onto a Simplex  Input: A ∈ Rm, c > 0 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' a1 ≥ a2 ≥ · · · ≥ am  1: I ← maxi≥1{i | (�m  j=1 aj − c)/i < ai  2: τ ← (�m  j=1 aj − c)/I  3: for j = 1 to m do  4:  a∗  j ← max{aj − τ, 0}  Output: A∗  The runtime of Algorithm 4 is linear in the input size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Therefore, by using a binary search and applying Algorithm 4  repeatedly, we can find index i∗ in nearly linear time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' the  details are given in Algorithm 5 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We now show that Algorithm 5 has low complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' By using HeapSort as the sorting method, the time  complexity of Algorithm 5 is O(N log N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Proof: We analyze the time complexity of Algorithm 5  line by line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' First, the complexity of lines 1–4 is O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Then,  the sorting operation in line 6 can be finished in O(N log N)  using HeapSort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Finally, the loop in binary search runs at most  log M times, each of which calls Algorithm 4 once and thus  takes only O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Therefore, the overall time complexity of  Algorithm 5 is O(N log N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We are ready to prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Proof of Theorem 2:  In each time slot, ROSC’s pro-  cedures include a single run of initialization, Algorithm 2,  Algorithm 3 and assignment of Xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We first analyze the time complexity of Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  According to (8) and Lemma 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' line 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3 and 4 in Algorithm 2  Algorithm 5 ΠD(Z): Projection onto a Bounded Simplex  Input: Z ∈ RN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' M > 0  1: Z ← max{Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 0}  2: V ← min{Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1}  3: if ⟨V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1⟩ ≤ M then  4:  Y ← V  5: else  6:  [Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Id] ← sort(Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' ′descend′)  7:  V ← 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' l ← 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' r ← M  8:  for n = 0 to ⌈log2(M)⌉ do  9:  i∗ ← ⌊(r + l)/2⌋  10:  Y  ′ ← Πsimplex(Z(i∗+1):N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' M − i∗)  11:  if i∗ == l then  12:  if any y  ′  i ≥ 1 then  13:  V ← [11:r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Πsimplex(Z(r+1):N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' M − r)]  14:  else  15:  V = [11:l,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Y  ′]  16:  break  17:  if any y  ′  i ≥ 1 then  18:  l ← i∗  19:  else  20:  r ← i∗  21:  Y (Id) ← V  Output: Y  run in O(N),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' O(N) and O(N log N),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Since the  for-loop in Algorithm 2 runs at most W times, the complexity  of Algorithm 2 is O(WN log(N)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Next, Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [5] shows that the complexity of Algo-  rithm 3 is O(KMN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For initialization and assignment in  ROSC, it is easy to verify that the complexity is O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Therefore, the total complexity of ROSC per time slot is  O(max{WN log(N), KMN}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' EVALUATION  In this section, we evaluate the performance of ROSC  through various simulations and compare it to that of other  state-of-the-art policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We also evaluate the case when the  prediction of future arrivals can be inaccurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Setup  Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We conduct experiments on two different data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The first data set is based on a random replacement model  presented by Elayoubi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The requests in this data  set follow a Zipf distribution, while the ranking of services  changes frequently according to real-world measured statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  We call this the Replacement data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The second data set  follows the model introduced by Traverso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Services  are divided into 5 groups in which services share the same  lifetime in the same group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' The beginnings of the services  follow a Poisson process determined by their group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We  call this the Poisson data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Table I summarizes important  parameters of data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Default parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Throughout the evaluation, we set  K = 100 for ROSC and assume β1 = β2 = · · · = βN = β∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  TABLE I  REQUEST MODEL PARAMETERS  Model  N  T  U  Ranking Lifetime∗  Replacement  103  104  200  Follow Table 2 in [22]  Poisson  103  104  Follow Trace 1 in [23]  ∗ Represent how often the popularity of each service changes  Since the forwarding cost and instantiating cost per service  vary for different edge servers, we fix α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='05 and then  evaluate the total cost using different  β∗  α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For the auxiliary  function, we set γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='05 as T and HT are not available to  the online algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We also set the step size to be η =  γ  12β∗  as suggested in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Comparison schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We compare ROSC with four other  algorithms:  Receding Horizon Control (RHC): RHC is introduced  in [16], [24], [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In each time slot t, it chooses  to cache Xt  by solving the optimization problem  arg minXt:t+W −1  �t+W −1  τ=t  Fτ(Xτ, Xτ−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Committed Horizon Control (CHC): CHC is generalized  RHC and has been proposed in [16], [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It’s caching  decision in time slot t is the average of RHC solutions  Xt in the previous W time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Static Optimal Offline Algorithm (SOPT): This is an  offline policy that has knowledge of all future requests  and caches the same services in all time slots that  minimize �T  t=1 Ft(Xt, Xt−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Specifically, it caches the  same M services with the largest total requests with  �T  t=1 λn,t ≥ β∗  α in all time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  ROSC, W=300: Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1 has proven that results of  ROSC with W prediction window size are the same as  the results of applying offline projected gradient descent  algorithm with W update times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hence, we can approx-  imate the optimal dynamic offline algorithm by using  ROSC with a large W = 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Noisy prediction model Considering predictions are im-  perfect in practice, we use the the prediction error model in  Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' [17] to simulate predictions with noisy errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In  detail, the error at time τ for the prediction of service n at  time t is calculated by λn,t  �t  s=τ Ren(s), where R is a noise  weight and en(s) is per-step noise for service n at time s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  In the simulations, we let en(s), ∀n, s follow standard normal  distribution and simulate on various R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Evaluation Results  We present results of our simulations in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' II, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1  and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Throughout the simulations, parameters are set as  β∗  α = 200, M = 10, W = 10 and R = 0 if they are not  specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We run 10 independent simulations for each setting  and report the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' II evaluates the runtimes of algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It can be seen  that ROSC runs much faster than RHC and CHC, and it is less  influenced by the increment of the prediction window size W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Both RHC and CHC require solving a complex finite-horizon  optimization problem with size O(NW),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' which is why their  0  100  200  300  400  /  16  18  20  22  24  26  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' W=300  (a) Variable cost ratio  0  5  10  15  20  M  16  18  20  22  24  26  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' W=300  (b) Variable caching limit  0  5  10  15  20  W  16  18  20  22  24  26  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' W=300  (c) Variable prediction window size  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='03  R  16  18  20  22  24  26  Cost per time slot  ROSC, W=1  ROSC, W=5  ROSC, W=10  ROSC, W=20  (d) Variable prediction error weight  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Simulation results of cost per time slot on the Replacement data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  0  100  200  300  400  /  0  2  4  6  8  10  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC, W=300  (a) Variable cost ratio  0  5  10  15  20  M  0  2  4  6  8  10  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC, W=300  (b) Variable caching limit  0  5  10  15  20  W  0  2  4  6  8  10  Cost per time slot  ROSC  SOPT  RHC  CHC  ROSC, W=300  (c) Variable prediction window size  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='03  R  0  2  4  6  8  10  Cost per time slot  ROSC, W=1  ROSC, W=5  ROSC, W=10  ROSC, W=20  (d) Variable prediction error weight  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Simulation results of cost per time slot on the Poisson data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  runtimes increase nearly exponentially as W increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In  contrast, under our ROSC, the runtime is linear in W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  TABLE II  AVERAGE RUNTIME OF ALGORITHMS  Algorithm  W = 1  5  10  15  20  RHC  426∗  739  1499  2585  4036  CHC  855  1463  2979  5100  8072  ROSC  124  130  137  144  150  ∗ Results are measured in seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1a – 1d and 2a – 2c compare the costs incurred under  different algorithms over various settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It can be observed  that RHC and CHC both perform much worse than our ROSC  in most cases, especially when W is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Based on the  algorithm design, RHC and CHC will only change their caches  to host a service n at time t if �t+W −1  τ=t  λn,τ > β∗  α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hence,  when W is small, RHC and CHC are not responsive to gradual  changes in long-term trends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It can also be observed that ROSC  performs better than the static optimal offline algorithm in the  Poisson data set, and has a close performance to SOPT in the  replacement data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In the Poisson data set, the popularity of  services changes over time, and no service is always popular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  The offline algorithm performs worse than ROSC as it cannot  catch the changes in popularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Finally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1d and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2d show the result of ROSC  with different W under different R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' It should be noticed that  the standard deviation of the prediction error at time t is  WRλn,t, which increases with both W and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Simulation  results show that ROSC is very robust against prediction  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' For example, even when W = 10 and R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='03, under  which case the prediction error is 30% of the arrival rate,  ROSC still outperforms RHC and CHC without prediction  error in both data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' CONCLUSION  This paper studies an online service caching problem with  predictions and analyzes the performance of the proposed  algorithm with expected dynamic regret and complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' In  detail, we introduce an auxiliary cost function and then pro-  pose a randomized online algorithm, ROSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' ROSC applies  an online projected gradient descent step with respect to the  auxiliary cost function and uses a randomized algorithm to  obtain integer solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We show that the expected dynamic  regret of ROSC is bounded by the total time horizon and  the path length of the requests, which represents changes  in requests over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' We further prove that this bound is  sublinear with the length of time horizon when the path length  is sublinear and parameters are properly chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Simulations  with two different data sets have shown that ROSC has much  better performance than two state-of-the-art algorithms, RHC  and CHC, under various parameter settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  ACKNOWLEDGMENT  This material is based upon work supported in part by  NSF under Award Number ECCS-2127721, in part by the  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Army Research Laboratory and the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Army Research  Office under Grant Number W911NF-22-1-0151, and in part  by Office of Naval Research under Contract N00014-21-1-  2385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  REFERENCES  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Paschos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Destounis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Vigneri, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Iosifidis, “Learning to  cache with no regrets,” in IEEE INFOCOM 2019-IEEE Conference on  Computer Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 235–243, IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [2] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Li, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lau, “Proactive vnf provisioning  with multi-timescale cloud resources: Fusing online learning and online  optimization,” in IEEE INFOCOM 2017-IEEE Conference on Computer  Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–9, IEEE, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [3] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Shen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Ling, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Giannakis, “Online learning  for “thing-adaptive” fog computing in iot,” in 2017 51st Asilomar  Conference on Signals, Systems, and Computers, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 664–668, IEEE,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Qu, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Li, “Online optimization with predictions and  switching costs: Fast algorithms and the fundamental limit,” IEEE  Transactions on Automatic Control, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Fan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hou, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Mai, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Benmohamed, “Online service  caching and routing at the edge with unknown arrivals,” in ICC 2022 -  IEEE International Conference on Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 383–388, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Salem, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Neglia, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Ioannidis, “No-regret caching via  online mirror descent,” in ICC 2021-IEEE International Conference on  Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–6, IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Tan and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Xia, “An adaptive learning approach for efficient  resource provisioning in cloud services,” ACM Sigmetrics Performance  Evaluation Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3–11, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Agarwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wierman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Barman, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Andrew,  “Online convex optimization using predictions,” in Proceedings of the  2015 ACM SIGMETRICS International Conference on Measurement and  Modeling of Computer Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 191–204, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wierman, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Andrew, “Online algorithms for  geographical load balancing,” in 2012 international green computing  conference (IGCC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–10, IEEE, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lin, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Jiao, “On the value of look-ahead in competitive  online convex optimization,” Proceedings of the ACM on Measurement  and Analysis of Computing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–42, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Zinkevich, “Online convex programming and generalized infinitesi-  mal gradient ascent,” in Proceedings of the 20th international conference  on machine learning (icml-03), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 928–936, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [12] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Jin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Jiao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Qian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Zhang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wang, “Pro-  visioning edge inference as a service via online learning,” in 2020 17th  Annual IEEE International Conference on Sensing, Communication, and  Networking (SECON), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–9, IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Jin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Jiao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Qian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wang, “Resource-  efficient and convergence-preserving online participant selection in  federated learning,” in 2020 IEEE 40th International Conference on  Distributed Computing Systems (ICDCS), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 606–616, IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [14] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Goel, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wierman, “Smoothed online convex optimiza-  tion in high dimensions via online balanced descent,” in Conference On  Learning Theory, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1574–1594, PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Goel and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wierman, “An online algorithm for smoothed regression  and lqr control,” in The 22nd International Conference on Artificial  Intelligence and Statistics, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 2504–2513, PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Comden, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Yao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Xing, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Liu, “Online optimization  in cloud resource provisioning: Predictions, regrets, and algorithms,”  Proceedings of the ACM on Measurement and Analysis of Computing  Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1–30, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [17] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Comden, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Gandhi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wierman, “Using  predictions in online optimization: Looking forward with an eye on  the past,” ACM SIGMETRICS Performance Evaluation Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 44,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 193–206, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Li and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Li, “Leveraging predictions in smoothed online convex  optimization via gradient-based algorithms,” in Advances in Neural  Information Processing Systems (H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Larochelle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Ranzato, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Hadsell,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Balcan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lin, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' ), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 14520–14531, Curran  Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Beck, First-order methods in optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' SIAM, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [20] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Wang and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Lu, “Projection onto the capped simplex,” arXiv  preprint arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='01002, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Duchi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Shalev-Shwartz, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Singer, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Chandra, “Efficient  projections onto the l 1-ball for learning in high dimensions,” in  Proceedings of the 25th international conference on Machine learning,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 272–279, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Elayoubi and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Roberts, “Performance and cost effectiveness of  caching in mobile access networks,” in Proceedings of the 2nd ACM  Conference on Information-Centric Networking, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 79–88, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Traverso, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Ahmed, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Garetto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Giaccone, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Leonardi, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Niccolini, “Temporal locality in today’s content caching: Why it mat-  ters and how to model it,” ACM SIGCOMM Computer Communication  Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 5–12, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [24] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Camacho and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Alba, Model predictive control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  Springer  science & business media, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content='  [25] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Garcia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Prett, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' Morari, “Model predictive control:  Theory and practice—a survey,” Automatica, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
+page_content=' 335–348,  1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE2T4oBgHgl3EQfzQgZ/content/2301.04128v1.pdf'}
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@@ -0,0 +1,1761 @@
+MNRAS 000, 1–14 (2023)
+Preprint 16 January 2023
+Compiled using MNRAS LATEX style file v3.0
+Size-selective accretion of dust onto CPDs: Low CPD masses and filtration
+of larger grains
+Samuel M. Karlin,1★ Olja Panić,1 and Sven van Loo1,2
+1School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
+2Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, Technicum blok 4 9000 Gent, Belgium
+Accepted 2023 January 12. Received 2022 December 22; in original form 2022 August 10
+ABSTRACT
+The major satellites of Jupiter and Saturn are believed to have formed in circumplanetary discs, which orbit forming giant
+protoplanets. Gas and dust in CPDs have different distributions and affect each other by drag, which varies with grain size.
+Yet simulations of multiple dust grain sizes with separate dynamics have not been done before. We seek to assess how much
+dust of each grain size there is in circumplanetary discs. We run multifluid 3D hydrodynamical simulations including gas and
+four discrete grain sizes of dust from 1 𝜇m to 1 mm, representing a continuous distribution. We consider a 1𝑀Jup protoplanet
+embedded in a protoplanetary disc around a 1𝑀⊙ star. Our results show a truncated MRN distribution at smaller grain sizes,
+which starts to tail off by 𝑎 = 100 𝜇m and is near zero at 1 mm. Large dust grains, which hold most of the dust mass, have
+very inefficient accretion to the CPD, due to dust filtration. Therefore CPDs’ dust masses must be small, with mass ratio ∼ a few
+×10−6 to the protoplanet. These masses and the corresponding millimetre opacities are in line with CPD fluxes observed to date.
+Key words: accretion – accretion discs – hydrodynamics – planets and satellites: formation – planets and satellites: gaseous
+planets – protoplanetary discs
+1 INTRODUCTION
+The major satellites of Jupiter and Saturn exhibit almost perfectly
+coplanar prograde circular orbits, with remarkably low eccentricities
+and inclinations. This lends itself to the suggestion that they formed
+in discs of gas and dust orbiting around their parent planets (Ko-
+rycansky et al. 1991; Ward & Canup 2010). These circumplanetary
+discs (CPDs) are thus the birthplaces of icy moons such as Europa
+and Enceladus, considered promising candidates for extraterrestrial
+life (Greenberg 2011; Blanc et al. 2020; Parkinson et al. 2008; Neveu
+et al. 2020). They also regulate the flow of material onto a protoplanet
+(Rivier et al. 2012), from which it follows that they determine the
+final mass that the mature planet can attain. Circumplanetary discs
+used to be a prediction of theorists alone, but in recent years, with
+VLT K-band observations of the protoplanet PDS 70 b (Christiaens
+et al. 2019) and ALMA submillimetre observations of the proto-
+planet PDS 70 c (Isella et al. 2019; Benisty et al. 2021), emission
+from CPDs has begun to be directly observed. As such, study of
+CPDs is both pertinent and timely.
+The dynamics of differently-sized dust particles in circumplane-
+tary discs remains an understudied topic. The grain size of dust in
+CPDs is important in multiple ways. It will govern their resulting
+opacity, in which dust, despite being greatly outmassed by gas, is
+the dominant component (Williams & Cieza 2011). That means it
+governs their temperature, which is crucial to our ability, or lack
+thereof, to detect CPDs observationally. Furthermore, dust size has
+★ Email: s.m.karlin@gmail.com
+implications for the feasibility of satellitesimal formation from dust,
+and thus of satellite formation.
+The earliest CPD modelling, done by Lunine & Stevenson (1982),
+takes the observed mass of Jupiter’s Galilean satellites, multiplies it
+by 100 to adjust for a dust-to-gas ratio of 10−2 and concludes that
+Jupiter’s circumplanetary disc must have had a minimum mass of
+∼ 0.02 times the mass of Jupiter. Applying the same reasoning to the
+Saturnian system gives a strikingly similar fraction. The combined
+satellites of each planet have about 2 × 10−4 times the mass of the
+planet (Canup & Ward 2009). Mosqueira & Estrada (2003) point
+out that a disc as dense as this ‘rich disc’ model proposes would
+drag satellitesimals into the protoplanet at extremely short migration
+timescales (< 103 yr), rendering the formation of satellites like
+those of Saturn and Jupiter unfeasible. They suggest an alternative
+‘gas-starved disc’ model, where the CPD is continuously being fed
+more matter from outside and losing matter to the protoplanet. The
+observations of Isella et al. (2019) and Benisty et al. (2021) constrain
+the dust masses of circumplanetary discs around protoplanets in the
+PDS 70 system. With the caveat that this is only one star-system
+and it may not be representative, their results tentatively suggest that
+observed dust masses seem too low for the rich disc models. The
+starved disc models are a better fit.
+Circumplanetary discs form inside gaps in the parent protoplane-
+tary disc; a gap is a necessary but not sufficient condition for a CPD
+to exist. Only a sufficiently massive protoplanet can exert sufficiently
+strong gravitational torque to form a gap;
+𝑀pl > 0.39𝑀Jup × 𝑀∗
+𝑀⊙
+×
+� 𝐻/𝑅
+0.05
+�3
+(1)
+© 2023 The Authors
+arXiv:2301.05662v1  [astro-ph.EP]  13 Jan 2023
+
+2
+S. M. Karlin et al.
+(Lin & Papaloizou 1993) where 𝑀pl and 𝑀∗ are the masses of
+the protoplanet and star, 𝑀Jup and 𝑀⊙ are the masses of Jupiter
+and the Sun, and 𝐻/𝑅 is the protoplanetary disc’s aspect ratio at
+the protoplanet’s location. Earth-like protoplanets are thus precluded
+from having circumplanetary discs, but giant protoplanets ought to.
+Several authors have perfomed three-dimensional single-fluid hy-
+drodynamical simulations of CPDs: Bate et al. (2003), Machida et al.
+(2008), Tanigawa et al. (2012), Szulágyi et al. (2014), Szulágyi et al.
+(2016), Szulágyi & Mordasini (2017), Szulágyi (2017) to name but a
+few. Among their many results they find that most of the protoplanet’s
+mass inflow comes vertically from above and below the midplane,
+not through the CPD on the midplane. This renders two-dimensional
+simulations impractical to capture protoplanet growth. CO gas veloc-
+ity observations by Teague et al. (2019) affirm simulations’ prediction
+that protoplanets should have these meridional flows. Another con-
+clusion from these simulations is that viscosity has a strong effect on
+the resultant accretion rate: more viscous CPDs grant their protoplan-
+ets faster accretion. The artificial numerical viscosity of simulations
+can be a problem for modelling low-viscosity cases (Szulágyi et al.
+2014) because it means that simulations intended to be inviscid, or
+nearly so, might be quite viscous in practice. The temperature of the
+CPD and of the protoplanet also plays a major role in determining the
+shape of the CPD and gap, the mass of the CPD, and even whether
+or not a CPD can exist at all. A hot enough protoplanet will have no
+CPD, only a gaseous envelope filling the whole Roche lobe (Szulágyi
+et al. 2016).
+However, in the literature, circumplanetary discs have been simu-
+lated assuming that gas and dust have the same distribution in space.
+The assumption is that they have the same dust-to-gas ratio, typically
+the interstellar medium value of 10−2 (Knapp & Kerr 1974), at all
+points in space. Sometimes this assumption is not made explicit; it
+is implicit in the work by using opacity tables which assume a dust-
+to-gas ratio of 10−2. It is well-known observationally that gas and
+dust do not share the same distribution in space in protoplanetary
+discs (e.g. Long et al. 2018; Pinte et al. 2016; among many others).
+According to theory they do not obey the same physics, so there is
+no reason to expect them to.
+The separate dynamics of dust from gas should not be neglected.
+Even if it is only 1% of the mass budget as per the ISM dust-to-
+gas ratio, the dust plays an outsized role in heating and cooling
+because it dominates the opacity: (𝜅𝜌)𝑑 ≫ (𝜅𝜌)𝑔 despite 𝜌𝑔 ≫ 𝜌𝑑
+(Williams & Cieza 2011) where 𝜅 is opacity and 𝜌 is density and
+𝑔 and 𝑑 denote gas and dust. For the same reason of high opacity,
+dust emits disproportionately much of the electromagnetic radiation
+we can see. Understanding dust dynamics as separate from the gas
+is a necessary prerequisite to capture the thermodynamic behaviour
+of a CPD and its environs. In models that presume perfect uniform
+mixing, the opacity and temperature at any given point in space will
+be dramatically overestimated or underestimated if the local dust-to-
+gas ratio at that point is greater or less than 10−2. Furthermore, there
+is no reason to expect dust of different grain sizes to share the same
+distribution in space, because dust particles of different sizes have
+different surface-area-to-mass ratios and thus experience different
+strengths of dust-gas drag.
+Previously published work by Binkert et al. (2021) and Szulá-
+gyi et al. (2022) concern three-dimensional hydrodynamical simula-
+tions of CPDs with separate gas and dust. The principal differences
+from this work are as follows: (I) they use only one dust grain size,
+𝑎 = 1 mm, whereas we allow dust of multiple grain sizes to exist
+simultaneously, with each dust size possessing its own dynamics;
+(II) they simulate a larger region of the protoplanetary disc than we
+do; (III) their simulations are radiative, whereas we adopt a locally
+isothermal approach; and (IV) they neglect turbulent diffusion of
+dust, which matters because the main flow feeding the protoplanet
+is vertical, sourced from far above and below the midplane, and tur-
+bulent stirring is what counteracts the gravitational settling of dust
+which would otherwise pull the dust onto the midplane to form an
+extremely thin layer. They conclude that planetary gravity vertically
+stirs the dust, so planet-hosting protoplanetary discs are thicker than
+expected in the dust and therefore the dust masses of observed pro-
+toplanetary discs may be being underestimated.
+The purpose of this paper is to assess not only how much dust there
+is in circumplanetary discs but how much dust there is of each grain
+size. The dust size distribution determines the opacity and, as such,
+is crucial to understand CPD observations. For example, Benisty
+et al. (2021) conclude that the circumplanetary disc of PDS 70 c
+has a dust mass 0.007𝑀⊕ if the dust grain size is 1 mm or a much
+more massive 0.031𝑀⊕ if the dust grain size is 1 𝜇m. Therefore,
+we run three-dimensional multifluid hydrodynamical simulations of
+a circumplanetary disc, covering the gap in which the CPD dwells
+and the protoplanet within the CPD. Gas and dust are permitted to
+exist separately, following their separate dynamics, albeit coupled
+to each other by dust-gas drag. Our approach differs from previous
+work in that we devote the available computing power to multifluid
+dust dynamics, rather than to a more sophisticated thermal treatment.
+We argue that temperature depends so strongly on opacity and thus
+on the distribution of different-sized dust grains in space that our
+approach is warranted. In Sect. 2, we lay out the numerical toolset
+we use, the setup of the simulations and the physical processes they
+model. Then we give the results of our simulations and compare them
+to observations in Sect. 3 and we discuss the implications of these
+results in Sect. 4. Finally, our conclusions are offered in Sect. 5.
+2 METHODS
+2.1 Numerical implementation
+We run 3D hydrodynamical simulations of a segment of a proto-
+planetary disc containing a Jupiter-mass protoplanet on a circular
+orbit at 10 AU around a solar-mass star. The orbital radius we use is
+wider than Jupiter’s orbit because we wish to consider protoplanets
+distant enough to be observable in practice. We use a grid-based
+Finite-Volume Adaptive Mesh Refinement code called MG (Falle
+1991; Van Loo et al. 2006). The governing equations for the gas are:
+𝜕𝜌𝑔
+𝜕𝑡 + ∇. �𝜌𝑔v𝑔
+� = 0
+(2)
+𝜕 �𝜌𝑔v𝑔
+�
+𝜕𝑡
++ ∇.
+�
+𝜌𝑔v𝑔 ⊗ v𝑔 − 𝝈∼
+�
+= −
+𝑛
+∑︁
+𝑖=1
+F𝐷,𝑖 − 𝜌𝑔∇Φ
+−𝜌𝑔Ω𝑐 × (Ω𝑐 × r) − 2𝜌𝑔Ω𝑐 × v𝑔
+(3)
+where 𝜌𝑔 is the gas density, v𝑔 the gas velocity, Φ the gravitational
+potential, 𝑛 the number of different dust species, F𝐷,𝑖 the drag force
+by the gas on the 𝑖th dust species, and Ω𝑐 = Ω𝑐ˆe𝑧 the corotation
+vector with Ω𝑐 the corotation frequency. In our simulations, we
+choose to use a frame corotating at frequency Ω𝑐 =
+√︃
+𝐺𝑀∗/𝑎3
+pl to
+keep the protoplanet stationary where 𝑀∗ is the star’s mass and 𝑎pl
+the orbital radius of the protoplanet around the star. The position r
+is defined relative to the star which is at the origin, i.e. r = 0. The
+turbulent-viscous stress tensor, 𝝈∼, is defined as follows:
+𝝈∼ = 𝜂turb
+�
+∇ ⊗ v𝑔 + �∇ ⊗ v𝑔
+�T�
+−
+� 2
+3𝜂turb∇.v𝑔 + 𝑃
+�
+I∼
+(4)
+MNRAS 000, 1–14 (2023)
+
+Size-selective accretion of dust onto CPDs
+3
+where 𝑃 is the pressure, 𝜂turb the turbulent viscosity and I∼ the
+identity matrix. The code is locally isothermal, for computational
+efficiency. See Sect. 2.2 for the temperature description. For the 𝑖th
+dust species, the governing equations are:
+𝜕𝜌𝑖
+𝜕𝑡 + ∇.
+�
+𝜌𝑖v𝑖 − 𝜂turb∇
+� 𝜌𝑖
+𝜌𝑔
+��
+= 0
+(5)
+𝜕 (𝜌𝑖v𝑖)
+𝜕𝑡
++ ∇.
+�
+𝜌𝑖v𝑖 ⊗ v𝑖 −
+�
+𝜂turb∇
+� 𝜌𝑖
+𝜌𝑔
+��
+⊗ v𝑖
+�
+=
+F𝐷,𝑖 − 𝜌𝑖∇Φ − 𝜌𝑖Ω𝑐 × (Ω𝑐 × r) − 2𝜌𝑖Ω𝑐 × v𝑖
+(6)
+where 𝜌𝑖 and v𝑖 are the density and velocity of the 𝑖th dust species,
+and all other variables are defined above (Morfill & Voelk 1984).
+Each dust species is treated as a pressureless fluid.
+The MG code uses a Godunov method which is 2nd order in space
+and time. For the gas we use a Kurganov-Tadmor Riemann solver,
+while for the dust Riemann solver we implement the algorithm of
+Paardekooper & Mellema (2006). The dust species are coupled to the
+gas by dust-gas drag; see Sect. 2.5. Once the drag coefficients have
+been calculated, our code uses the algorithm of Benítez-Llambay
+et al. (2019) to solve the effects of dust-gas drag upon all of the
+dust species and the gas, at once. It solves equations of the form
+F𝐷,𝑖 = − �
+𝑗 𝛽𝑖 𝑗
+�v𝑖 − v 𝑗
+� by a backward-in-time, implicit, linear-
+algebra method. Our version of MG is able to simulate an arbitrary
+number of dust species coexisting with gas, rather than just gas; to
+work in a corotating frame; and to have protoplanets which exert
+gravity, accrete matter, and provide heat to their surroundings.
+We run one gas-only simulation, four single grain size simula-
+tions with gas and one dust species at a time, and one multiple grain
+size simulation with gas and four dust species simultaneously, with
+quarter-annulus geometry, and we run one multiple grain size simu-
+lation (gas + 4 dust) with full-annulus geometry. The dust grain sizes
+are 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m and 1 mm. These grain sizes are
+consistent with the Miley et al. (2021) protoplanetary disc models
+that produced our initial conditions, as described in Sect. 2.6. We
+obtain the other grain sizes from our choice to use logarithmically
+even spacing with a factor of 10, in order to explore the behaviour of
+dust of a wide range of orders of magnitude.
+2.2 Temperature
+The disc is assumed to be locally isothermal, with an ideal gas
+equation of state:
+𝑃 =
+𝜌𝑔
+¯𝜇𝑚 𝑝
+𝑘𝐵𝑇
+(7)
+where ¯𝜇 is mean molecular mass, 𝑚 𝑝 the mass of a proton, 𝑘𝐵
+Boltzmann’s constant and 𝑇 temperature.
+The initial conditions give the temperature of the unperturbed
+protoplanetary disc at every point in space, as Sect. 2.6 explains. The
+temperature at every point in space is kept equal to its value in these
+initial conditions, unless the point is close enough that the luminosity
+of the hot young protoplanet dominates.
+𝑇 (r) = max ��
+�
+�
+𝐿pl
+4𝜋 �𝑑pl (r)�2 × 𝜎
+�1/4
+, 𝑇init (r)��
+�
+(8)
+where 𝐿pl is the protoplanet’s luminosity, and 𝑑pl (r) the distance
+from protoplanet is given by 𝑑pl (r) = max ���r − rpl
+�� , 𝑅eff
+�. 𝑅eff
+the “effective radius” serves to avoid a singularity at the location of
+the protoplanet. In this paper we set 𝑅eff to be 8 times the radius
+of Jupiter. For the protoplanet’s luminosity, we use 𝐿pl = 5.96 ×
+10−5𝐿⊙, which comes from the equation 𝐿pl = 4𝜋𝑅2
+pl × 𝜎𝑇4
+surf
+for a Jupiter-radius protoplanet with the same surface temperature
+1600 K that was observed by Christiaens et al. (2019) for the giant
+protoplanet PDS 70 b. This is not expected to be exact for all giant
+protoplanets but should be of the right order of magnitude.
+2.3 Gravity and accretion
+While the self-gravity of the disc material upon itself is neglected,
+the gravitational acceleration – which is the same for the gas and dust
+– can be straightforwardly calculated using
+∇Φ(r) =
+𝐺𝑀pl
+�r − rpl
+�
+���r − rpl
+��2 + (2𝑅eff)2�3/2 + 𝐺𝑀∗
+|r|3 r + 𝐺𝑀pl
+��rpl
+��3 rpl
+(9)
+Note that the first two terms arise directly from the gravitational
+potentials of the star and protoplanet, while the last term is an indirect,
+fictitious acceleration due to the gravitational pull of the protoplanet
+on the star. This is included because our choice of reference frame is
+keeping the star always at r = 0. Furthermore, the direct term of the
+protoplanet’s gravity is artificially smoothed close to the protoplanet
+using a smoothing radius of 2𝑅eff.
+For Eq. 9, the protoplanet’s mass is fixed at 1𝑀Jup throughout
+the simulations. These simulations are intended to capture the CPD
+instantaneously, not to simulate its entire lifetime, which would be
+computationally prohibitive for high-resolution 3D hydrodynamical
+simulations.
+Accretion has a major impact on the results because the mass bud-
+get of the circumplanetary disc is governed by input and output: the
+flow of mass from the parent protoplanetary disc, and the accretion
+of mass from the circumplanetary disc onto the protoplanet. There-
+fore, even though accretion happens on length-scales much smaller
+than every other length-scale in the problem, it still must be treated
+with great care. The accretion algorithm we use is Gaussian with
+distance from the protoplanet and near-linear with time. The mass
+accreted from a cell in a timestep of length Δ𝑡 is proportional to
+(1 − exp (−Δ𝑡/𝑡acc)) where 𝑡acc is an accretion timescale based on
+freefall. However, as close to the protoplanet Δ𝑡/𝑡acc ≪ 1, it is in
+effect linear. For the algorithmic details of the accretion treatment in
+this paper, see Appendix A.
+2.4 Turbulence
+Turbulence in protoplanetary discs is a source of angular momen-
+tum transport and can be treated like a viscosity where the kine-
+matic viscosity is given by 𝜈turb = 𝛼𝑐2
+𝑠,𝑖𝑠𝑜Ω−1
+K (Shakura & Sun-
+yaev 1973) where 𝑐𝑠,𝑖𝑠𝑜 =
+√︁
+𝑃/𝜌𝑔 is the isothermal sound speed
+and ΩK =
+√︁
+𝐺𝑀∗/𝑅3 is the Keplerian frequency. This equation is
+used to calculate the dynamic viscosity 𝜂turb = 𝜌𝑔𝜈turb through-
+out this paper, for both gas and dust. 𝜈turb in our simulations is
+not time-variable; it is calculated using the initial conditions. The
+turbulent/diffusive terms in Eqs 5 and 6 are for turbulent stirring,
+which must not be neglected because the balance between it and the
+settling due to drag and gravity sets the scale height for dust of each
+grain size (Youdin & Lithwick 2007). Without it, the dust would set-
+tle into a super-dense, gravitationally unstable layer at the midplane
+(Goldreich & Ward 1973).
+Observationally, the general consensus is that 𝛼 is around 10−4 -
+10−3 in Class II discs: for instance, Pinte et al. (2016) look at the
+continuum emission of the disc HL Tau and, by modelling the vertical
+MNRAS 000, 1–14 (2023)
+
+4
+S. M. Karlin et al.
+settling of dust, they deduce an 𝛼 of order a few times 10−4. With a
+different method, Trapman et al. (2020) analyse protoplanetary discs’
+viscous spreading by comparing PPDs’ ages to their outer radii for a
+sample in the Lupus star-forming region and they conclude that 𝛼 is
+generally in the 10−4 - 10−3 range. In this paper we take 𝛼 = 10−3.
+We choose the upper end of the 10−4 - 10−3 range because higher
+𝛼 means higher dust scale heights, which are less computationally
+expensive to capture.
+2.5 Dust-gas drag
+Dust-gas drag is treated as one of two regimes, depending on com-
+paring the dust grain size 𝑎 to the mean free path 𝜆 of the gas: the
+Epstein drag regime when 𝑎 ≤
+9
+4𝜆 and the Stokes regime when
+𝑎 > 9
+4𝜆. The mean free path can be expressed in terms of the gas
+density and collisional cross section 𝜎coll as 𝜆 = ¯𝜇𝑚 𝑝/�𝜌𝑔𝜎coll
+�
+with 𝜎coll taken to be 2 × 10−19 m2 and the mean molecular mass
+¯𝜇 = 2.3 (Dipierro et al. 2018). Following Dipierro et al. (2018), we
+use the following drag equations:
+F𝐷,𝑖 = − 𝜌𝑔𝑣𝑡ℎ
+𝜌𝑚𝑎 𝜌𝑖
+�v𝑖 − v𝑔
+� ×
+�
+1
+if 𝑎 ≤ 9
+4𝜆 (Epstein)
+9𝜆
+4𝑎
+if 𝑎 > 9
+4𝜆 (Stokes)
+(10)
+where 𝜌𝑚 is the material density of a dust grain which we take to be
+3000 kg m−3, 𝑣𝑡ℎ the thermal speed which is 𝑣𝑡ℎ = 𝑐𝑠,𝑖𝑠𝑜
+√︁
+8/𝜋 in
+the Boltzmann distribution. Of course, the 𝑖th dust species exerts an
+equal and opposite drag force on the gas: F𝐷,𝑔 = −Σ𝑛
+𝑖=1F𝐷,𝑖.
+2.6 Initial and boundary conditions
+The simulations are done in 3D cylindrical polar coordinates (𝑅, 𝜙, 𝑧)
+in a stellar-centric frame. That is, the star is always at r = 0. Compu-
+tational units are chosen so that 𝑎pl, the radius of the protoplanet’s
+orbit around the star, is 1 and the period of the protoplanet’s orbit
+is also 1. Thus, in this corotating frame, the protoplanet is always
+at 𝑅 = 1, 𝜙 = 0, 𝑧 = 0. The region we simulate is 0.7 ≤ 𝑅 ≤ 1.3,
+0 ≤ 𝑧 ≤ 0.2. For every simulation but the last, the simulated region
+is −1
+4 𝜋 ≤ 𝜙 ≤ 1
+4 𝜋, one quarter of an annulus. The 𝜙 (azimuthal)
+boundary conditions are periodic, so that information is not lost as
+matter orbits the star, following Ayliffe & Bate (2009a,b). For the
+final simulation, we simulate the full annulus, 2𝜋 rad, at the same
+resolution as was done for the quarter-annulus. The simulations only
+include the upper half of the disc because mirror-symmetry at the
+midplane is assumed. The upper 𝑧 (vertical) boundary condition and
+both of the 𝑅 (radial) boundary conditions are fixed at their values
+from the initial conditions described below.
+These are multi-resolution simulations, with the higher-resolution
+levels existing only in the vicinity of the protoplanet. The low-
+resolution level which covers the entire grid, Level 1, has resolution
+120 in 𝑅, 40 in 𝑧 and 316 in 𝜙 (for quarter-annulus). That yields cells
+of size ∼ 0.005𝑎pl in all three dimensions. The accretion near to
+the protoplanet takes place on length-scales ∼ the radius of Jupiter,
+5 × 10−4 AU. Using such high resolution for the entire simulation
+is prohibited by computation time. Therefore we use a static mesh
+refinement. If a Level-1 cell is within 512 Jupiter radii of the proto-
+planet, it is divided into 8 Level-2 cells. If one of these Level-2 cells
+then lies within 256 Jupiter radii, it is further divided into 8 Level-3
+cells, and so on. The base grid is fully resolved and the highest grid
+level is 6, so that our maximum resolution is 25 times the base grid’s
+resolution.
+Initial conditions and boundary conditions for the simulations
+come from star+protoplanetary disc models developed by Miley et al.
+Parameter
+Value
+Units
+Stellar mass
+1
+𝑀⊙
+Mass of protoplanetary disc
+0.05
+𝑀⊙
+Age of protoplanetary disc
+1 × 106
+yr
+Dust size distribution power-law
+−3.5
+Minimum dust grain size
+1 × 10−8
+m
+Maximum dust grain size
+1 × 10−3
+m
+Turbulent alpha parameter
+1 × 10−3
+Table 1. Input parameters for the Miley et al. (2021) models that we used to
+generate initial and boundary conditions for our simulations.
+(2021). These models use the Monte Carlo radiative transfer code
+mcmax (Min et al. 2009) to produce self-consistent 2D solutions for
+temperature and densities in an axisymmetric protoplanetary disc.
+The parameters of the Miley et al. (2021) model that we use are
+shown in Table 1.
+The Miley et al. (2021) models are static. We have taken from the
+models the temperature, gas density, and total dust density summed
+over all grain sizes: 𝑇 (𝑅, 𝑧), 𝜌𝑔 (𝑅, 𝑧), 𝜌all dust (𝑅, 𝑧). For veloci-
+ties, we initially approximate as follows: 𝑣𝑅 = 𝑣𝑧 = 0 for both gas
+and dust; 𝑣𝜙 =
+√︃
+𝐺𝑀∗𝑅−1 − 3𝑃𝜌−1
+𝑔
+for gas; and 𝑣𝜙 =
+√︁
+𝐺𝑀∗𝑅−1
+for dust. This is a simplified form of an analytical protoplanetary
+disc expression; see Eq. 13 of Nelson et al. (2013) and remove
+the 𝑞
+�
+1 − 𝑅/
+√
+𝑅2 + 𝑧2
+�
+term for simplicity. We set 𝑝 and 𝑞, the
+power-law indices for the dependence of midplane gas density and
+temperature (respectively) on 𝑅, to 𝑝 = −2.5 and 𝑞 − 0.5. Dust,
+being pressureless, lacks the gas’s (𝑝 + 𝑞) (𝐻/𝑅)2 term. Since the
+initial star+disc models span the whole protoplanetary disc from
+0.24 AU ≤ 𝑅 ≤ 200 AU, their grid is much coarser in space
+than this paper. That necessitates logarithmic interpolation to con-
+vert them to appropriate initial and boundary conditions. Thus, tak-
+ing temperatures and densities from the initial star+disc models and
+velocities from an approximate analytical prescription, we obtain
+{𝑇, 𝜌, 𝑣𝑅, 𝑣𝜙, 𝑣𝑧} as a function of 𝑅 and 𝑧.
+While this provides us the initial conditions for the gas-only and
+single-grain models with gas (where we assume that the grain size is
+either i.e. 1 𝜇m, 10 𝜇m, 100 𝜇m or 1 mm), it does not directly give
+us the dust distribution for the multiple grain size simulations. In
+the multiple grain size simulations, the dust mass is divided between
+four grain sizes and we must obtain the density for each individual
+grain size 𝜌𝑖 from the overall summed dust density. We assume that
+these grain sizes, i.e. ¯𝑎1 = 1 𝜇m, ¯𝑎2 = 10 𝜇m, ¯𝑎3 = 100 𝜇m and
+¯𝑎4 = 1 mm, are representative of a continuous grain size distribution
+given by d𝑁 (𝑎)
+d𝑎
+= 𝑁0𝑎−3.5 where 𝑁0 is a normalisation factor
+(Mathis et al. 1977). In principle the mass density for each grain
+radius can be calculated using
+𝜌𝑖 = 𝑚 (𝑎𝑖) d𝑁 (𝑎)
+d𝑎
+����𝑎𝑖
+= 4𝜋𝜌𝑚
+3
+𝑁0𝑎−0.5
+𝑖
+(11)
+The normalisation factor 𝑁0 would then be determined by summing
+the mass densities and setting this sum equal to the total dust density.
+However, such an approach ignores the fact that the given grain sizes
+represent a range of grain radii with ¯𝑎𝑖 ∈ [𝑎𝑖, 𝑎𝑖+1]. A meaningful
+choice for a characteristic grain size is such that both the number
+and mass density of the bin can be reproduced simultaneously. This
+requires
+4𝜋𝜌𝑚
+3
+¯𝑎3
+𝑖 = 𝑀 (𝑎𝑖, 𝑎𝑖+1)
+𝑁 (𝑎𝑖, 𝑎𝑖+1)
+(12)
+where 𝑁(𝑎𝑖, 𝑎𝑖+1) and 𝑀(𝑎𝑖, 𝑎𝑖+1) are the total number density and
+MNRAS 000, 1–14 (2023)
+
+Size-selective accretion of dust onto CPDs
+5
+mass density, respectively, of grains with radii between 𝑎𝑖 and 𝑎𝑖+1.
+𝑀 (𝑎𝑖, 𝑎𝑖+1) =
+∫ 𝑎𝑖+1
+𝑎𝑖
+𝑚 (𝑎) d𝑁 (𝑎)
+d𝑎
+d𝑎
+(13)
+With our choice of characteristic grain radii ¯𝑎𝑖, this actually sets the
+lower and upper limit of each grain size bin, i.e. 𝑎𝑖 ≈ 0.4517¯𝑎𝑖,
+while 𝑎𝑖+1 ≈ 4.517¯𝑎𝑖. Using these limits we can then calculate the
+mass densities and determine the normalisation factor 𝑁0, and thus
+𝜌𝑖 = 𝑀(𝑎𝑖, 𝑎𝑖+1). This method is applied at every point in space.
+However, as Sect. 1 elaborates, the dust grain size distribution is
+observably not the same everywhere in space. Hence, the initial and
+boundary conditions from the above procedure are only provisional.
+To obtain our true initial and boundary conditions, we take the pro-
+visional {𝑇, 𝜌, 𝑣𝑅, 𝑣𝜙, 𝑣𝑧} (𝑅, 𝑧) values and we plug them into the
+MG hydrodynamics code, now simulating a slightly larger region:
+0.65 ≤ 𝑅 ≤ 1.35, 0 ≤ 𝑧 ≤ 0.22. This protoplanetary disc is then
+allowed to evolve freely for 10 orbital periods, with all the same
+physics except that axisymmetry is assumed and no protoplanets are
+present. This serves to “relax” the values from the initial star+disc
+models to a stable steady state, prior to the implantation of proto-
+planets. During this relaxation phase, the dust settles to the scale
+height appropriate for its grain size, except at the boundaries where
+the boundary conditions are pinned to the initial conditions. For this
+reason we use a larger simulated region during relaxation which
+prevents any distortion near the boundaries from entering the main
+simulations. Furthermore it produces a flux of inward radial-drifting
+dust. It will not perfectly capture the phenomenon of radial drift be-
+cause that takes place on timescales of order the disc lifetime, which
+greatly exceeds the length of these simulations. The resultant relaxed,
+steady-state, fully hydrodynamic models are used as the initial and
+boundary conditions for the main simulations.
+2.7 Implanting protoplanets
+Protoplanet growth during the runaway gas accretion phase takes
+place on timescales ∼ 104 −106 yr (Helled et al. 2014). For contrast,
+the relevant dynamical timescale of our simulations is the orbital pe-
+riod, which is ∼ 30 yr at 𝑎pl ∼ 10 AU around a star of mass ∼ 1𝑀⊙.
+The timescale of protoplanet growth is so many orders of magnitude
+longer than the timescale of our simulations that protoplanet growth
+is effectively static on our timescales. Thus, for our simulations to be
+accurate, we need them to have settled into a quasi-static state.
+Numerical breakdown would be caused by instantaneous insertion
+of a Jupiter-mass protoplanet into an unperturbed protoplanetary disc
+model. To avoid this, the protoplanet’s mass is set to 𝑀pl = 0 at 𝑡 = 0
+and it is linearly grown to its desired mass over the first 3 orbital
+periods of the main simulation. For our simulations the desired mass
+is 1𝑀Jup. This super-fast linear growth is not a representation of
+the planet formation process but purely a tool to avert numerical
+breakdown.
+The super-fast protoplanet implantation excites the protoplanetary
+disc to a temporary unsustainable state with extremely large amounts
+of matter clustering around the protoplanet and thus extremely high
+accretion rates. Therefore, even though the protoplanet is at full mass
+at 𝑡 = 3 orbits, a snapshot of the simulation at 𝑡 = 3 orbits is not
+conclusive. It is necessary to give the simulation more time to allow
+it to relax into a sustainable steady state. How much time, and how
+we determine that, is discussed in Sect. 3.
+Figure 1. The density distribution of a circumplanetary disc, in a frame
+comoving with the protoplanet, in a gas-only simulation. The protoplanet
+is at (0,0). 𝑅 and 𝑧 are measured from the protoplanet. The densities and
+velocities presented here have been mass-averaged across 𝜙, the azimuthal
+coordinate from the protoplanet. The arrows show the mass-averaged velocity
+vectors, or rather their 𝑅 and 𝑧 components. The 𝜙 component of velocity,
+orbiting around the protoplanet, is not shown.
+3 RESULTS
+3.1 Gas dynamics
+First we start with a gas-only simulation. It serves as a fiduciary
+model to confirm that our code is working as it should, reproducing
+the opening of a gap and the formation of a circumplanetary disc seen
+in previous studies (e.g. Kley 1999; Nelson et al. 2000; Machida et al.
+2008). Fig. 2 shows the gas surface density 50 orbits after the pro-
+toplanet was introduced in the numerical domain. The tidal torques
+exerted by the protoplanet indeed perturb the disc gas density in the
+form of trailing spiral shock waves. These open up an annular gap
+in the disc, although, after 50 orbits, the disc is not yet fully cleared
+and some disc material on a co-rotating orbit with the protoplanet
+is still present. This gas oscillates on horseshoe-shaped orbits in the
+frame corotating with the protoplanet. Henceforth we refer to this as
+the horseshoe region.
+Simultaneously a CPD forms around the protoplanet. Fig. 1 shows
+the azimuthally averaged density distribution within one Hill radius,
+𝑅Hill = 0.69 AU and shows a flared disc structure which is notably
+denser than its surrounding material. The disc itself is rotationally
+supported, while additional gas is fed to the CPD by meridional flows
+(as seen in e.g. Szulágyi et al. 2016). The CPD extends to a distance
+of about ≈ 0.5𝑅Hill from the protoplanet corresponding roughly to
+the extent of protoplanet’s Roche lobe. Therefore, throughout this
+paper, we define the CPD mass as twice the mass in all cells within
+a distance ≤ 0.5𝑅Hill of the protoplanet. Note that the factor of 2 is
+because we use symmetry boundary conditions at the midplane.
+As previously stated (Sect. 2.7), after the implantation of the pro-
+toplanet, the system requires some time to settle down. Fig. 3 shows
+the temporal evolution of the gas mass in the CPD in the gas-only
+simulation. It shows a rapid increase in the CPD gas mass which
+reaches a maximum after 3 orbits. Then the CPD mass reduces as
+more gas is accreted by the protoplanet than is deposited on the CPD.
+After about 20-25 orbits the CPD mass loss and gain balance each
+other and the CPD gas mass remains constant at about 0.76𝑀⊕. The
+MNRAS 000, 1–14 (2023)
+
+Ip / kgm-3
+0.7
+10-6
+0.6
+0.5
+10-7
+/ AU
+0.4
+10-8
+0.3
+10-9
+0.2
+10-10
+0.1
+10-11
+0.0
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+R/ AU
+10-126
+S. M. Karlin et al.
+Figure 2. Gas surface density in units kg m−2 for the gas-only simulation at
+𝑡 = 50 orbits after the implantation of the protoplanet. The green semicircle
+denotes a distance of 0.5𝑅Hill from the protoplanet, which is marked with a
+cross.
+Figure 3. The mass of a CPD in a gas-only simulation, over time. The CPD
+is settling into a steady state after the implantation of a protoplanet to the
+parent protoplanetary disc at 𝑡 = 0. This metric serves to inform us of when
+the CPD has reached a steady state.
+extreme clustering of matter near the protoplanet in the early part
+of these simulations is a numerical artefact due to the super-fast im-
+plantation of the protoplanet between 𝑡 = 0 and 𝑡 = 3 orbits. Only
+some time after the implantation phase (about 20-30 orbits), the CPD
+reaches a quasi-steady state, and it is this state that we analyse in this
+paper. This does not mean the system does not continue to evolve.
+Two-dimensional simulations of the late-time behaviour shows that
+the gap first becomes devoid of gas and that subsequently the inner
+disc (between star and protoplanet) disappears as the gas is accreted
+by the star (Nelson et al. 2000). However, computational restrictions
+of high-resolution three-dimensional simulations do not allow us to
+follow the CPD evolution up to such long timescales.
+3.2 Single grain size dynamics
+Now we include single-sized dust grains as well as the gas. Fig. 4
+shows the gas’s surface density (density integrated along the 𝑧 axis)
+and Fig. 5 the density of a slice at 𝜙 = 0. From these it is clear that
+the general effect of the dust grains on the gas structure is small, i.e.
+the width of the annular gap in the disc and the structure of the spiral
+arms connecting the CPD with the disc do not change at all. The
+main differences are seen in the structure of the horseshoe region: its
+location and thickness differs compared to the gas-only simulation
+and even between the single grain size simulations.
+To interpret this we need to understand the interaction between
+the gas and dust grains. In a general situation when the dust density
+is much smaller than the gas density, the radial motion of the dust
+particles is given by (Dipierro et al. 2018; Zhu et al. 2012)
+𝑣𝑑,𝑅 =
+𝑣𝑔,𝑅St−1 + 𝑣𝑝
+St + St−1
++
+𝑣visc
+1 + St2 − 𝜂turb
+𝜌𝑑
+𝜕
+𝜕𝑅
+� 𝜌𝑑
+𝜌𝑔
+�
+(14)
+where St = 𝜌𝑚𝑎
+𝜌𝑔𝑣𝑡ℎ ΩK is the Stokes number of the dust grains, 𝑣𝑝 =
+1
+𝜌𝑔ΩK
+𝜕𝑃
+𝜕𝑅 the typical dust drift velocity due to pressure differences
+and 𝑣visc =
+2
+𝜌𝑔ΩK ∇. 𝝈∼|𝜙 the radial drift due to viscous torques. The
+last term is the drift due to dust diffusion. For low Stokes numbers
+the dust grains closely follow the gas: the gas-grain drag dominates
+and the viscous drift is small compared to the gas velocity. However,
+when there is a large gradient in the dust-to-gas mass ratio, dust
+diffusion can become important. Grains with a high Stokes number,
+i.e. St > 0.1, decouple from the gas and the drift due to pressure
+gradients plays a significant role. In our simulations only the 1 mm
+grain model has high enough Stokes numbers for the dust and gas to
+decouple from each other, although the decoupling transition already
+starts at the smaller grain size of 100 𝜇m. Fig. 6 shows the dust
+surface density for each single grain size simulation. The surface
+density structure is nearly identical for 1 𝜇m, 10 𝜇m and 100 𝜇m,
+but is significantly different for 1 mm. Especially the dust density
+within the annular gap is a few orders of magnitude lower. This is
+an effect of the pressure-gradient drift, i.e. at the outer edge of the
+gap a pressure bump forms an effective barrier for the grains to drift
+inward. As a consequence the gap becomes devoid of 1 mm dust
+grains. This process is referred to as dust filtering (Rice et al. 2006)
+and observed in many simulations (e.g. Zhu et al. 2012).
+Another significant difference seen for the 1 mm simulation is
+that, although the gap is devoid of dust grains, the dust grains in the
+corotating region are trapped because of pressure gradients. As gas
+moves out of the annular gap, the dust-to-gas mass ratio therefore
+increases significantly and dust grains actually become the dominant
+mass carriers. Fig. 7 shows that the dust-to-gas mass ratio in the
+horseshoe region is 3 orders of magnitude larger than for typical
+ISM values. When this happens the back-reaction (or drag force) of
+MNRAS 000, 1–14 (2023)
+
+3 ×103
+8
+6 
+1×103
+4
+2 
+3×102
+AU
+0
+1×102
+-2
+-4 
+3×101
+-6 
+1×10l
+-8 
+5
+6
+7
+8
+9
+10
+11
+12
+13
+X/ AU8
+mgas,CPD/M@
+6
+4
+2
+0
+0
+10
+20
+30
+40
+50
+Time/ orbitsSize-selective accretion of dust onto CPDs
+7
+Figure 4. Surface density of gas in protoplanetary discs, in units kg m−2, after 𝑡 = 50 orbits since the implantation of the protoplanet. From left to right, the
+subplots show the single grain size simulations for 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m and 1 mm and finally the (quarter-annulus) multiple grain size simulation on
+the far right. The green semicircle denotes a distance of 0.5𝑅Hill from the protoplanet, which is marked with a cross.
+the dust grains on the gas can no longer be neglected. The qualitative
+analysis of Dipierro et al. (2018) shows that the back-reaction already
+becomes important when 𝜌𝑑/𝜌𝑔 > 𝛼/(St − 𝛼). However, Dipierro
+et al. (2018) did not include the effect of dust diffusion. Dust diffusion
+actually acts earlier as can be seen in the comparison of the thickness
+of the horseshoe region between the gas-only and single grain size
+simulations (see Figs. 2 and 4). At the boundaries of the horseshoe
+region the dust-to-gas mass ratio changes rapidly which gives rise
+to dust diffusion drift and pushes the dust away from the horseshoe
+region. As the gas and dust are strongly coupled, it actually drags the
+gas with it. While dust diffusion is also important for the 1 mm grains,
+the gas and dust are only weakly coupled leading to a thin horseshoe
+region as in the gas-only simulation, but a thick region in the dust. As
+we mentioned earlier, the dust-gas decoupling can already be noticed
+in the 100 𝜇m model, as it shows a dust distribution in between the
+smallest grain size simulations and the largest grain size simulation.
+So, the inclusion of dust grains does not change the gas dynamics,
+especially not the formation of a CPD around the protoplanet. How-
+ever, as we have seen, the dynamics of the dust depends on the Stokes
+number and, thus, the size of the grains. This also has consequences
+for the dust content of the CPD. As seen in Sect. 3.1, gas form inside
+the annular gap is transported to the CPD via meridional flows. As
+in the 1 mm simulation, the gap is devoid of dust grains, it is likely
+that the CPD has no dust in it either. Fig. 8 shows the dust-to-gas
+ratio of the CPD and, indeed, the ratio for the 1 mm simulation de-
+creases to 10−6 while the smaller grain size simulations have equal
+values around 10−3 (although for the 100 𝜇m model it is a factor
+of 2 lower). Note that the smaller grain size simulations also have
+a lower dust-to-gas mass ratio than the default value of 10−2. This
+is because the pressure maximum at the centre of the gap traps the
+dust grains to form the horseshoe region. Although not as efficient
+as in the 1 mm simulation, dust in the smaller grain size simulations
+is still more efficiently trapped than the gas. This is why, as Fig. 9
+shows, the dust-to-gas ratio in the horseshoe region is slightly above
+10−2, whereas it is lower elsewhere in the gap. That is also seen in
+2D simulations, e.g. Drążkowska et al. (2019). Actually, the ratio we
+obtain in the CPD is the same as in the gap, reinforcing the notion
+that material in the CPD is replenished by meridional flows.
+3.3 Multiple grain size dynamics
+In the previous section, we studied the behaviour of each dust species
+separately. The results show that the dust content of the CPD depends
+directly on the dust content of the annular gap and, thus, is grain
+size dependent due to dust filtration. Furthermore, the grain size
+affects the dynamics of the system as grains with a high Stokes
+number (or large grain size) decouple from the gas and dust-to-gas
+feedback becomes important. As there is a dust grain size distribution
+within protoplanetary discs, it is therefore important to consider the
+dynamics of multiple grain species simultaneously. The large, weakly
+coupled grains potentially modify the dynamics of the smaller well-
+coupled grains.
+Figs. 4 and 5 show that the gas structure for the quarter-annulus
+multiple grain size simulation is similar to the 1 mm single grain
+size simulation. This is not surprising as Dipierro et al. (2018) show
+that, for a continuous dust distribution, the effect of dust-gas drag on
+both the dust and gas is set by the parameters
+𝜆𝑘 =
+𝑛
+∑︁
+𝑖=1
+St𝑘
+𝑖
+1 + St2
+𝑖
+𝜌𝑖
+𝜌𝑔
+(15)
+where 𝑘 ∈ {0, 1} and 𝑛 is the number of dust grain size bins. For an
+MRN (Mathis et al. 1977) distribution, the value of 𝜆0 and 𝜆1 are
+solely determined by the Stokes number of the largest grains. This is
+because the largest bin (represented by the average bin grain size of
+1 mm) not only has the highest Stokes number, it also contains most
+of the dust mass. Thus, the dynamics, and thus the structure, of the
+largest grains and the gas are extremely similar to the single grain
+size simulation for 1 mm. The dynamics of the smaller grains that
+are strongly coupled to the gas does change in relation to their single
+MNRAS 000, 1–14 (2023)
+
+lμm single gr. size
+10μm single gr. size
+100μm single gr. size
+1mm single gr. size
+3×103
+Multiple grain size
+8
+1×103
+6
+.
+2
+3 × 102
+y/AU
+0
+1×102
+-2
+-4
+3×101
+-6
+-8
+1×101
+6
+8
+ ９ 101112 ５ ６
+7
+8 9 101112 5 6
+7
+8 9 101112 5 6
+7
+8 9 10 11 12 5 6
+7
+8
+9 1011 12 13
+X/ AU
+X/ AU
+X/ AU
+X/ AU
+X / AU8
+S. M. Karlin et al.
+Figure 5. Vertical slice at 𝜙 = 0 of the gas density, in units kg m−3, after
+𝑡 = 50 orbits since the implantation of the protoplanet. From top to bottom, the
+subplots show the gas-only simulation, then the single grain size simulations
+with 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m, and 1 mm, and then the multiple grain size
+simulation (all quarter-annulus). The green semicircle denotes the distance
+of 0.5𝑅Hill from the protoplanet.
+grain size simulations. The density structure in these smaller grains
+now looks like the 1 mm dust grain structure. As seen in Sect. 3.2,
+most of the difference is in the horseshoe region and not the CPD.
+This can be seen from Fig. 8 which shows the dust-to-gas mass ratio
+in the CPD. While the 1 𝜇m and 10 𝜇m dust grain size bins follow
+roughly the expected MRN distribution, the dust mass in the 100 𝜇m
+bin is a factor of 2 less than would be expected if it followed the MRN
+distribution, and the 1 mm mass is 3 orders of magnitude smaller.
+Fig. 10 shows that the multiple grain size simulation has the same
+filtering efficiency – CPD dust-to-gas mass ratio of a dust species,
+normalised by the initial dust-to-gas ratio of that species – for the
+different dust species as in the single grain size simulations. It is thus
+clear that dust filtering acts in the multiple grain size simulation as it
+does in the single grain size simulations and that every dust species
+behaves dynamically as if it and the gas were an isolated system.
+An important consequence of the multiple grain size simulation
+is that, although the CPD is populated with a wide size range of
+dust grains that are well coupled to the gas, the total dust-to-gas
+mass ratio of the CPD is much less than in the single size grain
+simulations, i.e. ≈ 3 × 10−4 compared to 10−3. This is because most
+of the protoplanetary disc dust mass is in the 1 mm bin. Dust filtration
+stops these large dust grains from flowing into the protoplanet-carved
+gap and, thus, also onto the CPD.
+Figure 6. Dust surface density for the single grain size simulations, i.e.
+𝑎 = 1 𝜇m (top left), 10 𝜇m (top right), 100 𝜇m (bottom left), and 1 mm
+(bottom right) in kg m−2 after 𝑡 = 50 orbits since the implantation of the
+protoplanet. The green semicircle denotes a distance of 0.5𝑅Hill from the
+protoplanet, which is marked with a cross.
+3.4 Full-annulus geometry
+Our quarter-annulus simulations provide an excellent comparison
+between the gas-only, single-grain and multiple grain models, but the
+periodic boundary conditions potentially affect the obtained results.
+To assess the effects, we run one additional simulation, which is
+identical in every way to the quarter-annulus multiple grain size
+simulation from Sect. 3.3 except that it covers the full annulus, i.e.
+2𝜋 rad, without loss of resolution. This full-annulus multiple grain
+size simulation takes longer to settle into steady state than its quarter-
+annulus counterpart, because it has more mass in the gap. Therefore,
+we run it for longer up to 𝑡 = 100 orbits, not 𝑡 = 50 as before.
+From Fig. 11 it is apparent that the simulation has reached a quasi-
+steady state by then. Fig. 12 shows that, qualitatively, this full-annulus
+result does not dramatically differ from the quarter-annulus results as
+compared to e.g. Fig. 7. There are some small local structures in the
+horseshoe region in Fig. 7 that are absent from Fig. 12, but these are
+simply due to spiral arms interacting with the periodic 𝜙-boundary
+conditions of a less-than-full annulus. The global picture with a gap,
+an inner and outer disc, streamers and a CPD remains the same.
+Some quantitative difference can be observed between the quarter
+and full-annulus cases. From Fig. 13 it can be seen that the filtering
+efficiency for the different dust grain sizes, but especially 1 mm, is
+MNRAS 000, 1–14 (2023)
+
+2.0
+Gas-only
+1.5
+Z/ AU
+1.0
+10-6
+0.5
+0.0
+lμm singlegrain size
+1.5
+/AU
+1.0
+10-7
+0.5
+0.0
+10μm single grain size
+1.5
+Z/ AU
+1.0
+0.5
+10-8
+0.0
+100μmsinglegrainsize
+1.5
+Z/ AU
+1.0
+0.5
+10-9
+0.0
+1mmsingle grainsize
+1.5
+Z/ AU
+1.0
+0.5
+10-10
+0.0
+Multiple grain size
+1.5
+Z/ AU
+1.0
+0.5
+10-11
+0.0
+7
+8
+9
+10
+11
+12
+13
+R / AU8
+6
+101
+4
+2
+AU
+0
+④
+④
++100
+-2
+4
+10-1
+-6
+-8
+10-2
+8
+6
+4
+10-3
+2
+y/AU
+0
+-2 
+10-4
+-4
+-6 
+10-5
+-8
+56
+6
+7.8.91011125
+6
+7
+8 910111213
+X/ AU
+X / AUSize-selective accretion of dust onto CPDs
+9
+Figure 7. Dust-to-gas ratio in the midplane after 𝑡 = 50 orbits since the
+implantation of the protoplanet, for the single grain size simulation of grain
+size 1 mm. The green semicircle denotes a distance of 0.5𝑅Hill from the
+protoplanet, which is marked with a cross.
+Figure 8. Dust-to-gas mass ratio of the circumplanetary disc at 𝑡 = 50 orbits
+for single grain size (blue dash-dotted) and multiple grain size simulation
+with quarter-annulus (red dashed). The green solid line is a power-law Mathis
+et al. (1977) distribution normalised with the value at 1 𝜇m.
+Figure 9. Azimuthally and vertically averaged dust-to-gas mass ratio after
+𝑡 = 50 orbits for the different single grain size simulations.
+Figure 10. Dust-to-gas mass ratio in the CPD normalised to the initial dust-
+to-gas mass ratio for that grain species. The blue, solid line shows the single
+size grain simulations while the red, dashed line shows the quarter-annulus
+multiple grain size simulation.
+much reduced (by a factor of 37, for 1 mm) in the quarter-annulus
+case compared to the full-annulus case. This is because the proto-
+planet’s gravitational torque is responsible for carving out the gap,
+by transferring orbital angular momentum from matter interior to its
+orbit to matter exterior of it. In effect, the quarter-annulus geometry
+exaggerates the time-integrated gravitational torque and the result-
+ing planetary gap. Then, as more dust grains remain in the gap in
+the full-annulus case, more can be captured by the CPD. This ef-
+fect of quarter-annulus geometry is stronger for larger grain sizes, a
+key weakness of simulations which depict less than the full annulus.
+However, note that size dependence of the filtering efficiency remains
+the same.
+Also, the dust-to-gas mass ratio of the circumplanetary disc in the
+multiple grain size simulations – considering dust of all grain sizes
+– is 2.9 × 10−4 for the quarter-annulus while 7.6 × 10−4 for the full
+annulus. The diminution in the quarter-annulus case is likely due to
+the enhanced strength of gravitational torque discussed above. The
+torque particularly strongly affects 1 mm dust, which is the domi-
+nant dust-mass-carrier species. To visualise this effect whereby the
+quarter-annulus’s enhanced torque exaggerates the gap compared to
+MNRAS 000, 1–14 (2023)
+
+10-1
+10
+10-3
+Single grainsize simulations
+10-4
+Multiplegrain sizesimulation
+1μm
+10μm
+100μm
+1mm
+Dustgrain size101
+8 
+6
+10-1
+4
+10-3
+2 
+AU
+0
++
+10-5
+-2 
+10-7
+-4 
+-6 
+10-9
+-8 
+5
+6
+7
+8
+9
+10
+11
+12
+13
+X/ AU10-3
+10-
+10-5
+Initialdistributiontrendline
+Singlegrainsizesimulations
+10-6
+Multiple grain size simulation
+口
+1μm
+10μm
+100μm
+1mm
+Dust grain size1 um
+0.1
+10um
+0.1mm
+1mm
+0.01
+10-3
+10-4
+10-5
+8.5
+9
+9.5
+10
+10.5
+11
+11.5
+radius [AU]10
+S. M. Karlin et al.
+Figure 11. Circumplanetary disc masses and filtering efficiencies over time
+in the quarter-annulus and full-annulus multifluid simulations. Filtering effi-
+ciency is as defined in Sect. 3.3: a dimensionless ratio for each dust species,
+proportional to that dust species’s CPD mass.
+Figure 12. Dust-to-gas ratio of the 1 mm dust species in the midplane after
+𝑡 = 100 orbits since the implantation of the protoplanet, for the full-annulus
+multiple grain size simulation.
+a full annulus, especially for large dust grains, see Fig. 14. Similarly,
+the ratio of the CPD dust mass to the protoplanet’s mass is 7.0×10−7
+for the quarter-annulus while 4.5×10−6 for the full annulus. Not only
+is the dust-to-gas ratio higher in the full annulus, but also the CPD
+gas mass (see Fig. 13) because quarter-annulus geometry reduces the
+pool of available mass to accrete onto the CPD, which leads to this
+increase of a factor of 6.5.
+Thus, while there are some quantitative difference between the
+quarter-and full annulus simulations, these differences are moderate
+and the overall behaviour and results remain the same.
+Figure 13. Dust-to-gas mass ratio in the CPD normalised to the initial dust-
+to-gas mass ratio for that grain species. The blue, solid line is for the quarter-
+annulus multiple grain size simulation. The red, dashed line is for the full-
+annulus multiple grain size simulation.
+Figure 14. Azimuthally and vertically averaged dust-to-gas mass ratio for the
+multiple grain size simulations, in steady state. That is at 𝑡 = 50 orbits for the
+quarter-annulus and 𝑡 = 100 for the full annulus.
+4 DISCUSSION
+4.1 Benchmarking
+Our simulations show a qualitatively similar picture as in the litera-
+ture (e.g. Klahr & Kley 2006; Machida et al. 2008; Tanigawa et al.
+2012; Szulágyi et al. 2014); i.e. the protoplanet carves a gap in the
+protoplanetary disc and, at the same time, a CPD forms around the
+protoplanet. The CPD structure itself shows a rotationally supported
+density structure filling the protoplanet’s Roche lobe. Furthermore,
+the protoplanet accretes mass from the CPD while, at the same time,
+CPD material is replenished by meridional flows (Szulágyi et al.
+2014). Previous studies do not, however, model the CPD with gas
+and multiple dust grain sizes each having their own dynamics.
+Dust grains also exhibit the expected behaviour: as seen in Fig. 15,
+larger dust grains have a smaller vertical scale height (e.g. Naka-
+gawa et al. 1986; Garaud et al. 2004; Dullemond & Dominik 2005;
+Fromang & Papaloizou 2006). Small grains are strongly coupled to
+the gas by dust-gas drag and thus experience turbulent stirring, while
+large grains are weakly coupled and thus settle towards the midplane.
+Recently, observations have corroborated this picture. Observations
+of HL Tau show that ∼ mm dust have a scale height of 𝐻 ∼ 0.01𝑅
+which is much flatter than for the gas disc. In contrast, Rich et al.
+(2021) find that, in the discs of IM Lup, HD 163296 and HD 97048,
+MNRAS 000, 1–14 (2023)
+
+100
+10
+Gas
+10
+lμm dust
+10μm dust
+10-6,
+100μmdust
+0
+20
+40
+60
+80
+100
+1mm dust
+Time/orbits
+Full annulus
+100
+Ouarter-annulus
+10
+-2
+10
+0
+20
+40
+60
+80
+100
+Time/orbits100
+10
+10-1
+5
+10-2
+y/AU
+10-3
+0
+10-4
+-5 
+10-5
+-10
+10-6
+-10
+-5
+0
+5
+10
+X /AU10-1
+10-2
+10-3
+Quarter-annulus,multifluid
+10-4
+Full annulus, multifluid
+1μm
+10μm
+100μm
+1mm
+Dustgrain sizespecies:
+10-2
+lμm dust
+10umdust
+dust
+10
+100μm dust
+1mm dust
+ratio
+10-4
+Quarter-annulus
+Full annulus
+10-5
+10
+8.0
+8.5
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+Radius / AUSize-selective accretion of dust onto CPDs
+11
+Figure 15. Vertical slice at 𝜙 = 0 of the dust density, in units kg m−3, of
+a protoplanetary disc with no protoplanet yet inserted. Each subplot comes
+from a different single grain size simulation, with dust grain size 𝑎 = 1 𝜇m,
+10 𝜇m, 100 𝜇m and 1 mm from top to bottom.
+small-grain-size (∼ 𝜇m) dust at radii < 100 AU has similar vertical
+distribution to the gas.
+Furthermore, we also observe the effect of dust filtration, i.e. large
+grains are prevented from penetrating the annular gap, while small
+grains can flow in easily with the gas. This was already seen in 2D
+simulations (Rice et al. 2006; Zhu et al. 2012; Weber et al. 2018;
+Haugbølle et al. 2019) which study the effect of dust clearing of the
+inner protoplanetary disc. They, however, do not consider the effect
+on the CPD.
+4.2 CPD grain size distribution
+Our results show that the grain size distribution function of the CPD
+follows the MRN distribution (Mathis et al. 1977) at small grain
+sizes, but falls significantly below that distribution by grain size
+𝑎 = 100 𝜇m and is truncated to near zero by 𝑎 = 1 mm. Secondly,
+the total dust-to-gas ratio is significantly lower than the typical ISM
+value, i.e. 8 × 10−4 compared to 10−2. This is because of the lower
+dust content – particularly of larger dust – in the annular gap carved
+by the protoplanet due to dust filtration (Zhu et al. 2012). These
+results are similar to the findings of Bae et al. (2019) who used test
+particles for the dust grain dynamics in a 2D disc.
+One caveat of this result is that the distribution function is only
+described by a limited number of size bins. It is necessary to increase
+the number of bins to examine the grain size distribution near the
+truncation. It is likely that there is no sharp transition, but a smooth
+turnover between 100 𝜇m and 1 mm as grains start to decouple from
+the gas. Another caveat is that, while we find that the dust distribution
+function follows an MRN power-law distribution at small grain sizes
+and tails off below MRN at 𝑎 = 100 𝜇m to 1 mm, this is only valid
+in absence of any grain processes. Local variations are expected as
+the grain size distribution is set by balancing dust production, growth
+and destruction processes. In protoplanetary discs, there is no dust
+production, but both growth and fragmentation of dust grains take
+place (Brauer et al. 2008; Birnstiel et al. 2010, 2018; Dullemond
+et al. 2018; Homma & Nakamoto 2018; Tamfal et al. 2018). These
+restrictions are important when analysing observational data.
+Understanding the grain size distribution function is also key to
+understanding observations as the distribution determines the opac-
+ity. When considering single-sized grains, Benisty et al. (2021) find
+that the CPD of PDS 70 c has a dust mass 0.007𝑀⊕ if the grain
+size is 1 mm or 0.031𝑀⊕ if 𝑎 = 1 𝜇m. Using an MRN distribution
+adjusted with the calculated filtering efficiencies (see Fig. 10) via
+logarithmic linear interpolation to approximate the CPD’s grain size
+distribution, we find that the CPD’s opacity at wavelength 855 𝜇m
+– and thus the CPD dust mass – is close to that for single-sized
+grains of 1 mm. However, as said before, with the coarse bin sizes
+there is some uncertainty on the turnover grain radius. Furthermore,
+Zhu et al. (2012) show that the critical grain radius for filtration
+depends on Stcrit which is proportional to 𝛼. It follows that 𝑎crit de-
+pends on the local temperature, viscosity and gas density of the disc:
+𝑎crit ∝ 𝜈turb𝜌𝑔/�𝑐𝑠,𝑖𝑠𝑜𝜌𝑚
+�. We know that PDS 70 c lies further
+out in the protoplanetary disc at 34 AU and the local temperature is
+about 26 K (Benisty et al. 2021), compared to 10 AU and 45 K in our
+simulations. We need to assume some radial dependency for 𝜈turb
+and 𝜌𝑔. Let us assume that 𝛼 is constant; then 𝜈turb ∝ 𝑐2
+𝑠,𝑖𝑠𝑜𝑅3/2.
+If we adopt 𝜌𝑔 ∝ 𝑅−1, the critical grain size is 1.4 times that of our
+simulations, whereas if 𝜌𝑔 ∝ 𝑅−3/2, 𝑎crit is 0.76 times ours. Either
+way, such a small variation in 𝑎crit makes little difference to the CPD
+dust mass deduced, as per Fig. 9 of Benisty et al. (2021).
+Via the method stated above, we can also calculate an opacity for
+our grain size distribution at 𝜆 = 1.8 𝜇m, the wavelength correspond-
+ing to the protoplanet’s surface temperature 𝑇 = 1600 K by Wien’s
+displacement law. It is 3.1 times the opacity of the MRN distribu-
+tion at the same wavelength. This can be understood by thinking of
+opacity as an absorption area-to-mass ratio. Our simulations include
+dust filtration to deplete the mass of large ∼ 1 mm grains, which
+have a lot of mass but little absorption area. Thus a CPD would be
+> 3 times better at absorbing radiation emitted by its protoplanet
+than an MRN-distributed CPD and thus hotter, if it has the grain size
+distribution we obtain.
+The reason why our results differ from those of Szulágyi et al.
+(2022), who find that the CPD is enriched in dust compared to its
+parent PPD, is that they model the unperturbed PPD’s dust as verti-
+cally flat, while our dust PPD is not flat because we do not neglect
+turbulent diffusion as they do. They find that large dust grains can
+accrete efficiently onto the protoplanet because the protoplanet ver-
+tically stirs up their flat disc of dust, pushing dust to high altitude
+where it can flow to feed the protoplanet, when flows at the mid-
+plane cannot do so because large dust grains are blocked as per dust
+filtration (e.g. Haugbølle et al. 2019). We find, contrarily, that the
+protoplanet pulls down the dust towards the midplane. An alternative
+reason is that their 𝑎crit is larger than ours, so large dust grains are
+still small enough not to be blocked off. However, their 𝑎crit is only
+larger than ours for their 5.2 AU case, not their 30 AU and 50 AU
+cases.
+MNRAS 000, 1–14 (2023)
+
+IPiμm dust / kg m-3]
+2.0
+1.5
+10-9
+Z/ AU
+1.0
+0.5
+0.0
+7
+8
+9
+10
+11
+12
+13
+10-10
+R / AU
+IP1oμm dust / kg m-3]
+2.0
+1.5
+AU
+10-11
+1.0
+0.5
+0.0
+7
+8
+9
+10 
+11
+12
+13
+10-12
+R/AU
+IP100μm dust / kg m-3]
+2.0
+1.5
+AU
+1.0
+10-13
+//z
+0.5
+0.0
+7
+8
+9
+10
+11
+12
+13
+R / AU
+10-14
+IP1mm dust / kg m-3]
+2.0
+1.5
+AU
+1.0
+10-15
+0.5
+0.0
+7
+8
+9
+10
+11
+12
+13
+R/AU
+10-1612
+S. M. Karlin et al.
+4.3 Dust mass and satellite formation
+With the Benisty et al. (2021) 0.007𝑀⊕ estimate of the CPD dust
+mass for PDS 70 c, the ratio of the CPD dust mass to protoplanet
+mass is about 10−5 where we assume the protoplanet mass to be
+2𝑀Jup (Wang et al. 2020). In our simulation – meaning the full-
+annulus multiple grain size simulation, the most physically realistic
+one – the ratio is even lower than that: 4.5×10−6. This discrepancy is
+simply the result of differing temperature assumptions. For the same
+observed flux, the higher the assumed temperature, the lower the
+deduced mass. Benisty et al. (2021) assume a CPD temperature of
+26 K, whereas the mass-averaged temperature of the CPD in our full-
+annulus multiple grain size simulation is 105 K. This is likelier to be
+an underestimate of the temperature than an overestimate, because
+we may include the protoplanet’s luminosity but we neglect shock
+heating from the matter falling vertically at up to 15 km s−1 towards
+the CPD. Furthermore, Isella et al. (2019) observe a similar flux for
+PDS 70 c’s CPD to Benisty et al. (2021) and they estimate its dust
+mass at 0.004𝑀⊕ if 𝑇 ∼ 20 K and 0.002𝑀⊕ if 𝑇 ∼ 80 K. With
+a temperature in the latter case more similar to ours, they obtain
+a CPD dust to protoplanet mass ratio of 3.2 × 10−6. This brings
+our simulated value of the mass ratio and the value inferred from
+observed flux within decent agreement.
+If our numerical model is overestimating the accretion rate from
+the CPD onto the protoplanet, the true mass of the CPD may be
+greater than we calculate. Our simulation result should be understood
+as providing a lower limit for CPD dust mass, rather than exact.
+This observational comparison provides support that it is at least
+reasonable on an order-of-magnitude basis.
+The major satellites of Jupiter, combined, have a mass ∼ 2 × 10−4
+times the mass of their host planet, and the same ratio holds true
+for Saturn (Canup & Ward 2009). However, the CPD dust mass
+is determined by the balance of removal through accretion of the
+protoplanet and replenishment from the protoplanetary disc. This is
+different than for a protoplanetary disc as the CPD is embedded in a
+gas and dust reservoir, while the protoplanetary disc is not and can
+become depleted of dust (Canup & Ward 2002). Because of this, it is
+not actually necessary for the instantaneous dust mass of the CPD at
+any one moment to be high, for satellites to be formed. This is known
+in the literature as the ‘starved disc’ model as discussed in Sect. 1.
+Also, planetesimal capture can provide satellitesimal seeds for this
+dust to accrete onto (e.g. Ronnet & Johansen 2020) and Drążkowska
+& Szulágyi (2018) show that dust traps are an efficient way to form
+satellites within the CPD. This would limit the accretion of dust onto
+the protoplanet and make more dust available to accumulate and form
+satellites. However, our simulations do not have enough resolution to
+follow the detailed evolution of the CPD and its satellite formation
+process. It thus is beyond the scope of this paper to follow the detailed
+evolution of the CPD involving the formation of satellites.
+Furthermore, both the CPD dust to protoplanet mass ratio and the
+CPD dust-to-gas mass ratio can be expected to be higher at earlier
+times in planet formation. For these simulations, recall that the mass
+of the parent protoplanetary disc was set to 0.05𝑀⊙ around a 1𝑀⊙
+star. If gas density is higher, there is a larger 𝑎crit (Sect. 4.2). Most
+of the dust mass is in larger grains, so when the critical grain size is
+larger, much more of the dust mass is able to enter the CPD in spite
+of dust filtration. And of course, for a protoplanet which has not (or
+not yet) grown massive enough to carve out a gap in the PPD, the
+CPD dust-to-gas mass ratio can be very much higher than we find
+here, as the gap’s dust filtration effect is absent.
+5 CONCLUSIONS
+We run 3D hydrodynamical simulations of a segment of protoplan-
+etary disc with an embedded Jupiter-mass protoplanet orbiting a
+Solar-mass star at orbital radius 10 AU. We follow the dynamics of
+the gas and 4 different dust grain sizes (1 𝜇m, 10 𝜇m, 100 𝜇m and
+1 mm). We include the effects of turbulent viscosity and dust-gas
+drag, using either the Epstein or the Stokes drag law depending on
+the ratio of the dust grain size to the gas’s mean free path. We in-
+clude the back-reaction due to the drag force of the dust on the gas.
+The different dust grain sizes are not coupled directly by a force, but
+via their back-reaction on the gas, they can indirectly influence each
+other. This is the first time multiple dust grain sizes with separate
+dynamics have been simulated in a CPD.
+We obtain the following conclusions:
+(i) The dynamics of the grains in the multiple grain size simu-
+lation is similar to the dynamics observed in the single grain size
+simulations. As the large grains modify the gas dynamics due to the
+back-reaction of dust-gas drag, they also modify the dynamics of the
+small grains. However, these changes are not significant and do not
+affect the CPD.
+(ii) At small grain sizes < 100 𝜇m, the grain size distribution
+of the dust in the CPD shows an MRN distribution. It tails off sig-
+nificantly below MRN at 𝑎 = 100 𝜇m and falls to almost zero by
+𝑎 = 1 mm, due to dust filtration limiting the flow of large dust
+grains into the annular gap. The critical grain radius for dust filtra-
+tion depends on the local properties of the disc, i.e. the disc density,
+temperature and viscosity.
+(iii) The CPD is depleted in dust-to-gas ratio compared to the
+parent protoplanetary disc by an order of magnitude, but is similar
+to the value within the annular gap carved by the protoplanet.
+(iv) Because the truncation and the low dust-to-gas ratio in the
+CPD, the CPD dust mass is low. The ratio of the CPD dust mass to
+the protoplanetary mass is ∼ a few ×10−6. While this is considerably
+lower than the value of 2 × 10−4 of Jupiter’s mass that constitutes
+the total mass of its moons, the dust within the CPD is continuously
+replenished by dust flow from the protoplanetary disc, thus making
+satellite formation possible as per the ‘starved disc’ model in the
+literature.
+(v) The opacity, mass-averaged temperature, and CPD dust to pro-
+toplanet mass ratio derived from our multiple grain size simulation
+yield consistency with the fluxes observed from the CPD of PDS 70
+c by Isella et al. (2019) and Benisty et al. (2021).
+Our simulations consider only a singular environment while changing
+the dust distribution between simulations. To further understand how
+environmental conditions change the grain size distribution, we need
+to change these parameters. In a subsequent study we will consider
+different planetary masses and position within the protoplanetary
+disc and also consider finer size binning in order to refine the critical
+grain size affected by dust filtration.
+ACKNOWLEDGEMENTS
+S.M.K. acknowledges funding from the Royal Society through the
+Fellowship Enhancement Award (grant holder O.P.). The research of
+O.P. was supported by the Royal Society Dorothy Hodgkin Fellow-
+ship during the preparation of this publication. S.v.L. is supported by
+a STFC consolidated grant. S.M.K. would like to thank Dr James Mi-
+ley for the protoplanetary disc models that underlie these simulations.
+This work was undertaken on ARC4, part of the High Performance
+Computing facilities at the University of Leeds, UK.
+MNRAS 000, 1–14 (2023)
+
+Size-selective accretion of dust onto CPDs
+13
+DATA AVAILABILITY
+The data underlying this article will be shared on reasonable request
+to the corresponding author.
+REFERENCES
+Ayliffe B. A., Bate M. R., 2009a, MNRAS, 393, 49
+Ayliffe B. A., Bate M. R., 2009b, MNRAS, 397, 657
+Bae J., et al., 2019, ApJ, 884, L41
+Bate M. R., Lubow S. H., Ogilvie G. I., Miller K. A., 2003, MNRAS, 341,
+213
+Benisty M., et al., 2021, ApJ, 916, L2
+Benítez-Llambay P., Krapp L., Pessah M. E., 2019, ApJS, 241, 25
+Binkert F., Szulágyi J., Birnstiel T., 2021, MNRAS, 506, 5969
+Birnstiel T., Dullemond C. P., Brauer F., 2010, A&A, 513, A79
+Birnstiel T., et al., 2018, ApJ, 869, L45
+Blanc M., et al., 2020, Planet. Space Sci., 193, 104960
+Brauer F., Dullemond C. P., Henning T., 2008, A&A, 480, 859
+Canup R. M., Ward W. R., 2002, AJ, 124, 3404
+Canup R. M., Ward W. R., 2009, in Pappalardo R. T., McKinnon W. B.,
+Khurana K. K., eds, , Europa. University of Arizona Press, p. 59
+Christiaens V., Cantalloube F., Casassus S., Price D. J., Absil O., Pinte C.,
+Girard J., Montesinos M., 2019, ApJ, 877, L33
+Dipierro G., Laibe G., Alexander R., Hutchison M., 2018, MNRAS, 479,
+4187
+Drążkowska J., Szulágyi J., 2018, ApJ, 866, 142
+Drążkowska J., Li S., Birnstiel T., Stammler S. M., Li H., 2019, ApJ, 885, 91
+Dullemond C. P., Dominik C., 2005, A&A, 434, 971
+Dullemond C. P., et al., 2018, ApJ, 869, L46
+Falle S. A. E. G., 1991, MNRAS, 250, 581
+Fromang S., Papaloizou J., 2006, A&A, 452, 751
+Garaud P., Barrière-Fouchet L., Lin D. N. C., 2004, ApJ, 603, 292
+Goldreich P., Ward W. R., 1973, ApJ, 183, 1051
+Greenberg R., 2011, Astrobiology, 11, 183
+Haugbølle T., Weber P., Wielandt D. P., Benítez-Llambay P., Bizzarro M.,
+Gressel O., Pessah M. E., 2019, AJ, 158, 55
+Helled R., et al., 2014, in Beuther H., Klessen R. S., Dullemond C. P.,
+Henning T., eds, Protostars and Planets VI. p. 643 (arXiv:1311.1142),
+doi:10.2458/azu_uapress_9780816531240-ch028
+Homma K., Nakamoto T., 2018, ApJ, 868, 118
+Isella A., Benisty M., Teague R., Bae J., Keppler M., Facchini S., Pérez L.,
+2019, ApJ, 879, L25
+Klahr H., Kley W., 2006, A&A, 445, 747
+Kley W., 1999, MNRAS, 303, 696
+Knapp G. R., Kerr F. J., 1974, A&A, 35, 361
+Korycansky D. G., Bodenheimer P., Pollack J. B., 1991, Icarus, 92, 234
+Krumholz M. R., McKee C. F., Klein R. I., 2004, ApJ, 611, 399
+Lin D. N. C., Papaloizou J. C. B., 1993, in Levy E. H., Lunine J. I., eds,
+Protostars and Planets III. p. 749
+Long Z. C., et al., 2018, ApJ, 858, 112
+Lunine J. I., Stevenson D. J., 1982, Icarus, 52, 14
+Machida M. N., Kokubo E., Inutsuka S.-i., Matsumoto T., 2008, ApJ, 685,
+1220
+Mathis J. S., Rumpl W., Nordsieck K. H., 1977, ApJ, 217, 425
+Miley J. M., Panić O., Booth R. A., Ilee J. D., Ida S., Kunitomo M., 2021,
+MNRAS, 500, 4658
+Min M., Dullemond C. P., Dominik C., de Koter A., Hovenier J. W., 2009,
+A&A, 497, 155
+Morfill G. E., Voelk H. J., 1984, ApJ, 287, 371
+Mosqueira I., Estrada P. R., 2003, Icarus, 163, 198
+Nakagawa Y., Sekiya M., Hayashi C., 1986, Icarus, 67, 375
+Nelson R. P., Papaloizou J. C. B., Masset F., Kley W., 2000, MNRAS, 318,
+18
+Nelson R. P., Gressel O., Umurhan O. M., 2013, MNRAS, 435, 2610
+Neveu M., et al., 2020, Frontiers in Astronomy and Space Sciences, 7, 26
+Paardekooper S. J., Mellema G., 2006, A&A, 453, 1129
+Parkinson C. D., Liang M.-C., Yung Y. L., Kirschivnk J. L., 2008, Origins of
+Life and Evolution of the Biosphere, 38, 355
+Pinte C., Dent W. R. F., Ménard F., Hales A., Hill T., Cortes P., de Gregorio-
+Monsalvo I., 2016, ApJ, 816, 25
+Rice W. K. M., Armitage P. J., Wood K., Lodato G., 2006, MNRAS, 373,
+1619
+Rich E. A., et al., 2021, ApJ, 913, 138
+Rivier G., Crida A., Morbidelli A., Brouet Y., 2012, A&A, 548, A116
+Ronnet T., Johansen A., 2020, A&A, 633, A93
+Shakura N. I., Sunyaev R. A., 1973, A&A, 500, 33
+Szulágyi J., 2017, ApJ, 842, 103
+Szulágyi J., Mordasini C., 2017, MNRAS, 465, L64
+Szulágyi J., Morbidelli A., Crida A., Masset F., 2014, ApJ, 782, 65
+Szulágyi J., Masset F., Lega E., Crida A., Morbidelli A., Guillot T., 2016,
+MNRAS, 460, 2853
+Szulágyi J., Binkert F., Surville C., 2022, ApJ, 924, 1
+Tamfal T., Drążkowska J., Mayer L., Surville C., 2018, ApJ, 863, 97
+Tanigawa T., Ohtsuki K., Machida M. N., 2012, ApJ, 747, 47
+Teague R., Bae J., Bergin E. A., 2019, Nature, 574, 378
+Trapman L., Rosotti G., Bosman A. D., Hogerheijde M. R., van Dishoeck
+E. F., 2020, A&A, 640, A5
+Van Loo S., Falle S. A. E. G., Hartquist T. W., 2006, MNRAS, 370, 975
+Wang J. J., et al., 2020, AJ, 159, 263
+Ward W. R., Canup R. M., 2010, AJ, 140, 1168
+Weber P., Benítez-Llambay P., Gressel O., Krapp L., Pessah M. E., 2018,
+ApJ, 854, 153
+Williams J. P., Cieza L. A., 2011, Annual Review of Astronomy and Astro-
+physics, 49, 67
+Youdin A. N., Lithwick Y., 2007, Icarus, 192, 588
+Zhu Z., Nelson R. P., Dong R., Espaillat C., Hartmann L., 2012, ApJ, 755, 6
+APPENDIX A: ACCRETION ALGORITHM
+We wrote a Gaussian accretion algorithm, designed to prevent
+sharp, discontinuous, un-physical transitions for a protoplanet mov-
+ing across a grid of cells. The method bears some resemblance to,
+but is not identical to, that of Krumholz et al. (2004). The amount of
+matter accreted from a cell containing density 𝜌 in each timestep Δ𝑡
+is given by:
+Δ𝑚 = 𝑓 𝜌𝑉cell ×
+�
+1 − exp
+� −Δ𝑡
+𝑡acc
+��
+exp
+�
+−
+��r − rpl
+��2
+𝑟2
+𝐺
+�
+(A1)
+where 𝑓 is an order-unity constant and 𝑟𝐺 is the ‘Gaussian radius’ of
+the protoplanet, which is chosen to be 𝑟𝐺 = 3𝑅eff. Here 𝑅eff is the
+effective radius that was defined in Sect. 2.2. As Δ𝑡 ≪ 𝑡acc in practice,
+the amount of mass accreted from a cell in time Δ𝑡 is proportional
+to Δ𝑡. This is deliberate; a conclusion for the accretion rate should
+not depend on the user’s arbitrary numerical timestep. The accretion
+timescale works like a freefall timescale: 𝑡2acc = 𝜋2𝑅3
+𝑓 𝑓 /�8𝐺𝑀pl
+�,
+where 𝑅 𝑓 𝑓 = max ���r − rpl
+�� , 𝑅eff
+�. The truncation of distance from
+the protoplanet at minimum value 𝑅eff is to avoid a singularity at the
+position of the protoplanet.
+This accretion is applied separately to the gas and to every species
+of dust. Whenever the protoplanet accretes matter from a cell, it
+records – separately – how much gas and how much dust it has
+accreted. This enables the simulations to track how efficiently the
+protoplanet accretes dust, by comparison to its accretion of gas.
+Following Krumholz et al. (2004), it is not advisable to let the sink
+particle violate the conservation of angular momentum around it
+when it accretes matter onto itself. Accordingly, whenever accretion
+is carried out for a fluid in the cell, the velocity of that fluid in that
+cell is decomposed into a component comoving with the protoplanet
+and the remainder ‘peculiar’ velocity. The peculiar velocity vector is
+MNRAS 000, 1–14 (2023)
+
+14
+S. M. Karlin et al.
+further decomposed using a cell-specific spherical coordinate system
+centred on the protoplanet, with unit-vectors �ˆe𝑟,pl, ˆe𝜙,pl, ˆe𝜃,pl
+�.
+Hence v = vpl + Σ𝑖𝑣rel,𝑖 where we define 𝑣rel,𝑖 = ˆe𝑖,pl . �v − vpl
+�
+where 𝑖 ∈ {𝑟, 𝜃, 𝜙}. When some mass is removed from the cell onto
+the sink particle, the component of momentum comoving with the
+protoplanet 𝑚vpl and the peculiar component 𝑚𝑣rel,𝑟 are accreted,
+whereas the peculiar components 𝑚𝑣rel,𝜃 and 𝑚𝑣rel,𝜙 are conserved
+during accretion. If mass of a fluid Δ𝑚 is accreted from a cell,
+the momentum of that same fluid accreted from the same cell is
+Δp = �vpl + 𝑣rel,𝑟ˆe𝑟,pl
+� × Δ𝑚.
+This paper has been typeset from a TEX/LATEX file prepared by the author.
+MNRAS 000, 1–14 (2023)
+
diff --git a/o9E5T4oBgHgl3EQfkQ_G/content/tmp_files/load_file.txt b/o9E5T4oBgHgl3EQfkQ_G/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..638e13ec75890604f7d5e1505bbb4a3ded0d2287
--- /dev/null
+++ b/o9E5T4oBgHgl3EQfkQ_G/content/tmp_files/load_file.txt
@@ -0,0 +1,1219 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf,len=1218
+page_content='MNRAS 000, 1–14 (2023)  Preprint 16 January 2023  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  Size-selective accretion of dust onto CPDs: Low CPD masses and filtration  of larger grains  Samuel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin,1★ Olja Panić,1 and Sven van Loo1,2  1School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK  2Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, Technicum blok 4 9000 Gent, Belgium  Accepted 2023 January 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Received 2022 December 22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' in original form 2022 August 10  ABSTRACT  The major satellites of Jupiter and Saturn are believed to have formed in circumplanetary discs, which orbit forming giant  protoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Gas and dust in CPDs have different distributions and affect each other by drag, which varies with grain size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Yet simulations of multiple dust grain sizes with separate dynamics have not been done before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We seek to assess how much  dust of each grain size there is in circumplanetary discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We run multifluid 3D hydrodynamical simulations including gas and  four discrete grain sizes of dust from 1 𝜇m to 1 mm, representing a continuous distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We consider a 1𝑀Jup protoplanet  embedded in a protoplanetary disc around a 1𝑀⊙ star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Our results show a truncated MRN distribution at smaller grain sizes,  which starts to tail off by 𝑎 = 100 𝜇m and is near zero at 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Large dust grains, which hold most of the dust mass, have  very inefficient accretion to the CPD, due to dust filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore CPDs’ dust masses must be small, with mass ratio ∼ a few  ×10−6 to the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These masses and the corresponding millimetre opacities are in line with CPD fluxes observed to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Key words: accretion – accretion discs – hydrodynamics – planets and satellites: formation – planets and satellites: gaseous  planets – protoplanetary discs  1 INTRODUCTION  The major satellites of Jupiter and Saturn exhibit almost perfectly  coplanar prograde circular orbits, with remarkably low eccentricities  and inclinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This lends itself to the suggestion that they formed  in discs of gas and dust orbiting around their parent planets (Ko-  rycansky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Ward & Canup 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These circumplanetary  discs (CPDs) are thus the birthplaces of icy moons such as Europa  and Enceladus, considered promising candidates for extraterrestrial  life (Greenberg 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Blanc et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Parkinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Neveu  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' They also regulate the flow of material onto a protoplanet  (Rivier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2012), from which it follows that they determine the  final mass that the mature planet can attain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Circumplanetary discs  used to be a prediction of theorists alone, but in recent years, with  VLT K-band observations of the protoplanet PDS 70 b (Christiaens  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2019) and ALMA submillimetre observations of the proto-  planet PDS 70 c (Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2021), emission  from CPDs has begun to be directly observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As such, study of  CPDs is both pertinent and timely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The dynamics of differently-sized dust particles in circumplane-  tary discs remains an understudied topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The grain size of dust in  CPDs is important in multiple ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It will govern their resulting  opacity, in which dust, despite being greatly outmassed by gas, is  the dominant component (Williams & Cieza 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That means it  governs their temperature, which is crucial to our ability, or lack  thereof, to detect CPDs observationally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore, dust size has  ★ Email: s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='karlin@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='com  implications for the feasibility of satellitesimal formation from dust,  and thus of satellite formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The earliest CPD modelling, done by Lunine & Stevenson (1982),  takes the observed mass of Jupiter’s Galilean satellites, multiplies it  by 100 to adjust for a dust-to-gas ratio of 10−2 and concludes that  Jupiter’s circumplanetary disc must have had a minimum mass of  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='02 times the mass of Jupiter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Applying the same reasoning to the  Saturnian system gives a strikingly similar fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The combined  satellites of each planet have about 2 × 10−4 times the mass of the  planet (Canup & Ward 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Mosqueira & Estrada (2003) point  out that a disc as dense as this ‘rich disc’ model proposes would  drag satellitesimals into the protoplanet at extremely short migration  timescales (< 103 yr), rendering the formation of satellites like  those of Saturn and Jupiter unfeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' They suggest an alternative  ‘gas-starved disc’ model, where the CPD is continuously being fed  more matter from outside and losing matter to the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  observations of Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) and Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) constrain  the dust masses of circumplanetary discs around protoplanets in the  PDS 70 system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' With the caveat that this is only one star-system  and it may not be representative, their results tentatively suggest that  observed dust masses seem too low for the rich disc models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  starved disc models are a better fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Circumplanetary discs form inside gaps in the parent protoplane-  tary disc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' a gap is a necessary but not sufficient condition for a CPD  to exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Only a sufficiently massive protoplanet can exert sufficiently  strong gravitational torque to form a gap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  𝑀pl > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='39𝑀Jup × 𝑀∗  𝑀⊙  ×  � 𝐻/𝑅  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='05  �3  (1)  © 2023 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='05662v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='EP]  13 Jan 2023  2  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (Lin & Papaloizou 1993) where 𝑀pl and 𝑀∗ are the masses of  the protoplanet and star, 𝑀Jup and 𝑀⊙ are the masses of Jupiter  and the Sun, and 𝐻/𝑅 is the protoplanetary disc’s aspect ratio at  the protoplanet’s location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Earth-like protoplanets are thus precluded  from having circumplanetary discs, but giant protoplanets ought to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Several authors have perfomed three-dimensional single-fluid hy-  drodynamical simulations of CPDs: Bate et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2003), Machida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (2008), Tanigawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2012), Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2014), Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (2016), Szulágyi & Mordasini (2017), Szulágyi (2017) to name but a  few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Among their many results they find that most of the protoplanet’s  mass inflow comes vertically from above and below the midplane,  not through the CPD on the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This renders two-dimensional  simulations impractical to capture protoplanet growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' CO gas veloc-  ity observations by Teague et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) affirm simulations’ prediction  that protoplanets should have these meridional flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Another con-  clusion from these simulations is that viscosity has a strong effect on  the resultant accretion rate: more viscous CPDs grant their protoplan-  ets faster accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The artificial numerical viscosity of simulations  can be a problem for modelling low-viscosity cases (Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2014) because it means that simulations intended to be inviscid, or  nearly so, might be quite viscous in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The temperature of the  CPD and of the protoplanet also plays a major role in determining the  shape of the CPD and gap, the mass of the CPD, and even whether  or not a CPD can exist at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A hot enough protoplanet will have no  CPD, only a gaseous envelope filling the whole Roche lobe (Szulágyi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  However, in the literature, circumplanetary discs have been simu-  lated assuming that gas and dust have the same distribution in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The assumption is that they have the same dust-to-gas ratio, typically  the interstellar medium value of 10−2 (Knapp & Kerr 1974), at all  points in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Sometimes this assumption is not made explicit;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' it  is implicit in the work by using opacity tables which assume a dust-  to-gas ratio of 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is well-known observationally that gas and  dust do not share the same distribution in space in protoplanetary  discs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Long et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' among many others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  According to theory they do not obey the same physics, so there is  no reason to expect them to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The separate dynamics of dust from gas should not be neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Even if it is only 1% of the mass budget as per the ISM dust-to-  gas ratio, the dust plays an outsized role in heating and cooling  because it dominates the opacity: (𝜅𝜌)𝑑 ≫ (𝜅𝜌)𝑔 despite 𝜌𝑔 ≫ 𝜌𝑑  (Williams & Cieza 2011) where 𝜅 is opacity and 𝜌 is density and  𝑔 and 𝑑 denote gas and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the same reason of high opacity,  dust emits disproportionately much of the electromagnetic radiation  we can see.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Understanding dust dynamics as separate from the gas  is a necessary prerequisite to capture the thermodynamic behaviour  of a CPD and its environs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In models that presume perfect uniform  mixing, the opacity and temperature at any given point in space will  be dramatically overestimated or underestimated if the local dust-to-  gas ratio at that point is greater or less than 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore, there  is no reason to expect dust of different grain sizes to share the same  distribution in space, because dust particles of different sizes have  different surface-area-to-mass ratios and thus experience different  strengths of dust-gas drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Previously published work by Binkert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) and Szulá-  gyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2022) concern three-dimensional hydrodynamical simula-  tions of CPDs with separate gas and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The principal differences  from this work are as follows: (I) they use only one dust grain size,  𝑎 = 1 mm, whereas we allow dust of multiple grain sizes to exist  simultaneously, with each dust size possessing its own dynamics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (II) they simulate a larger region of the protoplanetary disc than we  do;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (III) their simulations are radiative, whereas we adopt a locally  isothermal approach;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' and (IV) they neglect turbulent diffusion of  dust, which matters because the main flow feeding the protoplanet  is vertical, sourced from far above and below the midplane, and tur-  bulent stirring is what counteracts the gravitational settling of dust  which would otherwise pull the dust onto the midplane to form an  extremely thin layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' They conclude that planetary gravity vertically  stirs the dust, so planet-hosting protoplanetary discs are thicker than  expected in the dust and therefore the dust masses of observed pro-  toplanetary discs may be being underestimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The purpose of this paper is to assess not only how much dust there  is in circumplanetary discs but how much dust there is of each grain  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The dust size distribution determines the opacity and, as such,  is crucial to understand CPD observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For example, Benisty  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) conclude that the circumplanetary disc of PDS 70 c  has a dust mass 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='007𝑀⊕ if the dust grain size is 1 mm or a much  more massive 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='031𝑀⊕ if the dust grain size is 1 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore,  we run three-dimensional multifluid hydrodynamical simulations of  a circumplanetary disc, covering the gap in which the CPD dwells  and the protoplanet within the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Gas and dust are permitted to  exist separately, following their separate dynamics, albeit coupled  to each other by dust-gas drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Our approach differs from previous  work in that we devote the available computing power to multifluid  dust dynamics, rather than to a more sophisticated thermal treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  We argue that temperature depends so strongly on opacity and thus  on the distribution of different-sized dust grains in space that our  approach is warranted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2, we lay out the numerical toolset  we use, the setup of the simulations and the physical processes they  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Then we give the results of our simulations and compare them  to observations in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3 and we discuss the implications of these  results in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Finally, our conclusions are offered in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2 METHODS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1 Numerical implementation  We run 3D hydrodynamical simulations of a segment of a proto-  planetary disc containing a Jupiter-mass protoplanet on a circular  orbit at 10 AU around a solar-mass star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The orbital radius we use is  wider than Jupiter’s orbit because we wish to consider protoplanets  distant enough to be observable in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We use a grid-based  Finite-Volume Adaptive Mesh Refinement code called MG (Falle  1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Van Loo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The governing equations for the gas are:  𝜕𝜌𝑔  𝜕𝑡 + ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' �𝜌𝑔v𝑔  � = 0  (2)  𝜕 �𝜌𝑔v𝑔  �  𝜕𝑡  + ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  �  𝜌𝑔v𝑔 ⊗ v𝑔 − 𝝈∼  �  = −  𝑛  ∑︁  𝑖=1  F𝐷,𝑖 − 𝜌𝑔∇Φ  −𝜌𝑔Ω𝑐 × (Ω𝑐 × r) − 2𝜌𝑔Ω𝑐 × v𝑔  (3)  where 𝜌𝑔 is the gas density, v𝑔 the gas velocity, Φ the gravitational  potential, 𝑛 the number of different dust species, F𝐷,𝑖 the drag force  by the gas on the 𝑖th dust species, and Ω𝑐 = Ω𝑐ˆe𝑧 the corotation  vector with Ω𝑐 the corotation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In our simulations, we  choose to use a frame corotating at frequency Ω𝑐 =  √︃  𝐺𝑀∗/𝑎3  pl to  keep the protoplanet stationary where 𝑀∗ is the star’s mass and 𝑎pl  the orbital radius of the protoplanet around the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The position r  is defined relative to the star which is at the origin, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  turbulent-viscous stress tensor, 𝝈∼, is defined as follows:  𝝈∼ = 𝜂turb  �  ∇ ⊗ v𝑔 + �∇ ⊗ v𝑔  �T�  −  � 2  3𝜂turb∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='v𝑔 + 𝑃  �  I∼  (4)  MNRAS 000, 1–14 (2023)  Size-selective accretion of dust onto CPDs  3  where 𝑃 is the pressure, 𝜂turb the turbulent viscosity and I∼ the  identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The code is locally isothermal, for computational  efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' See Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 for the temperature description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the 𝑖th  dust species, the governing equations are:  𝜕𝜌𝑖  𝜕𝑡 + ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  �  𝜌𝑖v𝑖 − 𝜂turb∇  � 𝜌𝑖  𝜌𝑔  ��  = 0  (5)  𝜕 (𝜌𝑖v𝑖)  𝜕𝑡  + ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  �  𝜌𝑖v𝑖 ⊗ v𝑖 −  �  𝜂turb∇  � 𝜌𝑖  𝜌𝑔  ��  ⊗ v𝑖  �  =  F𝐷,𝑖 − 𝜌𝑖∇Φ − 𝜌𝑖Ω𝑐 × (Ω𝑐 × r) − 2𝜌𝑖Ω𝑐 × v𝑖  (6)  where 𝜌𝑖 and v𝑖 are the density and velocity of the 𝑖th dust species,  and all other variables are defined above (Morfill & Voelk 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Each dust species is treated as a pressureless fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The MG code uses a Godunov method which is 2nd order in space  and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the gas we use a Kurganov-Tadmor Riemann solver,  while for the dust Riemann solver we implement the algorithm of  Paardekooper & Mellema (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The dust species are coupled to the  gas by dust-gas drag;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Once the drag coefficients have  been calculated, our code uses the algorithm of Benítez-Llambay  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) to solve the effects of dust-gas drag upon all of the  dust species and the gas, at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It solves equations of the form  F𝐷,𝑖 = − �  𝑗 𝛽𝑖 𝑗  �v𝑖 − v 𝑗  � by a backward-in-time, implicit, linear-  algebra method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Our version of MG is able to simulate an arbitrary  number of dust species coexisting with gas, rather than just gas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' to  work in a corotating frame;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' and to have protoplanets which exert  gravity, accrete matter, and provide heat to their surroundings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  We run one gas-only simulation, four single grain size simula-  tions with gas and one dust species at a time, and one multiple grain  size simulation with gas and four dust species simultaneously, with  quarter-annulus geometry, and we run one multiple grain size simu-  lation (gas + 4 dust) with full-annulus geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The dust grain sizes  are 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m and 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These grain sizes are  consistent with the Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) protoplanetary disc models  that produced our initial conditions, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We  obtain the other grain sizes from our choice to use logarithmically  even spacing with a factor of 10, in order to explore the behaviour of  dust of a wide range of orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 Temperature  The disc is assumed to be locally isothermal, with an ideal gas  equation of state:  𝑃 =  𝜌𝑔  ¯𝜇𝑚 𝑝  𝑘𝐵𝑇  (7)  where ¯𝜇 is mean molecular mass, 𝑚 𝑝 the mass of a proton, 𝑘𝐵  Boltzmann’s constant and 𝑇 temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The initial conditions give the temperature of the unperturbed  protoplanetary disc at every point in space, as Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6 explains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  temperature at every point in space is kept equal to its value in these  initial conditions, unless the point is close enough that the luminosity  of the hot young protoplanet dominates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  𝑇 (r) = max ��  �  �  𝐿pl  4𝜋 �𝑑pl (r)�2 × 𝜎  �1/4  , 𝑇init (r)��  �  (8)  where 𝐿pl is the protoplanet’s luminosity, and 𝑑pl (r) the distance  from protoplanet is given by 𝑑pl (r) = max ���r − rpl  �� , 𝑅eff  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝑅eff  the “effective radius” serves to avoid a singularity at the location of  the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In this paper we set 𝑅eff to be 8 times the radius  of Jupiter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the protoplanet’s luminosity, we use 𝐿pl = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='96 ×  10−5𝐿⊙, which comes from the equation 𝐿pl = 4𝜋𝑅2  pl × 𝜎𝑇4  surf  for a Jupiter-radius protoplanet with the same surface temperature  1600 K that was observed by Christiaens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) for the giant  protoplanet PDS 70 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is not expected to be exact for all giant  protoplanets but should be of the right order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3 Gravity and accretion  While the self-gravity of the disc material upon itself is neglected,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  the gravitational acceleration – which is the same for the gas and dust  – can be straightforwardly calculated using  ∇Φ(r) =  𝐺𝑀pl  �r − rpl  �  ���r − rpl  ��2 + (2𝑅eff)2�3/2 + 𝐺𝑀∗  |r|3 r + 𝐺𝑀pl  ��rpl  ��3 rpl  (9)  Note that the first two terms arise directly from the gravitational  potentials of the star and protoplanet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' while the last term is an indirect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  fictitious acceleration due to the gravitational pull of the protoplanet  on the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is included because our choice of reference frame is  keeping the star always at r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore, the direct term of the  protoplanet’s gravity is artificially smoothed close to the protoplanet  using a smoothing radius of 2𝑅eff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  For Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 9, the protoplanet’s mass is fixed at 1𝑀Jup throughout  the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These simulations are intended to capture the CPD  instantaneously, not to simulate its entire lifetime, which would be  computationally prohibitive for high-resolution 3D hydrodynamical  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Accretion has a major impact on the results because the mass bud-  get of the circumplanetary disc is governed by input and output: the  flow of mass from the parent protoplanetary disc, and the accretion  of mass from the circumplanetary disc onto the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' There-  fore, even though accretion happens on length-scales much smaller  than every other length-scale in the problem, it still must be treated  with great care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The accretion algorithm we use is Gaussian with  distance from the protoplanet and near-linear with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The mass  accreted from a cell in a timestep of length Δ𝑡 is proportional to  (1 − exp (−Δ𝑡/𝑡acc)) where 𝑡acc is an accretion timescale based on  freefall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, as close to the protoplanet Δ𝑡/𝑡acc ≪ 1, it is in  effect linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the algorithmic details of the accretion treatment in  this paper, see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4 Turbulence  Turbulence in protoplanetary discs is a source of angular momen-  tum transport and can be treated like a viscosity where the kine-  matic viscosity is given by 𝜈turb = 𝛼𝑐2  𝑠,𝑖𝑠𝑜Ω−1  K (Shakura & Sun-  yaev 1973) where 𝑐𝑠,𝑖𝑠𝑜 =  √︁  𝑃/𝜌𝑔 is the isothermal sound speed  and ΩK =  √︁  𝐺𝑀∗/𝑅3 is the Keplerian frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This equation is  used to calculate the dynamic viscosity 𝜂turb = 𝜌𝑔𝜈turb through-  out this paper, for both gas and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝜈turb in our simulations is  not time-variable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' it is calculated using the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  turbulent/diffusive terms in Eqs 5 and 6 are for turbulent stirring,  which must not be neglected because the balance between it and the  settling due to drag and gravity sets the scale height for dust of each  grain size (Youdin & Lithwick 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Without it, the dust would set-  tle into a super-dense, gravitationally unstable layer at the midplane  (Goldreich & Ward 1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Observationally, the general consensus is that 𝛼 is around 10−4 -  10−3 in Class II discs: for instance, Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2016) look at the  continuum emission of the disc HL Tau and, by modelling the vertical  MNRAS 000, 1–14 (2023)  4  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  settling of dust, they deduce an 𝛼 of order a few times 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' With a  different method, Trapman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2020) analyse protoplanetary discs’  viscous spreading by comparing PPDs’ ages to their outer radii for a  sample in the Lupus star-forming region and they conclude that 𝛼 is  generally in the 10−4 - 10−3 range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In this paper we take 𝛼 = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  We choose the upper end of the 10−4 - 10−3 range because higher  𝛼 means higher dust scale heights, which are less computationally  expensive to capture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5 Dust-gas drag  Dust-gas drag is treated as one of two regimes, depending on com-  paring the dust grain size 𝑎 to the mean free path 𝜆 of the gas: the  Epstein drag regime when 𝑎 ≤  9  4𝜆 and the Stokes regime when  𝑎 > 9  4𝜆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The mean free path can be expressed in terms of the gas  density and collisional cross section 𝜎coll as 𝜆 = ¯𝜇𝑚 𝑝/�𝜌𝑔𝜎coll  �  with 𝜎coll taken to be 2 × 10−19 m2 and the mean molecular mass  ¯𝜇 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3 (Dipierro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Following Dipierro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2018), we  use the following drag equations:  F𝐷,𝑖 = − 𝜌𝑔𝑣𝑡ℎ  𝜌𝑚𝑎 𝜌𝑖  �v𝑖 − v𝑔  � ×  �  1  if 𝑎 ≤ 9  4𝜆 (Epstein)  9𝜆  4𝑎  if 𝑎 > 9  4𝜆 (Stokes)  (10)  where 𝜌𝑚 is the material density of a dust grain which we take to be  3000 kg m−3, 𝑣𝑡ℎ the thermal speed which is 𝑣𝑡ℎ = 𝑐𝑠,𝑖𝑠𝑜  √︁  8/𝜋 in  the Boltzmann distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Of course, the 𝑖th dust species exerts an  equal and opposite drag force on the gas: F𝐷,𝑔 = −Σ𝑛  𝑖=1F𝐷,𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6 Initial and boundary conditions  The simulations are done in 3D cylindrical polar coordinates (𝑅, 𝜙, 𝑧)  in a stellar-centric frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That is, the star is always at r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Compu-  tational units are chosen so that 𝑎pl, the radius of the protoplanet’s  orbit around the star, is 1 and the period of the protoplanet’s orbit  is also 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Thus, in this corotating frame, the protoplanet is always  at 𝑅 = 1, 𝜙 = 0, 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The region we simulate is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='7 ≤ 𝑅 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3,  0 ≤ 𝑧 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For every simulation but the last, the simulated region  is −1  4 𝜋 ≤ 𝜙 ≤ 1  4 𝜋, one quarter of an annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The 𝜙 (azimuthal)  boundary conditions are periodic, so that information is not lost as  matter orbits the star, following Ayliffe & Bate (2009a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the  final simulation, we simulate the full annulus, 2𝜋 rad, at the same  resolution as was done for the quarter-annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The simulations only  include the upper half of the disc because mirror-symmetry at the  midplane is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The upper 𝑧 (vertical) boundary condition and  both of the 𝑅 (radial) boundary conditions are fixed at their values  from the initial conditions described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  These are multi-resolution simulations, with the higher-resolution  levels existing only in the vicinity of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The low-  resolution level which covers the entire grid, Level 1, has resolution  120 in 𝑅, 40 in 𝑧 and 316 in 𝜙 (for quarter-annulus).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That yields cells  of size ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='005𝑎pl in all three dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The accretion near to  the protoplanet takes place on length-scales ∼ the radius of Jupiter,  5 × 10−4 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Using such high resolution for the entire simulation  is prohibited by computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore we use a static mesh  refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' If a Level-1 cell is within 512 Jupiter radii of the proto-  planet, it is divided into 8 Level-2 cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' If one of these Level-2 cells  then lies within 256 Jupiter radii, it is further divided into 8 Level-3  cells, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The base grid is fully resolved and the highest grid  level is 6, so that our maximum resolution is 25 times the base grid’s  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Initial conditions and boundary conditions for the simulations  come from star+protoplanetary disc models developed by Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Parameter  Value  Units  Stellar mass  1  𝑀⊙  Mass of protoplanetary disc  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='05  𝑀⊙  Age of protoplanetary disc  1 × 106  yr  Dust size distribution power-law  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Minimum dust grain size  1 × 10−8  m  Maximum dust grain size  1 × 10−3  m  Turbulent alpha parameter  1 × 10−3  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Input parameters for the Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) models that we used to  generate initial and boundary conditions for our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These models use the Monte Carlo radiative transfer code  mcmax (Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2009) to produce self-consistent 2D solutions for  temperature and densities in an axisymmetric protoplanetary disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The parameters of the Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) model that we use are  shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) models are static.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We have taken from the  models the temperature, gas density, and total dust density summed  over all grain sizes: 𝑇 (𝑅, 𝑧), 𝜌𝑔 (𝑅, 𝑧), 𝜌all dust (𝑅, 𝑧).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For veloci-  ties, we initially approximate as follows: 𝑣𝑅 = 𝑣𝑧 = 0 for both gas  and dust;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝑣𝜙 =  √︃  𝐺𝑀∗𝑅−1 − 3𝑃𝜌−1  𝑔  for gas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' and 𝑣𝜙 =  √︁  𝐺𝑀∗𝑅−1  for dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is a simplified form of an analytical protoplanetary  disc expression;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 13 of Nelson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2013) and remove  the 𝑞  �  1 − 𝑅/  √  𝑅2 + 𝑧2  �  term for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We set 𝑝 and 𝑞, the  power-law indices for the dependence of midplane gas density and  temperature (respectively) on 𝑅, to 𝑝 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5 and 𝑞 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust,  being pressureless, lacks the gas’s (𝑝 + 𝑞) (𝐻/𝑅)2 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Since the  initial star+disc models span the whole protoplanetary disc from  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='24 AU ≤ 𝑅 ≤ 200 AU, their grid is much coarser in space  than this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That necessitates logarithmic interpolation to con-  vert them to appropriate initial and boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Thus, tak-  ing temperatures and densities from the initial star+disc models and  velocities from an approximate analytical prescription, we obtain  {𝑇, 𝜌, 𝑣𝑅, 𝑣𝜙, 𝑣𝑧} as a function of 𝑅 and 𝑧.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  While this provides us the initial conditions for the gas-only and  single-grain models with gas (where we assume that the grain size is  either i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1 𝜇m, 10 𝜇m, 100 𝜇m or 1 mm), it does not directly give  us the dust distribution for the multiple grain size simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In  the multiple grain size simulations, the dust mass is divided between  four grain sizes and we must obtain the density for each individual  grain size 𝜌𝑖 from the overall summed dust density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We assume that  these grain sizes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' ¯𝑎1 = 1 𝜇m, ¯𝑎2 = 10 𝜇m, ¯𝑎3 = 100 𝜇m and  ¯𝑎4 = 1 mm, are representative of a continuous grain size distribution  given by d𝑁 (𝑎)  d𝑎  = 𝑁0𝑎−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5 where 𝑁0 is a normalisation factor  (Mathis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In principle the mass density for each grain  radius can be calculated using  𝜌𝑖 = 𝑚 (𝑎𝑖) d𝑁 (𝑎)  d𝑎  ����𝑎𝑖  = 4𝜋𝜌𝑚  3  𝑁0𝑎−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  𝑖  (11)  The normalisation factor 𝑁0 would then be determined by summing  the mass densities and setting this sum equal to the total dust density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  However, such an approach ignores the fact that the given grain sizes  represent a range of grain radii with ¯𝑎𝑖 ∈ [𝑎𝑖, 𝑎𝑖+1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A meaningful  choice for a characteristic grain size is such that both the number  and mass density of the bin can be reproduced simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This  requires  4𝜋𝜌𝑚  3  ¯𝑎3  𝑖 = 𝑀 (𝑎𝑖, 𝑎𝑖+1)  𝑁 (𝑎𝑖, 𝑎𝑖+1)  (12)  where 𝑁(𝑎𝑖, 𝑎𝑖+1) and 𝑀(𝑎𝑖, 𝑎𝑖+1) are the total number density and  MNRAS 000, 1–14 (2023)  Size-selective accretion of dust onto CPDs  5  mass density, respectively, of grains with radii between 𝑎𝑖 and 𝑎𝑖+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  𝑀 (𝑎𝑖, 𝑎𝑖+1) =  ∫ 𝑎𝑖+1  𝑎𝑖  𝑚 (𝑎) d𝑁 (𝑎)  d𝑎  d𝑎  (13)  With our choice of characteristic grain radii ¯𝑎𝑖, this actually sets the  lower and upper limit of each grain size bin, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝑎𝑖 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4517¯𝑎𝑖,  while 𝑎𝑖+1 ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='517¯𝑎𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Using these limits we can then calculate the  mass densities and determine the normalisation factor 𝑁0, and thus  𝜌𝑖 = 𝑀(𝑎𝑖, 𝑎𝑖+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This method is applied at every point in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  However, as Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1 elaborates, the dust grain size distribution is  observably not the same everywhere in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Hence, the initial and  boundary conditions from the above procedure are only provisional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  To obtain our true initial and boundary conditions, we take the pro-  visional {𝑇, 𝜌, 𝑣𝑅, 𝑣𝜙, 𝑣𝑧} (𝑅, 𝑧) values and we plug them into the  MG hydrodynamics code, now simulating a slightly larger region:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='65 ≤ 𝑅 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='35, 0 ≤ 𝑧 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This protoplanetary disc is then  allowed to evolve freely for 10 orbital periods, with all the same  physics except that axisymmetry is assumed and no protoplanets are  present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This serves to “relax” the values from the initial star+disc  models to a stable steady state, prior to the implantation of proto-  planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' During this relaxation phase, the dust settles to the scale  height appropriate for its grain size, except at the boundaries where  the boundary conditions are pinned to the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For this  reason we use a larger simulated region during relaxation which  prevents any distortion near the boundaries from entering the main  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore it produces a flux of inward radial-drifting  dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It will not perfectly capture the phenomenon of radial drift be-  cause that takes place on timescales of order the disc lifetime, which  greatly exceeds the length of these simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The resultant relaxed,  steady-state, fully hydrodynamic models are used as the initial and  boundary conditions for the main simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='7 Implanting protoplanets  Protoplanet growth during the runaway gas accretion phase takes  place on timescales ∼ 104 −106 yr (Helled et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For contrast,  the relevant dynamical timescale of our simulations is the orbital pe-  riod, which is ∼ 30 yr at 𝑎pl ∼ 10 AU around a star of mass ∼ 1𝑀⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The timescale of protoplanet growth is so many orders of magnitude  longer than the timescale of our simulations that protoplanet growth  is effectively static on our timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Thus, for our simulations to be  accurate, we need them to have settled into a quasi-static state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Numerical breakdown would be caused by instantaneous insertion  of a Jupiter-mass protoplanet into an unperturbed protoplanetary disc  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' To avoid this, the protoplanet’s mass is set to 𝑀pl = 0 at 𝑡 = 0  and it is linearly grown to its desired mass over the first 3 orbital  periods of the main simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For our simulations the desired mass  is 1𝑀Jup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This super-fast linear growth is not a representation of  the planet formation process but purely a tool to avert numerical  breakdown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The super-fast protoplanet implantation excites the protoplanetary  disc to a temporary unsustainable state with extremely large amounts  of matter clustering around the protoplanet and thus extremely high  accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore, even though the protoplanet is at full mass  at 𝑡 = 3 orbits, a snapshot of the simulation at 𝑡 = 3 orbits is not  conclusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is necessary to give the simulation more time to allow  it to relax into a sustainable steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' How much time, and how  we determine that, is discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The density distribution of a circumplanetary disc, in a frame  comoving with the protoplanet, in a gas-only simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The protoplanet  is at (0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝑅 and 𝑧 are measured from the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The densities and  velocities presented here have been mass-averaged across 𝜙, the azimuthal  coordinate from the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The arrows show the mass-averaged velocity  vectors, or rather their 𝑅 and 𝑧 components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The 𝜙 component of velocity,  orbiting around the protoplanet, is not shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  3 RESULTS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1 Gas dynamics  First we start with a gas-only simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It serves as a fiduciary  model to confirm that our code is working as it should, reproducing  the opening of a gap and the formation of a circumplanetary disc seen  in previous studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Kley 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Nelson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Machida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2 shows the gas surface density 50 orbits after the pro-  toplanet was introduced in the numerical domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The tidal torques  exerted by the protoplanet indeed perturb the disc gas density in the  form of trailing spiral shock waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These open up an annular gap  in the disc, although, after 50 orbits, the disc is not yet fully cleared  and some disc material on a co-rotating orbit with the protoplanet  is still present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This gas oscillates on horseshoe-shaped orbits in the  frame corotating with the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Henceforth we refer to this as  the horseshoe region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Simultaneously a CPD forms around the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1 shows  the azimuthally averaged density distribution within one Hill radius,  𝑅Hill = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='69 AU and shows a flared disc structure which is notably  denser than its surrounding material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The disc itself is rotationally  supported, while additional gas is fed to the CPD by meridional flows  (as seen in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The CPD extends to a distance  of about ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the protoplanet corresponding roughly to  the extent of protoplanet’s Roche lobe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore, throughout this  paper, we define the CPD mass as twice the mass in all cells within  a distance ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Note that the factor of 2 is  because we use symmetry boundary conditions at the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  As previously stated (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='7), after the implantation of the pro-  toplanet, the system requires some time to settle down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3 shows  the temporal evolution of the gas mass in the CPD in the gas-only  simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It shows a rapid increase in the CPD gas mass which  reaches a maximum after 3 orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Then the CPD mass reduces as  more gas is accreted by the protoplanet than is deposited on the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  After about 20-25 orbits the CPD mass loss and gain balance each  other and the CPD gas mass remains constant at about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='76𝑀⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  MNRAS 000, 1–14 (2023)  Ip / kgm-3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='7  10-6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-7  / AU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4  10-8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3  10-9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2  10-10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1  10-11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6  R/ AU  10-126  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Gas surface density in units kg m−2 for the gas-only simulation at  𝑡 = 50 orbits after the implantation of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green semicircle  denotes a distance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the protoplanet, which is marked with a  cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The mass of a CPD in a gas-only simulation, over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The CPD  is settling into a steady state after the implantation of a protoplanet to the  parent protoplanetary disc at 𝑡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This metric serves to inform us of when  the CPD has reached a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  extreme clustering of matter near the protoplanet in the early part  of these simulations is a numerical artefact due to the super-fast im-  plantation of the protoplanet between 𝑡 = 0 and 𝑡 = 3 orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Only  some time after the implantation phase (about 20-30 orbits), the CPD  reaches a quasi-steady state, and it is this state that we analyse in this  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This does not mean the system does not continue to evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Two-dimensional simulations of the late-time behaviour shows that  the gap first becomes devoid of gas and that subsequently the inner  disc (between star and protoplanet) disappears as the gas is accreted  by the star (Nelson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, computational restrictions  of high-resolution three-dimensional simulations do not allow us to  follow the CPD evolution up to such long timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 Single grain size dynamics  Now we include single-sized dust grains as well as the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 4  shows the gas’s surface density (density integrated along the 𝑧 axis)  and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 5 the density of a slice at 𝜙 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' From these it is clear that  the general effect of the dust grains on the gas structure is small, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  the width of the annular gap in the disc and the structure of the spiral  arms connecting the CPD with the disc do not change at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  main differences are seen in the structure of the horseshoe region: its  location and thickness differs compared to the gas-only simulation  and even between the single grain size simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  To interpret this we need to understand the interaction between  the gas and dust grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In a general situation when the dust density  is much smaller than the gas density, the radial motion of the dust  particles is given by (Dipierro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2012)  𝑣𝑑,𝑅 =  𝑣𝑔,𝑅St−1 + 𝑣𝑝  St + St−1  +  𝑣visc  1 + St2 − 𝜂turb  𝜌𝑑  𝜕  𝜕𝑅  � 𝜌𝑑  𝜌𝑔  �  (14)  where St = 𝜌𝑚𝑎  𝜌𝑔𝑣𝑡ℎ ΩK is the Stokes number of the dust grains, 𝑣𝑝 =  1  𝜌𝑔ΩK  𝜕𝑃  𝜕𝑅 the typical dust drift velocity due to pressure differences  and 𝑣visc =  2  𝜌𝑔ΩK ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 𝝈∼|𝜙 the radial drift due to viscous torques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  last term is the drift due to dust diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For low Stokes numbers  the dust grains closely follow the gas: the gas-grain drag dominates  and the viscous drift is small compared to the gas velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However,  when there is a large gradient in the dust-to-gas mass ratio, dust  diffusion can become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Grains with a high Stokes number,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' St > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1, decouple from the gas and the drift due to pressure  gradients plays a significant role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In our simulations only the 1 mm  grain model has high enough Stokes numbers for the dust and gas to  decouple from each other, although the decoupling transition already  starts at the smaller grain size of 100 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 6 shows the dust  surface density for each single grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The surface  density structure is nearly identical for 1 𝜇m, 10 𝜇m and 100 𝜇m,  but is significantly different for 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Especially the dust density  within the annular gap is a few orders of magnitude lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is  an effect of the pressure-gradient drift, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' at the outer edge of the  gap a pressure bump forms an effective barrier for the grains to drift  inward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As a consequence the gap becomes devoid of 1 mm dust  grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This process is referred to as dust filtering (Rice et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2006)  and observed in many simulations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Another significant difference seen for the 1 mm simulation is  that, although the gap is devoid of dust grains, the dust grains in the  corotating region are trapped because of pressure gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As gas  moves out of the annular gap, the dust-to-gas mass ratio therefore  increases significantly and dust grains actually become the dominant  mass carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 7 shows that the dust-to-gas mass ratio in the  horseshoe region is 3 orders of magnitude larger than for typical  ISM values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' When this happens the back-reaction (or drag force) of  MNRAS 000, 1–14 (2023)  3 ×103  8  6  1×103  4  2  3×102  AU  0  1×102  2  4  3×101  6  1×10l  8  5  6  7  8  9  10  11  12  13  X/ AU8  mgas,CPD/M@  6  4  2  0  0  10  20  30  40  50  Time/ orbitsSize-selective accretion of dust onto CPDs  7  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Surface density of gas in protoplanetary discs, in units kg m−2, after 𝑡 = 50 orbits since the implantation of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' From left to right, the  subplots show the single grain size simulations for 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m and 1 mm and finally the (quarter-annulus) multiple grain size simulation on  the far right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green semicircle denotes a distance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the protoplanet, which is marked with a cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  the dust grains on the gas can no longer be neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The qualitative  analysis of Dipierro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2018) shows that the back-reaction already  becomes important when 𝜌𝑑/𝜌𝑔 > 𝛼/(St − 𝛼).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, Dipierro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2018) did not include the effect of dust diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust diffusion  actually acts earlier as can be seen in the comparison of the thickness  of the horseshoe region between the gas-only and single grain size  simulations (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2 and 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' At the boundaries of the horseshoe  region the dust-to-gas mass ratio changes rapidly which gives rise  to dust diffusion drift and pushes the dust away from the horseshoe  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As the gas and dust are strongly coupled, it actually drags the  gas with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' While dust diffusion is also important for the 1 mm grains,  the gas and dust are only weakly coupled leading to a thin horseshoe  region as in the gas-only simulation, but a thick region in the dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As  we mentioned earlier, the dust-gas decoupling can already be noticed  in the 100 𝜇m model, as it shows a dust distribution in between the  smallest grain size simulations and the largest grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  So, the inclusion of dust grains does not change the gas dynamics,  especially not the formation of a CPD around the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' How-  ever, as we have seen, the dynamics of the dust depends on the Stokes  number and, thus, the size of the grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This also has consequences  for the dust content of the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As seen in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1, gas form inside  the annular gap is transported to the CPD via meridional flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As  in the 1 mm simulation, the gap is devoid of dust grains, it is likely  that the CPD has no dust in it either.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 8 shows the dust-to-gas  ratio of the CPD and, indeed, the ratio for the 1 mm simulation de-  creases to 10−6 while the smaller grain size simulations have equal  values around 10−3 (although for the 100 𝜇m model it is a factor  of 2 lower).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Note that the smaller grain size simulations also have  a lower dust-to-gas mass ratio than the default value of 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This  is because the pressure maximum at the centre of the gap traps the  dust grains to form the horseshoe region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Although not as efficient  as in the 1 mm simulation, dust in the smaller grain size simulations  is still more efficiently trapped than the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is why, as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 9  shows, the dust-to-gas ratio in the horseshoe region is slightly above  10−2, whereas it is lower elsewhere in the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That is also seen in  2D simulations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Drążkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Actually, the ratio we  obtain in the CPD is the same as in the gap, reinforcing the notion  that material in the CPD is replenished by meridional flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3 Multiple grain size dynamics  In the previous section, we studied the behaviour of each dust species  separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The results show that the dust content of the CPD depends  directly on the dust content of the annular gap and, thus, is grain  size dependent due to dust filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore, the grain size  affects the dynamics of the system as grains with a high Stokes  number (or large grain size) decouple from the gas and dust-to-gas  feedback becomes important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As there is a dust grain size distribution  within protoplanetary discs, it is therefore important to consider the  dynamics of multiple grain species simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The large, weakly  coupled grains potentially modify the dynamics of the smaller well-  coupled grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 4 and 5 show that the gas structure for the quarter-annulus  multiple grain size simulation is similar to the 1 mm single grain  size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is not surprising as Dipierro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2018) show  that, for a continuous dust distribution, the effect of dust-gas drag on  both the dust and gas is set by the parameters  𝜆𝑘 =  𝑛  ∑︁  𝑖=1  St𝑘  𝑖  1 + St2  𝑖  𝜌𝑖  𝜌𝑔  (15)  where 𝑘 ∈ {0, 1} and 𝑛 is the number of dust grain size bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For an  MRN (Mathis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1977) distribution, the value of 𝜆0 and 𝜆1 are  solely determined by the Stokes number of the largest grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is  because the largest bin (represented by the average bin grain size of  1 mm) not only has the highest Stokes number, it also contains most  of the dust mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Thus, the dynamics, and thus the structure, of the  largest grains and the gas are extremely similar to the single grain  size simulation for 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The dynamics of the smaller grains that  are strongly coupled to the gas does change in relation to their single  MNRAS 000, 1–14 (2023)  lμm single gr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' size  10μm single gr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' size  100μm single gr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' size  1mm single gr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' size  3×103  Multiple grain size  8  1×103  6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2  3 × 102  y/AU  0  1×102  2  4  3×101  6  8  1×101  6  8  ９ 101112 ５ ６  7  8 9 101112 5 6  7  8 9 101112 5 6  7  8 9 10 11 12 5 6  7  8  9 1011 12 13  X/ AU  X/ AU  X/ AU  X/ AU  X / AU8  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Vertical slice at 𝜙 = 0 of the gas density, in units kg m−3, after  𝑡 = 50 orbits since the implantation of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' From top to bottom, the  subplots show the gas-only simulation, then the single grain size simulations  with 𝑎 = 1 𝜇m, 10 𝜇m, 100 𝜇m, and 1 mm, and then the multiple grain size  simulation (all quarter-annulus).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green semicircle denotes the distance  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  grain size simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The density structure in these smaller grains  now looks like the 1 mm dust grain structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As seen in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2,  most of the difference is in the horseshoe region and not the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  This can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 8 which shows the dust-to-gas mass ratio  in the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' While the 1 𝜇m and 10 𝜇m dust grain size bins follow  roughly the expected MRN distribution, the dust mass in the 100 𝜇m  bin is a factor of 2 less than would be expected if it followed the MRN  distribution, and the 1 mm mass is 3 orders of magnitude smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 10 shows that the multiple grain size simulation has the same  filtering efficiency – CPD dust-to-gas mass ratio of a dust species,  normalised by the initial dust-to-gas ratio of that species – for the  different dust species as in the single grain size simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is thus  clear that dust filtering acts in the multiple grain size simulation as it  does in the single grain size simulations and that every dust species  behaves dynamically as if it and the gas were an isolated system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  An important consequence of the multiple grain size simulation  is that, although the CPD is populated with a wide size range of  dust grains that are well coupled to the gas, the total dust-to-gas  mass ratio of the CPD is much less than in the single size grain  simulations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' ≈ 3 × 10−4 compared to 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is because most  of the protoplanetary disc dust mass is in the 1 mm bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust filtration  stops these large dust grains from flowing into the protoplanet-carved  gap and, thus, also onto the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust surface density for the single grain size simulations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  𝑎 = 1 𝜇m (top left), 10 𝜇m (top right), 100 𝜇m (bottom left), and 1 mm  (bottom right) in kg m−2 after 𝑡 = 50 orbits since the implantation of the  protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green semicircle denotes a distance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the  protoplanet, which is marked with a cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4 Full-annulus geometry  Our quarter-annulus simulations provide an excellent comparison  between the gas-only, single-grain and multiple grain models, but the  periodic boundary conditions potentially affect the obtained results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  To assess the effects, we run one additional simulation, which is  identical in every way to the quarter-annulus multiple grain size  simulation from Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3 except that it covers the full annulus, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2𝜋 rad, without loss of resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This full-annulus multiple grain  size simulation takes longer to settle into steady state than its quarter-  annulus counterpart, because it has more mass in the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Therefore,  we run it for longer up to 𝑡 = 100 orbits, not 𝑡 = 50 as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 11 it is apparent that the simulation has reached a quasi-  steady state by then.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 12 shows that, qualitatively, this full-annulus  result does not dramatically differ from the quarter-annulus results as  compared to e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' There are some small local structures in the  horseshoe region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 7 that are absent from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 12, but these are  simply due to spiral arms interacting with the periodic 𝜙-boundary  conditions of a less-than-full annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The global picture with a gap,  an inner and outer disc, streamers and a CPD remains the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Some quantitative difference can be observed between the quarter  and full-annulus cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 13 it can be seen that the filtering  efficiency for the different dust grain sizes, but especially 1 mm, is  MNRAS 000, 1–14 (2023)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  Gas-only  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10-6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  lμm singlegrain size  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  /AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10-7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10μm single grain size  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  100μmsinglegrainsize  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  1mmsingle grainsize  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  Multiple grain size  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  7  8  9  10  11  12  13  R / AU8  6  101  4  2  AU  0  ④  ④  +100  2  4  10-1  6  8  10-2  8  6  4  10-3  2  y/AU  0  2  10-4  4  6  10-5  8  56  6  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='91011125  6  7  8 910111213  X/ AU  X / AUSize-selective accretion of dust onto CPDs  9  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust-to-gas ratio in the midplane after 𝑡 = 50 orbits since the  implantation of the protoplanet, for the single grain size simulation of grain  size 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green semicircle denotes a distance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5𝑅Hill from the  protoplanet, which is marked with a cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust-to-gas mass ratio of the circumplanetary disc at 𝑡 = 50 orbits  for single grain size (blue dash-dotted) and multiple grain size simulation  with quarter-annulus (red dashed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The green solid line is a power-law Mathis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (1977) distribution normalised with the value at 1 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Azimuthally and vertically averaged dust-to-gas mass ratio after  𝑡 = 50 orbits for the different single grain size simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust-to-gas mass ratio in the CPD normalised to the initial dust-  to-gas mass ratio for that grain species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The blue, solid line shows the single  size grain simulations while the red, dashed line shows the quarter-annulus  multiple grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  much reduced (by a factor of 37, for 1 mm) in the quarter-annulus  case compared to the full-annulus case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is because the proto-  planet’s gravitational torque is responsible for carving out the gap,  by transferring orbital angular momentum from matter interior to its  orbit to matter exterior of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In effect, the quarter-annulus geometry  exaggerates the time-integrated gravitational torque and the result-  ing planetary gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Then, as more dust grains remain in the gap in  the full-annulus case, more can be captured by the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This ef-  fect of quarter-annulus geometry is stronger for larger grain sizes, a  key weakness of simulations which depict less than the full annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  However, note that size dependence of the filtering efficiency remains  the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Also, the dust-to-gas mass ratio of the circumplanetary disc in the  multiple grain size simulations – considering dust of all grain sizes  – is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='9 × 10−4 for the quarter-annulus while 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='6 × 10−4 for the full  annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The diminution in the quarter-annulus case is likely due to  the enhanced strength of gravitational torque discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The  torque particularly strongly affects 1 mm dust, which is the domi-  nant dust-mass-carrier species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' To visualise this effect whereby the  quarter-annulus’s enhanced torque exaggerates the gap compared to  MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1–14 (2023)  10-1  10  10-3  Single grainsize simulations  10-4  Multiplegrain sizesimulation  1μm  10μm  100μm  1mm  Dustgrain size101  8  6  10-1  4  10-3  2  AU  0  +  10-5  2  10-7  4  6  10-9  8  5  6  7  8  9  10  11  12  13  X/ AU10-3  10-  10-5  Initialdistributiontrendline  Singlegrainsizesimulations  10-6  Multiple grain size simulation  口  1μm  10μm  100μm  1mm  Dust grain size1 um  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1  10um  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1mm  1mm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='01  10-3  10-4  10-5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  9  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  11  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  radius [AU]10  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Circumplanetary disc masses and filtering efficiencies over time  in the quarter-annulus and full-annulus multifluid simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Filtering effi-  ciency is as defined in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3: a dimensionless ratio for each dust species,  proportional to that dust species’s CPD mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust-to-gas ratio of the 1 mm dust species in the midplane after  𝑡 = 100 orbits since the implantation of the protoplanet, for the full-annulus  multiple grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  a full annulus, especially for large dust grains, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Similarly,  the ratio of the CPD dust mass to the protoplanet’s mass is 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0×10−7  for the quarter-annulus while 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5×10−6 for the full annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Not only  is the dust-to-gas ratio higher in the full annulus, but also the CPD  gas mass (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 13) because quarter-annulus geometry reduces the  pool of available mass to accrete onto the CPD, which leads to this  increase of a factor of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Thus, while there are some quantitative difference between the  quarter-and full annulus simulations, these differences are moderate  and the overall behaviour and results remain the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dust-to-gas mass ratio in the CPD normalised to the initial dust-  to-gas mass ratio for that grain species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The blue, solid line is for the quarter-  annulus multiple grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The red, dashed line is for the full-  annulus multiple grain size simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Azimuthally and vertically averaged dust-to-gas mass ratio for the  multiple grain size simulations, in steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' That is at 𝑡 = 50 orbits for the  quarter-annulus and 𝑡 = 100 for the full annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  4 DISCUSSION  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1 Benchmarking  Our simulations show a qualitatively similar picture as in the litera-  ture (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Klahr & Kley 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Machida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Tanigawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' the protoplanet carves a gap in the  protoplanetary disc and, at the same time, a CPD forms around the  protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The CPD structure itself shows a rotationally supported  density structure filling the protoplanet’s Roche lobe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore,  the protoplanet accretes mass from the CPD while, at the same time,  CPD material is replenished by meridional flows (Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Previous studies do not, however, model the CPD with gas  and multiple dust grain sizes each having their own dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Dust grains also exhibit the expected behaviour: as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 15,  larger dust grains have a smaller vertical scale height (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Naka-  gawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1986;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Garaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dullemond & Dominik 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Fromang & Papaloizou 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Small grains are strongly coupled to  the gas by dust-gas drag and thus experience turbulent stirring, while  large grains are weakly coupled and thus settle towards the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Recently, observations have corroborated this picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Observations  of HL Tau show that ∼ mm dust have a scale height of 𝐻 ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='01𝑅  which is much flatter than for the gas disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In contrast, Rich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (2021) find that,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' in the discs of IM Lup,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' HD 163296 and HD 97048,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1–14 (2023)  100  10  Gas  10  lμm dust  10μm dust  10-6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  100μmdust  0  20  40  60  80  100  1mm dust  Time/orbits  Full annulus  100  Ouarter-annulus  10  2  10  0  20  40  60  80  100  Time/orbits100  10  10-1  5  10-2  y/AU  10-3  0  10-4  5  10-5  10  10-6  10  5  0  5  10  X /AU10-1  10-2  10-3  Quarter-annulus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='multifluid  10-4  Full annulus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' multifluid  1μm  10μm  100μm  1mm  Dustgrain sizespecies:  10-2  lμm dust  10umdust  dust  10  100μm dust  1mm dust  ratio  10-4  Quarter-annulus  Full annulus  10-5  10  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  Radius / AUSize-selective accretion of dust onto CPDs  11  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Vertical slice at 𝜙 = 0 of the dust density, in units kg m−3, of  a protoplanetary disc with no protoplanet yet inserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Each subplot comes  from a different single grain size simulation, with dust grain size 𝑎 = 1 𝜇m,  10 𝜇m, 100 𝜇m and 1 mm from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  small-grain-size (∼ 𝜇m) dust at radii < 100 AU has similar vertical  distribution to the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Furthermore, we also observe the effect of dust filtration, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' large  grains are prevented from penetrating the annular gap, while small  grains can flow in easily with the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This was already seen in 2D  simulations (Rice et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Weber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Haugbølle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2019) which study the effect of dust clearing of the  inner protoplanetary disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' They, however, do not consider the effect  on the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 CPD grain size distribution  Our results show that the grain size distribution function of the CPD  follows the MRN distribution (Mathis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1977) at small grain  sizes, but falls significantly below that distribution by grain size  𝑎 = 100 𝜇m and is truncated to near zero by 𝑎 = 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Secondly,  the total dust-to-gas ratio is significantly lower than the typical ISM  value, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 8 × 10−4 compared to 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is because of the lower  dust content – particularly of larger dust – in the annular gap carved  by the protoplanet due to dust filtration (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These  results are similar to the findings of Bae et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) who used test  particles for the dust grain dynamics in a 2D disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  One caveat of this result is that the distribution function is only  described by a limited number of size bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is necessary to increase  the number of bins to examine the grain size distribution near the  truncation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is likely that there is no sharp transition, but a smooth  turnover between 100 𝜇m and 1 mm as grains start to decouple from  the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Another caveat is that, while we find that the dust distribution  function follows an MRN power-law distribution at small grain sizes  and tails off below MRN at 𝑎 = 100 𝜇m to 1 mm, this is only valid  in absence of any grain processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Local variations are expected as  the grain size distribution is set by balancing dust production, growth  and destruction processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In protoplanetary discs, there is no dust  production, but both growth and fragmentation of dust grains take  place (Brauer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Birnstiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2010, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Dullemond  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Homma & Nakamoto 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Tamfal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' These  restrictions are important when analysing observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Understanding the grain size distribution function is also key to  understanding observations as the distribution determines the opac-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' When considering single-sized grains, Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) find  that the CPD of PDS 70 c has a dust mass 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='007𝑀⊕ if the grain  size is 1 mm or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='031𝑀⊕ if 𝑎 = 1 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Using an MRN distribution  adjusted with the calculated filtering efficiencies (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 10) via  logarithmic linear interpolation to approximate the CPD’s grain size  distribution, we find that the CPD’s opacity at wavelength 855 𝜇m  – and thus the CPD dust mass – is close to that for single-sized  grains of 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, as said before, with the coarse bin sizes  there is some uncertainty on the turnover grain radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore,  Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2012) show that the critical grain radius for filtration  depends on Stcrit which is proportional to 𝛼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It follows that 𝑎crit de-  pends on the local temperature, viscosity and gas density of the disc:  𝑎crit ∝ 𝜈turb𝜌𝑔/�𝑐𝑠,𝑖𝑠𝑜𝜌𝑚  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We know that PDS 70 c lies further  out in the protoplanetary disc at 34 AU and the local temperature is  about 26 K (Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2021), compared to 10 AU and 45 K in our  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We need to assume some radial dependency for 𝜈turb  and 𝜌𝑔.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Let us assume that 𝛼 is constant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' then 𝜈turb ∝ 𝑐2  𝑠,𝑖𝑠𝑜𝑅3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  If we adopt 𝜌𝑔 ∝ 𝑅−1, the critical grain size is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='4 times that of our  simulations, whereas if 𝜌𝑔 ∝ 𝑅−3/2, 𝑎crit is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='76 times ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Either  way, such a small variation in 𝑎crit makes little difference to the CPD  dust mass deduced, as per Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 9 of Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Via the method stated above, we can also calculate an opacity for  our grain size distribution at 𝜆 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='8 𝜇m, the wavelength correspond-  ing to the protoplanet’s surface temperature 𝑇 = 1600 K by Wien’s  displacement law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1 times the opacity of the MRN distribu-  tion at the same wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This can be understood by thinking of  opacity as an absorption area-to-mass ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Our simulations include  dust filtration to deplete the mass of large ∼ 1 mm grains, which  have a lot of mass but little absorption area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Thus a CPD would be  > 3 times better at absorbing radiation emitted by its protoplanet  than an MRN-distributed CPD and thus hotter, if it has the grain size  distribution we obtain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The reason why our results differ from those of Szulágyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (2022), who find that the CPD is enriched in dust compared to its  parent PPD, is that they model the unperturbed PPD’s dust as verti-  cally flat, while our dust PPD is not flat because we do not neglect  turbulent diffusion as they do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' They find that large dust grains can  accrete efficiently onto the protoplanet because the protoplanet ver-  tically stirs up their flat disc of dust, pushing dust to high altitude  where it can flow to feed the protoplanet, when flows at the mid-  plane cannot do so because large dust grains are blocked as per dust  filtration (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Haugbølle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We find, contrarily, that the  protoplanet pulls down the dust towards the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' An alternative  reason is that their 𝑎crit is larger than ours, so large dust grains are  still small enough not to be blocked off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, their 𝑎crit is only  larger than ours for their 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 AU case, not their 30 AU and 50 AU  cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2023)  IPiμm dust / kg m-3]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  10-9  Z/ AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  7  8  9  10  11  12  13  10-10  R / AU  IP1oμm dust / kg m-3]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  AU  10-11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  7  8  9  10  11  12  13  10-12  R/AU  IP100μm dust / kg m-3]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10-13  //z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  7  8  9  10  11  12  13  R / AU  10-14  IP1mm dust / kg m-3]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  AU  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  10-15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='0  7  8  9  10  11  12  13  R/AU  10-1612  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='3 Dust mass and satellite formation  With the Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='007𝑀⊕ estimate of the CPD dust  mass for PDS 70 c, the ratio of the CPD dust mass to protoplanet  mass is about 10−5 where we assume the protoplanet mass to be  2𝑀Jup (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In our simulation – meaning the full-  annulus multiple grain size simulation, the most physically realistic  one – the ratio is even lower than that: 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='5×10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This discrepancy is  simply the result of differing temperature assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For the same  observed flux, the higher the assumed temperature, the lower the  deduced mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) assume a CPD temperature of  26 K, whereas the mass-averaged temperature of the CPD in our full-  annulus multiple grain size simulation is 105 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is likelier to be  an underestimate of the temperature than an overestimate, because  we may include the protoplanet’s luminosity but we neglect shock  heating from the matter falling vertically at up to 15 km s−1 towards  the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Furthermore, Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) observe a similar flux for  PDS 70 c’s CPD to Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021) and they estimate its dust  mass at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='004𝑀⊕ if 𝑇 ∼ 20 K and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='002𝑀⊕ if 𝑇 ∼ 80 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' With  a temperature in the latter case more similar to ours, they obtain  a CPD dust to protoplanet mass ratio of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2 × 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This brings  our simulated value of the mass ratio and the value inferred from  observed flux within decent agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  If our numerical model is overestimating the accretion rate from  the CPD onto the protoplanet, the true mass of the CPD may be  greater than we calculate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Our simulation result should be understood  as providing a lower limit for CPD dust mass, rather than exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  This observational comparison provides support that it is at least  reasonable on an order-of-magnitude basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The major satellites of Jupiter, combined, have a mass ∼ 2 × 10−4  times the mass of their host planet, and the same ratio holds true  for Saturn (Canup & Ward 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, the CPD dust mass  is determined by the balance of removal through accretion of the  protoplanet and replenishment from the protoplanetary disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is  different than for a protoplanetary disc as the CPD is embedded in a  gas and dust reservoir, while the protoplanetary disc is not and can  become depleted of dust (Canup & Ward 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Because of this, it is  not actually necessary for the instantaneous dust mass of the CPD at  any one moment to be high, for satellites to be formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is known  in the literature as the ‘starved disc’ model as discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Also, planetesimal capture can provide satellitesimal seeds for this  dust to accrete onto (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Ronnet & Johansen 2020) and Drążkowska  & Szulágyi (2018) show that dust traps are an efficient way to form  satellites within the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This would limit the accretion of dust onto  the protoplanet and make more dust available to accumulate and form  satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, our simulations do not have enough resolution to  follow the detailed evolution of the CPD and its satellite formation  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It thus is beyond the scope of this paper to follow the detailed  evolution of the CPD involving the formation of satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Furthermore, both the CPD dust to protoplanet mass ratio and the  CPD dust-to-gas mass ratio can be expected to be higher at earlier  times in planet formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' For these simulations, recall that the mass  of the parent protoplanetary disc was set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='05𝑀⊙ around a 1𝑀⊙  star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' If gas density is higher, there is a larger 𝑎crit (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Most  of the dust mass is in larger grains, so when the critical grain size is  larger, much more of the dust mass is able to enter the CPD in spite  of dust filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' And of course, for a protoplanet which has not (or  not yet) grown massive enough to carve out a gap in the PPD, the  CPD dust-to-gas mass ratio can be very much higher than we find  here, as the gap’s dust filtration effect is absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  5 CONCLUSIONS  We run 3D hydrodynamical simulations of a segment of protoplan-  etary disc with an embedded Jupiter-mass protoplanet orbiting a  Solar-mass star at orbital radius 10 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We follow the dynamics of  the gas and 4 different dust grain sizes (1 𝜇m, 10 𝜇m, 100 𝜇m and  1 mm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We include the effects of turbulent viscosity and dust-gas  drag, using either the Epstein or the Stokes drag law depending on  the ratio of the dust grain size to the gas’s mean free path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' We in-  clude the back-reaction due to the drag force of the dust on the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  The different dust grain sizes are not coupled directly by a force, but  via their back-reaction on the gas, they can indirectly influence each  other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is the first time multiple dust grain sizes with separate  dynamics have been simulated in a CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  We obtain the following conclusions:  (i) The dynamics of the grains in the multiple grain size simu-  lation is similar to the dynamics observed in the single grain size  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As the large grains modify the gas dynamics due to the  back-reaction of dust-gas drag, they also modify the dynamics of the  small grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' However, these changes are not significant and do not  affect the CPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (ii) At small grain sizes < 100 𝜇m, the grain size distribution  of the dust in the CPD shows an MRN distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' It tails off sig-  nificantly below MRN at 𝑎 = 100 𝜇m and falls to almost zero by  𝑎 = 1 mm, due to dust filtration limiting the flow of large dust  grains into the annular gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The critical grain radius for dust filtra-  tion depends on the local properties of the disc, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' the disc density,  temperature and viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (iii) The CPD is depleted in dust-to-gas ratio compared to the  parent protoplanetary disc by an order of magnitude, but is similar  to the value within the annular gap carved by the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (iv) Because the truncation and the low dust-to-gas ratio in the  CPD, the CPD dust mass is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The ratio of the CPD dust mass to  the protoplanetary mass is ∼ a few ×10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' While this is considerably  lower than the value of 2 × 10−4 of Jupiter’s mass that constitutes  the total mass of its moons, the dust within the CPD is continuously  replenished by dust flow from the protoplanetary disc, thus making  satellite formation possible as per the ‘starved disc’ model in the  literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  (v) The opacity, mass-averaged temperature, and CPD dust to pro-  toplanet mass ratio derived from our multiple grain size simulation  yield consistency with the fluxes observed from the CPD of PDS 70  c by Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2019) and Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Our simulations consider only a singular environment while changing  the dust distribution between simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' To further understand how  environmental conditions change the grain size distribution, we need  to change these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' In a subsequent study we will consider  different planetary masses and position within the protoplanetary  disc and also consider finer size binning in order to refine the critical  grain size affected by dust filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' acknowledges funding from the Royal Society through the  Fellowship Enhancement Award (grant holder O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The research of  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' was supported by the Royal Society Dorothy Hodgkin Fellow-  ship during the preparation of this publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' is supported by  a STFC consolidated grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' would like to thank Dr James Mi-  ley for the protoplanetary disc models that underlie these simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  This work was undertaken on ARC4, part of the High Performance  Computing facilities at the University of Leeds, UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2023)  Size-selective accretion of dust onto CPDs  13  DATA AVAILABILITY  The data underlying this article will be shared on reasonable request  to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  REFERENCES  Ayliffe B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2009a, MNRAS, 393, 49  Ayliffe B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2009b, MNRAS, 397, 657  Bae J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, ApJ, 884, L41  Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lubow S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ogilvie G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Miller K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2003, MNRAS, 341,  213  Benisty M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2021, ApJ, 916, L2  Benítez-Llambay P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Krapp L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pessah M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, ApJS, 241, 25  Binkert F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Birnstiel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2021, MNRAS, 506, 5969  Birnstiel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Brauer F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2010, A&A, 513, A79  Birnstiel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 869, L45  Blanc M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2020, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 193, 104960  Brauer F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2008, A&A, 480, 859  Canup R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ward W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2002, AJ, 124, 3404  Canup R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ward W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2009, in Pappalardo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', McKinnon W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=',  Khurana K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', eds, , Europa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' University of Arizona Press, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 59  Christiaens V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Cantalloube F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Casassus S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Price D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Absil O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pinte C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=',  Girard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Montesinos M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, ApJ, 877, L33  Dipierro G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Laibe G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Alexander R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hutchison M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, MNRAS, 479,  4187  Drążkowska J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 866, 142  Drążkowska J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Birnstiel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Stammler S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Li H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, ApJ, 885, 91  Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dominik C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2005, A&A, 434, 971  Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 869, L46  Falle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1991, MNRAS, 250, 581  Fromang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Papaloizou J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2006, A&A, 452, 751  Garaud P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Barrière-Fouchet L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lin D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2004, ApJ, 603, 292  Goldreich P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ward W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1973, ApJ, 183, 1051  Greenberg R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2011, Astrobiology, 11, 183  Haugbølle T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Weber P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Wielandt D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Benítez-Llambay P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bizzarro M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=',  Gressel O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pessah M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, AJ, 158, 55  Helled R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2014, in Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Klessen R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=',  Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', eds, Protostars and Planets VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 643 (arXiv:1311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='1142),  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2458/azu_uapress_9780816531240-ch028  Homma K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Nakamoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 868, 118  Isella A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Benisty M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Teague R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bae J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Keppler M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Facchini S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pérez L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=',  2019, ApJ, 879, L25  Klahr H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kley W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2006, A&A, 445, 747  Kley W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1999, MNRAS, 303, 696  Knapp G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kerr F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1974, A&A, 35, 361  Korycansky D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bodenheimer P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pollack J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1991, Icarus, 92, 234  Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', McKee C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Klein R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2004, ApJ, 611, 399  Lin D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Papaloizou J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1993, in Levy E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lunine J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', eds,  Protostars and Planets III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 749  Long Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 858, 112  Lunine J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Stevenson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1982, Icarus, 52, 14  Machida M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kokubo E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Inutsuka S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Matsumoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2008, ApJ, 685,  1220  Mathis J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Rumpl W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Nordsieck K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1977, ApJ, 217, 425  Miley J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Panić O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Booth R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ilee J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ida S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kunitomo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2021,  MNRAS, 500, 4658  Min M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dominik C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', de Koter A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hovenier J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2009,  A&A, 497, 155  Morfill G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Voelk H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1984, ApJ, 287, 371  Mosqueira I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Estrada P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2003, Icarus, 163, 198  Nakagawa Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Sekiya M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hayashi C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1986, Icarus, 67, 375  Nelson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Papaloizou J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Masset F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kley W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2000, MNRAS, 318,  18  Nelson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Gressel O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Umurhan O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2013, MNRAS, 435, 2610  Neveu M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2020, Frontiers in Astronomy and Space Sciences, 7, 26  Paardekooper S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Mellema G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2006, A&A, 453, 1129  Parkinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Liang M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Yung Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Kirschivnk J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2008, Origins of  Life and Evolution of the Biosphere, 38, 355  Pinte C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dent W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ménard F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hales A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hill T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Cortes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', de Gregorio-  Monsalvo I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2016, ApJ, 816, 25  Rice W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Armitage P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Wood K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lodato G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2006, MNRAS, 373,  1619  Rich E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2021, ApJ, 913, 138  Rivier G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Crida A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Morbidelli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Brouet Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2012, A&A, 548, A116  Ronnet T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Johansen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2020, A&A, 633, A93  Shakura N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Sunyaev R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 1973, A&A, 500, 33  Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2017, ApJ, 842, 103  Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Mordasini C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2017, MNRAS, 465, L64  Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Morbidelli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Crida A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Masset F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2014, ApJ, 782, 65  Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Masset F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lega E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Crida A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Morbidelli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Guillot T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2016,  MNRAS, 460, 2853  Szulágyi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Binkert F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Surville C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2022, ApJ, 924, 1  Tamfal T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Drążkowska J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Mayer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Surville C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018, ApJ, 863, 97  Tanigawa T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Ohtsuki K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Machida M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2012, ApJ, 747, 47  Teague R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bae J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bergin E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2019, Nature, 574, 378  Trapman L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Rosotti G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Bosman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hogerheijde M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', van Dishoeck  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2020, A&A, 640, A5  Van Loo S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Falle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hartquist T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2006, MNRAS, 370, 975  Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2020, AJ, 159, 263  Ward W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Canup R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2010, AJ, 140, 1168  Weber P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Benítez-Llambay P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Gressel O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Krapp L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Pessah M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2018,  ApJ, 854, 153  Williams J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Cieza L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2011, Annual Review of Astronomy and Astro-  physics, 49, 67  Youdin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Lithwick Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2007, Icarus, 192, 588  Zhu Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Nelson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Dong R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Espaillat C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', Hartmann L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=', 2012, ApJ, 755, 6  APPENDIX A: ACCRETION ALGORITHM  We wrote a Gaussian accretion algorithm, designed to prevent  sharp, discontinuous, un-physical transitions for a protoplanet mov-  ing across a grid of cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The method bears some resemblance to,  but is not identical to, that of Krumholz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The amount of  matter accreted from a cell containing density 𝜌 in each timestep Δ𝑡  is given by:  Δ𝑚 = 𝑓 𝜌𝑉cell ×  �  1 − exp  � −Δ𝑡  𝑡acc  ��  exp  �  −  ��r − rpl  ��2  𝑟2  𝐺  �  (A1)  where 𝑓 is an order-unity constant and 𝑟𝐺 is the ‘Gaussian radius’ of  the protoplanet, which is chosen to be 𝑟𝐺 = 3𝑅eff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Here 𝑅eff is the  effective radius that was defined in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' As Δ𝑡 ≪ 𝑡acc in practice,  the amount of mass accreted from a cell in time Δ𝑡 is proportional  to Δ𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This is deliberate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' a conclusion for the accretion rate should  not depend on the user’s arbitrary numerical timestep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The accretion  timescale works like a freefall timescale: 𝑡2acc = 𝜋2𝑅3  𝑓 𝑓 /�8𝐺𝑀pl  �,  where 𝑅 𝑓 𝑓 = max ���r − rpl  �� , 𝑅eff  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The truncation of distance from  the protoplanet at minimum value 𝑅eff is to avoid a singularity at the  position of the protoplanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  This accretion is applied separately to the gas and to every species  of dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Whenever the protoplanet accretes matter from a cell, it  records – separately – how much gas and how much dust it has  accreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' This enables the simulations to track how efficiently the  protoplanet accretes dust, by comparison to its accretion of gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Following Krumholz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' (2004), it is not advisable to let the sink  particle violate the conservation of angular momentum around it  when it accretes matter onto itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Accordingly, whenever accretion  is carried out for a fluid in the cell, the velocity of that fluid in that  cell is decomposed into a component comoving with the protoplanet  and the remainder ‘peculiar’ velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' The peculiar velocity vector is  MNRAS 000, 1–14 (2023)  14  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' Karlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  further decomposed using a cell-specific spherical coordinate system  centred on the protoplanet, with unit-vectors �ˆe𝑟,pl, ˆe𝜙,pl, ˆe𝜃,pl  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  Hence v = vpl + Σ𝑖𝑣rel,𝑖 where we define 𝑣rel,𝑖 = ˆe𝑖,pl .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' �v − vpl  �  where 𝑖 ∈ {𝑟, 𝜃, 𝜙}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' When some mass is removed from the cell onto  the sink particle, the component of momentum comoving with the  protoplanet 𝑚vpl and the peculiar component 𝑚𝑣rel,𝑟 are accreted,  whereas the peculiar components 𝑚𝑣rel,𝜃 and 𝑚𝑣rel,𝜙 are conserved  during accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content=' If mass of a fluid Δ𝑚 is accreted from a cell,  the momentum of that same fluid accreted from the same cell is  Δp = �vpl + 𝑣rel,𝑟ˆe𝑟,pl  � × Δ𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2023)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfkQ_G/content/2301.05662v1.pdf'}
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+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+SKILL DECISION TRANSFORMER
+Shyam Sudhakaran & Sebastian Risi
+IT University of Copenhagen
+Copenhagen, Denmark
+{shsu,sebr}@itu.dk
+ABSTRACT
+Recent work has shown that Large Language Models (LLMs) can be incredibly
+effective for offline reinforcement learning (RL) by representing the traditional
+RL problem as a sequence modelling problem (Chen et al., 2021; Janner et al.,
+2021). However many of these methods only optimize for high returns, and may
+not extract much information from a diverse dataset of trajectories. Generalized
+Decision Transformers (GDTs) (Furuta et al., 2021) have shown that utilizing fu-
+ture trajectory information, in the form of information statistics, can help extract
+more information from offline trajectory data. Building upon this, we propose
+Skill Decision Transformer (Skill DT). Skill DT draws inspiration from hindsight
+relabelling (Andrychowicz et al., 2017) and skill discovery methods to discover
+a diverse set of primitive behaviors, or skills. We show that Skill DT can not
+only perform offline state-marginal matching (SMM), but can discovery descrip-
+tive behaviors that can be easily sampled. Furthermore, we show that through
+purely reward-free optimization, Skill DT is still competitive with supervised of-
+fline RL approaches on the D4RL benchmark. The code and videos can be found
+on our project page: https://github.com/shyamsn97/skill-dt .
+1
+INTRODUCTION
+Reinforcement Learning (RL) has been incredibly effective in a variety of online scenarios such
+as games and continuous control environments (Li, 2017). However, they generally suffer from
+sample inefficiency, where millions of interactions with an environment are required. In addition,
+efficient exploration is needed to avoid local minimas (Pathak et al., 2017; Campos et al., 2020).
+Because of these limitations, there is interest in methods that can learn diverse and useful primitives
+without supervision, enabling better exploration and re-usability of learned skills (Eysenbach et al.,
+2018; Strouse et al., 2021; Campos et al., 2020). However, these online skill discovery methods still
+require interactions with an environment, where access may be limited.
+This requirement has sparked interest in Offline RL, where a dataset of trajectories is provided.
+Some of these datasets (Fu et al., 2020) are composed of large and diverse trajectories of varying
+performance, making it non trivial to actually make proper use of these datasets; simply applying
+behavioral cloning (BC) leads to sub-optimal performance. Recently, approaches such as the Deci-
+sion Transformer (DT) (Chen et al., 2021) and the Trajectory Transformer (TT) (Janner et al., 2021),
+utilize Transformer architectures (Vaswani et al., 2017) to achieve high performance on Offline RL
+benchmarks. Furuta et al. (2021) showed that these methods are effectively doing hindsight infor-
+mation matching (HIM), where the policies are trained to estimate a trajectory that matches given
+target statistics of future information. The work also generalizes DT as an information-statistic con-
+ditioned policy, Generalized Decision Transformer (GDT). This results in policies with different
+capabilities, such as supervised learning and State Marginal Matching (SMM) (Lee et al., 2019),
+just by simply varying different information statistics.
+In the work presented here, we take inspiration from the previously mentioned skill discovery meth-
+ods and introduce Skill Decision Transformers (Skill DT), a special case of GDT, where we wish
+to condition action predictions on skill embeddings and also future skill distributions. We show
+that Skill DT is not only able to discovery a number of discrete behaviors, but it is also able to ef-
+fectively match target trajectory distributions. Furthermore, we empirically show that through pure
+unsupervised skill discovery, Skill DT is actually able to discover high performing behaviors that
+1
+arXiv:2301.13573v1  [cs.LG]  31 Jan 2023
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+Figure 1: Skill Decision Transformer. States are encoded and clustered via VQ-VAE codebook
+embeddings. A Causal Transformer, similar to the original DT architecture, takes in a sequence
+of states, a latent skill distribution, represented as the normalized summed future counts of VQ-
+VAE encoding indices (details can be found in the ”generate histogram” function in A.5), and the
+corresponding skill encoding of the state at timestep t. The skill histogram captures ”future” skill
+behavior, while the skill embedding represents current skill behavior as timestep t.
+match or achieve higher performance on D4RL benchmarks (Fu et al., 2020) compared to other
+state-of-the-art offline RL approaches.
+Our method is completely unsupervised and predicts actions, conditioned by previous states, skills,
+and distributions of future skills. Empirically, we show that Skill DT can not only perform SMM
+on target trajectories, but can also match or achieve higher performance on D4RL benchmarks (Fu
+et al., 2020) compared to other state-of-the-art offline RL approaches.
+2
+RELATED WORK
+2.1
+SKILL DISCOVERY
+Many skill methods attempt to learn a latent skill conditioned policy π(a|s, z), where state s ∼
+p(s) and skill z ∼ Z, that maximizes mutual information between S and Z (Gregor et al., 2016;
+Sharma et al., 2019; Eysenbach et al., 2018). Another way of learning meaningful skills is through
+variational inference, where z is learned via a reconstruction loss (Campos et al., 2020). Explore,
+Discover and Learn (EDL) (Campos et al., 2020) is an approach, which discovers a discrete set of
+skills by encoding states via a VQ-VAE: p(z|s), and reconstructing them: p(s|z). We use a similar
+approach, but instead of reconstructing states, we utilize offline trajectories and optimize action
+reconstruction directly (p(a|s, z)). Since our policy is autoregressive, our skill encoding actually
+takes into account temporal information, leading to more descriptive skill embeddings. Offline
+Primitive Discovery for Accelerating Offline Reinforcement Learning (OPAL) (Ajay et al., 2020),
+also discovers offline skills temporally, but instead uses a continuous distribution of skills. These
+continuous skills are then sample by a hierarchical policy that is optimized by task rewards. Because
+our approach is completely unsupervised, we wish to easily sample skills. To simplify this, we opt to
+use a discrete distribution of skills. This makes it trivial to query the highest performing behaviors,
+accomplished by just iterating through the discrete skills.
+2.2
+STATE MARGINAL MATCHING
+State marginal matching (SMM) (Lee et al., 2019) involves finding policies that minimize the dis-
+tance between the marginal state distribution that the policy represents pπ(s), and a target distribu-
+tion p∗(s). These objectives have an advantage over traditional RL objectives in that they do not
+require any rewards and are guided towards exploration (Campos et al., 2020). CDT has shown
+impressive SMM capabilities by utilizing binned target state distributions to condition actions in
+order to match the given target state distributions. However, using CDT in a real environment is
+2
+
+VQVAE Codebook
+02122
+min
+Causal Transformer
+Encoder
+K
+one_hot(zt)
+t<TFoundation Models for Decision Making Workshop at NeurIPS, 2022
+difficult because target distributions must be provided, while Skill DT learns discrete skills that can
+be sampled easily. Also, CDT requires a low dimensional state space, while Skill DT can – in theory
+– work on any type of input as long as it can be encoded effectively into a vector.
+3
+PRELIMINARIES
+In this work, we consider learning in environments modelled as Markov decision processes (MDPs),
+which can be described using varibles (S, A, P, R), where S represents the state space, A represents
+the action space, and P(st+1|st, at) represents state transition dynamics of the environment.
+3.1
+GENERALIZED DECISION TRANSFORMER
+The Decision Transformer (DT) (Chen et al., 2021) represents RL as a sequence modelling problem
+and uses a GPT architecture (Radford et al., 2018) to predict actions autoregressively. Specifi-
+cally, DT takes in a sequence of RTGs, states, and actions, where Rt = �T
+t rt, and trajectory
+τ = (R0, s0, a0, ..., R|τ|, s|τ|, a|τ|). DT uses K previous tokens to predict at with a deterministic
+policy which is optimized by a mean squared error loss between target and predicted actions. For
+evaluation, a target return ˆRtarget is provided and DT attempts to achieve the targeted return in the
+actual environment. Furuta et al. (2021) introduced a generalized version of DT, Generalized De-
+cision Transformer (GDT). GDT provides a simple interface for representing a variety of different
+objectives, configurable by different information statistics (for consistency, we represent variations
+of GDT with πgdt):
+τt = st, at, rt, ..., sT , aT , rT , Iφ = information statistics function
+Generalized Decision Transformer (GDT):
+πgdt(at|Iφ(τ0), s0, a0..., Iφ(τt), st−1, at−1)
+Decision Transformer (DT):
+πgdt
+dt (at|Iφ
+dt(τ0), s0, a0, ..., Iφ
+dt(τt), st−1, at−1), where Iφ
+dt(τt) = �T
+t γ ∗ rt, γ = discount factor
+Categorical Decision Transformer (CDT):
+πgdt
+cdt(at|Iφ
+cdt(τ0), s0, a0, ..., Iφ
+cdt(τt), st, at), where Iφ
+cdt(τt) = histogram(st, ..., sT )
+CDT is the most similar to Skill DT – CDT captures future trajectory information using future state
+distributions, represented as histograms for each state dimension, essentially binning and counting
+the bin ids for each state dimension. Skill DT instead utilizes learned skill embeddings to generate
+future skill distributions, represented as histograms of full embeddings. In addition, Skill DT also
+makes use of the representation learnt by the skill embedding by also using it in tandem with the
+skill distributions.
+4
+SKILL DECISION TRANSFORMER
+4.1
+FORMULATION
+Our Skill DT architecture is very similar to the original Decision Transformer presented in Chen
+et al. (2021). While the classic DT uses summed future returns to condition trajectories, we instead
+make use of learned skill embeddings and future skill distributions, represented as a histogram of
+skill embedding indices, similar to the way Categorical Decision Transformer (CDT) (Furuta et al.,
+2021) utilizes future state counts. One notable difference Skill DT has to the original Decision
+Transformer (Chen et al., 2021) and the GDT (Furuta et al., 2021) variant is that we omit actions in
+predictions. This is because we are interested in SMM through skills, where we want to extract as
+much information from states.
+3
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+Formally, Skill DT represents a policy:
+π(at|Zt−K, zt−K, st−K, ...Zt−1, zt−1, st−1),
+where K is the context length, and θ are the learnable parameters of the model. States are encoded
+as skill embeddings ˆzt, which are then quantized using a learned codebook of embeddings z =
+argminn||ˆz − zn||2
+2. The future skill distributions are represented as the normalized histogram of
+summed future one hot encoded skill indices: Zt = �T
+t one hot(zt). Connecting this to GDT, our
+policy can be viewed as:
+πgdt
+skill(at|Iφ
+skill(τ0), s0, ..., Iφ
+skill(τt), st), where Iφ
+skill(τt) = (histogram(zt, ..., zT ), zt).
+4.1.1
+HINDSIGHT SKILL RE-LABELLING
+Hindsight experience replay (HER) is a method that has been effective in improving sample-
+efficiency of goal-oriented agents (Andrychowicz et al., 2017; Rauber et al., 2017). The core concept
+revolves around goal relabelling, where trajectory goals are replaced by achieved goals vs. inteded
+goals. This concept of re-labelling information has been utilized in a number of works (Ghosh
+et al., 2019; Zheng et al., 2022; Faccio et al., 2022), to iteratively learn an condition predictions on
+target statistics. Bi-Directional Decision Transformer (BDT) (Furuta et al., 2021), utilizes an anti-
+causal transformer to encode trajectory information, and passes it into a causal transformer action
+predictor. At every training iteration, BDT re-labels trajectory information with the anti-causal trans-
+former. Similarly, Skill DT re-labels future skill distributions at every training iteration. Because
+the skill encoder is being updated consistently and skill representations change during training, the
+re-labelling of skill distributions is required to ensure stability in action predictions.
+4.2
+ARCHITECTURE
+VQ-VAE Skill Encoder. Many previous works have represented discrete skills as categorical vari-
+ables, sampled from a categorical distribution prior (Strouse et al., 2021; Eysenbach et al., 2018).
+VQ-VAEs (van den Oord et al., 2017) have shown impressive capabilities with discrete variational
+inference in the space of computer vision (Razavi et al., 2019; Esser et al., 2020), planning (Ozair
+et al., 2021), and online skill discovery (Campos et al., 2020). Because of this, we use a VQ-VAE
+to quantize encoded states into a set of continuous skill embeddings. We encode states into vectors
+z, and quantize to nearest skill embeddings ˆz. To ensure stability, we minimize the regularization
+term:
+V QLOSS(z, ˆz) = MSE(z, ˆz)
+(1)
+Where ˆz is the output of the MLP encoder and z is the nearest embedding in the VQ-VAE codebook.
+Optimizing this loss minimizes the distance of our skill encodings with their corresponding nearest
+VQ-VAE embeddings. This is analagous to clustering, where we are trying to minimize the distance
+between datapoints and their actual cluster centers. In practice, we optimize this loss using an
+exponential moving average, as detailed in Lai et al. (2022).
+Causal Transformer. The Causal Transformer portion of Skill DT shares a similar architecture to
+that of the original DT (Chen et al., 2021), utilizing a GPT (Radford et al., 2018) model. It takes
+in input the last K states st−K:t, skill encodings zt−K:t, and future skill embedding distributions
+Zt−K:t. As mentioned above, the future skill embedding distributions are calculated by generating
+a histogram of skill indices from timestep t : T, and normalizing them so that they add up to 1. For
+states and skill embedding distributions, we use learned linear layers to create token embeddings. To
+capture temporal information, we also learn a timestep embedding that is added to each token. Note
+that we don’t tokenize our skill embeddings because we want to ensure that we don’t lose important
+skill embedding information. It’s important to note that even though we don’t add timestep embed-
+dings to the skill embeddings, they still capture temporal behavior because the attention mechanism
+(Vaswani et al., 2017) of the causal transformer attends the embeddings to temporally conditioned
+states and skill embedding distributions. The VQ-VAE and Causal Transformer components are
+shown visually in Fig. 1.
+4
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+4.3
+TRAINING PROCEDURE
+Figure 2: Training procedure for Skill Decision Transformer. Sub-trajectories of states of length k
+are sampled from the dataset and encoded into latents and discretized. All three variables are passed
+into the causal transformer to output actions. The VQ-VAE parameters and Causal Transformer
+parameters are backpropagated directly using an MSE loss and VQ-VAE regularization loss, shown
+in Equation 1.
+Training Skill DT is very similar to how other variants of GDT are trained (CDT, BDT, DT, etc.).
+First, before every training iteration we re-label skill distributions for every trajectory using our VQ-
+VAE encoder. Afterwards, we sample minibatches of sequence length K, where timesteps are sam-
+pled uniformly. Specifically, at every training iteration, we sample τ = (st, ...st+K, at, ...at+K),
+where t is sampled uniformly for each trajectory in the batch. The sampled states, (st, ...st+K),
+are encoded into skill embeddings using the VQ-VAE encoder. We then pass in the states, encoded
+skills, and skill distributions into the causal transformer to output actions. Like the original DT
+(Chen et al., 2021), we also did not find it useful to predict states or skill distributions, but it could
+be useful for actively predicting skill distributions without having to actually provide states to en-
+code. This is a topic we hope to explore more in the future. The VQ-VAE encoder and causal
+transformer are updated by backpropagation through an MSE loss between target actions and pre-
+dicted actions and the VQ-VAE regularization loss referenced in Equation 1. The simplified training
+procedure is shown in Algorithm 0.
+Algorithm 1 Offline Skill Discovery with Skill Decision Transformer
+Initialize offline dataset D, Causal Transformer fθ, VQ-VAE Encoder eφ, context length K, num
+updates per iteration J
+for training iterations i = 1...N do
+Sample timesteps uniformly: t ∈ 1, ...max len
+Label dataset trajectories with skill distributions Zτt = �T
+t one hot(zt) for all t, ..|τ|
+Sample batch of trajectory states: τ = (st, ...st+K, at, ...at+K)
+for j = 1...J do
+ˆzτt:t+K = (eφ(st), ...eφ(st+K)) Encode skills
+zτt:t+K = quantize(ˆzτt:t+K) Quantize skills with VQ-VAE
+ˆaτt:t+K = fθ(Zτt, zτt, st, ..., Zτt+K, zτt+K, st+K)
+Lθ,φ = 1
+K
+�t+K
+t
+(at − ˆat)2 + V QLOSSφ(zτt:t+K, ˆzτt:t+K)
+backprop Lθ,φ w.r.t θ, φ
+end for
+end for
+5
+
+v(Φ) :
+Zt+K
+quantize
+Zt,...Zt+K
+Z+K
+discretize + histogram
+VQVAE Encoder 
+V(0)
+(at, ...at+K)
+Causal Transformer f
+(St,...St+K)
+Training
+Data
+(at,...at+K)
+MSE((at,...at+K), (at,..., at+K))
+(++?...“***Y++·..*+z)SSOTOA+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+5
+EXPERIMENTS
+5.1
+TASKS AND DATASETS
+For evaluating the performance of Skill DT, we use tasks and datasets from the D4RL benchmark
+(Fu et al., 2020). D4RL has been used as a standard for evaluating many offline RL methods (Kumar
+et al., 2020; Chen et al., 2021; Kostrikov et al., 2021; Zheng et al., 2022). We evaluate our methods
+on mujoco gym continuous control tasks, as well as two antmaze tasks. Images of some of these
+environments can be seen in Section A.4.
+5.2
+EVALUATING SUPERVISED RETURN
+Can Skill DT achieve near or competitive performance, using only trajectory information,
+compared to supervised offline RL approaches?
+Mujoco Mean Results
+Env Name
+DT CQL IQL
+OPAL KMeans
+DT
+Skill
+DT
+(best
+skill)
+num
+skills
+(Skill
+DT)
+Dataset
+Max
+Reward
+walker2d-medium
+74
+79
+78.3
+—
+76
+82
+10
+92
+halfcheetah-medium
+43
+44
+47
+—
+43
+44
+10
+45
+ant-medium
+94
+—
+101
+—
+100
+106
+10
+107
+hopper-medium
+68
+58
+66
+—
+66
+76
+32
+100
+halfcheetah-medium-replay
+37
+46
+44
+—
+39
+41
+32
+42
+hopper-medium-replay
+63
+95
+95
+—
+71
+81
+32
+99
+antmaze-umaze
+59
+75
+88
+—
+73
+100
+32
+100
+antmaze-umaze-diverse
+53
+84
+62
+—
+67
+100
+32
+100
+antmaze-medium-diverse
+0
+61
+71
+—
+0
+13
+64
+100
+antmaze-medium-play
+0
+54
+70
+81
+0
+0
+64
+100
+Table 1: Average normalized returns on Gym and AntMaze tasks. We obtain the same results for
+baselines as reported in other works (Chen et al., 2021; Kumar et al., 2020; Kostrikov et al., 2021;
+Zheng et al., 2022), and calculate Skill DT’s returns as an average over 4 seeds (for gym) and 15 (for
+antmaze). Skill DT outperforms the baselines on most tasks, but fails to beat them on replay tasks
+and antmaze-medium. However, Skill DT can consistently solve the antmaze-umaze tasks.
+Other offline skill discovery algorithms optimize hierarchical policies via supervised RL, utilizing
+the learned primitives to maximize rewards of downstream tasks (Ajay et al., 2020). However,
+because we are interested in evaluating Skill DT without rewards, we have to rely on learning
+enough skills such that high performing trajectories are represented. To evaluate this in practice,
+we run rollouts for each unique skill and take the maximum reward achieved. Detailed python
+sudocode for this is provided in A.5. For a close skill-based comparison to Skill DT, we use a K-
+Means augmented Decision Transformer (K-Means DT). K-Means DT differs from Skill DT in that
+instead of learning skill embeddings, instead we cluster states via K-Means and utilize the cluster
+centers as the skill embeddings.
+Surprisingly, through just pure unsupervised skill discovery, we are able to achieve competitive re-
+sults on Mujoco continuous control environments compared to state-of-the-art offline reinforcement
+learning algorithms (Kumar et al., 2020; Kostrikov et al., 2021; Chen et al., 2021). As we can see
+in our results in Table 1, Skill DT outperforms other baselines on most of the tasks and DT on all
+of the tasks. However, it performs worse than the other baselines on the antmaze-medium / -replay
+tasks. We hypothesize that Skill DT performs worse in these tasks because they contain multimodal
+and diverse behaviors. We think that with additional return context or online play, Skill DT may
+be able to perform better in these environments, and we hope to explore this as future work. Skill
+DT, like the original Decision Transformer (Chen et al., 2021), also struggles on harder exploration
+problems like the antmaze-medium environments. Methods that perform well on these tasks usually
+utilize dynamic programming like Trajectory Transformer(Janner et al., 2021) or hierarchical rein-
+6
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+forcement learning like OPAL (Ajay et al., 2020). Even though Skill DT performs marginally better
+than DT, there is still a lot of room for improvement in future work.
+6
+DISCUSSION
+6.1
+ABLATION STUDY
+What is the effect of the number of skills?
+Ablation Results
+Env Name
+5 skills
+10 skills
+16 skills
+32 skills
+walker2d-medium
+80
+82
+82
+82
+halfcheetah-medium
+44
+44
+44
+44
+ant-medium
+100
+106
+106
+106
+hopper-medium
+65
+70
+76
+76
+hopper-medium-replay
+28
+31
+46
+81
+halfcheetah-medium-replay
+34
+39
+41
+41
+ant-umaze
+80
+100
+100
+100
+ant-umaze-diverse
+66
+100
+100
+100
+Table 2: Best reward obtained from skills for a varying number of skills
+Because Skill DT is a completely unsupervised algorithm, evaluating supervised return requires
+evaluating every learnt skill and taking the one that achieves the maximum reward. This means
+we are relying entirely on Skill DT’s ability to capture behaviors from high performing trajecto-
+ries from the offline dataset. We found that increasing the number of skills has less of an effect on
+performance, in environments that have a large number of successful trajectories (-medium environ-
+ments). We hypothesize that these datasets have unimodal behaviors, and Skill DT does not need
+many skills to capture descriptive information from the dataset. However, for multimodal datasets
+(such as the -replay environments), Skill DT’s performance improves with an increasing number of
+skills. In general, using a larger number of skills can help performance, but the tradeoff is increased
+computation time because each skill needs to be evaluated in the environment. These results are
+reported in Table 2. Images of skills learnt can be seen in Section A.4.
+6.2
+SMM WITH LEARNED SKILLS
+How well can Skill DT reconstruct target trajectories and perform SMM in a zero shot man-
+ner?
+Ideally, if an algorithm is effective at SMM, it should be able to reconstruct a target trajectory in an
+actual environment. That is, given a target trajectory, the algorithm should be able to rollout a sim-
+ilar trajectory. The original DT can actually perform SMM well, on offline trajectories. However,
+when actually attempting this in an actual environment, it is unable to reconstruct a target trajec-
+tory because it is unable to be conditioned on accurate future state trajectory information. Skill DT,
+similar to CDT, is able to perform SMM in an actual environment because it encodes future state
+information into skill embedding histograms. The practical process for this is fairly simple and de-
+tailed in Algorithm 2. In addition to state trajectories, learned skill distributions of the reconstructed
+trajectory and the target trajectory should also be close. We investigate this by looking into target
+trajectories from antmaze-umaze-v2, antmaze-umaze-diverse-v2. For a more challenging example,
+we handpicked a trajectory from antmaze-umaze-diverse that is unique in that it has a loop. Even
+though the trajectory is unique, Skill DT is still able to roughly recreate it in a zero shot manner
+(Fig. 3), with rollouts also including a loop in the trajectory. Additional results can be found in A.3.
+7
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+(a) Target antmaze-umaze trajectory
+(b) Target antmaze-umaze-diverse skill dist.
+(c) reconstructed trajectories
+(d) reconstructed skill dist.
+Figure 3: From the antmaze-umaze-diverse Environment: The target trajecty is complex, with a loop
+and with noisy movement. Reconstructed rollouts also contain a loop.
+6.3
+SKILL DIVERSITY AND DESCRIPTIVENESS
+How diverse and descriptive are the skills that Skill DT discovers?
+In order to evaluate Skill DT as a skill discovery method, we must show that behaviors are not
+only diverse but are descriptive, or more intuitively, distinguishable. We are able to visualize the
+diversity of learned behaviors by plotting each trajectory generated by a skill on both antmaze-umaze
+and ant environments, shown below. To visualize Skill DT’s ability to describe states, we show the
+the projected skill embeddings and quantized skill embedding clusters (Fig. 5). For a diversity
+metric, we utilize a Wasserstein Distance metric between skill distributions (normalized between [0,
+1]), similar to the method proposed in Furuta et al. (2021). We report this metric in Table 3.
+Wasserstein Distances
+Env Name
+min
+max
+avg
+walker2d-medium
+0.007
+0.015
+0.010
+ant-medium
+0.007
+0.012
+0.008
+hopper-medium-replay
+0.009
+0.036
+0.027
+halfcheetah-medium-replay
+0.011
+0.033
+0.019
+ant-umaze-diverse
+0.008
+0.026
+0.011
+Table 3: Wasserstein distance metric (computed between each skill and all others). In tasks with
+unimodal behaviors (-medium), Skill DT discovers skills that result in trajectories that are more
+similar to each other than more complex tasks (-replay and antmaze).
+8
+
+0.16 
+0.12
+o10
+0.DB
+0.06
+0.02 -
+0.L0
+2f
+25
+3I2
+00.12
+0.10
+0.DB
+0.06
+0.02
+0.LC
+15
+3'1910
+0.14
+0.12
+ot0
+0.DB 
+0.06
+0.02
+15
+21
+25
+3I0.125
+0.075
+DSIO
+0.025
+25Foundation Models for Decision Making Workshop at NeurIPS, 2022
+Figure 5: t-SNE projections of Ant-v2 states. Left: States are encoded into unquantized skill em-
+beddings and projected via t-SNE. Right: States are encoded into quantized skill embeddings and
+projected via t-SNE.
+Figure 4: Left: ant-umaze-v2, Right: ant-umaze-diverse-v2. Trajectories made using 32 skills for
+both ant-umaze variants. The diverse variant contains many noisy trajectories, but Skill DT is still
+able to learn diverse and distinguishable skills.
+6.4
+LIMITATIONS AND FUTURE WORK
+Our approach is powerful because it is unsupervised, but it is also limited because of it. Because we
+do not have access to rewards, we rely on pure offline diversity to ensure that high performing tra-
+jectories are learned and encoded into skills that can be sampled. However, this is not very effective
+for tasks that require dynamic programming or longer sequence prediction. Skill DT could bene-
+fit from borrowing concepts from hierarchical skill discovery (Ajay et al., 2020) to re-use learned
+skills on downstream tasks by using an additional return-conditioned model. In addition, it would be
+interesting to explore an online component to the training procedure, similar to the work in Zheng
+et al. (2022).
+7
+CONCLUSION
+We proposed Skill DT, a variant of Generalized DT, to explore the capabilities of offline skill dis-
+covery with sequence modelling. We showed that a combination of LLMs, hindsight-relabelling
+can be useful for extracting information from diverse offline trajectories.. On standard offline RL
+environments, we showed that Skill DT is capable of learning a rich set of behaviors and can per-
+form zero-shot SMM through state-encoded skill embeddings. Skill DT can further be improved
+by adding an online component, a hierarchical component that utilizes returns, and improved explo-
+ration.
+9
+
++
+2
+1+114I
+-10
+201
+301
+40
+-20
+2DE
+ 
+0 -
+-10
+20 -
+30
+30
+-20
+-10
+0
+21Foundation Models for Decision Making Workshop at NeurIPS, 2022
+ACKNOWLEDGEMENTS
+This project was supported by a DFF-Research Project1 grant (9131- 00042B) and GoodAI Research
+Award.
+REFERENCES
+Anurag Ajay, Aviral Kumar, Pulkit Agrawal, Sergey Levine, and Ofir Nachum.
+OPAL: offline
+primitive discovery for accelerating offline reinforcement learning. CoRR, abs/2010.13611, 2020.
+URL https://arxiv.org/abs/2010.13611.
+Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob
+McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. CoRR,
+abs/1707.01495, 2017. URL http://arxiv.org/abs/1707.01495.
+V´ıctor Campos, Alexander Trott, Caiming Xiong, Richard Socher, Xavier Gir´o-i-Nieto, and Jordi
+Torres. Explore, discover and learn: Unsupervised discovery of state-covering skills. CoRR,
+abs/2002.03647, 2020. URL https://arxiv.org/abs/2002.03647.
+Lili Chen, Kevin Lu, Aravind Rajeswaran, Kimin Lee, Aditya Grover, Michael Laskin, Pieter
+Abbeel, Aravind Srinivas, and Igor Mordatch. Decision transformer: Reinforcement learning
+via sequence modeling. arXiv preprint arXiv:2106.01345, 2021.
+Patrick Esser, Robin Rombach, and Bj¨orn Ommer. Taming transformers for high-resolution image
+synthesis. CoRR, abs/2012.09841, 2020. URL https://arxiv.org/abs/2012.09841.
+Benjamin Eysenbach, Abhishek Gupta, Julian Ibarz, and Sergey Levine.
+Diversity is all you
+need: Learning skills without a reward function. CoRR, abs/1802.06070, 2018. URL http:
+//arxiv.org/abs/1802.06070.
+Francesco Faccio, Vincent Herrmann, Aditya Ramesh, Louis Kirsch, and J¨urgen Schmidhuber.
+Goal-conditioned generators of deep policies, 2022.
+URL https://arxiv.org/abs/
+2207.01570.
+Justin Fu, Aviral Kumar, Ofir Nachum, George Tucker, and Sergey Levine. D4rl: Datasets for deep
+data-driven reinforcement learning, 2020.
+Hiroki Furuta, Yutaka Matsuo, and Shixiang Shane Gu. Generalized decision transformer for offline
+hindsight information matching. CoRR, abs/2111.10364, 2021. URL https://arxiv.org/
+abs/2111.10364.
+Dibya Ghosh, Abhishek Gupta, Justin Fu, Ashwin Reddy, Coline Devin, Benjamin Eysenbach, and
+Sergey Levine. Learning to reach goals without reinforcement learning. CoRR, abs/1912.06088,
+2019. URL http://arxiv.org/abs/1912.06088.
+Karol Gregor, Danilo Jimenez Rezende, and Daan Wierstra. Variational intrinsic control. CoRR,
+abs/1611.07507, 2016. URL http://arxiv.org/abs/1611.07507.
+Michael Janner, Qiyang Li, and Sergey Levine. Offline reinforcement learning as one big sequence
+modeling problem. In Advances in Neural Information Processing Systems, 2021.
+Ilya Kostrikov, Ashvin Nair, and Sergey Levine. Offline reinforcement learning with implicit q-
+learning. CoRR, abs/2110.06169, 2021. URL https://arxiv.org/abs/2110.06169.
+Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline
+reinforcement learning. CoRR, abs/2006.04779, 2020. URL https://arxiv.org/abs/
+2006.04779.
+Chieh-Hsin Lai, Dongmian Zou, and Gilad Lerman. Robust vector quantized-variational autoen-
+coder. CoRR, abs/2202.01987, 2022. URL https://arxiv.org/abs/2202.01987.
+Lisa Lee, Benjamin Eysenbach, Emilio Parisotto, Eric P. Xing, Sergey Levine, and Ruslan Salakhut-
+dinov. Efficient exploration via state marginal matching. CoRR, abs/1906.05274, 2019. URL
+http://arxiv.org/abs/1906.05274.
+10
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+Yuxi Li. Deep reinforcement learning: An overview. arXiv preprint arXiv:1701.07274, 2017.
+Sherjil Ozair, Yazhe Li, Ali Razavi, Ioannis Antonoglou, A¨aron van den Oord, and Oriol Vinyals.
+Vector quantized models for planning. CoRR, abs/2106.04615, 2021. URL https://arxiv.
+org/abs/2106.04615.
+Deepak Pathak, Pulkit Agrawal, Alexei A. Efros, and Trevor Darrell. Curiosity-driven exploration by
+self-supervised prediction. CoRR, abs/1705.05363, 2017. URL http://arxiv.org/abs/
+1705.05363.
+Alec Radford, Karthik Narasimhan, Tim Salimans, and Ilya Sutskever. Improving language under-
+standing by generative pre-training. 2018.
+Paulo E. Rauber, Filipe Mutz, and J¨urgen Schmidhuber.
+Hindsight policy gradients.
+CoRR,
+abs/1711.06006, 2017. URL http://arxiv.org/abs/1711.06006.
+Ali Razavi, A¨aron van den Oord, and Oriol Vinyals. Generating diverse high-fidelity images with
+VQ-VAE-2. CoRR, abs/1906.00446, 2019. URL http://arxiv.org/abs/1906.00446.
+Archit Sharma, Shixiang Gu, Sergey Levine, Vikash Kumar, and Karol Hausman. Dynamics-aware
+unsupervised discovery of skills. CoRR, abs/1907.01657, 2019. URL http://arxiv.org/
+abs/1907.01657.
+DJ Strouse, Kate Baumli, David Warde-Farley, Vlad Mnih, and Steven Hansen. Learning more
+skills through optimistic exploration. CoRR, abs/2107.14226, 2021. URL https://arxiv.
+org/abs/2107.14226.
+A¨aron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural discrete representation learn-
+ing. CoRR, abs/1711.00937, 2017. URL http://arxiv.org/abs/1711.00937.
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez,
+Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. CoRR, abs/1706.03762, 2017.
+URL http://arxiv.org/abs/1706.03762.
+Qinqing Zheng, Amy Zhang, and Aditya Grover. Online decision transformer, 2022. URL https:
+//arxiv.org/abs/2202.05607.
+11
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+A
+APPENDIX
+A.1
+DATASET STATISTICS
+Dataset Stats
+Env Name
+state
+dim
+act dim
+num
+trajec-
+tories
+avg
+dataset
+reward
+max
+dataset
+reward
+min
+dataset
+reward
+avg
+dataset
+d4rl
+max
+dataset
+d4rl
+min
+dataset
+d4rl
+walker2d -
+medium
+17
+6
+1190
+2852
+4227
+-7
+62
+92
+0
+halfcheetah
+-medium
+17
+6
+1000
+4770
+5309
+-310
+41
+45
+0
+ant
+-
+medium
+111
+8
+1202
+3051
+4187
+-530
+80
+107
+-5
+hopper
+-medium
+11
+3
+2186
+1422
+3222
+316
+44
+100
+10
+halfcheetah
+-medium
+-replay
+17
+6
+202
+3093
+4985
+-638
+27
+42
+-3
+hopper-
+medium
+-replay
+11
+3
+1801
+529
+3193
+-0.5
+17
+99
+1
+antmaze-
+umaze
+29
+8
+2815
+0.5
+1
+0
+52
+100
+0
+antmaze-
+umaze
+-diverse
+29
+8
+1011
+0.012
+1
+0
+1.2
+100
+0
+antmaze-
+medium
+-diverse
+29
+8
+1137
+0.125
+1
+0
+12.5
+100
+0
+antmaze-
+medium
+-play
+29
+8
+1204
+0.2
+1
+0
+20.0
+100
+0
+Table 4: Dataset statistics.
+A.2
+HYPERPARAMETERS
+Common Hyper Parameters for Causal Transformer
+hyperparameter
+value
+Number of layers
+4
+Number of attention heads
+4
+Embedding dimension
+256
+Context Length
+20
+Dropout
+0.0
+Batch Size
+256
+Updates between rollouts
+50
+lr
+1e-4
+gradient norm
+0.25
+Table 5: The hyperparameters used for the causal transformer.
+A.3
+FEW SHOT TARGET TRAJECTORY RECONSTRUCTION
+Skill DT, like other skill discovery methods, can use its state-to-skill encoder to guide its actions
+towards a particular goal. In this case, we are interested in recreating target trajectories as close as
+12
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+(a) Target Ant Skill Distribution
+(b) Reconstructed Ant Skill Distribution
+Figure 7: From the Ant-v2 Environment: Skill distributions of a target trajectory and the recon-
+structed trajectory from rolling out in the environment. Because Ant-v2 is a simpler environment,
+we can see that the reconstructed skill distributions are very close to the target.
+possible. The detailed sudocode and its description for few shot skill reconstruction can be found in
+Section A.5.
+(a) Target antmaze-umaze x-y trajectory
+(b) Reconstructed antmaze-umaze x-y trajectory
+(c) Target antmaze-umaze skill dist.
+(d) Reconstructed antmaze-umaze skill dist.
+Figure 6: From the Antmaze-Umaze Envidiverseronment: One of the longer and highest performing
+trajectories in the dataset is reconstructed by Skill DT. The trajectory is not quite identical to the
+target, but it follows a similar path, where it hugs the edges of the maze just like the target.
+Algorithm 2 Reconstructing target trajectories
+Initialize target trajectory τ, skill encoder Eφ, Skill DT transformer π
+1. (starget
+0
+, ..., starget
+T
+) ← τ,
+▷ Extract states from target trajectory
+2. (z0, ..., zT ), (zindex0, ..., zindexT ) = Eφ(starget
+0
+, ..., starget
+T
+),
+▷ encode states
+3. (Z0, ..., ZT ) = histogram (zindex0, ..., zindexT ),
+▷ Create skill distributions by creating a
+histogram of skill encoding indices
+4. ˆτ ∼ π(a|Z0, z0, s0, ...),
+▷ rollout in real environment, see A.5 for details
+13
+
+-Doz.0
+0.15
+0.125
+DSIO
+0.025
+0.0.00.25
+0.20
+0.15
+0.D5
+0
+150.200
+0.15
+0.125
+0.100
+0.075
+0.050
+0.025
+0.000
+00.200
+0.15
+0.125
+0.100
+0.075
+0.050
+0.025
+0.000
+0Foundation Models for Decision Making Workshop at NeurIPS, 2022
+A.4
+TRAJECTORY SKILL VISUALIZATIONS
+Figure 8: Skills learned in the ant-medium-v2 environment. Each row corresponds to a skill.
+Figure 9: Skills learned in the halfcheetah-medium-replay-v2 environment. Each row corresponds
+to a skill.
+Figure 10: Skills learned in the hopper-medium-replay-v2 environment. Each row corresponds to a
+skill.
+14
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+Figure 11: Skills learned in the walker-medium-v2 environment. Each row corresponds to a skill.
+Figure 12: Skills learned in the ant-umaze-diverse-v2 environment. Each row corresponds to a skill.
+15
+
+Foundation Models for Decision Making Workshop at NeurIPS, 2022
+A.5
+EVALUATING SKILL DT’S PERFORMANCE
+Because Skill DT is a purely unsupervised algorithm, to evaluate the performance in an actual en-
+vironment, we perform rollouts for each skill and evaluate each to determine which is the best. To
+do this, we first populate a buffer of skills (here denoted with z) and skill histograms Z. When we
+rollout in the actual environment, the causal transformer utilizes this buffer to actually make pre-
+dictions. However, it updates the skill encodings that it actually sees in the environment at each
+timestep. This is because even though the policy is completely conditioned to follow a single skill,
+it may end up reaching states that are classified under another. Python sudocode shown below:
+def generate_histogram(one_hot_skill_ids):
+trajectory_length = len(one_hot_skill_ids)
+histogram = torch.tensor(copy(one_hot_skill_ids))
+for i in range(trajectory_length-1, -1, -1):
+# reverse order
+if i != trajectory_length - 1
+histogram[i] = histogram[i] + histogram[i+1]
+return histogram / histogram.sum(-1) # normalize in range [0, 1]
+def evaluate_skill_dt(skill_dt, env, max_steps, context_len):
+num_skills = skill_dt.num_skills
+rewards = []
+for skill_id in range(num_skills):
+skill_ids = repeat(skill_id, max_steps)
+# create on_hot skill ids
+# ex: one_hot([1,1], 5) = [[0, 1, 0, 0, 0],[0, 1, 0, 0, 0]]
+one_hot_skill_ids = one_hot(skill_ids, num_skills)
+state = env.reset()
+# initialize_state
+t = 0
+total_reward = 0
+state_buffer = zeros(max_steps)
+z_buffer = zeros(max_steps)
+while t < max_steps:
+# z is vqvae embedding
+# skill_id is the index of the vqvae embedding in codebook
+z, skill_id = skill_dt.encode_skill(state)
+one_hot_skill_ids[t] = one_hot(skill_id)
+Z = skill_dt.generate_histogram(one_hot_skill_ids) # create
+histograms
+state_buffer[t] = state
+z_buffer[t] = z
+if t < context_len:
+curr_states = state_buffer[t:t+context_len]
+curr_z = z_buffer[t:t+context_len]
+curr_Z = Z[t:t+context_len]
+actions = skill_dt.causal_transformer(curr_Z, curr_z,
+curr_states)
+action = actions[t]
+else:
+curr_states = state_buffer[t-context_len+1:t+1]
+curr_z = z_buffer[t-context_len+1:t+1]
+curr_Z = Z[t-context_len+1:t+1]
+actions = skill_dt.causal_transformer(curr_Z, curr_z,
+curr_states)
+action = actions[-1]
+state, reward, done = env.step(action)
+total_reward += reward
+if done:
+break
+rewards.append(total_reward)
+return max(rewards)
+16
+
diff --git a/q9FRT4oBgHgl3EQfezfQ/content/tmp_files/load_file.txt b/q9FRT4oBgHgl3EQfezfQ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..16cb90c7b67f9d2427275442f32816c71ba9ee06
--- /dev/null
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@@ -0,0 +1,829 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf,len=828
+page_content='Foundation Models for Decision Making Workshop at NeurIPS, 2022  SKILL DECISION TRANSFORMER  Shyam Sudhakaran & Sebastian Risi  IT University of Copenhagen  Copenhagen, Denmark  {shsu,sebr}@itu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='dk  ABSTRACT  Recent work has shown that Large Language Models (LLMs) can be incredibly  effective for offline reinforcement learning (RL) by representing the traditional  RL problem as a sequence modelling problem (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Janner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=',  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However many of these methods only optimize for high returns, and may  not extract much information from a diverse dataset of trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Generalized  Decision Transformers (GDTs) (Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) have shown that utilizing fu-  ture trajectory information, in the form of information statistics, can help extract  more information from offline trajectory data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Building upon this, we propose  Skill Decision Transformer (Skill DT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT draws inspiration from hindsight  relabelling (Andrychowicz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017) and skill discovery methods to discover  a diverse set of primitive behaviors, or skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We show that Skill DT can not  only perform offline state-marginal matching (SMM), but can discovery descrip-  tive behaviors that can be easily sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Furthermore, we show that through  purely reward-free optimization, Skill DT is still competitive with supervised of-  fline RL approaches on the D4RL benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The code and videos can be found  on our project page: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='com/shyamsn97/skill-dt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  1  INTRODUCTION  Reinforcement Learning (RL) has been incredibly effective in a variety of online scenarios such  as games and continuous control environments (Li, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, they generally suffer from  sample inefficiency, where millions of interactions with an environment are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In addition,  efficient exploration is needed to avoid local minimas (Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Because of these limitations, there is interest in methods that can learn diverse and useful primitives  without supervision, enabling better exploration and re-usability of learned skills (Eysenbach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=',  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Strouse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, these online skill discovery methods still  require interactions with an environment, where access may be limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  This requirement has sparked interest in Offline RL, where a dataset of trajectories is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Some of these datasets (Fu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020) are composed of large and diverse trajectories of varying  performance, making it non trivial to actually make proper use of these datasets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' simply applying  behavioral cloning (BC) leads to sub-optimal performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Recently, approaches such as the Deci-  sion Transformer (DT) (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) and the Trajectory Transformer (TT) (Janner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021),  utilize Transformer architectures (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017) to achieve high performance on Offline RL  benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2021) showed that these methods are effectively doing hindsight infor-  mation matching (HIM), where the policies are trained to estimate a trajectory that matches given  target statistics of future information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The work also generalizes DT as an information-statistic con-  ditioned policy, Generalized Decision Transformer (GDT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This results in policies with different  capabilities, such as supervised learning and State Marginal Matching (SMM) (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2019),  just by simply varying different information statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  In the work presented here, we take inspiration from the previously mentioned skill discovery meth-  ods and introduce Skill Decision Transformers (Skill DT), a special case of GDT, where we wish  to condition action predictions on skill embeddings and also future skill distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We show  that Skill DT is not only able to discovery a number of discrete behaviors, but it is also able to ef-  fectively match target trajectory distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Furthermore, we empirically show that through pure  unsupervised skill discovery, Skill DT is actually able to discover high performing behaviors that  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='13573v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='LG]  31 Jan 2023  Foundation Models for Decision Making Workshop at NeurIPS, 2022  Figure 1: Skill Decision Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' States are encoded and clustered via VQ-VAE codebook  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' A Causal Transformer, similar to the original DT architecture, takes in a sequence  of states, a latent skill distribution, represented as the normalized summed future counts of VQ-  VAE encoding indices (details can be found in the ”generate histogram” function in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5), and the  corresponding skill encoding of the state at timestep t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The skill histogram captures ”future” skill  behavior, while the skill embedding represents current skill behavior as timestep t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  match or achieve higher performance on D4RL benchmarks (Fu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020) compared to other  state-of-the-art offline RL approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Our method is completely unsupervised and predicts actions, conditioned by previous states, skills,  and distributions of future skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Empirically, we show that Skill DT can not only perform SMM  on target trajectories, but can also match or achieve higher performance on D4RL benchmarks (Fu  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020) compared to other state-of-the-art offline RL approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  2  RELATED WORK  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  SKILL DISCOVERY  Many skill methods attempt to learn a latent skill conditioned policy π(a|s, z), where state s ∼  p(s) and skill z ∼ Z, that maximizes mutual information between S and Z (Gregor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Sharma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Eysenbach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Another way of learning meaningful skills is through  variational inference, where z is learned via a reconstruction loss (Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Explore,  Discover and Learn (EDL) (Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020) is an approach, which discovers a discrete set of  skills by encoding states via a VQ-VAE: p(z|s), and reconstructing them: p(s|z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We use a similar  approach, but instead of reconstructing states, we utilize offline trajectories and optimize action  reconstruction directly (p(a|s, z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Since our policy is autoregressive, our skill encoding actually  takes into account temporal information, leading to more descriptive skill embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Offline  Primitive Discovery for Accelerating Offline Reinforcement Learning (OPAL) (Ajay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020),  also discovers offline skills temporally, but instead uses a continuous distribution of skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' These  continuous skills are then sample by a hierarchical policy that is optimized by task rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Because  our approach is completely unsupervised, we wish to easily sample skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To simplify this, we opt to  use a discrete distribution of skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This makes it trivial to query the highest performing behaviors,  accomplished by just iterating through the discrete skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  STATE MARGINAL MATCHING  State marginal matching (SMM) (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2019) involves finding policies that minimize the dis-  tance between the marginal state distribution that the policy represents pπ(s), and a target distribu-  tion p∗(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' These objectives have an advantage over traditional RL objectives in that they do not  require any rewards and are guided towards exploration (Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CDT has shown  impressive SMM capabilities by utilizing binned target state distributions to condition actions in  order to match the given target state distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, using CDT in a real environment is  2  VQVAE Codebook  02122  min  Causal Transformer  Encoder  K  one_hot(zt)  t<TFoundation Models for Decision Making Workshop at NeurIPS, 2022  difficult because target distributions must be provided, while Skill DT learns discrete skills that can  be sampled easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Also, CDT requires a low dimensional state space, while Skill DT can – in theory  – work on any type of input as long as it can be encoded effectively into a vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  3  PRELIMINARIES  In this work, we consider learning in environments modelled as Markov decision processes (MDPs),  which can be described using varibles (S, A, P, R), where S represents the state space, A represents  the action space, and P(st+1|st, at) represents state transition dynamics of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  GENERALIZED DECISION TRANSFORMER  The Decision Transformer (DT) (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) represents RL as a sequence modelling problem  and uses a GPT architecture (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2018) to predict actions autoregressively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Specifi-  cally, DT takes in a sequence of RTGs, states, and actions, where Rt = �T  t rt, and trajectory  τ = (R0, s0, a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', R|τ|, s|τ|, a|τ|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' DT uses K previous tokens to predict at with a deterministic  policy which is optimized by a mean squared error loss between target and predicted actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' For  evaluation, a target return ˆRtarget is provided and DT attempts to achieve the targeted return in the  actual environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2021) introduced a generalized version of DT, Generalized De-  cision Transformer (GDT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' GDT provides a simple interface for representing a variety of different  objectives, configurable by different information statistics (for consistency, we represent variations  of GDT with πgdt):  τt = st, at, rt, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', sT , aT , rT , Iφ = information statistics function  Generalized Decision Transformer (GDT):  πgdt(at|Iφ(τ0), s0, a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', Iφ(τt), st−1, at−1)  Decision Transformer (DT):  πgdt  dt (at|Iφ  dt(τ0), s0, a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', Iφ  dt(τt), st−1, at−1), where Iφ  dt(τt) = �T  t γ ∗ rt, γ = discount factor  Categorical Decision Transformer (CDT):  πgdt  cdt(at|Iφ  cdt(τ0), s0, a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', Iφ  cdt(τt), st, at), where Iφ  cdt(τt) = histogram(st, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', sT )  CDT is the most similar to Skill DT – CDT captures future trajectory information using future state  distributions, represented as histograms for each state dimension, essentially binning and counting  the bin ids for each state dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT instead utilizes learned skill embeddings to generate  future skill distributions, represented as histograms of full embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In addition, Skill DT also  makes use of the representation learnt by the skill embedding by also using it in tandem with the  skill distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  4  SKILL DECISION TRANSFORMER  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  FORMULATION  Our Skill DT architecture is very similar to the original Decision Transformer presented in Chen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' While the classic DT uses summed future returns to condition trajectories, we instead  make use of learned skill embeddings and future skill distributions, represented as a histogram of  skill embedding indices, similar to the way Categorical Decision Transformer (CDT) (Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=',  2021) utilizes future state counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' One notable difference Skill DT has to the original Decision  Transformer (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) and the GDT (Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) variant is that we omit actions in  predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This is because we are interested in SMM through skills, where we want to extract as  much information from states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  3  Foundation Models for Decision Making Workshop at NeurIPS, 2022  Formally, Skill DT represents a policy:  π(at|Zt−K, zt−K, st−K, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='Zt−1, zt−1, st−1),  where K is the context length, and θ are the learnable parameters of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' States are encoded  as skill embeddings ˆzt, which are then quantized using a learned codebook of embeddings z =  argminn||ˆz − zn||2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The future skill distributions are represented as the normalized histogram of  summed future one hot encoded skill indices: Zt = �T  t one hot(zt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Connecting this to GDT, our  policy can be viewed as:  πgdt  skill(at|Iφ  skill(τ0), s0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', Iφ  skill(τt), st), where Iφ  skill(τt) = (histogram(zt, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', zT ), zt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  HINDSIGHT SKILL RE-LABELLING  Hindsight experience replay (HER) is a method that has been effective in improving sample-  efficiency of goal-oriented agents (Andrychowicz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Rauber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The core concept  revolves around goal relabelling, where trajectory goals are replaced by achieved goals vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' inteded  goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This concept of re-labelling information has been utilized in a number of works (Ghosh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Faccio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2022), to iteratively learn an condition predictions on  target statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Bi-Directional Decision Transformer (BDT) (Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021), utilizes an anti-  causal transformer to encode trajectory information, and passes it into a causal transformer action  predictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' At every training iteration, BDT re-labels trajectory information with the anti-causal trans-  former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Similarly, Skill DT re-labels future skill distributions at every training iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Because  the skill encoder is being updated consistently and skill representations change during training, the  re-labelling of skill distributions is required to ensure stability in action predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  ARCHITECTURE  VQ-VAE Skill Encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Many previous works have represented discrete skills as categorical vari-  ables, sampled from a categorical distribution prior (Strouse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Eysenbach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  VQ-VAEs (van den Oord et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017) have shown impressive capabilities with discrete variational  inference in the space of computer vision (Razavi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Esser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020), planning (Ozair  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021), and online skill discovery (Campos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Because of this, we use a VQ-VAE  to quantize encoded states into a set of continuous skill embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We encode states into vectors  z, and quantize to nearest skill embeddings ˆz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To ensure stability, we minimize the regularization  term:  V QLOSS(z, ˆz) = MSE(z, ˆz)  (1)  Where ˆz is the output of the MLP encoder and z is the nearest embedding in the VQ-VAE codebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Optimizing this loss minimizes the distance of our skill encodings with their corresponding nearest  VQ-VAE embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This is analagous to clustering, where we are trying to minimize the distance  between datapoints and their actual cluster centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In practice, we optimize this loss using an  exponential moving average, as detailed in Lai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Causal Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The Causal Transformer portion of Skill DT shares a similar architecture to  that of the original DT (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021), utilizing a GPT (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2018) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' It takes  in input the last K states st−K:t, skill encodings zt−K:t, and future skill embedding distributions  Zt−K:t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' As mentioned above, the future skill embedding distributions are calculated by generating  a histogram of skill indices from timestep t : T, and normalizing them so that they add up to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' For  states and skill embedding distributions, we use learned linear layers to create token embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To  capture temporal information, we also learn a timestep embedding that is added to each token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Note  that we don’t tokenize our skill embeddings because we want to ensure that we don’t lose important  skill embedding information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' It’s important to note that even though we don’t add timestep embed-  dings to the skill embeddings, they still capture temporal behavior because the attention mechanism  (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2017) of the causal transformer attends the embeddings to temporally conditioned  states and skill embedding distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The VQ-VAE and Causal Transformer components are  shown visually in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  4  Foundation Models for Decision Making Workshop at NeurIPS, 2022  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='3  TRAINING PROCEDURE  Figure 2: Training procedure for Skill Decision Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Sub-trajectories of states of length k  are sampled from the dataset and encoded into latents and discretized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' All three variables are passed  into the causal transformer to output actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The VQ-VAE parameters and Causal Transformer  parameters are backpropagated directly using an MSE loss and VQ-VAE regularization loss, shown  in Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Training Skill DT is very similar to how other variants of GDT are trained (CDT, BDT, DT, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  First, before every training iteration we re-label skill distributions for every trajectory using our VQ-  VAE encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Afterwards, we sample minibatches of sequence length K, where timesteps are sam-  pled uniformly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Specifically, at every training iteration, we sample τ = (st, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='st+K, at, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='at+K),  where t is sampled uniformly for each trajectory in the batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The sampled states, (st, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='st+K),  are encoded into skill embeddings using the VQ-VAE encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We then pass in the states, encoded  skills, and skill distributions into the causal transformer to output actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Like the original DT  (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021), we also did not find it useful to predict states or skill distributions, but it could  be useful for actively predicting skill distributions without having to actually provide states to en-  code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This is a topic we hope to explore more in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The VQ-VAE encoder and causal  transformer are updated by backpropagation through an MSE loss between target actions and pre-  dicted actions and the VQ-VAE regularization loss referenced in Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The simplified training  procedure is shown in Algorithm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Algorithm 1 Offline Skill Discovery with Skill Decision Transformer  Initialize offline dataset D, Causal Transformer fθ, VQ-VAE Encoder eφ, context length K, num  updates per iteration J  for training iterations i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='N do  Sample timesteps uniformly: t ∈ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='max len  Label dataset trajectories with skill distributions Zτt = �T  t one hot(zt) for all t, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='.|τ|  Sample batch of trajectory states: τ = (st, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='st+K, at, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='at+K)  for j = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='J do  ˆzτt:t+K = (eφ(st), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='eφ(st+K)) Encode skills  zτt:t+K = quantize(ˆzτt:t+K) Quantize skills with VQ-VAE  ˆaτt:t+K = fθ(Zτt, zτt, st, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', Zτt+K, zτt+K, st+K)  Lθ,φ = 1  K  �t+K  t  (at − ˆat)2 + V QLOSSφ(zτt:t+K, ˆzτt:t+K)  backprop Lθ,φ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='t θ, φ  end for  end for  5  v(Φ) :  Zt+K  quantize  Zt,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='Zt+K  Z+K  discretize + histogram  VQVAE Encoder  V(0)  (at, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='at+K)  Causal Transformer f  (St,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='St+K)  Training  Data  (at,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='at+K)  MSE((at,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='at+K), (at,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', at+K))  (++?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='.“***Y++·.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='. *+z)SSOTOA+Foundation Models for Decision Making Workshop at NeurIPS, 2022  5  EXPERIMENTS  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  TASKS AND DATASETS  For evaluating the performance of Skill DT, we use tasks and datasets from the D4RL benchmark  (Fu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' D4RL has been used as a standard for evaluating many offline RL methods (Kumar  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Kostrikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We evaluate our methods  on mujoco gym continuous control tasks, as well as two antmaze tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Images of some of these  environments can be seen in Section A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  EVALUATING SUPERVISED RETURN  Can Skill DT achieve near or competitive performance, using only trajectory information,  compared to supervised offline RL approaches?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Mujoco Mean Results  Env Name  DT CQL IQL  OPAL KMeans  DT  Skill  DT  (best  skill)  num  skills  (Skill  DT)  Dataset  Max  Reward  walker2d-medium  74  79  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='Table 1: Average normalized returns on Gym and AntMaze tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We obtain the same results for  baselines as reported in other works (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Kostrikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2022), and calculate Skill DT’s returns as an average over 4 seeds (for gym) and 15 (for  antmaze).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT outperforms the baselines on most tasks, but fails to beat them on replay tasks  and antmaze-medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, Skill DT can consistently solve the antmaze-umaze tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Other offline skill discovery algorithms optimize hierarchical policies via supervised RL, utilizing  the learned primitives to maximize rewards of downstream tasks (Ajay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However,  because we are interested in evaluating Skill DT without rewards, we have to rely on learning  enough skills such that high performing trajectories are represented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To evaluate this in practice,  we run rollouts for each unique skill and take the maximum reward achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Detailed python  sudocode for this is provided in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' For a close skill-based comparison to Skill DT, we use a K-  Means augmented Decision Transformer (K-Means DT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' K-Means DT differs from Skill DT in that  instead of learning skill embeddings, instead we cluster states via K-Means and utilize the cluster  centers as the skill embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Surprisingly, through just pure unsupervised skill discovery, we are able to achieve competitive re-  sults on Mujoco continuous control environments compared to state-of-the-art offline reinforcement  learning algorithms (Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Kostrikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' As we can see  in our results in Table 1, Skill DT outperforms other baselines on most of the tasks and DT on all  of the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, it performs worse than the other baselines on the antmaze-medium / -replay  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We hypothesize that Skill DT performs worse in these tasks because they contain multimodal  and diverse behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We think that with additional return context or online play, Skill DT may  be able to perform better in these environments, and we hope to explore this as future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill  DT, like the original Decision Transformer (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021), also struggles on harder exploration  problems like the antmaze-medium environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Methods that perform well on these tasks usually  utilize dynamic programming like Trajectory Transformer(Janner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2021) or hierarchical rein-  6  Foundation Models for Decision Making Workshop at NeurIPS, 2022  forcement learning like OPAL (Ajay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Even though Skill DT performs marginally better  than DT, there is still a lot of room for improvement in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  6  DISCUSSION  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='1  ABLATION STUDY  What is the effect of the number of skills?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Ablation Results  Env Name  5 skills  10 skills  16 skills  32 skills  walker2d-medium  80  82  82  82  halfcheetah-medium  44  44  44  44  ant-medium  100  106  106  106  hopper-medium  65  70  76  76  hopper-medium-replay  28  31  46  81  halfcheetah-medium-replay  34  39  41  41  ant-umaze  80  100  100  100  ant-umaze-diverse  66  100  100  100  Table 2: Best reward obtained from skills for a varying number of skills  Because Skill DT is a completely unsupervised algorithm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' evaluating supervised return requires  evaluating every learnt skill and taking the one that achieves the maximum reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This means  we are relying entirely on Skill DT’s ability to capture behaviors from high performing trajecto-  ries from the offline dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We found that increasing the number of skills has less of an effect on  performance, in environments that have a large number of successful trajectories (-medium environ-  ments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We hypothesize that these datasets have unimodal behaviors, and Skill DT does not need  many skills to capture descriptive information from the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, for multimodal datasets  (such as the -replay environments), Skill DT’s performance improves with an increasing number of  skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In general, using a larger number of skills can help performance, but the tradeoff is increased  computation time because each skill needs to be evaluated in the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' These results are  reported in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Images of skills learnt can be seen in Section A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  SMM WITH LEARNED SKILLS  How well can Skill DT reconstruct target trajectories and perform SMM in a zero shot man-  ner?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Ideally, if an algorithm is effective at SMM, it should be able to reconstruct a target trajectory in an  actual environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' That is, given a target trajectory, the algorithm should be able to rollout a sim-  ilar trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The original DT can actually perform SMM well, on offline trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However,  when actually attempting this in an actual environment, it is unable to reconstruct a target trajec-  tory because it is unable to be conditioned on accurate future state trajectory information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT,  similar to CDT, is able to perform SMM in an actual environment because it encodes future state  information into skill embedding histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The practical process for this is fairly simple and de-  tailed in Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In addition to state trajectories, learned skill distributions of the reconstructed  trajectory and the target trajectory should also be close.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We investigate this by looking into target  trajectories from antmaze-umaze-v2, antmaze-umaze-diverse-v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' For a more challenging example,  we handpicked a trajectory from antmaze-umaze-diverse that is unique in that it has a loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Even  though the trajectory is unique, Skill DT is still able to roughly recreate it in a zero shot manner  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' 3), with rollouts also including a loop in the trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Additional results can be found in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  7  Foundation Models for Decision Making Workshop at NeurIPS, 2022  (a) Target antmaze-umaze trajectory  (b) Target antmaze-umaze-diverse skill dist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  (c) reconstructed trajectories  (d) reconstructed skill dist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 3: From the antmaze-umaze-diverse Environment: The target trajecty is complex, with a loop  and with noisy movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Reconstructed rollouts also contain a loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='3  SKILL DIVERSITY AND DESCRIPTIVENESS  How diverse and descriptive are the skills that Skill DT discovers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  In order to evaluate Skill DT as a skill discovery method, we must show that behaviors are not  only diverse but are descriptive, or more intuitively, distinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We are able to visualize the  diversity of learned behaviors by plotting each trajectory generated by a skill on both antmaze-umaze  and ant environments, shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To visualize Skill DT’s ability to describe states, we show the  the projected skill embeddings and quantized skill embedding clusters (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' For a diversity  metric, we utilize a Wasserstein Distance metric between skill distributions (normalized between [0,  1]), similar to the method proposed in Furuta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We report this metric in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Wasserstein Distances  Env Name  min  max  avg  walker2d-medium  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='010  ant-medium  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='008  hopper-medium-replay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='036  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='027  halfcheetah-medium-replay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='033  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='019  ant-umaze-diverse  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='011  Table 3: Wasserstein distance metric (computed between each skill and all others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In tasks with  unimodal behaviors (-medium), Skill DT discovers skills that result in trajectories that are more  similar to each other than more complex tasks (-replay and antmaze).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='12  o10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='02 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='L0  2f  25  3I2  00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='02  15  21  25  3I0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='075  DSIO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='025  25Foundation Models for Decision Making Workshop at NeurIPS, 2022  Figure 5: t-SNE projections of Ant-v2 states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Left: States are encoded into unquantized skill em-  beddings and projected via t-SNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Right: States are encoded into quantized skill embeddings and  projected via t-SNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 4: Left: ant-umaze-v2, Right: ant-umaze-diverse-v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Trajectories made using 32 skills for  both ant-umaze variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The diverse variant contains many noisy trajectories, but Skill DT is still  able to learn diverse and distinguishable skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='4  LIMITATIONS AND FUTURE WORK  Our approach is powerful because it is unsupervised, but it is also limited because of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Because we  do not have access to rewards, we rely on pure offline diversity to ensure that high performing tra-  jectories are learned and encoded into skills that can be sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, this is not very effective  for tasks that require dynamic programming or longer sequence prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT could bene-  fit from borrowing concepts from hierarchical skill discovery (Ajay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', 2020) to re-use learned  skills on downstream tasks by using an additional return-conditioned model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In addition, it would be  interesting to explore an online component to the training procedure, similar to the work in Zheng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  7  CONCLUSION  We proposed Skill DT, a variant of Generalized DT, to explore the capabilities of offline skill dis-  covery with sequence modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' We showed that a combination of LLMs, hindsight-relabelling  can be useful for extracting information from diverse offline trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='. On standard offline RL  environments, we showed that Skill DT is capable of learning a rich set of behaviors and can per-  form zero-shot SMM through state-encoded skill embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Skill DT can further be improved  by adding an online component, a hierarchical component that utilizes returns, and improved explo-  ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  9  +  2  1+114I  10  201  301  40  20  2DE  0 -  10  20 -  30  30  20  10  0  21Foundation Models for Decision Making Workshop at NeurIPS, 2022  ACKNOWLEDGEMENTS  This project was supported by a DFF-Research Project1 grant (9131- 00042B) and GoodAI Research  Award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  REFERENCES  Anurag Ajay, Aviral Kumar, Pulkit Agrawal, Sergey Levine, and Ofir Nachum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  OPAL: offline  primitive discovery for accelerating offline reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='13611, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='13611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob  McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Hindsight experience replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR,  abs/1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01495, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  V´ıctor Campos, Alexander Trott, Caiming Xiong, Richard Socher, Xavier Gir´o-i-Nieto, and Jordi  Torres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Explore, discover and learn: Unsupervised discovery of state-covering skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR,  abs/2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='03647, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='03647.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Lili Chen, Kevin Lu, Aravind Rajeswaran, Kimin Lee, Aditya Grover, Michael Laskin, Pieter  Abbeel, Aravind Srinivas, and Igor Mordatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Decision transformer: Reinforcement learning  via sequence modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01345, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Patrick Esser, Robin Rombach, and Bj¨orn Ommer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Taming transformers for high-resolution image  synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='09841, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='09841.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Benjamin Eysenbach, Abhishek Gupta, Julian Ibarz, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Diversity is all you  need: Learning skills without a reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06070, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL http:  //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06070.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Francesco Faccio, Vincent Herrmann, Aditya Ramesh, Louis Kirsch, and J¨urgen Schmidhuber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Goal-conditioned generators of deep policies, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/  2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Justin Fu, Aviral Kumar, Ofir Nachum, George Tucker, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' D4rl: Datasets for deep  data-driven reinforcement learning, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Hiroki Furuta, Yutaka Matsuo, and Shixiang Shane Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Generalized decision transformer for offline  hindsight information matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='10364, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/  abs/2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='10364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Dibya Ghosh, Abhishek Gupta, Justin Fu, Ashwin Reddy, Coline Devin, Benjamin Eysenbach, and  Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Learning to reach goals without reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06088,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Karol Gregor, Danilo Jimenez Rezende, and Daan Wierstra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Variational intrinsic control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR,  abs/1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='07507, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='07507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Michael Janner, Qiyang Li, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Offline reinforcement learning as one big sequence  modeling problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Ilya Kostrikov, Ashvin Nair, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Offline reinforcement learning with implicit q-  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06169, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='06169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Conservative q-learning for offline  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='04779, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/  2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='04779.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Chieh-Hsin Lai, Dongmian Zou, and Gilad Lerman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Robust vector quantized-variational autoen-  coder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01987, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='01987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Lisa Lee, Benjamin Eysenbach, Emilio Parisotto, Eric P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Xing, Sergey Levine, and Ruslan Salakhut-  dinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Efficient exploration via state marginal matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' CoRR, abs/1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='05274, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' URL  http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='org/abs/1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='05274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  10  Foundation Models for Decision Making Workshop at NeurIPS, 2022  Yuxi Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Deep reinforcement learning: An overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' arXiv preprint arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='07274, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Sherjil Ozair, Yazhe Li, Ali Razavi, Ioannis Antonoglou, A¨aron van den Oord, and Oriol Vinyals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Vector quantized models for planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='5  17  99  1  antmaze-  umaze  29  8  2815  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='012  1  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='125  1  0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5  100  0  antmaze-  medium  play  29  8  1204  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  1  0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='0  100  0  Table 4: Dataset statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='2  HYPERPARAMETERS  Common Hyper Parameters for Causal Transformer  hyperparameter  value  Number of layers  4  Number of attention heads  4  Embedding dimension  256  Context Length  20  Dropout  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='0  Batch Size  256  Updates between rollouts  50  lr  1e-4  gradient norm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='25  Table 5: The hyperparameters used for the causal transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='3  FEW SHOT TARGET TRAJECTORY RECONSTRUCTION  Skill DT, like other skill discovery methods, can use its state-to-skill encoder to guide its actions  towards a particular goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' In this case, we are interested in recreating target trajectories as close as  12  Foundation Models for Decision Making Workshop at NeurIPS, 2022  (a) Target Ant Skill Distribution  (b) Reconstructed Ant Skill Distribution  Figure 7: From the Ant-v2 Environment: Skill distributions of a target trajectory and the recon-  structed trajectory from rolling out in the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Because Ant-v2 is a simpler environment,  we can see that the reconstructed skill distributions are very close to the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The detailed sudocode and its description for few shot skill reconstruction can be found in  Section A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  (a) Target antmaze-umaze x-y trajectory  (b) Reconstructed antmaze-umaze x-y trajectory  (c) Target antmaze-umaze skill dist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  (d) Reconstructed antmaze-umaze skill dist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 6: From the Antmaze-Umaze Envidiverseronment: One of the longer and highest performing  trajectories in the dataset is reconstructed by Skill DT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' The trajectory is not quite identical to the  target, but it follows a similar path, where it hugs the edges of the maze just like the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Algorithm 2 Reconstructing target trajectories  Initialize target trajectory τ, skill encoder Eφ, Skill DT transformer π  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (starget  0  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', starget  T  ) ← τ,  ▷ Extract states from target trajectory  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (z0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', zT ), (zindex0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', zindexT ) = Eφ(starget  0  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', starget  T  ),  ▷ encode states  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' (Z0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', ZT ) = histogram (zindex0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=', zindexT ),  ▷ Create skill distributions by creating a  histogram of skill encoding indices  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' ˆτ ∼ π(a|Z0, z0, s0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='),  ▷ rollout in real environment, see A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5 for details  13  Doz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+page_content='000  0Foundation Models for Decision Making Workshop at NeurIPS, 2022  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='4  TRAJECTORY SKILL VISUALIZATIONS  Figure 8: Skills learned in the ant-medium-v2 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Each row corresponds to a skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 9: Skills learned in the halfcheetah-medium-replay-v2 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Each row corresponds  to a skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 10: Skills learned in the hopper-medium-replay-v2 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Each row corresponds to a  skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  14  Foundation Models for Decision Making Workshop at NeurIPS, 2022  Figure 11: Skills learned in the walker-medium-v2 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Each row corresponds to a skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  Figure 12: Skills learned in the ant-umaze-diverse-v2 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Each row corresponds to a skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='  15  Foundation Models for Decision Making Workshop at NeurIPS, 2022  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='5  EVALUATING SKILL DT’S PERFORMANCE  Because Skill DT is a purely unsupervised algorithm, to evaluate the performance in an actual en-  vironment, we perform rollouts for each skill and evaluate each to determine which is the best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' To  do this, we first populate a buffer of skills (here denoted with z) and skill histograms Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' When we  rollout in the actual environment, the causal transformer utilizes this buffer to actually make pre-  dictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' However, it updates the skill encodings that it actually sees in the environment at each  timestep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' This is because even though the policy is completely conditioned to follow a single skill,  it may end up reaching states that are classified under another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content=' Python sudocode shown below:  def generate_histogram(one_hot_skill_ids):  trajectory_length = len(one_hot_skill_ids)  histogram = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='tensor(copy(one_hot_skill_ids))  for i in range(trajectory_length-1, -1, -1):  # reverse order  if i !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='= trajectory_length - 1  histogram[i] = histogram[i] + histogram[i+1]  return histogram / histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='sum(-1) # normalize in range [0, 1]  def evaluate_skill_dt(skill_dt, env, max_steps, context_len):  num_skills = skill_dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='num_skills  rewards = []  for skill_id in range(num_skills):  skill_ids = repeat(skill_id, max_steps)  # create on_hot skill ids  # ex: one_hot([1,1], 5) = [[0, 1, 0, 0, 0],[0, 1, 0, 0, 0]]  one_hot_skill_ids = one_hot(skill_ids, num_skills)  state = env.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='reset()  # initialize_state  t = 0  total_reward = 0  state_buffer = zeros(max_steps)  z_buffer = zeros(max_steps)  while t < max_steps:  # z is vqvae embedding  # skill_id is the index of the vqvae embedding in codebook  z, skill_id = skill_dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='encode_skill(state)  one_hot_skill_ids[t] = one_hot(skill_id)  Z = skill_dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='generate_histogram(one_hot_skill_ids) # create  histograms  state_buffer[t] = state  z_buffer[t] = z  if t < context_len:  curr_states = state_buffer[t:t+context_len]  curr_z = z_buffer[t:t+context_len]  curr_Z = Z[t:t+context_len]  actions = skill_dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='causal_transformer(curr_Z, curr_z,  curr_states)  action = actions[t]  else:  curr_states = state_buffer[t-context_len+1:t+1]  curr_z = z_buffer[t-context_len+1:t+1]  curr_Z = Z[t-context_len+1:t+1]  actions = skill_dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='causal_transformer(curr_Z, curr_z,  curr_states)  action = actions[-1]  state, reward, done = env.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='step(action)  total_reward += reward  if done:  break  rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
+page_content='append(total_reward)  return max(rewards)  16' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FRT4oBgHgl3EQfezfQ/content/2301.13573v1.pdf'}
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+MNRAS 000, 1–42 (2022)
+Preprint 12 January 2023
+Compiled using MNRAS LATEX style file v3.0
+[CII] 158 𝜇m emission as an indicator of galaxy star formation rate
+Lichen Liang1,2★ , Robert Feldmann2 , Norman Murray1,3 , Desika Narayanan4,5,6 ,
+Christopher C. Hayward7 , Daniel Anglés-Alcázar8,7 , Luigi Bassini2 , Alexander J. Richings9,10
+Claude-André Faucher-Giguère11 , Dongwoo T. Chung1,12 , Jennifer Y. H. Chan1,12 ,
+Onur Çatmabacak2 , Dušan Kereš13 , Philip F. Hopkins14
+1Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
+2Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, Zurich CH-8057, Switzerland
+3Canada Research Chair in Theoretical Astrophysics
+4Department of Astronomy, University of Florida, 211 Bryant Space Sciences Center, Gainesville, FL 32611, USA
+5University of Florida Informatics Institute, 432 Newell Drive, CISE Bldg E251, Gainesville, FL 32611, USA
+6Cosmic Dawn Center at the Niels Bohr Institute, University of Copenhagen and DTU-Space, Technical University of Denmark, Denmark
+7Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
+8Department of Physics, University of Connecticut, 196 Auditorium Road, U-3046, Storrs, CT 06269-3046, USA
+9E. A. Milne Centre for Astrophysics, University of Hull, Cottingham Road, Hull, HU6 7RX, UK
+10DAIM, University of Hull, Cottingham Road, Hull, HU6 7RX, UK
+11Department of Physics and Astronomy and CIERA, Northwestern University, Evanston, IL 60208, USA
+12Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
+13Department of Physics, Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093, USA
+14TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
+Accepted 2022. Received 2022; in original form 2022
+ABSTRACT
+Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity
+(𝐿 [CII]) and star formation rate (SFR), suggesting that 𝐿 [CII] may be a useful SFR tracer for galaxies. Some other galaxy
+populations, however, are found to have lower 𝐿 [CII]/SFR than the local SFGs, including the infrared-luminous, starburst
+galaxies at low and high redshifts, as well as some moderately star-forming galaxies at the epoch of re-ionization (EoR). The
+origin of this ‘[CII] deficit’ is unclear. In this work, we study the 𝐿 [CII]-SFR relation of galaxies using a sample of 𝑧 = 0−8 galaxies
+with 𝑀∗ ≈ 107 − 5 × 1011 𝑀⊙ extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic
+Environments (FIRE) project. We find a simple analytic expression for 𝐿 [CII]/SFR of galaxies in terms of the following parameters:
+mass fraction of [CII]-emitting gas ( 𝑓[CII]), gas metallicity (𝑍gas), gas density (𝑛gas) and gas depletion time (𝑡dep = 𝑀gas/SFR).
+We find two distinct physical regimes, where 𝑡dep (𝑍gas) is the main driver of the [CII] deficit in H2-rich (H2-poor) galaxies.
+The observed [CII] deficit of IR-luminous galaxies and early EoR galaxies, corresponding to the two different regimes, is due to
+short gas depletion time and low gas metallicity, respectively. Our result indicates that [CII] deficit is a common phenomenon
+of galaxies, and caution needs to be taken when applying a constant 𝐿 [CII]-to-SFR conversion factor derived from local SFGs to
+estimate cosmic SFR density at high redshifts and interpret data from upcoming [CII] line intensity mapping experiments.
+Key words: evolution — galaxies: high-redshift — galaxies: ISM — infrared: galaxies
+1 INTRODUCTION
+The census of cosmic star formation from the present day to the
+highest redshifts imposes a key constraint on galaxy evolution theory
+and physical cosmology (see e.g., Madau & Dickinson 2014; Dayal
+& Ferrara 2018, and references therein). The rest-frame ultra-violet
+(UV) luminosity (𝐿UV) of galaxies, tracing the young, massive stars,
+is a common star formation rate (SFR) indicator of galaxies. How-
+ever, a large fraction of the UV light from galaxies in the Universe
+is absorbed by interstellar dust and gets re-emitted as thermal ra-
+diation at far-infrared (far-IR) wavelength (e.g. Fixsen et al. 1998;
+★ Email: lliang@cita.utoronto.ca
+Takeuchi et al. 2005; Dole et al. 2006; Magnelli et al. 2009; Gruppi-
+oni et al. 2013; Burgarella et al. 2013; Whitaker et al. 2017; Salim
+& Narayanan 2020). Therefore, an accurate estimate of the cosmic
+SF history depends on a multi-wavelength, UV-to-millimetre (mm)
+analysis that accounts for both the direct, unobscured stellar light and
+the dust thermal emission of galaxies over cosmic time.
+In practice, however, our capability of constraining the two com-
+ponents of stellar radiation is largely imbalanced (e.g. Casey et al.
+2018a). While the rest-frame UV-based, unobscured component has
+been constrained to as early as redshift 𝑧 ∼ 15 (e.g. Bouwens et al.
+2007, 2011, 2015, 2019; Oesch et al. 2012, 2016, 2018; Ellis et al.
+2013; McLure et al. 2013; Finkelstein et al. 2015; McLeod et al. 2015;
+Bowler et al. 2020; Leethochawalit et al. 2022a,b; Naidu et al. 2022;
+© 2022 The Authors
+arXiv:2301.04149v1  [astro-ph.GA]  10 Jan 2023
+
+2
+Liang et al.
+Donnan et al. 2022; Harikane et al. 2022) through deep imaging with
+the Hubble and the James Webb Space Telescopes, the obscured com-
+ponent is still not well constrained beyond 𝑧 ∼ 3 due to the lack of
+statistically-representative, unbiased galaxy samples in that regime
+(Casey et al. 2014; Casey et al. 2018a; Dayal & Ferrara 2018; Zavala
+et al. 2021). It is therefore important to have other SFR diagnostics
+in addition to UV+IR for early galaxies (see e.g. Khusanova et al.
+2021, and references therein).
+The 158 𝜇m (1900.5 GHz) fine structure transition (2𝑃3/2 →
+2𝑃1/2) of singly ionized carbon ([CII]) has been thought as a promis-
+ing alternative SFR indicator, particularly for high-𝑧 galaxies (Hodge
+& da Cunha 2020). It is a major coolant of the neutral atomic gas of
+the interstellar medium (ISM) and the strongest emission line of star-
+forming galaxies at rest-frame far-IR wavelength (Carilli & Walter
+2013). The [CII] line of galaxies is usually not much affected by dust
+extinction.
+To first order, a correlation between 𝐿[CII] and global SFR of
+galaxies is expected. Much of the [CII] emission of galaxy originates
+from the neutral atomic gas regions (Hollenbach & Tielens 1999;
+Wolfire et al. 2003; Ferrara et al. 2019), where the far-UV (FUV)
+photons produced by the young O and B-type stars heat the gas via the
+photoelectric (PE) effect on small dust grains and polycyclic aromatic
+hydrocarbon (PAH) molecules (Tielens & Hollenbach 1985; Hollen-
+bach et al. 1991; Weingartner & Draine 2001a; Helou et al. 2001).
+The photo-electrons ejected from the dust grains/PAH molecules
+collisionally couple to and heat the gas. Since the PE heating rate
+( �𝐸PE) traces galaxy SFR, and 𝐿[CII] balances �𝐸PE given that [CII]
+line is the dominant coolant in those regions (assuming a thermal
+equilibrium), 𝐿[CII] should therefore be correlated to SFR. Obser-
+vations of local star-forming galaxies (SFGs) have indeed found a
+linear correlation between 𝐿[CII] and SFR over the broad SFR range
+of ≈ 10−4 − 10 𝑀⊙ yr−1 (e.g. Stacey et al. 1991; Leech et al. 1999;
+Boselli et al. 2002; De Looze et al. 2011, 2014; Herrera-Camus et al.
+2015). These observations suggest that the [CII] line can be a useful
+SFR indicator for galaxies.
+There is evidence, however, showing that this scaling relation-
+ship does not hold on all occasions. For instance, observations find
+that local ultra-luminous infrared galaxies (ULIRGs, galaxies having
+𝐿IR >∼ 1012 𝐿⊙) show a significant lower 𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR)
+ratio than normal star-forming galaxies by up to an order of magni-
+tude (Malhotra et al. 1997, 2001; Luhman et al. 1998, 2003; Brauher
+et al. 2008; Farrah et al. 2013; Magdis et al. 2014), the so-called ‘[CII]
+deficit’ problem. This result was at first revealed with the Infrared
+Space Observatory (ISO; Kessler et al. 1996) and later confirmed
+by observations with the Herschel Space Observatory (hereafter
+Herschel; Pilbratt et al. 2010) that has improved far-IR observing
+capabilities. Subsequent observations with Herschel also show that
+the [CII] deficit extends to lower 𝐿IR and that the 𝐿[CII]/𝐿IR ratio
+of galaxies exhibits a continuous decrease with increasing 𝐿IR at
+𝐿IR >∼ 1011 𝐿⊙ (e.g. Graciá-Carpio et al. 2011; Sargsyan et al. 2012;
+Díaz-Santos et al. 2013; Cormier et al. 2015; Herrera-Camus et al.
+2015, 2018; Díaz-Santos et al. 2017; Hughes et al. 2017; Contursi
+et al. 2017).
+Studies have investigated the 𝐿[CII]-SFR relation of galaxies at
+higher redshifts (e.g. Stacey et al. 2010; Gullberg et al. 2015, 2018;
+Brisbin et al. 2015; Spilker et al. 2016; Zanella et al. 2018; Cooke
+et al. 2018; Rybak et al. 2019; McKinney et al. 2020). At 𝑧 ≈ 1−5, the
+selected galaxies are mostly uncovered by sub-mm surveys, which are
+traditionally classified as ‘sub-millimetre-bright galaxies (SMGs1)’.
+1 In the literature, ‘SMGs’ typically refer to the galaxies detectable by single-
+These are heavily dust-obscured systems having 𝐿IR >∼1012 𝐿⊙ (cor-
+responding to SFR >∼ 100 𝑀⊙ yr−1; Kennicutt 1998). In general, it is
+found that [CII] deficit persists at high 𝐿IR at high redshifts, although
+the high-𝑧 populations appear to show larger scatter of 𝐿[CII]/SFR
+at given 𝐿IR than the local ones.
+The advent of the Atacama Large Millimetre/submillimetre Array
+(ALMA) Telescope (e.g. Wootten & Thompson 2009) has triggered
+particular interest in searching for [CII] emitters at 𝑧 >∼ 5, and accu-
+mulating efforts have been made to constrain the 𝐿[CII]-SFR relation
+of galaxies at this epoch (e.g. Ouchi et al. 2013; Ota et al. 2014;
+Maiolino et al. 2015; Capak et al. 2015; Willott et al. 2015b; Penter-
+icci et al. 2016; Matthee et al. 2017, 2019; Carniani et al. 2018a; Smit
+et al. 2018; Schaerer et al. 2020; Fujimoto et al. 2021; Ferrara et al.
+2022; Schouws et al. 2022a). The ALMA observational programs are
+often designed to target the Lyman-𝛼 emitters (LAEs), Lyman-break
+galaxies (LBGs) and the quasar host galaxies (hereafter quasar hosts
+for simplicity) having pre-determined redshift (Hodge & da Cunha
+2020). Though the earliest attempts targeting the bright LAEs were
+mostly unsuccessful (e.g. Maiolino et al. 2005; Ouchi et al. 2013;
+Ota et al. 2014; Inoue et al. 2016), follow-up programs targeting the
+LBGs and quasar hosts generally have had much higher success rate
+of [CII] line detection. Overall, there have been > 200 galaxies at
+𝑧 >∼ 5 that have confirmed detection of [CII] line to date. While the
+quasar hosts are typically very luminous and have substantial SFR
+(e.g. Bañados et al. 2016; Decarli et al. 2018; Venemans et al. 2020),
+many of the selected LBGs/LAEs at 𝑧 >∼ 5 are normal star-forming
+galaxies having moderate SFR (≈ 10 𝑀⊙ yr−1). In particular, the
+ALMA Large Program to INvestigate [CII] at Early times (ALPINE)
+survey (Le Fèvre et al. 2020; Béthermin et al. 2020; Faisst et al.
+2020a) in Cycle-5, targeting a sample of 118 star-forming galaxies at
+𝑧 ≈ 5 − 6, has contributed more than a third (∼ 75/200) of the total
+number of successful detections at 𝑧 >∼ 5 (Schaerer et al. 2020). More
+recently, the ALMA Reionization Era Bright Emission Line Survey
+(REBELS; Bouwens et al. 2022) in Cycle-7 has targeted a sample of
+40 UV-bright, star-forming galaxies at 𝑧 ≈ 7 and confirmed [CII]
+line detection for 18 galaxies in their sample (Ferrara et al. 2022).
+Observations have drawn divergent conclusions on the 𝐿[CII]-SFR
+relation at 𝑧 >∼ 5. While some have argued a clear [CII] deficit of
+galaxies at 𝑧 >∼ 5 with respect to the local normal SFGs (e.g. Ouchi
+et al. 2013; Ota et al. 2014; Maiolino et al. 2015; Inoue et al. 2016;
+Knudsen et al. 2016; Pentericci et al. 2016; Bradač et al. 2017; Ferrara
+et al. 2019; Laporte et al. 2019; Carniani et al. 2020; Fujimoto et al.
+2022), others have argued that they follow the same linear scaling
+relation (e.g. Matthee et al. 2017; Carniani et al. 2018a; Schaerer
+et al. 2020; Fujimoto et al. 2021; Ferrara et al. 2022; Schouws et al.
+2022a). It should be noted, however, that the SFR estimates at such
+high redshifts can be highly uncertain. Galaxies at 𝑧 >∼ 5 typically
+have very few reliable photometric data points in the dust thermal
+continuum that are measured with ALMA (at band 6 or 7). A number
+of recent studies, both observational (Capak et al. 2015; Bouwens
+et al. 2016; Casey et al. 2018a; Faisst et al. 2020b) and theoretical
+(Liang et al. 2019, 2021; Ma et al. 2019; Sommovigo et al. 2020,
+2021), have pointed out that based on the ALMA broad-band flux(es)
+alone, 𝐿IR (and hence the obscured SFR) of galaxies at 𝑧 >∼5 is likely
+to be poorly constrained due to the large variation in the shape of
+the spectral energy distribution (SED) of their dust emission. The
+reported (in)consistencies of the 𝐿[CII]-SFR relation at 𝑧 >∼5 with the
+dish sub-mm telescopes, of which the observed sub-mm flux density is above
+∼ 1 mJy (Casey et al. 2014; Hodge & da Cunha 2020).
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+3
+local SFGs by the observations therefore need to be more carefully
+assessed.
+Much effort has been made to model [CII] emission of galaxies
+and explain the origins of the observed [CII] deficit over the last
+two decades. A broad variety of different methods are used by dif-
+ferent studies, including pure analytic approaches (e.g. Muñoz & Oh
+2016; Ferrara et al. 2019), numerical models of idealized gas clouds
+(e.g. Abel et al. 2009; Narayanan & Krumholz 2017), semi-analytic
+galaxy models (SAMs, e.g. Popping et al. 2014, 2016, 2019; Lagache
+et al. 2018; Yang et al. 2021, 2022) and cosmological hydrodynamic
+galaxy simulations (e.g. Vallini et al. 2013, 2015; Olsen et al. 2015,
+2017; Pallottini et al. 2017, 2019; Katz et al. 2019; Leung et al. 2020;
+Lupi et al. 2020; Lupi & Bovino 2020; Kannan et al. 2022; Richings
+et al. 2022; Bisbas et al. 2022). A pure analytic approach and/or a
+simplified cloud model can capture the key physical mechanisms that
+determine 𝐿[CII] of galaxies and provide useful insights at low com-
+putational cost, but does not provide the necessary galaxy statistics.
+SAMs can produce statistically significant galaxy samples probing a
+very wide dynamic range (in stellar mass, SFR, redshift and etc.) and
+are computationally efficient (Somerville & Davé 2015), but they do
+not provide any information of structures on the sub-galactic scales.
+Hydrodynamic simulations, in contrast, can calculate the detailed
+sub-galactic structures and thus provide more accurate prediction
+for the [CII] emission properties of galaxies, at the cost of more
+computational expense.
+Different explanations for the [CII] deficit in the high 𝐿IR regime
+have been proposed by the theory groups (see also e.g. Casey et al.
+2014; Narayanan & Krumholz 2017, for a summary). For instance,
+some studies argue that the deficit is due to a strong UV radiative
+intensity (𝐺) in the IR luminous galaxies (e.g. Malhotra et al. 1997;
+Luhman et al. 1998; Genzel & Cesarsky 2000; Helou et al. 2001;
+Luhman et al. 2003; Abel et al. 2009; Stacey et al. 2010; Graciá-
+Carpio et al. 2011; Lagache et al. 2018). This can have two important
+effects on the thermal balance of [CII]-emitting gas. First of all, a
+high 𝐺 leads to large positive grain charges, thereby reducing the
+kinetic energy of the ejected photo-electrons and hence the rate of
+PE heating ( �𝐸PE) of gas (Tielens & Hollenbach 1985; Kaufman et al.
+1999). As a result, [CII] cooling rate drops. Besides, HII regions in
+those galaxies may become ‘dust bounded’ rather than ‘ionization
+bounded’ (e.g. Bottorff et al. 1998; Abel et al. 2009; see also Ferrara
+et al. 2019). In this scenario, most of the UV radiation from young
+stars is absorbed by dust in the HII regions, leading to both an excess
+of IR emission in the HII regions and a reduced �𝐸PE (and hence
+𝐿[CII]) in gas outside the HII regions due to a starvation of UV
+photons there.
+Alternatively, Narayanan & Krumholz (2017) suggest that a high
+gas density can lead to a [CII] deficit of galaxy in addition to having
+a high 𝐺. Using a stratified gas cloud model, the authors demonstrate
+that with increasing gas density, a larger fraction of carbon in gas
+turns into neutral (i.e. in CO and CI) and 𝐿[CII] decreases due to a
+reduced mass fraction of [CII]-emitting gas.
+Apart from these studies, Muñoz & Oh (2016) posit an analytic
+model where [CII] deficit is due to thermal saturation of the upper fine
+structure transition state (2𝑃3/2) of CII ions2. At above 91.8 K (note:
+𝑇∗ = 91.8 K is the equivalent temperature of the [CII] transition),
+𝐿[CII] does not increase much with gas kinetic temperature and this
+has been suggested to be the reason for 𝐿[CII] not increasing much
+2 Throughout this paper, we use ‘[CII]’ when referring to the observable
+emission line, and ‘CII’ when discussing ionized carbon under the context of
+chemical abundances of gas.
+with SFR at high 𝐿IR (∼ SFR). Note, however, that the Muñoz & Oh
+(2016) model assumes that the bulk of the [CII] emission of galaxies
+originates from the gas having density in excess of the critical density
+for the [CII] transition (Goldsmith et al. 2012).
+With the recent success of the ALMA programs in searching for
+[CII]-emitters, there has been an increasing amount of effort to pre-
+dict [CII] emission properties of galaxies at 𝑧 >∼ 5 by coupling cos-
+mological hydrodynamic simulations or SAMs with photo-ionization
+codes (e.g. CLOUDY, Ferland et al. 1998, 2013; DESPOTIC, Krumholz
+2014; RADMC-3D, Dullemond et al. 2012). The predicted 𝐿[CII]-SFR
+relation for galaxies, however, shows non-trivial discrepancy between
+different groups in both normalization and slope (see summary in
+e.g. Katz et al. 2019; Leung et al. 2020), which can be ascribed to
+the differences in the simulation methodology and [CII] modelling
+techniques adopted by the different groups. Despite the discrepancy,
+many have predicted a [CII] deficit of galaxies at 𝑧 >∼5 with respect to
+the local normal star-forming galaxies. For instance, Lagache et al.
+(2018) couple a sample of ∼ 20 K SAM galaxies at 4 ≤ 𝑧 ≤ 8
+with CLOUDY and report a [CII] deficit of > 0.5 dex and a trend of
+decreasing normalization of the relation with redshift. Olsen et al.
+(2017) post-process 30 star-forming galaxies at 𝑧 = 6 extracted from
+the MUFASA ‘zoom-in’ simulations (Davé et al. 2016) using CLOUDY
+and predict a [CII] deficit of about one decade. A similarly strong
+[CII] deficit is reported by Pallottini et al. (2017, 2019) using the
+SERRA ‘zoom-in’ simulations that include more sophisticated chem-
+ical networks. More recently, Kannan et al. (2022) predict an even
+more prominent [CII] deficit at 𝑧 ≥ 5 than the above-mentioned ear-
+lier studies, especially at low SFR, using a galaxy sample produced
+by the THESAN ‘zoom-in’ suite, which includes the Illustris-TNG
+galaxy formation model (Pillepich et al. 2018a,b).
+It has been generally thought that gas metallicity (𝑍gas) is the key
+factor in determining the [CII] luminosity of the early galaxies (e.g.
+Vallini et al. 2015; Olsen et al. 2017; Ferrara et al. 2019) since [CII]
+emissivity is linearly scaled with 𝑍gas. The early work by Vallini et al.
+(2015) shows that the 𝐿[CII]-SFR relation of EoR galaxies depends
+sensitively on 𝑍gas, and the significant [CII] deficit found with the
+LAEs at 𝑧 ≈ 5−7, such as Himiko (Ouchi et al. 2013; Ota et al. 2014)
+and IOK-1 (Ota et al. 2014), can be well accounted for by assigning
+a very low gas metallicity (𝑍gas < 0.05 𝑍⊙) to the simulated galaxy
+in an ad hoc manner. The [CII] deficit of galaxies at 𝑧 >∼ 5 commonly
+found in the recent simulations, as mentioned above, is likely due to
+the much lower 𝑍gas of the early galaxies than the 𝑧 = 0 ones predicted
+by these simulations. Observationally, however, direct measurement
+of 𝑍gas at 𝑧 >∼ 5 is still very challenging, though some preliminary
+attempts have been made recently (e.g. Rigopoulou et al. 2018; Curti
+et al. 2022; Heintz et al. 2022a,b; Rhoads et al. 2022; Schaerer et al.
+2022; Trump et al. 2022).
+A few recent studies have predicted [CII] emission of galaxies at
+lower redshifts using simulations. For instance, Popping et al. (2019)
+and Yang et al. (2021) predict the 𝐿[CII]-SFR relation for the catalog
+derived from the ‘Santa Cruz’ semi-analytic models (Somerville &
+Primack 1999; Somerville et al. 2015) using DESPOTIC. Their result
+is in good agreement with the observational data at 𝑧 ≈ 2, except
+that at high SFR (i.e. SFR >∼ 10 𝑀⊙ yr−1), they produce a noticeably
+weaker [CII] deficit than is observed. More recently, Richings et al.
+(2022) ran a set of hydrodynamic simulations of isolated (dwarf
+and Milky Way-mass) galaxies implemented with the CHIMES non-
+equilibrium chemistry module (Richings et al. 2014a,b) (including a
+dust-depletion model) and predict the [CII] emission of their galaxy
+sample using RADMC-3D. Despite having a small sample size, the
+predicted 𝐿[CII] of their galaxies appears to be in agreement with
+the observational result of local galaxies (e.g. De Looze et al. 2011,
+MNRAS 000, 1–42 (2022)
+
+4
+Liang et al.
+2014; Herrera-Camus et al. 2015) at similar SFR (see also another
+recent work by Bisbas et al. 2022 using isolated dwarf simulations).
+Apart from these studies, there has been limited effort to predict
+the 𝐿[CII]-SFR relation of galaxies at 𝑧 = 0 − 5 using statistically
+representative galaxy samples and compare the result to the fruitful
+observational data in this regime. In particular, the origin of the [CII]
+deficit of the IR-luminous galaxies has not yet been studied in detail
+using cosmological hydrodynamic simulations. This is largely be-
+cause producing a statistically representative sample in this regime
+with well-resolved ISM is computationally demanding, which is pos-
+sible only for a few large simulation consortiums. It is, however, of
+critical importance that a robust [CII] model should be able to simul-
+taneously reproduce the data of different galaxy populations over the
+entire SFR and redshift ranges.
+In this study, we conduct a comprehensive analysis of the galaxy
+𝐿[CII]-SFR relation using a simulated sample spanning an unprece-
+dentedly broad redshift range of 𝑧 = 0−8 extracted from the Massive-
+FIRE (Feldmann et al. 2016, 2017; Anglés-Alcázar et al. 2017) and
+FIREbox (Feldmann et al. 2022) cosmological hydrodynamic simu-
+lations from the Feedback in Realistic Environments (FIRE) project3
+(Hopkins et al. 2014, 2018; Hopkins et al. 2022). The sample cov-
+ers a very broad range of galaxy stellar mass and SFR, allowing
+us to make direct comparison with the observational data in differ-
+ent regimes. In particular, the sample includes local normal SFGs
+(having SFR ≈ 0.1 − 10 𝑀⊙ yr−1) that can be compared with the
+observations where a linear 𝐿[CII]-SFR correlation has been found
+by the observations. It also includes IR-luminous (𝐿IR > 1011 𝐿⊙)
+galaxies at 𝑧 = 0 − 5 that are candidates for (U)LIRGs and SMGs,
+where observations have shown to have [CII] deficit. Moreover, the
+sample includes early galaxies at above 𝑧 = 5 spanning a broad SFR
+range. Many of these galaxies have similar mass and SFR to the
+samples of the ALPINE and REBELS projects and therefore can be
+used to provide useful interpretations for a variety of their recent
+observational results (e.g. Fujimoto et al. 2020; Ginolfi et al. 2020;
+Schaerer et al. 2020; Fudamoto et al. 2021, 2022; Ferrara et al. 2022;
+Sommovigo et al. 2022).
+The main goal of this work is to predict the 𝐿[CII]-SFR relation
+for the FIRE galaxy sample (spanning 𝑧 = 0 − 8 and SFR ≈ 0.1 −
+103 𝑀⊙ yr−1) and to understand what physical parameters of galaxies
+determine their overall 𝐿[CII]-to-SFR ratio. This will then help us
+find the origin of the observed [CII] deficit of galaxies at both high
+𝐿IR and high redshifts.
+Note that the results from this work will be useful for interpreting
+the data of several upcoming [CII] line intensity mapping (LIM)
+experiments (see e.g. Kovetz et al. 2017, 2019; Bernal & Kovetz
+2022, and references therein), such as TIME4 (Crites et al. 2014; Sun
+et al. 2021), CCAT-prime5 (CCAT-Prime collaboration et al. 2021),
+CONCERTO6 (CONCERTO Collaboration et al. 2020; Gkogkou et al.
+2022) and EXCLAIM (Ade et al. 2020). The LIM experiments have
+been designed to measure the emission from spectral lines originat-
+ing from galaxies at all luminosities, including the ones that cannot be
+resolved by the current surveys (e.g. with ALMA). The experiments
+that will target [CII] emission, in particular, will be useful for con-
+straining the cosmic star-formation history (see e.g. Gong et al. 2012;
+Silva et al. 2015; Serra et al. 2016; Fonseca et al. 2017; Padmanabhan
+2019; Yue & Ferrara 2019; Chung et al. 2020; Padmanabhan et al.
+3 FIRE project website: http://fire.northwestern.edu
+4 https://cosmology.caltech.edu/projects/TIME
+5 http://www.ccatobservatory.org
+6 https://www.apex-telescope.org/ns/concerto/
+2022; Sun et al. 2022; ?). It is, however, not yet certain whether the
+[CII] line always acts as a reliable SFR tracer for galaxies of all types
+and at all redshifts.
+This paper is structured as follows. We describe in Section 2 the
+simulation methodology and in Section 3, the method used to simu-
+late [CII] emission. In Section 4, we compare the predicted 𝐿[CII]-
+SFR relation of the FIRE galaxy sample with the observational data at
+different redshifts. In Section 5, we investigate the origin of the tight
+𝐿[CII]-SFR linear scaling relation of normal star-forming galaxies
+at 𝑧 = 0 and the causes of the [CII] deficit of galaxies. We discuss
+our results in Section 6 and finally summarize and conclude this
+study in Section 7. Throughout this paper, we adopt the cosmologi-
+cal parameters of the Planck 2015 Cosmology (Planck Collaboration
+et al. 2016), specifically Ωm = 0.309, ΩΛ = 0.691, Ωb = 0.049,
+𝜎8 = 0.816, and 𝐻0 = 67.74 km s−1 Mpc−1.
+2 SIMULATION METHODOLOGY
+In this section, we introduce the simulation suites (FIREbox and
+MassiveFIRE) from which we extract the galaxy sample used for this
+study.
+2.1 Simulation set-up and galaxy catalogue
+We adopt a sample that spans the wide redshift range 𝑧 = 0−8, stellar
+mass (𝑀∗) range 𝑀∗ ≈ 107−5×1011 𝑀⊙ and SFR range SFR ≈ 0.1−
+103 𝑀⊙ yr−1. The sample consists primarily of galaxies at 𝑧 = 0 − 8
+produced by FIREbox (Feldmann et al. 2022), the new-generation
+simulation suite of FIRE run with full cosmological volume boxes. It
+is supplemented by a number of high-𝑧 (𝑧 = 1 − 8) massive galaxies
+(𝑀∗ >∼ 1010 𝑀⊙) extracted from the ‘zoom-in’ suite, MassiveFIRE
+(Feldmann et al. 2016, 2017), rerun with FIRE-2 physics (Anglés-
+Alcázar et al. 2017; Çatmabacak et al. 2022; Bassini et al. 2022).
+Many of the MassiveFIRE galaxies have the 𝐿IR close to that of the
+SMGs (Liang et al. 2018; Cochrane et al. 2019) that are used by the
+observational studies on the 𝐿[CII]-SFR relation at high redshifts. All
+simulations used for this study are run with the same FIRE-2 physics
+and numerics (Hopkins et al. 2018).
+FIREbox simulations
+FIREbox (Feldmann et al. 2022) is a new-generation simulation suite
+using FIRE physics. Different from all previous simulations of FIRE,
+FIREbox simulates full cosmological volumes instead of using ‘zoom-
+in’ set-up to study galaxy evolution. FIREbox simulations are run
+in cubic boxes with periodic boundary conditions, and with initial
+conditions at redshift 𝑧 = 120 generated using the MUSIC (Multi-
+Scale Initial Conditions) code (Hahn & Abel 2011). The simulations
+use the Planck 2015 Cosmology (Planck Collaboration et al. 2016).
+All FIREbox simulations use the same initial conditions and cos-
+mology but differ in numerical resolution. For this study, we extract
+galaxies from the fiducial FIREbox hydrodynamic simulation, which
+is run with a box length of 15 ℎ−1 cMpc and with the following
+number of dark matter (DM) and baryonic particles: 𝑁DM = 10243
+and 𝑁b = 10243. The mass resolution of DM and baryon particles
+are 𝑚DM = 3.3 × 105 and 𝑚b = 6.3 × 104 𝑀⊙. The gravitational
+softening lengths are kept fixed in proper (comoving) coordinates at
+𝑧 ≤ 9 (𝑧 ≥ 9) and are set to ℎDM = 80 pc for DM particles and
+ℎ∗ = 12 pc for star particles. The softening length for gas particles
+(ℎgas) is fully adaptive and is set equal to their kernel smoothing
+length down to a minimum of 1.5 proper pc, which is reached in the
+densest parts of the ISM. FIREbox is evolved down to 𝑧 = 0.
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+5
+SFR > 10 M⊙ yr−1
+Total
+z = 8
+FIREBox galaxies
+z = 6
+z = 4
+z = 2
+z = 1
+z = 0
+z = 3
+Figure 1. Histograms of the stellar mass distribution of the FIREbox sample
+at different redshifts. Violet, green, magenta, blue, red, yellow and cyan
+histograms correspond to 𝑧 = 8, 𝑧 = 6, 𝑧 = 4, 𝑧 = 3, 𝑧 = 2, 𝑧 = 1 and 𝑧 = 0,
+respectively. For each redshift, the unfilled histograms indicate the result of
+the entire galaxy sample, whereas the filled histograms indicate specifically
+the result of the galaxies having SFR ≥ 10 𝑀⊙ yr−1 (corresponding to 𝐿IR >∼
+1011 𝐿⊙ based on the Kennicutt 1998 relation. Note: [CII] deficit is observed
+at 𝐿IR >∼ 1011 𝐿⊙.). For clarity of presentation, we separately show the result
+of the 7 snapshots in 3 separate panels (top panel for 𝑧 = 8 and 𝑧 = 6, middle
+panel for 𝑧 = 3 and 𝑧 = 4 and bottom panel for 𝑧 = 0, 𝑧 = 1 and 𝑧 = 2).
+We identify galaxies in different snapshots of the FIREbox simula-
+tion using the AMIGA Halo Finder7 (AHF; Gill et al. 2004; Knollmann
+& Knebe 2009). We use the galaxies extracted from 7 snapshots cor-
+responding to redshift 𝑧 = 0, 1, 2, 3, 4, 6 and 8. For each snapshot,
+we include the central galaxy of the 30 most massive halos iden-
+tified by AHF. To enlarge our sample, we also include the central
+galaxy of a number of additional, randomly chosen halos having
+log (𝑀vir/𝑀⊙) > 10. We show in Fig. 1 the histograms of the 𝑀∗
+distribution of the selected FIREbox galaxies at different redshifts.
+The number of galaxies selected at 𝑧 = 0, 1, 2, 3, 4, 6, and 8 are
+113, 84, 80, 75, 64, 61 and 30, respectively. As is shown in Fig. 1,
+all but a few selected galaxies have stellar mass greater than 107 𝑀⊙
+(corresponding to ∼ 160 times of the mass resolution). The most
+7 Code available at: popia.ft.uam.es/AHF/Download.html
+massive galaxy of the FIREbox sample has 𝑀∗ = 4.8 × 1011 𝑀⊙ (at
+𝑧 = 0).
+In the same figure, we also show the 𝑀∗ distribution of the galaxies
+having SFR >∼ 10 𝑀⊙ yr−1 (filled histograms). These galaxies have
+𝐿IR ≥ 1011 𝐿⊙, the regime where a [CII] deficit is observed (see
+Section 3). They apparently are more massive than the galaxies hav-
+ing SFR < 10 𝑀⊙ yr−1. In our catalogue, we find most galaxies with
+SFR ≥ 10 𝑀⊙ yr−1 at 𝑧 = 2 (red histogram, 𝑁 = 29) and 𝑧 = 3
+(blue histogram, 𝑁 = 28). These redshifts are at the ‘cosmic noon’,
+where massive galaxies start to form and they are more gas-rich and
+actively star-forming than galaxies at lower redshifts.
+Since the
+FIREbox simulation is run with a volume of
+(15 ℎ−1cMpc)3, it does not produce enough galaxies at high redshifts
+that are as massive and luminous as the galaxy samples selected by
+the observational studies. We therefore supplement our sample with a
+handful of more massive galaxies (𝑀∗ ≈ 109−5×1011 𝑀⊙) extracted
+from the MassiveFIRE ‘zoom-in’ simulations (see below).
+MassiveFIRE simulations
+MassiveFIRE (Feldmann et al. 2016, 2017) is a set of simulations
+of massive galaxies at high redshifts using the ‘zoom-in’ method. A
+number of low-resolution (LR) DM-only simulations were run with
+the initial conditions generated using the MUSIC code within periodic
+boxes. From the outputs of these LR DM-runs, we then select a
+number of model haloes to re-simulate at much higher resolution and
+with baryons included (HR runs). The selected haloes have a variety
+of masses, accretion history, and environmental over-densities.
+For this study, we use the galaxies produced by 10 MassiveFIRE
+simulations, which are from the A (Anglés-Alcázar et al. 2017), D and
+E Series (Çatmabacak et al. 2022; Bassini et al. 2022). The A, D and
+E Series were run in the periodic boxes with size of (100 ℎ−1 Mpc)3,
+(400 ℎ−1 Mpc)3 and (762 ℎ−1 Mpc)3, respectively. The model haloes
+of the A Series are selected from the snapshot of 𝑧final = 1, those
+of the D and E Series are selected from the snapshot of 𝑧final = 6.
+All the HR runs were run down to 𝑧final except D7, where the HR
+run is evolved to only 𝑧 = 7.2. This is because part of the ISM in
+D7 became too compact so that the gas particles with the highest
+densities were evolved at extremely small time-steps and it became
+infeasible to run the simulation down to the target redshift.
+Initial conditions for the HR runs are set up using a convex hull
+surrounding all particles within 3𝑅vir at 𝑧final of the chosen halo
+defining the Lagrangian HR region following the method of Hahn &
+Abel (2011). The mass resolutions and force softening lengths of the
+HR runs are similar to those of the FIREbox simulation. Specifically,
+𝑚DM and 𝑚b are set to 1.9 × 105 𝑀⊙, 3.6 × 104 𝑀⊙, respectively.
+Both ℎDM and ℎ∗ are fixed in proper (comoving) coordinates at 𝑧 ≤ 9
+(𝑧 ≥ 9) and are set equal to 57 pc and 7 pc, respectively. ℎgas is set
+equal to the smoothing length of the gas particles down to a minimum
+of 0.7 proper pc.
+We include the central galaxy of the chosen haloes at 𝑧final except
+for that of the D7 run. In addition, we also include the most massive
+progenitors (MMPs) of the central galaxies at higher redshifts.
+Specifically, for the 4 A Series runs, we include the MMPs at 𝑧 = 2,
+𝑧 = 3 and 𝑧 = 4, while for the D and E Series, we include the MMPs
+at 𝑧 = 8. The galaxies are identified in the simulation snapshots
+using AHF (Gill et al. 2004; Knollmann & Knebe 2009). In Table 1,
+we summarize the information8 of the 10 MassiveFIRE simulations
+8 Physical properties, including e.g. 𝑀∗ , SFR, 𝐿IR and 𝐿[CII], of the FIRE
+galaxies reported in this paper are estimated using a radial kernel of 0.1𝑅vir
+MNRAS 000, 1–42 (2022)
+
+25
+20
+10
+5
+-
+6
+8
+9
+10
+11
+7
+12
+log (Mstar/Mo)2025
+20
+10
+5
+8
+9
+10
+11
+6
+12
+log (Mstar/Mo)25
+20
+gal
+10
+5
+6
+8
+9
+10
+11
+12
+log (Mstar/Mo)6
+Liang et al.
+Table 1. List of MassiveFIRE simulations used for this work.
+Sim ID †
+Box Size
+𝑧final
+𝑀vir ‡
+𝑀∗ (𝑀⊙)
+(ℎ−1 Mpc)
+(1012 𝑀⊙)
+𝑧 = 1
+𝑧 = 2
+𝑧 = 3
+𝑧 = 4
+𝑧 = 6
+𝑧 = 8
+A1
+100
+1
+2.4
+5.4 × 1011
+5.1 × 1010
+9.6 × 109
+1.2 × 109
+/
+/
+A2
+100
+1
+3.0
+4.1 × 1011
+2.9 × 1011
+1.3 × 1011
+2.7 × 1010
+/
+/
+A4
+100
+1
+2.9
+2.3 × 1011
+1.3 × 1011
+2.2 × 1010
+6.5 × 109
+/
+/
+A8
+100
+1
+3.6
+2.8 × 1011
+1.8 × 1011
+9.8 × 1010
+5.1 × 1010
+/
+/
+D3
+400
+6
+4.5
+/
+/
+/
+/
+3.9 × 1011
+7.0 × 1010
+D7§
+400
+6
+2.5
+/
+/
+/
+/
+/
+5.8 × 1010
+D9
+400
+6
+1.0
+/
+/
+/
+/
+3.9 × 1010
+1.3 × 109
+E1
+762
+6
+6.8
+/
+/
+/
+/
+1.6 × 1010
+3.2 × 109
+E2
+762
+6
+6.5
+/
+/
+/
+/
+7.2 × 109
+5.3 × 109
+E3
+762
+6
+6.1
+/
+/
+/
+/
+8.6 × 109
+2.7 × 109
+† The A (D and E) Series of MassiveFIRE were published in Anglés-Alcázar et al. (2017) (Çatmabacak et al. 2022) for the first time.
+‡ Virial mass at 𝑧final.
+§ The HR simulation of D7 has been run only down to 𝑧 = 7.2.
+used for this study.
+Both the MassiveFIRE and FIREbox simulations used in this work
+are run using the N-body+hydrodynamics code GIZMO (FIRE-2 ver-
+sion) in the Meshless-Finite-Mass (MFM) mode (Hopkins et al.
+2018). The simulations incorporate various gas cooling processes
+(free-free, photoionization/recombination, Compton, photoelectric,
+metal-line, molecular and fine structure processes) and a uniform
+UV background following the FG09 prescription (Faucher-Giguère
+et al. 2009), Star formation occurs in dense, self-gravitating and self-
+shielding molecular gas based on a sink-particle prescription. The
+simulations explicitly incorporate several different stellar feedback
+channels (but not feedback from supermassive black holes) includ-
+ing 1) local and long-range momentum flux from radiative pressure,
+2) energy, momentum, mass and metal injection from supernovae
+(Types Ia and II), 3) stellar mass loss (both OB and AGB stars)
+and 4) photo-ionization and photo-electric heating processes. We re-
+fer the reader to Hopkins et al. (2014, 2018) for details of the star
+formation and feedback prescriptions of FIRE.
+FIRE has demonstrated success at reproducing a variety of key
+galaxy properties that are relevant to this work, such as the stellar-to-
+halo mass relation (Hopkins et al. 2014; Feldmann et al. 2017), the
+specific SFR (sSFR) of galaxies at the cosmic noon (𝑧 ∼ 2) (Hopkins
+et al. 2014; Feldmann et al. 2016; Sparre et al. 2017; Feldmann
+et al. 2022), the galaxy molecular (atomic) hydrogen gas mass and
+stellar mass relations at 𝑧 = 0 (Feldmann et al. 2022), the gas-phase
+and stellar mass-metallicity relation at 𝑧 = 0 − 2 (Ma et al. 2016;
+Feldmann et al. 2022), the observational effective dust temperatures
+at 𝑧 = 2−4 (Liang et al. 2019) as well as the UV luminosity functions
+and UV-based cosmic star formation rate density (CSFRD) at 𝑧 > 5
+(Ma et al. 2019).
+3 SIMULATING OBSERVATIONAL PROPERTIES
+In this section, we describe the method used to predict the observa-
+tional properties for the FIRE galaxy sample, which we compare to
+the observational data. In Section 3.1, we describe our [CII] emission
+model. In Section 3.2, we describe the prescription for the dust RT
+modelling of the FIRE galaxies using SKIRT code, based on which we
+around the DM halo centre, i.e. the maximum density centre provided by
+AHF.
+derive the multi-wavelength SED and the distribution of the interstel-
+lar radiation field (ISRF) for the galaxies. The ISRF distribution is
+essential for predicting the [CII] emission properties of the galaxies.
+3.1 Predicting [CII] emission using CLOUDY
+We predict the [CII] line luminosity for the FIRE sample using the
+spectral synthesis code CLOUDY version 17.01 (Ferland et al. 2017).
+CLOUDY is a plasma simulation code designed to simulate the ion-
+ization, level populations, molecular state and thermal state of gas
+over a wide range of density and temperature in different astrophys-
+ical environments (e.g. black hole accretion disks, PDRs, molecular
+clouds, etc). It solves for the ionization structure for all stages of
+ionization for the lightest 30 elements (Abel et al. 2008).
+We treat each gas particle of the galaxies as an idealized spher-
+ical uniform ‘gas cloud’. The [CII] luminosity of each ‘cloud’ is
+calculated based on its physical conditions, including ‘cloud’ (or
+gas particle) mass (𝑀cl), gas density9 (𝑛H), gas metallicity (𝑍gas),
+gas turbulent velocity dispersion (𝜎) and local UV ISRF strength
+(𝐺10). 𝑀cl, 𝑛H, 𝑍gas of each ‘cloud’ are known directly from the
+FIRE simulations. 𝜎 is the mass-weighted standard deviation of the
+velocities in gas at the location of the ‘cloud’, which is calculated
+in post-processing. Finally, 𝐺 at the location of each ‘cloud’ in the
+galaxy is calculated using the dust RT code SKIRT (Baes et al. 2011;
+Baes & Camps 2015; Camps & Baes 2015) in post-processing (see
+Section 3.2 for the details).
+We calculate the [CII] luminosity for each ‘cloud’ (𝐿[CII], cl) by
+integrating the [CII] line cooling rate, Λ[CII] (erg s−1 cm−3; see Ap-
+pendix A for its analytic expression), obtained from the output of the
+CLOUDY simulations, over the volume of the cloud:
+𝐿[CII], cl = 4𝜋
+∫ 𝑅cl
+0
+Λ[CII] (𝑥) 𝑥2d𝑥,
+(1)
+9 ‘Gas density’ here refers to H nuclei number density of gas, 𝑛H ≡
+𝑋 (𝜌gas/𝑚H), where 𝑋 and 𝑚H represent the mass fraction of hydrogen
+in gas and the proton mass, respectively. CLOUDY uses 𝑛H as input instead
+of mass density 𝜌gas. In this paper, we constantly use ‘gas density’ to refer to
+𝑛H for simplicity.
+10 Conventionally, 𝐺 is used to denote the mean ISRF in the Habing band
+(6.0 − 13.6 eV). It is indicated in units of 𝐺0 = 1.6 × 10−3 erg s−1 cm−2, the
+observed value in the solar neighbourhood (Habing 1968).
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+7
+where
+𝑅cl =
+� 3
+4𝜋
+�1/3 �
+𝑀cl
+𝜇H𝑚H𝑛H
+�1/3
+(2)
+represents the radius of the cloud11 and 𝜇H in equation (2) represents
+the mean molecular weight of the gas. The [CII] luminosity of the
+galaxy (𝐿[CII]) is then derived by summing over 𝐿[CII], cl of all gas
+clouds calculated using equation (1). We treat the [CII] emission of
+our galaxy sample as being optically thin.
+In practice, to run CLOUDY simulations for every gas particle
+for the whole FIRE sample (> 400 galaxies in total) is computa-
+tionally formidable: a CLOUDY simulation is typically completed
+(i.e. when iterative convergence is reached) in 0.1 − 0.5 CPU hour,
+depending on the gas column density, and hence to analyze one sin-
+gle galaxy snapshot that contains ∼ 1 million gas particles would
+cost 100 − 500 K CPU hours in total. We therefore use a lookup-
+table method similar to the previous studies (e.g. Vallini et al. 2015,
+2018, 2021; Katz et al. 2017, 2019; Olsen et al. 2017; Lagache et al.
+2018; Li et al. 2018; Pallottini et al. 2019; Leung et al. 2020; Lupi
+et al. 2020; Yang et al. 2021; Lupi & Bovino 2020). Specifically,
+for each of the 7 snapshots, we build a grid of CLOUDY models
+that covers a gas density range −1 < log (𝑛H/cm−3) < 5, a gas
+metallicity range −2 < log (𝑍gas/𝑍⊙) < 0.8, a turbulent velocity
+dispersion range 0 < log (𝜎/km s−1) < 2.4 and a UV ISRF range
+−1 < log (𝐺/𝐺0) < 4. The grid spacing is set 0.5 dex for 𝑛H and 𝐺,
+and 0.4 dex for 𝑍gas and 𝜎. In total, the default look-up table that we
+use for calculating the [CII] luminosity of our galaxy sample consists
+of 8,008 (13 × 8 × 7 × 11) models for each redshift. We include the
+CMB background in the CLOUDY simulations for each redshift and
+the predicted [CII] luminosity is corrected for the CMB attenuation
+effect (da Cunha et al. 2013). Cosmic-ray (CR) hydrogen ionization
+rate in these models is fixed to the fiducial value of 2 × 10−16 s−1,
+the observed value in the Milky Way (Indriolo et al. 2007; Indriolo
+& McCall 2012; Neufeld & Wolfire 2017). We assume a constant
+dust-to-metal mass ratio 𝛿dzr = 0.4 (Dwek 1998; Draine et al. 2007;
+Watson 2011; Li et al. 2019) and adopt the default interstellar medium
+metal abundances (abundance ISM) stored in CLOUDY. The simula-
+tions are run till sufficiently large distance from the surface of the
+slab is reached. Given 𝑛H, 𝑍gas, 𝐺 and 𝑁H of each gas cloud, we
+interpolate [CII] luminosity of the cloud from the values found in
+the computed grid.
+CLOUDY simulation: an example
+Here we show the conditions of a plane-parallel gas slab calculated by
+CLOUDY (Fig. 2). The slab has a uniform gas density 𝑛H = 50 cm−3
+and is illuminated by an external radiation field having 𝐺 = 200 𝐺0.
+We present CLOUDY simulations for two different models, where 𝑍gas
+is set to 𝑍⊙ and 1/10 𝑍⊙. We include the 𝑧 = 0 CMB background
+and the CR hydrogen ionization rate is set to the default value. We
+show the results of the dust-rich and dust-poor models in the left and
+right panels of Fig. 2, respectively.
+The slab is characterized by three distinct zones based on the ion-
+ization state of hydrogen gas. In the upper panels, we show the abun-
+dance profiles for ionized hydrogen (HII; dashed red line), atomic
+hydrogen (HI; solid green line) and molecular hydrogen (H2; dotted
+11 Note that we do not derive 𝐿[CII], cl using the ‘emergent intensity’ (𝐼em,
+with physical unit erg s−1 cm−2) output by CLOUDY because 𝐼em is calculated
+for a plane-parallel geometry instead of a spherical geometry. The conversion
+factor between the two geometries is not simply a constant but depends on
+the profile of [CII] emissivity (Olsen et al. 2017, 2018).
+blue line), as well as the profile for gas temperature (solid black line).
+We can see that a HII region (Zone I) is created near the surface of
+the slab by the ionizing photons (𝐸𝛾 > 13.6 eV) of the incident radi-
+ation field. Gas in this region is heated to high temperature (𝑇 ≈ 104
+K). The slab then transits to a HI-dominating region (Zone II) at a
+distance where ionizing radiation gets fully absorbed. The photons
+in the Lyman-Werner (LW) band (11.2 < 𝐸𝛾 < 13.6 eV) dissociate
+H2 in this region, while maintaining gas temperature at about 102 K.
+Finally, the slab transits to a H2-dominating region (Zone III) at some
+larger distance, beyond which the LW radiation becomes sufficiently
+absorbed and the majority of hydrogen turns into H2.
+Like hydrogen, carbon has a very different ionization state in the
+three zones. This can be seen from the middle panels of Fig. 2, where
+we explicitly show the abundance profiles for atomic carbon (CI;
+dotted blue line), singly ionized carbon (CII; solid green line) and
+doubly ionized carbon (CIII; dashed red line) for the two models.
+Carbon is mostly ionized in Zone I and II. Specifically, in Zone I, it
+gets excited to CII level as well as higher ionization levels (e.g. CIII).
+In Zone II, on the contrary, carbon is singly ionized by LW photons
+but not excited to higher levels since ionizing photons are shielded
+from the region12. Finally, in Zone III, carbon turns into CI since the
+region is UV-dark13.
+[CII] emission originates mostly from the ionized (Zone I) and
+atomic hydrogen (Zone II) phases. We show in the middle panels
+the profile for [CII] cooling rate (erg s−1 cm−3), Λ[CII], for the two
+models (solid magenta line). It is clear that Λ[CII] drops sharply in
+Zone III, which is due to the very low abundance of CII ions (solid
+green line) in this region (note: most carbon is in CI state in Zone III).
+For the chosen models, Λ[CII] appears to be similar in the ionized
+and atomic hydrogen phases, varying by less than a factor of few.
+Comparing the metal-rich (left panel) and metal-poor (right panel)
+models, it can be seen that Λ[CII] of the metal-rich model is about
+a factor of ten higher. This is due to the fact that Λ[CII] is linearly
+scaled to 𝑍gas and 𝑍gas of the metal-rich model is set as ten times
+that of the metal-poor model.
+Using the Λ[CII] profile output by CLOUDY, we subsequently de-
+rive the [CII] luminosity profile (cumulative [CII] luminosity as a
+function of column depth from the surface) for a uniform spherical
+cloud having 𝑛H = 50 cm−3 (same as the gas slab) and 𝑀cl = 105 𝑀⊙
+that is irradiated by an external field having 𝐺 = 200 𝐺0 (same as the
+gas slab) following equation (1). We calculate the result for the metal-
+rich (𝑍gas = 𝑍⊙) and metal-poor (𝑍gas = 0.1𝑍⊙) models, which are
+shown in the lower left and lower right panels of the figure, re-
+spectively. It can be seen that about 30% (20%) of the total [CII]
+luminosity of the cloud is produced by the HII region for the metal-
+rich (poor) model, while the remainder originates almost totally from
+the HI region. The H2 region contributes very limited fraction of the
+[CII] luminosity. Note that the Λ[CII] profile, the size of the different
+zones, and their relatively contribution to the total [CII] luminosity
+of the cloud depends on 𝐺, 𝑛H and 𝑍gas (see Section 5.1 for a detailed
+discussion).
+One major difference between the two models (metal-rich vs.
+metal-poor) is whether or not the gas cloud has an H2 region in
+the core, as can be seen from the bottom panels. For the metal-poor
+model (bottom right panel), because dust column density is small,
+12 Note: the ionization energy of CIII is 24.39 eV, which is above the ioniza-
+tion energy of hydrogen atom (13.6 eV).
+13 Note: the first ionization energy of carbon is 11.26 eV. This coincides with
+the lower frequency limit of the LW band (11.2 eV). Hence, carbon is neutral
+in the H2 region.
+MNRAS 000, 1–42 (2022)
+
+8
+Liang et al.
+1019
+1020
+1021
+1022
+10-2
+10-1
+100
+1019
+1020
+1021
+1022
+10-3
+10-2
+10-1
+100
+1019
+1020
+1021
+1022
+10-2
+10-1
+100
+T / 104K
+HII /H
+H2/H
+HI /H
+ZONE I
+ZONE III
+Z = Z⊙
+L[CII] ( < NH) / L[CII]
+V ( < NH) / Vtot
+Spherical gas cloud
+ZONE II
+T / 104K
+CIII /C
+CI /C
+CII /C
+Λ[CII]
+10−22 ergs s−1 cm−3
+1019
+1020
+1021
+1022
+10-3
+10-2
+10-1
+100 1019
+1020
+1021
+1022
+10-2
+10-1
+100
+1019
+1020
+1021
+1022
+10-2
+10-1
+100
+T / 104K
+HII /H
+H2/H
+HI /H
+Z = 0.1Z⊙
+T / 104K
+CIII /C
+CI /C
+CII /C
+Λ[CII]
+10−22 ergs s−1 cm−3
+ZONE I
+ZONE II
+L[CII] ( < NH) / L[CII]
+V ( < NH) / Vtot
+Spherical gas cloud
+Figure 2. Top and middle panels: Ionization structures of a plane-parallel gas slab (𝑛H = 50 cm−3) irradiated by an external radiation field (𝐺 = 200 𝐺0)
+incident from the left in the figure predicted by the CLOUDY code. Dashed red, solid green and dotted blue lines in the top (middle) panels represent the
+abundance profiles for HII (CIII), HI (CII) and H2 (CI), respectively. Solid black line in the top and middle panels shows the profile of gas kinetic temperature
+(normalized by 104 K). Solid magenta line in the middle panels indicates the profile of [CII] cooling rate (normalized by 10−22 erg s−1 cm−3). Bottom panels:
+Cumulative fraction of [CII] luminosity (thick orange line) and volume (thin blue) as a function of gas column density (from the surface) of a spherical gas
+cloud (𝑀cl = 105 𝑀⊙, 𝑛H = 50 cm−3) irradiated by an external radiation field (𝐺 = 200 𝐺0). Red dotted line marks the surface-to-centre column density of the
+cloud (𝑁H = 4 × 1021 cm−2). The left and right columns correspond to the metal-rich and metal-poor models where gas metallicity of the slab (cloud) is set to
+𝑍⊙ and 1/10 𝑍⊙. For the metal-poor model, the dust-to-gas mass ratio (𝛿dgr) becomes lower and therefore Lyman-Werner photons can penetrate deeper into the
+slab (cloud), resulting in larger [CII]-emitting region (Zone I + Zone II).
+LW photons are able to penetrate the entire cloud, making it H2-free.
+The metal-rich model (bottom left panel), in contrast, has an H2 core
+owing to the high dust column density, which accounts for nearly half
+of 𝑀cl. The two cloud models correspond to the two distinct regimes
+where 𝐿[CII] ,cl has different scaling with 𝑍gas. When the cloud has
+no H2 core, 𝐿[CII] ,cl scales linearly with 𝑍gas. As 𝑍gas (and hence
+the dust-to-gas mass ratio, 𝛿dgr) increases, the depth of Zone I+Zone
+II decreases (Ferrara et al. 2019). When 𝑍gas is high enough that H2
+becomes abundant (i.e. , Zone III forms), 𝐿[CII] ,cl saturates and no
+longer depends sensitively on 𝑍gas. In Section 5, we will discuss in
+detail how the 𝐿[CII]/SFR ratio of the FIRE galaxies depends on gas
+metallicity, and interpret the results using the insights obtained from
+the toy models presented here.
+3.2 Calculating ISRF distribution and multi-wavelength SEDs
+of galaxies using SKIRT
+To predict the [CII] luminosity of the ISM, it is essential to know
+the local UV ISRF strength. We calculate the ISRF distribution for
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+9
+-2  
+-1.5
+-1  
+-0.5
+0   
+0.5 
+1   
+-0.5
+0   
+0.5 
+1   
+1.5 
+2   
+2.5 
+4  
+4.5
+5  
+5.5
+6  
+6.5
+7  
+4  
+4.5
+5  
+5.5
+6  
+6.5
+7  
+UVJ
+z = 0
+z = 6
+Σ[CII]
+G
+10 pkpc
+5 pkpc
+5 pkpc
+10 pkpc
+10 pkpc
+5 pkpc
+4  
+4.5
+5  
+5.5
+6  
+6.5
+7  -2  
+-1.5
+-1  
+-0.5
+0   
+0.5 
+1   
+log (G/G0)
+log (G/G0)
+Figure 3. The UVJ false-colour image (left), [CII] surface brightness (middle) and the distribution of UV ISRF strength (𝐺) (right) of selected FIRE galaxies.
+The upper panels show the results of a 𝑧 = 0 disc galaxy from FIREbox (c.f. Fig.3 of Feldmann et al. 2022), while the lower panels correspond to a galaxy
+undergoing multiple mergers at 𝑧 = 6 extracted from the MassiveFIRE ‘zoom-in’ suite.
+the FIRE galaxies using the open-source14 3D Monte Carlo dust RT
+code SKIRT (Baes et al. 2011; Baes & Camps 2015; Camps & Baes
+2015) (version 8). SKIRT provides full treatment of absorption and
+anisotropic scattering by dust, and self-consistently computes dust
+thermal re-emission and dust temperature distribution for various
+astrophysical systems.
+To prepare the galaxy snapshots as RT input models for SKIRT,
+we follow the prescription of Camps et al. (2016) (see also Trayford
+et al. 2017; Camps et al. 2018). We summarize the key points of the
+prescription here, and refer interested readers to the above-mentioned
+papers for the details.
+For the analysis, each star particle of the galaxy is treated as a
+‘single stellar population’ (SSP), and a spectrum of stellar emission
+is assigned to each particle using the STARBURST99 (Leitherer et al.
+1999; Vazquez & Leitherer 2005) SED libraries according to the
+age, metallicity and initial mass of the particle. The RT calculations
+are performed on an equally spaced logarithmic wavelength grid
+consisting of 250 wavelength points spanning the wavelength range
+𝜆 = 0.05 − 1000 𝜇m. We launch 106 photon packages for each of the
+250 point in the wavelength grid and for each of the stellar emission
+14 Code repository: https://skirt.ugent.be/version8/
+and following dust emission stages. The calculation iterates until
+convergence. To produce mock images and SEDs for the galaxies, we
+place mock detectors at an arbitrary ‘local’ distance of 10 Mpc from
+galaxy along multiple viewing angles to accumulate both spatially
+resolved as well as integrated fluxes at each wavelength grid point.
+We assume that dust mass traces metal mass in galaxies (Hayward
+et al. 2011; Narayanan et al. 2015; Camps et al. 2016; Trayford
+et al. 2017; Liang et al. 2018, 2019, 2021; Ma et al. 2019; Cochrane
+et al. 2019, 2022; Vogelsberger et al. 2020; Shen et al. 2022) and
+adopt a constant dust-to-metal mass ratio 𝛿dzr = 0.4 in gas cooler
+than 106 K. Hotter gas is assumed to be dust-free due to thermal
+sputtering (Draine & Salpeter 1979; Tielens et al. 1994). We adopt
+the Weingartner & Draine (2001b) dust model with Milky-Way size
+distribution for the case of 𝑅V = 3.1. We discretize the spatial domain
+using an octree grid and keep subdividing grid cells until the cell
+contains less than 𝑓 = 3×10−6 of the total dust mass and the 𝑉-band
+(0.55 𝜇m) optical depth in each cell is less than unity. The highest
+grid level corresponds to a cell width of ∼ 20 pc, i.e. about twice
+the minimal SPH smoothing length. We self-consistently calculate
+the self-absorption of dust emission and include the transient heating
+function to calculate non-local thermal equilibrium dust emission
+by transiently heated small grains and PAH molecules (Baes et al.
+2011; Camps & Baes 2015). To account for the heating of dust by
+MNRAS 000, 1–42 (2022)
+
+10
+Liang et al.
+the cosmic microwave background, we adopt a correction to the dust
+temperature using equation (12) of da Cunha et al. (2013).
+The final output of the SKIRT simulations includes the ISRF, 𝐽𝜆
+(W cm−3 sr−1), of each adaptive grid cell. We calculate the UV ISRF
+strength (𝐺) for each cell by integrating 𝐽𝜆 over the Habing band
+(6 − 13.6 eV) and solid angle (Ω). 𝐺 is assigned to every gas particle
+(‘cloud’) inside the cell for predicting its [CII] luminosity.
+In Fig. 3, we show the UVJ composite image (left panels), [CII]
+surface brightness (middle panels), and 𝐺 distribution (right panels)
+for the two selected FIRE galaxies calculated using CLOUDY and
+SKIRT. The upper panels show the results of a disc galaxy at 𝑧 = 0
+extracted from FIREbox, whilst the lower panels show the results of
+a galaxy undergoing multiple mergers at 𝑧 = 6 extracted from the
+MassiveFIRE simulation (Sim ID: D9). The 𝑧 = 6 galaxy system
+has much stronger strength of ISRF (right panels) due to its higher
+SFR (220 𝑀⊙ yr−1 vs. 4.5 𝑀⊙ yr−1) and shows higher [CII] surface
+brightness. 𝐿[CII] of the 𝑧 = 6 system and the 𝑧 = 0 galaxy are
+4.8 × 108 𝐿⊙ and 2.8 × 108 𝐿⊙, respectively.
+4 COMPARISON WITH OBSERVATIONS
+In this section, we compare the 𝐿[CII]-SFR relation of the FIRE
+galaxies predicted by our model with the observational data at various
+redshifts. We separately discuss the results for three redshift regimes,
+𝑧 = 0 (Section 4.1), 1 <∼ 𝑧 <∼ 5 (Section 4.2) and 𝑧 >∼ 5 (Section 4.3).
+We make this distinction because observations use different sample
+selection methods and the SFR of galaxies is estimated by different
+means of calibration in the three different regimes.
+4.1 Local Universe (redshift 𝑧 = 0)
+Observations of the 𝐿[CII]-SFR relation at 𝑧 = 0 probe a very wide
+SFR range across several orders of magnitude. The selected sam-
+ples include low-SFR systems such as dwarf galaxies as well as the
+extreme IR-luminous starbursts.
+There are three main samples of nearby galaxies that have been
+used for calibrating the 𝐿[CII]-SFR relation of normal star-forming
+galaxies (SFR ≈ 10−5−10 𝑀⊙ yr−1): De Looze et al. (2011, hereafter
+L11), De Looze et al. (2014, hereafter L14) and Herrera-Camus
+et al. (2015, hereafter H15). The L11 sample consists of 24 star-
+forming galaxies selected from the early compilation by Brauher et al.
+(2008) that have measurements at both the Galaxy Evolution Explorer
+(GALEX) FUV and the Multiband Imaging Photometer for Spitzer
+(MIPS) 24 𝜇m bands. The sample of L14 includes 48 nearby low-
+metallicity (𝑍gas ≈ 0.03−0.55 𝑍⊙) dwarf galaxies extracted from the
+Dwarf Galaxy Survey (DGS, Madden et al. 2013) catalogue. Lastly,
+H15 study a sample consisting of 46 local star-forming galaxies
+chosen from the KINGFISH catalogue (Kennicutt et al. 2011), having
+very diverse integrated galaxy properties and ISM environments. All
+these studies have excluded the sources with AGN features.
+Both L11 and L14 derive the SFR of their sample using GALEX
+FUV and MIPS 24 𝜇m fluxes (i.e. SFR = 𝛽 (𝐿FUV, obs +𝛼 × 𝐿24 𝜇m))
+but with different calibration. Specifically, L11 and L14 use the
+calibration by Zhu et al. (2008) (𝛼 = 6.31) and Hao et al. (2011)
+(𝛼 = 3.89), respectively. H15, on the other hand, derive the SFR
+of their sample using a hybrid of different methods: for 27 galaxies
+in their sample, SFR is derived using the H𝛼+24 𝜇m calibration by
+Calzetti et al. (2007) (equation 7). For the other 8 galaxies, they
+use the FUV+24 𝜇m calibration by Leroy et al. (2008) (equations
+D10 and D11). And lastly, for the remaining 11 galaxies having
+no measurement of either H𝛼 nor FUV flux, SFR is derived based
+solely on their 24 𝜇m flux using the calibration by Calzetti et al.
+(2007) (equation 6). In Table 2, we show the SFR range as well as
+the median SFR of the three samples (L11, L14 and H15). We also
+show in the table the best-fit parameter values for the scaling relation
+log(𝐿[CII]/𝐿⊙) = 𝐴 + 𝐵 log(SFR/𝑀⊙ yr−1)
+(3)
+for the three samples as well as the 1𝜎 scatter (in dex) of the data
+around the best-fit relation. Note that for the galaxies of the L11 and
+H15 samples whose SFR is derived using the FUV+24 𝜇m fluxes,
+we have re-calibrated their SFR following Hao et al. (2011) as has
+been done by L14 for a fair comparison. All the SFR calibrations are
+based on the Kroupa (2002) initial mass function (IMF).
+From Table 2, we can see that the three samples all exhibit an
+almost linear correlation between 𝐿[CII] and SFR, though having
+noticeable difference in the normalization. The H15 sample has the
+highest normalization among the three samples. It is higher than that
+of the L11 sample by 0.32 dex. This offset may partly be due to the
+difference in sample selection. Another potential cause is that H15
+adopt different SFR indicators and calibration methods compared
+with L11 for a large fraction of the galaxies in their sample. The
+offset between the L11 and L14 samples (0.21 dex), on the other
+hand, is mainly due to the difference in sample selection since L11
+and L14 adopt the same SFR indicators (FUV+24 𝜇m fluxes) for
+their entire samples and we have re-calibrated their results following
+the same method of Hao et al. (2011). The lower normalization of
+the L14 relation is very likely due to the relatively lower 𝑍gas of the
+dwarf galaxies they use for the study, as has been explicitly stated in
+L14.
+In Fig. 4, we show the 𝐿[CII]-SFR relation of the three samples
+(L11, L14 and H15) in the left panel. To more clearly show the differ-
+ence in the normalization of these scaling relations, we present the
+𝐿[CII]/SFR vs. SFR relation of the same samples in the right panel.
+In both panels, we also present the results for the FIRE sample15
+𝑧 = 0 (filled cyan stars) for comparison with the observational data.
+Note that for the L11 and H15 samples, we show both the data of
+the individual sources as well as the best-fit scaling relation for each
+sample, whereas for the L14 sample, we only present the best-fit scal-
+ing relation (purple dashed line) for reference. The L14 sample has
+systematically lower gas metallicity than the other two observational
+samples as well as the FIRE galaxy sample at 𝑧 = 0.
+The FIRE simulations, combined with our line model, produce the
+𝐿[CII]-SFR relation at 𝑧 = 0 (cyan stars) that is in good agreement
+with the local star-forming samples of L11 (black diamonds) and
+H15 (black triangles). The best-fit parameter values for the FIRE
+galaxies (over the SFR range of 0.05 − 100 𝑀⊙ yr−1) are 𝐴 = 7.70 ±
+0.02 and 𝐵 = 0.80 ± 0.03, and the 1𝜎 scatter of the data points
+around the best-fit relation is 0.21 dex, similar to the L11 and H15
+samples (see Table 2). Note that we have excluded the galaxies having
+SFR < 0.05 𝑀⊙ yr−1 for the fitting to avoid the regime where galaxy
+statistics can be contaminated by the shot noise due to the resolution
+limit of the simulation (Feldmann 2017).
+The FIRE galaxies exhibit a sub-linear relation between 𝐿[CII]
+and SFR, i.e. 𝐿[CII] ∝ SFR0.80±0.03. The sub-linearity is due to the
+galaxies having SFR>∼3 𝑀⊙ yr−1, which have lower 𝐿[CII]/SFR ratio
+on average than the galaxies having lower SFR (see the right panel of
+Fig. 4). Such a trend of reduced 𝐿[CII]/SFR ratio at high SFR ([CII]
+deficit) is not clearly present in any of the three (L11, L14 and H15)
+15 We calculate the SFR of the FIRE galaxies by averaging over a timescale
+of the last 100 Myrs.
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+11
+FIRE galaxies  z = 0
+Herrera-Camus et al. 2015
+Local observations
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+FIRE galaxies  z = 0
+Herrera-Camus et al. 2015
+Local observations
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+Figure 4. The 𝐿[CII] vs. SFR (left panel) and 𝐿[CII]/SFR vs. SFR (right panel) relations of the 𝑧 = 0 galaxies. The filled cyan stars in the two panels show
+the result of the FIRE galaxies. Black triangles and diamonds show the observational data of Herrera-Camus et al. (2015) (H15) and De Looze et al. (2011)
+(L11), and the orange and green lines indicate the best-fit linear relation of the H15 and L11 samples, respectively. The coloured shaded regions indicate the 1𝜎
+scatter of the data around the best-fit linear relation of the observed samples. Purple dashed line in the two panels represents the best-fit linear relation to the
+low-metallicity dwarf galaxy sample of De Looze et al. (2014) (L14). The result of the FIRE galaxies at 𝑧 = 0 is in good agreement with the observational data.
+Table 2. Observed scaling relations between SFR and 𝐿[CII] of local galaxies, i.e. 𝐿[CII]/𝐿⊙ = 𝐴(SFR/𝑀⊙ yr−1) 𝐵.
+Galaxy
+sample
+SFR range (𝑀⊙ yr−1)
+Median SFR (𝑀⊙ yr−1)
+𝐴
+𝐵
+1𝜎 scatter
+De Looze et al. (2011)
+0.02 − 88
+1.75
+7.31 ± 0.06
+0.93 ± 0.06
+0.26 dex
+De Looze et al. (2014)
+6 × 10−4 − 56
+0.12
+7.10 ± 0.11
+1.05 ± 0.07
+0.43 dex
+Herrera-Camus et al. (2015)
+10−3 − 9.6
+0.34
+7.63 ± 0.03
+0.97 ± 0.03
+0.21 dex
+observational samples. We note, however, that these samples do not
+contain statistically large number of galaxies at SFR >∼ 3 𝑀⊙ yr−1.
+Some other studies probing the local LIRGs and ULIRGs have found
+clear evidence of [CII] deficit at high 𝐿IR (∼ SFR) (see below).
+The 𝐿[CII] vs. 𝐿IR relation of 𝑧 = 0 galaxies
+A number of observational studies have probed the relation between
+𝐿[CII] and 𝐿IR (or 𝐿FIR16) of local galaxies.
+𝐿IR (or 𝐿FIR) can be a good proxy for galaxy SFR when the stellar
+light of a galaxy is heavily absorbed by dust (e.g. Kennicutt 1998;
+Salim & Narayanan 2020). Galaxies having higher SFR tend to be
+more gas/dust-rich and have higher gas density. Therefore, they tend
+to have higher dust opacity (e.g. Whitaker et al. 2017). We show
+in Fig. 5 the 𝐿IR vs. SFR relation of the FIRE galaxies at different
+redshifts, where 𝐿IR is calculated using their SEDs produced by
+SKIRT. It can be seen that at 𝑧 = 0, the FIRE galaxies (cyan stars)
+16 In the literature, ‘𝐿IR’ is used to denote the bolometric IR luminosity of
+galaxy that is integrated over the wavelength range 8 − 1000 𝜇m, whereas
+‘𝐿FIR’ represents the FIR luminosity of galaxy (42.5 − 122.5 𝜇m). Both 𝐿IR
+and 𝐿FIR are commonly adopted as SFR indicators for heavily dust-obscured
+galaxies.
+well follow the Kennicutt (1998, hereafter K98) relation17, i.e.
+𝐿IR (𝐿⊙) = 1.36 × 1010 SFR (𝑀⊙ yr−1)
+(4)
+at SFR >∼ 1 M⊙ yr−1 (or 𝐿IR >∼ 1010 𝐿⊙). The K98 relation is derived
+assuming that all radiative energy of the young stars is absorbed
+and re-emitted by dust and AGN radiation does not contribute to dust
+heating. At SFR < 1 M⊙ yr−1, however, the 𝑧 = 0 FIRE galaxies show
+larger scatter. Some of these galaxies are below the K98 relation by
+over 0.3 dex (indicating that less than half of the radiative energy of
+the young stars gets re-emitted at FIR by dust). These are the galaxies
+having relatively low dust opacity18. Nonetheless, 𝐿IR appears to be
+17 We adopt the K98 relation for the Kroupa (2002) IMF using the stellar
+population synthesis (SPS) model STARBURST99, assuming a constant star
+formation history lasting for 1 Gyr (see Hao et al. 2011 for the details). The
+original relation (i.e., 𝐿IR/𝐿⊙ = 5.8 × 109 SFR/(𝑀⊙ yr−1)) was derived for
+the Salpeter IMF based on the older SPS model of Leitherer & Heckman
+(1995), and for a shorter starburst period (𝑡age = 10 − 100 Myrs).
+18 It can be seen from Fig. 5 that some of the simulated galaxies (particularly
+those having low SFR) lie above the K98 relation, which seem to break
+the energy conservation law. These are in fact the galaxies that are recently
+quenched after a strong starburst whose dust is heated mainly by the stars
+older than 100 Myrs (see e.g. Hayward et al. 2014).
+MNRAS 000, 1–42 (2022)
+
+10
+L(CI) (Lo)
+106
+10-1
+100
+101
+102
+SFR(Mo yr-1)LicIm /SFR(Lo M1
+10
+10
+10-1
+100
+101
+102
+SFR(Mo yr-1)12
+Liang et al.
+10-2
+10-1
+100
+101
+102
+103
+108
+109
+1010
+1011
+1012
+1013
+Kennicutt et al. 1998 (K98) relation 
+K98 relation × 1/2
+K98 relation × 1/10
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+Figure 5. The 𝐿IR vs. SFR relation of FIRE galaxies at different redshifts
+(cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2, blue
+squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6 and
+purple downward diamonds for 𝑧 = 8). The diagonal solid black line indicates
+the K98 relation, i.e. 𝐿IR (𝐿⊙) = 1.36 × 1010 SFR (𝑀⊙ yr−1). The dashed
+and dotted lines indicate the modified K98 relations where the normalization
+is lower than the solid black line by a factor of 2 and 10, respectively. The
+K98 relation (solid black line) fits well to the galaxies at high SFR.
+a good SFR tracer for the 𝑧 = 0 galaxies at SFR >∼ 1 M⊙ yr−1 in the
+FIRE simulations.
+We show in Fig. 6 the observed 𝐿[CII] vs. 𝐿IR (left panel) and
+the 𝐿[CII]/𝐿IR vs. 𝐿IR (right panel) relations of the local galaxy
+samples of Malhotra et al. (2001), Brauher et al. (2008), Sargsyan
+et al. (2012), Farrah et al. (2013), Díaz-Santos et al. (2013), Magdis
+et al. (2014), Cormier et al. (2015), Herrera-Camus et al. (2015),
+Hughes et al. (2017) and Contursi et al. (2017). Note that for those
+having used 𝐿FIR as SFR indicator, we convert the reported 𝐿FIR of
+the galaxies to 𝐿IR by multiplying it with 1.6 (Sanders et al. 2003).
+For comparison, we also show in the same figure the data of the 𝑧 = 0
+FIRE galaxies. 𝐿IR of the FIRE galaxies is computed by integrating
+the SKIRT-produced SED over the wavelength range 8 − 1000 𝜇m.
+The observed samples contain a large number of galaxies that are
+IR-luminous (𝐿IR >∼ 1011 𝐿⊙, corresponding to SFR >∼ 10 𝑀⊙ yr−1
+following equation 4). With these statistically large samples, the
+𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR) ratio of the 𝑧 = 0 galaxies appear to
+show a clear decline with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙ ([CII] deficit), albeit
+with a large scatter (1𝜎 = 0.3 dex) at given 𝐿IR. From 𝐿IR = 1011 to
+1013 𝐿⊙, 𝐿[CII]/𝐿IR decreases from 2×10−3 to 10−4, over a factor of
+ten. At 𝐿IR <∼1011 𝐿⊙, on the other hand, 𝐿[CII]/𝐿IR of the observed
+galaxies is a constant. Overall, the observational and the simulated
+data agree well with each other (on both the mean value and level of
+scatter). In particular, the FIRE sample exhibits a mild [CII] deficit at
+𝐿IR >∼1011 𝐿⊙ at 𝑧 = 0, which is in agreement with the observational
+data. Note, however, that our FIRE sample at 𝑧 = 0 does not include
+any ULIRGs (i.e. 𝐿IR >∼ 1012 𝐿⊙) at 𝑧 = 0.
+4.2 High redshifts (1 <∼ 𝑧 <∼ 5)
+Observational studies have investigated the 𝐿[CII]-SFR relation of
+galaxies at 1 <∼ 𝑧 <∼ 5, including e.g. Ivison et al. (2010); Stacey
+et al. (2010); Valtchanov et al. (2011); Brisbin et al. (2015); Gullberg
+et al. (2015, 2018); Schaerer et al. (2015b); Umehata et al. (2017);
+Zanella et al. (2018); Hashimoto et al. (2019b); McKinney et al.
+(2020). Their samples consist of roughly 80 galaxies in total (see
+Table 3 for the details). Most of these galaxies have substantial SFR
+(SFR >∼ 100 𝑀⊙ yr−1) and are IR-luminous (𝐿IR >∼ 1012 𝐿⊙). This is
+in stark contrast with the local observations (see Section 4.1), which
+probe the galaxies having much lower SFR (see Table 2). Note that
+a large fraction of the selected galaxies in this redshift regime are
+uncovered by wide-field sub-mm galaxy surveys, e.g. the South Pole
+Telescope (SPT; Vieira et al. 2010; Carlstrom et al. 2011) survey
+(Weiß et al. 2013; Gullberg et al. 2015).
+We derive the SFR of the selected galaxies from their measured
+𝐿IR (see Table 3) using the K98 relation (equation 4) assuming that
+the galaxies are heavily dust-obscured. Note that at high redshifts,
+the K98 relation may only apply to the more massive and starburst
+galaxies. High-𝑧 galaxies are metal and dust-poorer than the 𝑧 =
+0 galaxies at given mass (or SFR), and therefore only the more
+massive and gas-rich systems have high enough dust opacity leading
+to total obscuration of stellar light. We can see from Fig. 5 that the
+K98 relation (solid black line) fits well the high-𝑧 FIRE galaxies at
+SFR >∼ 100 𝑀⊙ yr−1 (or 𝐿IR >∼ 1012 𝐿⊙. Note: For the 𝑧 = 1 galaxies,
+the K98 relation fits well to the data down to 𝐿IR ≈ 1011 𝐿⊙). At
+lower SFR, the high-𝑧 galaxies exhibit larger scatter and they, on the
+average, have lower 𝐿IR at given SFR than the 𝑧 = 0 galaxies due to
+their reduced dust opacity.
+The galaxies selected at 1 <∼ 𝑧 <∼ 5 typically have a good sampling
+of photometric data points in the dust continuum, which are ob-
+tained by observations with multiple IR and millimetre instruments
+(Spitzer, Herschel, ALMA and etc). The shape of the dust SED of
+these galaxies is therefore well constrained. This results in relatively
+small uncertainty in the estimate of their 𝐿IR.
+The [CII] line of these galaxies is measured with different instru-
+ments (see Table 3). For instance, Stacey et al. (2010) and Brisbin
+et al. (2015) measure the [CII] line of the 20 galaxies at 𝑧 ≈ 1 − 2
+of their samples using the redshift (𝑧) and Early Universe Spec-
+trometer (ZEUS; Stacey et al. 2007; Hailey-Dunsheath 2009) on the
+10.4 m Caltech Submillimeter Observatory (CSO). Gullberg et al.
+(2015) measure the [CII] line of the 16 SMGs selected from the
+SPT catalogue (Weiß et al. 2013) using the SPIRE Fourier Transform
+Spectrometer (FTS; Griffin et al. 2010) onboard Herschel (for the
+galaxies at 𝑧 < 3) and the First Light APEX Sub-millimetre Het-
+erodyne receiver (FLASH; Heyminck et al. 2006) (for the galaxies
+at 𝑧 > 3). For the remaining galaxies (∼ 40), their [CII] line is
+measured with ALMA (at Band 7, 8 and 9 for the galaxies at 𝑧 ∼ 4,
+𝑧 ∼ 3 and 𝑧 ∼ 2, respectively). ALMA observations often marginally
+resolve a galaxy spatially in [CII], whereas observations with ZEUS,
+APEX/FLASH and SPIRE FTS do not.
+It should be particularly noted that a large number (26) of the
+selected galaxies (mostly SMGs) in this regime are gravitationally-
+lensed systems (see Table 3). Hence, one important source of un-
+certainty in the estimates of their intrinsic 𝐿[CII] and 𝐿IR (∼SFR) is
+the lensing magnification factor 𝜇. To observationally determine 𝜇
+of a lensed source requires spatially resolved imaging. Note that 16
+of the selected SPT galaxies in this regime, however, are not spatially
+resolved by the observations and their 𝜇 is unknown. Gullberg et al.
+(2015) adopt a constant 𝜇 = 14.1 to de-magnify the luminosities of
+all the 16 galaxies. This is the mean of the 𝜇 of the only 4 galaxies
+in their selected SPT sample, which is determined using the spatially
+resolved ALMA 860 𝜇m broadband imaging of dust continuum by
+Hezaveh et al. (2013).
+In Fig. 7, we show the 𝐿[CII]-SFR relation (left panel) of the
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+13
+FIRE galaxies  z = 0
+FIRE galaxies  z = 0
+Local observations
+Sargsyan + 2012
+Malhotra + 2001
+Brauher + 2008
+Farrah + 2013
+Diaz-Santos + 2013
+Hughes + 2017
+Coutursi + 2017
+Madgis + 2014
+Cormier + 2015
+* 
+Herrara-Camus + 2015
+Local observations
+Sargsyan + 2012
+Malhotra + 2001
+Brauher + 2008
+Farrah + 2013
+Diaz-Santos + 2013
+Hughes + 2017
+Coutursi + 2017
+Madgis + 2014
+Cormier + 2015
+* 
+Herrara-Camus + 2015
+Figure 6. The 𝐿[CII] vs. 𝐿IR (left panel) and the 𝐿[CII]/𝐿IR vs. 𝐿IR (right panel) relations of 𝑧 = 0 galaxies. In the two panels, cyan stars show the result
+of the FIRE galaxies, whereas black symbols indicate the observational data from different studies, including Malhotra et al. (2001) (diamond), Brauher et al.
+(2008) (vertical crosses), Sargsyan et al. (2012) (filled squares), Farrah et al. (2013) (empty squares), Díaz-Santos et al. (2013) (filled circles), Magdis et al.
+(2014) (diagonal crosses), Cormier et al. (2015) (empty stars), Herrera-Camus et al. (2015) (asterisks), Hughes et al. (2017) (triangles) and Contursi et al. (2017)
+(empty circles). Observations show that 𝐿[CII]/𝐿IR ratio of galaxies is nearly a constant at 109 <∼ 𝐿IR <∼ 1011 𝐿⊙, but declines with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙. In
+the two panels, black line (solid at 𝐿IR < 1011 𝐿⊙ and dotted at 𝐿IR ≥ 1011 𝐿⊙) indicates the median 𝐿[CII]/𝐿IR ratio (≈ 2 × 10−3) of the galaxies having
+𝐿IR < 1011 𝐿⊙ and grey shaded bar (dark grey at 𝐿IR < 1011 𝐿⊙ and light grey at 𝐿IR ≥ 1011 𝐿⊙) indicates the 1𝜎 scatter of the 𝐿[CII]/𝐿IR ratio of the same
+galaxies. FIREbox successfully reproduces the observed 𝐿[CII] vs. 𝐿IR (and the 𝐿[CII]/𝐿IR vs. 𝐿IR) relation at 𝑧 = 0.
+FIRE galaxies
+Herrera-Camus et al. 2015
+Local observations
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+Observational data at 1 < z < 5
+Star-forming galaxies
+SMGs  (un-lensed or  determined)
+μ
+SMGs  (lensed but  undetermined)
+μ
+Observations by ZEUS
+1010
+1011
+1012
+1013
+1014
+10-6
+10-5
+10-4
+10-3
+10-2
+10-1
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+Observational data at 1 < z < 5
+Star-forming galaxies
+SMGs  (un-lensed or  determined)
+μ
+SMGs  (lensed but  undetermined)
+μ
+Observations by ZEUS
+Local observations  
+(same as in fig.6)
+* 
+Figure 7. The 𝐿[CII] vs. SFR (left panel) and the 𝐿[CII]/𝐿IR vs. 𝐿IR (right panel) relations of galaxies at 𝑧 = 0 and high redshifts. In both panels, filled coloured
+symbols represent the FIRE galaxies (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2, blue squares for 𝑧 = 3 and magenta circles for
+𝑧 = 4). Black symbols (filled and empty) show the observational data of galaxies at 1 <∼ 𝑧 <∼ 5 (see Table 3 for the details). Specifically, black circles and black
+triangles correspond to SMGs and other star-forming galaxies, respectively. For the gravitationally-lensed galaxies, their [CII] and IR luminosities have been
+corrected by the lensing magnification factor 𝜇 reported in the literature. Those having direct measurement of 𝜇 as well as the un-lensed galaxies are marked
+by filled symbols (triangles and circles), whereas the 16 lensed SPT galaxies whose 𝜇 is extrapolated (𝜇 has been assumed to be 14.1 by Gullberg et al. 2015)
+are shown by empty circles. The two grey empty squares represent the stacked result of the galaxy samples of Stacey et al. (2010) and Brisbin et al. (2015).
+The [CII] line of the two samples is measured with the redshift and Early Universe Spectrometer (ZEUS) and their data systematically offsets from that of the
+other galaxy samples. For reference, we also show in the left (right) panel the observational results of the local galaxy samples as shown in Fig. 4 (Fig. 6). Both
+observations and FIRE simulations show that high-𝑧 (1 <∼ 𝑧 <∼ 5) galaxies exhibit a [CII] deficit at high 𝐿IR similar to local galaxies.
+MNRAS 000, 1–42 (2022)
+
+10
+中
+() [I
+8
+10
+10
+10
+109
+10
+LIR (Lo)3101010
+LIR
+10
+[CII
+L
+0
+10
+109
+10
+LIR (Lo)10-110
+10
+10
+() [I
+108
+10
+10
+101
+100
+102
+103
+10
+SFR(Mo yr-14101114
+Liang et al.
+Table 3. The observed 𝐿[CII]-SFR relation of galaxies at high redshifts.
+Name†
+𝑧
+log (𝐿IR/𝐿⊙)§
+log (𝐿[CII]/𝐿⊙)‡, §, ∥
+Galaxy type#
+AGN
+𝜇
+References∗
+ID 7118
+1.7290
+12.06±0.01
+< 9.70 (ALMA 9)
+MS
+No
+−
+[1, 2]
+GS IRS61
+1.759
+12.46±0.13
+< 8.31 (ALMA 9)
+SB
+No
+−
+[3, 4]
+ID 9834
+1.7644
+11.99±0.02
+9.11 ± 0.07 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 2910
+1.7686
+11.76±0.08
+< 9.08 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 2861
+1.8102
+12.00±0.03
+< 9.58 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 6515
+1.8438
+11.68±0.04
+9.09 ± 0.12 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 9347
+1.8505
+11.80±0.05
+8.98 ± 0.14 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 9681
+1.8852
+11.84±0.04
+9.26 ± 0.20 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 8490
+1.9056
+11.54±0.06
+8.85 ± 0.20 (ALMA 9)
+MS
+No
+−
+[1, 2]
+ID 10049
+1.9200
+11.60±0.06
+< 8.78 (ALMA 9)
+MS
+Yes
+−
+[1, 2]
+GS IRS20
+1.923
+13.06±0.12
+9.17 ± 0.01 (ALMA 9)
+SB
+Yes
+−
+[3, 4]
+ID 10076
+1.9462
+11.91±0.03
+9.38 ± 0.14 (ALMA 9)
+MS
+No
+−
+[1, 2]
+MACS J0451+0006
+2.013
+11.08±0.04
+8.08 ± 0.04 (ALMA 9)
+MS
+No
+49 ± 5
+[5, 6, 7]
+GRB 080207
+2.0865
+12.26±0.05
+8.89 ± 0.12 (ALMA 9)
+MS
+No
+−
+[8]
+SPT 0551-50
+2.123
+11.89±0.05
+< 9.33 (SPIRE FTS)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0512-59
+2.234
+12.29±0.04
+9.45 ± 0.09 (SPIRE FTS)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SMM J2135
+2.3259
+12.08±0.07
+8.25 ± 0.11 (SPIRE FTS)
+SMG
+No
+32.5 ± 4.5
+[12, 13]
+SDP.130
+2.625
+12.40±0.02
+< 10.14 (SPIRE FTS)
+SMG
+No
+6 ± 1
+[14, 15]
+SPT 0538-50
+2.782
+12.44±0.03
+< 9.95 (SPIRE FTS)
+SMG
+No
+20.9 ± 4.2
+[9, 10]
+ALESS 49.1
+2.943
+12.85±0.06
+9.48 ± 0.12 (ALMA 8)
+SMG
+No
+−
+[16, 17, 18]
+ALESS 57.1
+2.943
+12.87±0.06
+9.04 ± 0.17 (ALMA 8)
+SMG
+No
+−
+[16, 17, 18]
+SDP.81
+3.042
+12.32±0.08
+10.06 ± 0.01 (SPIRE FTS)
+SMG
+No
+25 ± 7
+[14, 15]
+SPT 0103-45
+3.090
+12.38±0.02
+9.41 ± 0.06 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+LAB1-ALMA3
+3.0993
+11.76
+9.41 ± 0.06 (ALMA 8)
+MS
+No
+−
+[19, 20]
+LAB1-ALMA1
+3.1
+11.54
+< 8.9 (ALMA 8)
+MS
+No
+−
+[19, 20]
+LAB1-ALMA2
+3.1
+11.60
+< 8.9 (ALMA 8)
+MS
+No
+−
+[19, 20]
+SPT 0550-53
+3.129
+12.08±0.09
+9.46 ± 0.09 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0529-54
+3.369
+12.36±0.04
+9.74 ± 0.04 (APEX/FLASH)
+SMG
+No
+9.4 ± 1.0
+[9, 10]
+SPT 0532-50
+3.399
+12.69±0.07
+9.46 ± 0.08 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0300-46
+3.596
+12.40±0.11
+9.05 ± 0.11 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 2147-50
+3.761
+12.39±0.06
+9.38 ± 0.06 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0418-47
+4.224
+12.48±0.03
+9.49 ± 0.03 (APEX/FLASH)
+SMG
+No
+21.0 ± 3.5
+[9, 10]
+SPT 0113-46
+4.232
+12.20±0.09
+9.51 ± 0.10 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SDP.141
+4.24
+12.52±0.12
+9.48 ± 0.07 (APEX/FLASH)
+SMG
+No
+10 − 30
+[11]
+SPT 2311-54
+4.281
+12.40±0.04
+9.23 ± 0.06 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0345-47
+4.296
+12.84±0.04
+9.37 ± 0.04 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+COSMOS-AzTEC-1
+4.342
+13.21±0.09
+9.80 ± 0.04 (ALMA 7)
+SMG
+No
+−
+[21, 22]
+AS2UDS.0568.0
+4.404
+13.30±0.08
+9.20 ± 0.08 (ALMA 7)
+SMG
+No
+−
+[23, 24]
+ALESS 61.1
+4.4189
+12.49±0.03
+9.18 ± 0.17 (ALMA 7)
+SMG
+No
+−
+[24, 25, 26]
+UDS 47.0
+4.4201
+12.50±0.06
+9.42 ± 0.12 (ALMA 7)
+SMG
+No
+−
+[24, 26]
+AS2UDS.0051.0
+4.421
+12.85±0.20
+9.38 ± 0.05 (ALMA 7)
+SMG
+No
+−
+[23, 24]
+AS2UDS.0104.0
+4.423
+12.85±0.20
+9.46 ± 0.05 (ALMA 7)
+SMG
+No
+−
+[23, 24]
+SGP 38326 (SMG1)
+4.4237
+13.20±0.09
+9.92 ± 0.05 (ALMA 7)
+SMG (SB)
+No
+−
+[27]
+SGP 38326 (SMG2)
+4.4289
+12.90±0.09
+9.46 ± 0.05 (ALMA 7)
+SMG (SB)
+No
+−
+[27]
+BRI 0952-0115
+4.4337
+12.40±0.25
+9.66 ± 0.25 (APEX/FLASH)
+SMG (SB)
+No
+4.5 ± 2.8
+[28, 29, 30]
+SPT 2103-60
+4.435
+12.41±0.03
+9.70 ± 0.06 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+AS2UDS.0232.0
+4.443
+13.26±0.15
+8.70 ± 0.09 (ALMA 7)
+SMG
+No
+−
+[23, 24]
+ALESS 65.1
+4.4445
+12.49±0.03
+9.51 ± 0.09 (ALMA 7)
+SMG
+No
+−
+[24, 25, 26]
+AS2UDS.0109.0
+4.450
+12.90±0.06
+9.42 ± 0.03 (ALMA 7)
+SMG
+No
+−
+[23, 24]
+AS2UDS.0002.1
+4.4611
+13.38±0.08
+8.90 ± 0.11 (ALMA 7)
+SMG
+No
+<∼1.5 − 2
+[23, 24]
+AS2UDS.0643.0
+4.4614
+13.11±0.22
+8.95 ± 0.15 (ALMA 7)
+SMG
+No
+<∼1.5 − 2
+[23, 24]
+AS2UDS.0208.0
+4.4615
+12.89±0.01
+9.42 ± 0.06 (ALMA 7)
+SMG
+No
+<∼1.5 − 2
+[23, 24]
+SPT 0441-46
+4.477
+12.45±0.02
+9.13 ± 0.11 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 2146-55
+4.567
+12.31±0.05
+9.19 ± 0.10 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+W2246–0526
+4.601
+14.34±0.08
+9.79 ± 0.03 (ALMA 7)
+DOG
+Yes
+−
+[31]
+ALESS 73.1
+4.7555
+12.46±0.03
+9.69 ± 0.14 (ALMA 7)
+SMG (SB)
+Yes
+−
+[24, 26, 32]
+SPT 2132-58
+4.768
+12.37±0.04
+9.17 ± 0.08 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+HDF850.1
+5.185
+12.58±0.07
+9.38 ± 0.05 (IRAM/PdBI)
+SMG
+No
+1.5 − 1.7
+[33, 34]
+HLSJ091828.6+514223 5.24
+13.04±0.10
+9.98 ± 0.01 (SMA)
+SMG
+No
+8.9 ± 1.9
+[35]
+SPT 2319-55
+5.293
+12.28±0.03
+9.00 ± 0.06 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+SPT 0346-52
+5.656
+13.39±0.02
+9.97 ± 0.06 (APEX/FLASH)
+SMG
+No
+5.4 ± 0.2
+[9, 10]
+SPT 0243-49
+5.699
+12.40±0.04
+< 9.40 (APEX/FLASH)
+SMG
+No
+(14.1 ± 7.8)
+[9, 10]
+(Continue on next page)
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+15
+Table 3 – continued The observed 𝐿[CII]-SFR relation of galaxies at high redshifts.
+Name†
+𝑧
+log (𝐿IR/𝐿⊙)§
+log (𝐿[CII]/𝐿⊙)‡, §, ∥
+Galaxy type#
+AGN
+𝜇
+References∗
+HerMESFLS3
+6.3369
+13.34±0.05
+9.83 ± 0.10 (CARMA)
+SMG
+No
+2.2 ± 0.3
+[36, 37]
+SPT 0311-58-E
+6.900
+12.66±0.12
+9.62 ± 0.06 (ALMA 6)
+SMG
+No
+1.3
+[38]
+SPT 0311-58-W
+6.900
+13.52±0.09
+9.66 ± 0.06 (ALMA 6)
+SMG
+No
+2.2
+[38]
+† The table does not include the 20 galaxies (𝑧 ≈ 2) in the samples of Stacey et al. (2010) and Brisbin et al. (2015), of which the [CII] line is
+measured by ZEUS. The 𝐿[CII]/𝐿IR vs 𝐿IR relation of these two samples systematically offsets from the others that use different instrument to
+measure [CII] line (see Fig. 7).
+§ For the gravitationally-lensed galaxies, 𝐿[CII] and 𝐿IR have been de-magnified by the reported lensing magnification factor 𝜇. For those SPT
+galaxies having no direct measurement of 𝜇 (galaxies are not spatially resolved by any observation), we adopt a constant 𝜇 = 14.1 as is done by
+Gullberg et al. (2015), which is the mean of the four galaxies (SPT 0538-50, SPT 0529-54, SPT 0418-47 and SPT 0346-52) in the same sample
+that is observationally determined via lensing modelling.
+‡ For the [CII]-undetected galaxies, we show the 3𝜎 upper confidence limit.
+∥ IRAM/PdBI: the IRAM Plateau de Bure Interferometer (Guilloteau et al. 1992); SMA: the Submillimeter Array (Ho et al. 2004); CARMA: the
+Combined Array for Research in Millimeter-wave Astronomy (Woody et al. 2004). Note that the three telescopes have produced spatially resolved
+line emission maps of [CII] for high-𝑧 SMGs (HDF850.1, HLSJ091828.6+514223 and HerMESFLS3) as ALMA does.
+# SMG: sub-mm galaxies; MS: ‘main-sequence’ galaxies; SB: starburst galaxies; DOG: hot dust-obscured galaxies (galaxies uncovered by surveys
+at near-infrared wavelengths, which have strong IR emission from warm dust, e.g. Dey et al. 2008; Eisenhardt et al. 2012).
+∗ References: (1): Zanella et al. (2018), [2]: Elbaz et al. (2011), [3]: McKinney et al. (2020), [4]: Kirkpatrick et al. (2015), [5]:Schaerer et al. (2015b),
+[6]: Sklias et al. (2014), [7]: Jones et al. (2010), [8]: Hashimoto et al. (2019b), [9]: Gullberg et al. (2015), [10]: Weiß et al. (2013), [11]: Cox et al.
+(2011), [12]: Ivison et al. (2010), [13]: Swinbank et al. (2010), [14]: Valtchanov et al. (2011), [15]: Hopwood et al. (2011), [16]: Rybak et al.
+(2019), [17]: Wardlow et al. (2018), [18]: da Cunha et al. (2021), [19]: Umehata et al. (2017), [20]: Geach et al. (2016), [21]: Tadaki et al. (2018),
+[22]: Tadaki et al. (2020), [23]: Cooke et al. (2018), [24]: Swinbank et al. (2014), [25]: Swinbank et al. (2012), [26]: Gullberg et al. (2018), [27]:
+Oteo et al. (2016), [28]: Maiolino et al. (2009), [29]: Priddey & McMahon (2001), [30]: Lehar et al. (2000), [31]: Díaz-Santos et al. (2015), [32]:
+Breuck et al. (2014), [33]: Neri et al. (2014), [34]: Walter et al. (2012), [35]: Rawle et al. (2014), [36]: Riechers et al. (2013), [37]: Cooray et al.
+(2014), [38]: Marrone et al. (2018).
+observed samples at 1 <∼ 𝑧 <∼ 5, where we have converted the SFR
+of all galaxies from their 𝐿IR using the K98 relation following the
+observational studies. We show the stacked result for the samples
+of Stacey et al. (2010) and Brisbin et al. (2015) by grey empty
+squares. Both studies measure [CII] line with ZEUS, and both obtain
+systematically higher 𝐿[CII]/SFR ratio of galaxies than the other
+studies using different instruments (by about one dex) at similar
+SFR. For the other studies, we explicitly show the data of each
+individual source in their samples. Specifically, we show the result
+of the SMGs by black circles (empty and filled), whilst the other star-
+forming galaxies are denoted by black triangles. For all the lensed
+galaxies, both 𝐿[CII] and 𝐿IR are de-magnified by the observationally
+determined 𝜇 when available. For the 16 SPT galaxies having no
+determined 𝜇 (indicated by empty black circles in Fig. 7), we correct
+their luminosities by an assumed 𝜇 = 14.1 following Gullberg et al.
+(2015). For reference, we also show the 𝐿[CII]-SFR relation of local
+galaxies by L11, L14 and H15 in the same (left) panel.
+The bulk of the selected samples at 1 <∼ 𝑧 <∼ 5 have higher SFR
+than the local samples of L11, L14 and H15. Only the few galaxies
+at 𝑧 ≈ 1 − 2 of the Zanella et al. (2018) sample overlap with the
+SFR range of the most actively star-forming galaxies of the L11
+sample, and they appear to follow the same 𝐿[CII]-SFR relation.
+At higher SFR (i.e. SFR >∼ 100 𝑀⊙ yr−1), the high-𝑧 galaxy samples
+show a larger scatter in the 𝐿[CII]-SFR relation compared to the local
+samples (L11, L14 and H15) . Apart from that, the high-𝑧 samples
+show a decline of 𝐿[CII]/SFR ratio with increasing SFR at above
+100 𝑀⊙ yr−1 (corresponding to 𝐿IR >∼ 1012 𝐿⊙). This trend can be
+more clearly seen in the right panel, where we show the 𝐿[CII]/𝐿IR
+(≈ 𝐿[CII]/SFR at high SFR) ratio of the same high-𝑧 galaxy samples
+as a function of their 𝐿IR (∼SFR). From 𝐿IR = 1012 𝐿⊙ to 1013 𝐿⊙,
+the 𝐿[CII]/𝐿IR (or 𝐿[CII]/SFR) ratio of the high-𝑧 samples decreases
+by roughly a factor of 50 (excluding the Stacey et al. 2010 and Brisbin
+et al. 2015 samples). This [CII] deficit at high 𝐿IR is similar to what
+has been found with the local galaxy samples (indicated by the filled
+grey symbols in Fig. 7).
+In the same figure, we also show the results of the FIRE galaxies
+at high redshifts. Specifically, we show the 𝐿[CII]-SFR (left panel)
+and the 𝐿[CII]/𝐿IR-𝐿IR (right panel) relations of the FIRE galaxies at
+𝑧 = 1 (yellow hexagons), 𝑧 = 2 (red triangles), 𝑧 = 3 (blue squares)
+and 𝑧 = 4 (magenta circles). For reference, we also show in the two
+panels the results of the FIRE sample at 𝑧 = 0 (cyan stars).
+The FIRE galaxies follow a roughly linear 𝐿[CII]-SFR scaling rela-
+tion over the SFR range of ≈ 0.05−100 𝑀⊙ yr−1 at each redshift (left
+panel), though having considerable scatter (1𝜎 ≈ 0.2 − 0.35 dex).
+The normalization of the relation, however, shows clear redshift evo-
+lution. From 𝑧 = 0 to 𝑧 = 4, the mean 𝐿[CII]/SFR ratio of the FIRE
+sample declines by about one dex (see the left panel of Fig. 7). This
+indicates that using the 𝐿[CII]-SFR relation derived by L11 or H15
+will lead to a systematic underestimate of SFR of galaxies at high
+redshifts.
+On the other hand, the 𝐿[CII]/𝐿IR ratio of the FIRE galaxies does
+not evolve as much with redshift between 𝑧 = 0−4 (right panel). From
+𝑧 = 0 to 𝑧 = 4, the mean 𝐿[CII]/𝐿IR ratio of the FIRE galaxies de-
+creases by 0.5 dex, which is less than the decrease of the 𝐿[CII]/SFR
+ratio (∼ 1 dex). Obviously, the reason for the discrepancy in the red-
+shift evolution of the two ratios (𝐿[CII]/SFR and 𝐿[CII]/𝐿IR) is the
+redshift evolution of the 𝐿IR-SFR relation of the galaxies (see Fig. 5
+for the result of the FIRE galaxies, and also the observational data of
+e.g. Whitaker et al. 2017) — at fixed SFR, galaxies at higher red-
+shift have on average lower dust opacity and thus a smaller fraction
+of stellar radiation is absorbed and re-emitted at far-IR. The mean
+𝐿IR/SFR ratio of galaxies therefore decreases with redshift.
+Apart from that, it is clear from the right panel that the FIRE
+galaxies at 𝑧 = 1 − 4 show a similar decrease of 𝐿[CII]/𝐿IR ratio
+with 𝐿IR like the local 𝑧 = 0 FIRE galaxies (cyan stars), and the
+decrease appears to be more significant at 𝐿IR >∼ 5 × 1011 𝐿⊙. The
+MNRAS 000, 1–42 (2022)
+
+16
+Liang et al.
+sharp decrease of 𝐿[CII]/𝐿IR at the high 𝐿IR end is in line with the
+trend in the observational data at similar redshifts. In Section 5, we
+will examine in detail the origin of this ‘[CII] deficit’ at high 𝐿IR
+and we will show that it is mainly driven by the decrease of gas mass
+per unit SFR, or depletion timescale (𝑡dep ≡ 𝑀gas/SFR), of galaxies
+with SFR.
+Note that at 𝐿IR ≈ 1012 𝐿⊙, the observed 𝐿[CII]/𝐿IR ratio of the
+galaxies at high redshifts (black symbols) appears to be higher than
+that of the observed 𝑧 = 0 galaxy samples (grey symbols) as well
+as the FIRE galaxies (coloured symbols). The mean 𝐿[CII]/𝐿IR ratio
+is roughly in agreement with the upper bound of the FIRE galaxies
+at similar 𝐿IR. This can possibly be due to selection effect. Those
+galaxies at 𝐿IR ≈ 1012 𝐿⊙ are mostly the ‘main-sequence’ (MS)
+galaxies at 𝑧 ≈ 1.5 − 2 selected by Zanella et al. (2018), which are
+expected to have longer 𝑡dep (i.e. gas mass per unit SFR) than starburst
+galaxies at the same redshift (e.g. Genzel et al. 2015; Aravena et al.
+2016; Miettinen et al. 2017; Tacconi et al. 2018; Feldmann 2020)
+and hence higher 𝐿[CII]/𝐿IR (note: 𝐿[CII]/SFR ∝ 𝑡0.7
+dep, equation 30).
+The FIRE sample as well as the local observed galaxy samples, on
+the contrary, consist of galaxies across the star-forming MS as well
+as starburst galaxies, exhibiting a wide range of 𝑡dep.
+Finally, we note that the observational data in this redshift regime
+has large uncertainties due to the large fraction of gravitationally-
+lensed galaxies included in the samples (see Table 3). First of all,
+as mentioned above, many of the lensed galaxies do not have deter-
+mined magnification factor 𝜇 (marked by empty circles in Fig. 7).
+Even for those whose 𝜇 is derived from either the rest-UV (with
+Hubble Space Telescope) or dust continuum imaging (with ALMA),
+it is not yet certain whether their [CII] luminosity is magnified by the
+same level, given that the [CII] and stellar/dust emission of galaxies
+may have different spatial configuration (e.g. Cochrane et al. 2019;
+Fujimoto et al. 2019; Matthee et al. 2019; Novak et al. 2020; Fu-
+damoto et al. 2022) and thus the different emission components may
+have different 𝜇 due to the effect of differential lensing (e.g. Blain
+1999; Hezaveh et al. 2012; Serjeant 2012; Cañameras et al. 2018;
+Yang et al. 2019a; Harrington et al. 2021). Hence, it is important
+to obtain spatially resolved imaging of both [CII] and dust emission
+for lensed galaxies and re-examine the intrinsic 𝐿[CII]/𝐿IR ratio of
+these galaxies (note: most of the lensed SMGs do not have spatially
+resolved [CII] imaging, see Table 3).
+4.3 Early galaxies (redshift 𝑧 >∼ 5)
+Observational studies on the 𝐿[CII]-SFR relation at 𝑧 >∼ 5 depend
+mainly on the rest-frame UV-selected galaxies whose redshift has
+previously been confirmed either spectroscopically or via the Ly-
+man break ‘drop-out’ technique (Hodge & da Cunha 2020). Their
+[CII] and dust emission are constrained in follow-up observational
+campaigns with ALMA, which has the power to spatially resolve the
+distant galaxies down to the scale of ∼ 1 physical kpc. The majority
+of the UV-selected galaxies at this epoch are unlensed.
+There have been two major observational campaigns for searching
+for [CII] line of galaxies at 𝑧 >∼5. The ALPINE ALMA Large Program
+(Le Fèvre et al. 2020; Béthermin et al. 2020) in cycle-5 targeted a
+sample of 118 UV-selected star-forming galaxies at 4.5 < 𝑧 < 6 with
+𝑀UV, AB < −20.2 and identified [CII] emission (at > 3.5𝜎 level) in
+75 galaxies of them (Schaerer et al. 2020). More recently, the REBELS
+Large Program (Bouwens et al. 2022) in Cycle-7 studied a sample
+of 40 UV-bright (𝑀UV, AB < −21.4) galaxies at 6.5 < 𝑧 < 7.7 and
+confirmed [CII] detection (at > 7𝜎) in 18 galaxies in their sample
+(Ferrara et al. 2022). Other observations targeting the LBGs/LAEs
+at 𝑧 >∼ 5 have identified [CII] emission in another > 35 sources in
+total. The most distant galaxy that has a [CII] detection to date is
+MACS1149-JD1 (Hashimoto et al. 2018), a gravitationally-lensed
+(𝜇 = 10) galaxy at 𝑧 = 9.11 (Carniani et al. 2020; see also Inoue
+et al. 2016 and Laporte et al. 2019). We provide a summary of the
+star-forming galaxies at 𝑧 >∼ 5 having confirmed [CII] detection in
+Table 4 (excluding quasar host galaxies).
+The SFR of these UV-selected galaxies has been derived based on
+their 𝐿UV and 𝐿IR. Because the galaxies at 𝑧>∼5 typically do not have
+good photometric sampling of the dust continuum (e.g. Casey et al.
+2018b; Liang et al. 2019; Faisst et al. 2020b), 𝐿IR has frequently been
+converted from the ALMA broad-band flux density (measured at band
+6 or 7 for galaxies at 𝑧 >∼ 5) using the standard modified-blackbody
+(MBB) function of the form (e.g. Hildebrand 1983; Hayward et al.
+2011)
+𝑆𝜈0 = (1 + 𝑧)
+𝑑2
+L
+𝜅𝜈𝑀dust𝐵𝜈(𝑇),
+(5)
+where 𝜈0 is the observing frequency (note: 𝜈0 = 345 GHz for ALMA
+band 7 and 𝜈0 = 230 GHz for ALMA band 6), 𝑆𝜈0 is the broad-band
+flux density at 𝜈0, 𝜈 = (1 + 𝑧)𝜈0 is the rest-frame frequency, 𝜅𝜈 is
+the dust opacity (per unit dust mass) at 𝜈, 𝑀dust is the dust mass of
+galaxy, 𝑇 is the ‘dust temperature’, 𝐵𝜈(𝑇) is the Planck function and
+𝑑L is the luminosity distance. 𝐿IR is then converted from 𝑆𝜈0 using
+(see Section 3.1.3 of Liang et al. 2019 for the details)
+𝐿IR =
+D𝑑2
+L𝑇4+𝛽dust
+(1 + 𝑧)𝜅𝜈𝐵𝜈(𝑇) 𝑆𝜈0,
+(6)
+where 𝛽dust ≈ 2.0 is the dust emissivity spectral index (e.g. Dunne
+et al. 2000; Draine et al. 2007) and D is a parameter that depends
+on the shape of the dust opacity curve. The derived 𝐿IR (and hence
+the obscured SFR) therefore depends mainly on the assumed ‘dust
+temperature’. It should be noted that recent cosmological simulations
+show that the true SED of high-𝑧 galaxies may significantly differ
+from the standard MBB function (e.g. Liang et al. 2019; Ma et al.
+2019, and also Casey 2012, Casey et al. 2018b) and 𝑇 does not
+faithfully reflect the physical temperature of dust in galaxies (e.g.
+Behrens et al. 2018; Liang et al. 2019). Liang et al. (2019) defines
+the ‘dust temperature’ that one would need to obtain the correct
+𝐿IR and match the observed 𝑆𝜈0 under the assumption that the SED
+has the shape of a standard MBB function (equation 5) to be the
+‘equivalent dust temperature’ (𝑇eqv).
+Using a sample of high-𝑧 galaxies produced by the MassiveFIRE
+suite (Feldmann et al. 2016, 2017), Liang et al. (2019) derived the
+best-fitting formula for 𝑇eqv using redshift and dust-to-gas mass ratio
+(𝛿dzr) as variables, i.e.
+𝑇eqv = 𝑇0 (1 + 𝑧)𝛼(𝛿dzr/0.4)𝛾. (L19)
+(7)
+For ALMA band 7 (6) fluxes, the best-fitting parameter values are
+𝑇0 = 26.9 (24.5) K, 𝛼 = 0.31 (0.36) and 𝛾 = − 0.13 (−0.15). The
+increase of 𝑇eqv with redshift is related to the enhanced level of star
+formation activity in galaxies (i.e. higher specific SFR) (Safarzadeh
+et al. 2016; Ma et al. 2019; Liang et al. 2019; Sommovigo et al.
+2020). The anti-correlation with 𝛿dzr, on the other hand, is due to the
+fact that an increase of 𝛿dzr leads to a higher dust opacity, which in
+turn results in a ‘colder’ dust SED shape of galaxies (Scoville 2013;
+Faisst et al. 2017; Liang et al. 2019). Observationally, 𝛿dzr of high-𝑧
+galaxies has not yet been constrained.
+Often, it is easier to detect the [CII] line than the dust continuum
+of galaxies at 𝑧 >∼ 5. For example, 75 out of the 118 (63.6%) galaxies
+in the ALPINE sample have confirmed detection of [CII] emission,
+whilst only 21 (17.8%) of them have confirmed detection of dust
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+17
+Table 4. Properties of the star-forming galaxies at 𝑧 >∼ 5 targeted for search for [CII] emission.
+Name†
+𝑧
+SFRUV§, #
+(𝑀⊙ yr−1)
+𝑆 (𝜇Jy)‡, ¶, #
+log (𝐿IR/𝐿⊙) ∥
+SFR††
+(𝑀⊙ yr−1)
+log (𝐿[CII]/𝐿⊙) ¶, #
+𝜇
+References ∗
+HZ7
+5.253
+31.2
+< 108 (ALMA 7)
+< 11.6
+< 62.7
+8.74 (ALMA 7)
+−
+[1, 2, 3]
+HZ9
+5.541
+22.1
+516 (ALMA 7)
+11.9
+174.5
+9.21 (ALMA 7)
+−
+[1, 2, 3]
+HZ10
+5.657
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+1261 (ALMA 7)
+12.7
+432.8
+9.13 (ALMA 7)
+−
+[1, 2, 3]
+NB816-S-61269
+5.684
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+< 66 (ALMA 7)
+< 11.4
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+−
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+WMH13
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+−
+[4, 5]
+A383-5.1
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+< 2.9 (ALMA 6)
+< 10.5
+< 6.2
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+11.4 ± 1.9
+[6]
+J1211-0118
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+220 (ALMA 6)
+12.4
+257.3
+9.15 (ALMA 6)
+−
+[7]
+WMH5
+6.070
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+218 (ALMA 6)
+12.4
+263.5
+8.82 (ALMA 6)
+−
+[9, 10]
+NTTDF2313
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+< 54 (ALMA 6)
+< 11.8
+< 68.0
+< 7.7 (ALMA 6)
+−
+[8]
+RXCJ0600-z6
+6.0719
+2.8
+9.5 (ALMA 6)
+11.0
+11.5
+8.04 (ALMA 6)
+21 ± 10
+[11]
+J0235-0532
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+< 101 (ALMA 6)
+< 12.1
+< 150.5
+8.63 (ALMA 6)
+−
+[7]
+BDF2203
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+< 69 (ALMA 6)
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+−
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+CLM1
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+1.13
+[4, 9]
+J0217-0208
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+−
+[7]
+GOODS3203
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+< 123 (ALMA 6)
+< 12.2
+< 140.4
+< 8.1 (ALMA 6)
+−
+[8]
+COSMOS20521
+6.36
+20.2
+< 60 (ALMA 6)
+< 11.8
+< 75.5
+< 7.7 (ALMA 6)
+−
+[8]
+VR7
+6.529
+58.2
+< 31.8 (ALMA 6)
+< 11.6
+< 87.5
+8.68 (ALMA 6)
+−
+[12]
+MASOSA
+6.543
+13.0
+< 27.6 (ALMA 6)
+< 11.5
+< 35.5
+< 7.34 (ALMA 6)
+−
+[12]
+HCM6A
+6.56
+5.9
+< 680 (PdBI)
+< 12.9
+< 631.1
+< 7.81 (PdBI)
+4.5
+[13, 14]
+UDS4812
+6.561
+19.3
+< 72 (ALMA 6)
+< 11.9
+< 85.7
+< 7.8 (ALMA 6)
+−
+[8]
+Himiko
+6.591
+19.8
+< 27 (ALMA 6)
+< 11.5
+< 44.8
+8.08 (ALMA 6)
+−
+[15, 16]
+CR7
+6.600
+41.7
+< 21 (ALMA 6)
+< 11.4
+< 61.1
+8.34 (ALMA 6)
+−
+[17, 18]
+COSMOS24108
+6.629
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+< 54 (ALMA 6)
+< 11.8
+< 68.2
+8.04 (ALMA 6)
+−
+[19]
+UDS16291
+6.638
+13.4
+< 60 (ALMA 6)
+< 11.8
+< 65.4
+7.85 (ALMA 6)
+−
+[19]
+NTTDF6345
+6.701
+21.2
+< 48 (ALMA 6)
+< 11.7
+< 60.2
+8.26 (ALMA 6)
+−
+[19]
+MS0451-H
+6.703
+0.4
+< 0.33 (ALMA 6)
+< 9.6
+< 0.7
+< 5.48 (ALMA 6)
+100 ± 20
+[6]
+UVISTA-Z-007
+6.7496
+23.7
+< 52.2 (ALMA 6)
+< 11.8
+< 72.0
+8.75 (ALMA 6)
+−
+[20, 21]
+UVISTA-Z-019
+6.7534
+15.8
+66 (ALMA 6)
+11.9
+74.1
+8.94 (ALMA 6)
+−
+[20, 21]
+RXJ1347-1216
+6.766
+2.4
+< 45 (ALMA 6)
+< 11.7
+< 44.8
+7.18 (ALMA 6)
+5.0 ± 0.3
+[22]
+COS-2987030247
+6.808
+24.6
+< 75 (ALMA 6)
+< 11.9
+< 94.3
+8.56 (ALMA 6)
+−
+[23]
+A1703-zD1
+6.827
+10.1
+< 24.5 (NOEMA)
+< 11.5
+< 32.8
+7.54 (NOEMA)
+9.0 ± 2.7
+[24]
+SDF-46975
+6.844
+15.4
+< 57.6 (ALMA 6)
+< 11.8
+< 68.7
+< 7.75 (ALMA 6)
+−
+[25]
+COS-3018555981
+6.854
+20.8
+< 87 (ALMA 6)
+< 12.0
+< 101.3
+8.67 (ALMA 6)
+−
+[23]
+UVISTA-Z-009
+6.86
+16.9
+< 38.0 (ALMA 6)
+< 11.6
+< 52.1
+< 8.12 (ALMA 6)
+<∼1.5
+[20, 21]
+IOK-1
+6.965
+20.0
+< 63 (ALMA 6)
+< 11.9
+< 78.4
+< 7.53 (ALMA 6)
+−
+[26]
+BDF-512
+7.008
+6.0
+< 55.2 (ALMA 6)
+< 11.8
+< 54.2
+< 7.78 (ALMA 6)
+−
+[25]
+UVISTA-Z-013
+7.02
+22.1
+< 45.0 (ALMA 6)
+< 11.7
+< 63.8
+< 8.30 (ALMA 6)
+−
+[20, 21]
+UVISTA-Z-001
+7.0599
+45.8
+104 (ALMA 6)
+12.1
+137.8
+8.83 (ALMA 6)
+−
+[20, 21]
+UVISTA-Z-010
+7.06
+17.4
+< 44.1 (ALMA 6)
+< 11.7
+< 58.3
+< 8.30 (ALMA 6)
+−
+[20, 21]
+BDF-3299
+7.109
+5.7
+< 23.4 (ALMA 6)
+< 11.4
+< 27.4
+7.83 (ALMA 6)
+−
+[25, 27, 28]
+A1689-zD1
+7.137
+4.7
+60.2 (ALMA 6)
+11.9
+67.5
+7.87 (ALMA 6)
+9.3
+[29, 30, 31]
+COSMOS13679
+7.145
+21.1
+< 42 (ALMA 6)
+< 11.7
+< 60.1
+7.85 (ALMA 6)
+−
+[19]
+B14-65666
+7.152
+50.2
+130 (ALMA 6)
+12.2
+170.2
+9.12 (ALMA 6)
+−
+[32, 33]
+SXDF-NB1006-2
+7.212
+21.6
+< 42 (ALMA 6)
+< 11.7
+< 60.6
+< 7.45 (ALMA 6)
+−
+[34]
+z8-GND-5296
+7.508
+16.6
+< 480 (PdBI)
+< 12.7
+< 464.1
+< 8.55 (PdBI)
+−
+[35, 36]
+MACS0416-Y1
+8.311
+11.7
+137 (ALMA 7)
+11.8
+56.8
+8.15 (ALMA 5)
+1.43 ± 0.04
+[37, 38, 39]
+A2744-YD4
+8.380
+11.2
+99 (ALMA 7)
+11.6
+43.8
+7.26 (ALMA 5)
+1.8 ± 0.3
+[28, 40, 41]
+S04590
+8.4931
+0.5
+< 4.81 (ALMA 7)
+< 10.3
+< 2.0
+7.22 (ALMA 5)
+8.69 ± 2.5
+[42, 43]
+MACS1149-JD1
+9.110
+4.5
+< 5.3 (ALMA 7)
+< 10.4
+< 6.5
+7.08 (ALMA 5)
+10
+[28, 41, 44]
+REBELS‡‡
+REBELS-05
+6.496
+15.1
+67.2 (ALMA 6)
+11.9
+77.2
+8.84 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-38
+6.577
+19.5
+163.0 (ALMA 6)
+12.3
+170.2
+9.23 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-29
+6.685
+27.0
+56.1 (ALMA 6)
+11.8
+78.9
+8.74 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-32
+6.729
+15.1
+60.4 (ALMA 6)
+11.8
+71.0
+8.89 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-08
+6.749
+17.3
+101.4 (ALMA 6)
+12.1
+111.2
+8.87 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-39
+6.847
+40.0
+79.6 (ALMA 6)
+12.0
+113.7
+8.90 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-14
+7.084
+37.9
+60.0 (ALMA 6)
+11.8
+93.6
+8.57 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-27
+7.090
+21.6
+50.6 (ALMA 6)
+11.8
+68.5
+8.79 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-25
+7.306
+16.2
+56.1 (ALMA 6)
+11.8
+68.3
+9.20 (ALMA 6)
+−
+[45, 46, 47]
+REBELS-12
+7.349
+32.5
+86.8 (ALMA 6)
+12.0
+113.2
+9.00 (ALMA 6)
+−
+[45, 46, 47]
+(Continue on next page)
+MNRAS 000, 1–42 (2022)
+
+18
+Liang et al.
+Observations of LBGs/LAEs at z > 5
+FIRE galaxies
+z = 4
+z = 6
+z = 8
+FIRE galaxies
+z = 4
+z = 6
+z = 8
+Observations of LBGs/LAEs at z > 5
+ and dust-detected
+[CII]
+ detected, but no dust-detection
+[CII]
+(SFR converted from 
+ )
+LUV
+ undetected
+[CII]
+REBELS
+ALPINE
+Others
+Herrera-Camus et al. 2015
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+REBELS
+ALPINE
+Others
+Herrera-Camus et al. 2015
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+ and dust-detected
+[CII]
+ detected, but no dust-detection
+[CII]
+(SFR corrected by 3  upper limit of 
+)
+σ
+LIR
+ undetected
+[CII]
+Figure 8. Comparison of the 𝐿[CII]-SFR relation of the FIRE galaxies with the observational data at high redshifts. In the two panels, we show the result of the
+FIRE galaxies at 𝑧 = 4, 𝑧 = 6 and 𝑧 = 8 by magenta circles, green diamonds and purple downward triangles, respectively. We also show in the two panels the
+observational data of the rest-UV-selected star-forming galaxies at 𝑧 >∼ 5, including the ones targeted by the ALPINE (blue symbols) and REBELS (red symbols)
+ALMA surveys as well as the others targeted by the other observations (black symbols) (see Table 4 for the details). The galaxies having both confirmed [CII]
+and dust continuum detection are indicated by vertical (REBELS) and diagonal (red for ALPINE and black for others) crosses. The galaxies having no [CII]
+detection are shown by downward arrows in both panels. The location of the arrows indicate the 3𝜎 upper limit of their 𝐿[CII]. For the ones having [CII] but
+without dust detection (meaning that their SFRIR is uncertain), we show the relation between their 𝐿[CII] and the lower (upper) SFR limit in the left (right) panel
+by rightward (leftward) triangles. For reference, we also show the result of local (𝑧 = 0) observations of normal star-forming galaxies (SFGs) by L11, L14 and
+H15 in the two panels. The FIRE sample at 𝑧 = 4 − 8 shows systematically lower 𝐿[CII]/SFR ratio than the local SFGs ([CII] deficit). The observed galaxy
+samples at 𝑧 >∼ 5 show similar [CII] deficit if 𝑇eqv follows equation (7) (assuming 𝛿dzr = 0.4).
+Table 4 – continued
+Name†
+𝑧
+SFRUV§, #
+(𝑀⊙ yr−1)
+𝑆 (𝜇Jy)‡, ¶, #
+log (𝐿IR/𝐿⊙) ∥
+SFR††
+(𝑀⊙ yr−1)
+log (𝐿[CII]/𝐿⊙) ¶, # 𝜇
+References ∗
+REBELS-40
+7.365
+18.4
+48.3 (ALMA 6)
+11.8
+64.5
+8.69 (ALMA 6)
+−
+[43, 44, 45]
+REBELS-19
+7.369
+15.1
+71.2 (ALMA 6)
+11.9
+81.3
+8.94 (ALMA 6)
+−
+[43, 44, 45]
+REBELS-18
+7.675
+33.5
+52.9 (ALMA 6)
+11.8
+82.8
+9.03 (ALMA 6)
+−
+[43, 44, 45]
+† The table does not include the 118 galaxies (4.5 <∼ 𝑧 <∼ 6) selected by the ALPINE project. The information of the ALPINE galaxies can be
+downloaded from the official webpage of the project: https://cesam.lam.fr/a2c2s/data_release.php. The ALPINE galaxies
+are unlensed.
+§ SFRUV is converted from 𝐿UV via SFRUV (𝑀⊙ yr−1) = 1.58 × 10−10 𝐿UV (𝐿⊙) following Hao et al. (2011) (see Table 3) for the Kroupa
+(2002) IMF.
+‡ The number in the brackets indicates the specific ALMA band at which dust continuum is measured.
+¶ For the galaxies having no detection of dust thermal continuum ([CII] emission), we show the 3𝜎 upper confidence limit of 𝑆 (𝐿[CII]).
+# For the gravitationally-lensed galaxies, 𝐿UV (and hence SFRUV), 𝑆, 𝐿IR and 𝐿[CII] are de-magnified by 𝜇.
+∥ 𝐿IR (or the upper limit of 𝐿IR for the dust-undetected sources) is converted from 𝑆 (the 3𝜎 upper limit of 𝑆) via the standard MBB function
+with 𝑇eqv calculated by equation (4) (assuming 𝛽dust = 2.0 and 𝛿dzr = 0.4).
+†† SFR is derived using SFR (𝑀⊙ yr−1) = SFRUV + SFRIR = 1.58 × 10−10 (𝐿UV + 0.46𝐿IR) (𝐿⊙) following Hao et al. (2011) (see Table 3) for
+the Kroupa (2002) IMF.
+‡‡ We only list here the 13 galaxies of the REBELS sample that have confirmed detection of both [CII] and dust continuum. The information of
+the other 5 galaxies having [CII] but no dust detection is not yet publicly available.
+∗ References: (1): Capak et al. (2015), [2]: Barisic et al. (2017), [3]: Faisst et al. (2017), [4]: Fujimoto et al. (2019), [5]: Fujimoto et al. (2016),
+[6]: Knudsen et al. (2016), [7]: Harikane et al. (2020), [8]: Carniani et al. (2018a), [9]: Willott et al. (2015b), [10]: Willott et al. (2013a), [11]:
+Fujimoto et al. (2021), [12]: Matthee et al. (2019), [13]: Kanekar et al. (2013), [14]: Hu et al. (2002), [15]: Ouchi et al. (2013), [16]: Carniani
+et al. (2018b), [17]: Sobral et al. (2015), [18]: Matthee et al. (2017), [19]: Pentericci et al. (2016), [20]: Schouws et al. (2022a), [21]: Schouws
+et al. (2022b), [22]: Bradač et al. (2017), [23]: Smit et al. (2018), [24]: Molyneux et al. (2022), [25]: Maiolino et al. (2015), [26]: Ota et al.
+(2014), [27]: Carniani et al. (2017), [28]: Carniani et al. (2020), [29]: Watson et al. (2015), [30]: Knudsen et al. (2017), [31]: Wong et al. (2022),
+[32]: Hashimoto et al. (2019a), [33]: Bowler et al. (2018), [34]: Inoue et al. (2016), [35]: Schaerer et al. (2015a), [36]: Finkelstein et al. (2013),
+[37]: Tamura et al. (2019), [38]: Bakx et al. (2020), [39]: Kawamata et al. (2016), [40]: Laporte et al. (2017), [41]: Laporte et al. (2019), [42]:
+Fujimoto et al. (2022), [43]: Heintz et al. (2022b), [44]: Hashimoto et al. (2018), [45]: Ferrara et al. (2022), [46]: Sommovigo et al. (2022),
+[47]: Bouwens et al. (2022).
+MNRAS 000, 1–42 (2022)
+
+X
+10
+() I
+108
+X
+10
+106
+10-1
+100
+101
+102
+103
+10
+SFR(Mo yr-14X
+10
+108
+10
+106
+100
+101
+10-1
+102
+103
+10
+SFR(Mo yr-1CII emission as an indicator of galaxy SFR
+19
+Table 5. Comparison between the mean ‘equivalent dust temperature’ (<𝑇eqv>) assumed by the ALPINE and REBELS projects and by this work.
+Project name
+Reference
+No. of galaxies
+<𝑧>
+<𝑇eqv/K>
+<𝑇eqv/K>†
+Δ<log(
+𝐿[CII ]
+SFR )>‡
+(literature)
+(this work)
+(dex)
+ALPINE
+Schaerer et al. (2020)
+118
+4.58
+42
+51.3
+-0.27
+REBELS
+Ferrara et al. (2022)
+40
+7.08
+55
+57.4
+-0.12
+† Calculated using equation (7) with 𝛿dzr = 0.4. Note that with a lower 𝛿dzr, 𝑇eqv is higher than the listed value in this column.
+‡ The resulting difference in the derived mean 𝐿[CII]/SFR ratio (in dex) of the galaxy samples due to the difference in 𝑇eqv used by the previous
+studies (Schaerer et al. 2020 and Ferrara et al. 2019) and this work.
+continuum. Almost all dust-detected galaxies have detection of [CII]
+line. The detection limit of [CII] of the current ALMA observations
+is about 108 𝐿⊙.
+We convert the sub-mm broad-band flux density (𝑆𝜈0) of the dust-
+detected galaxies (or the 3𝜎 upper limit of 𝑆𝜈0 for the dust-undetected
+galaxies) to 𝐿IR (the upper limit of 𝐿IR) consistently using 𝑇eqv that
+follows equation (7) (assuming 𝛿dzr = 0.4) to make a fair comparison
+between different observed samples and our theoretical predictions
+using FIRE galaxies. We compute the SFR of the observed galaxies
+using their measured 𝐿UV and the derived 𝐿IR following Hao et al.
+(2011), i.e. SFR (𝑀⊙ yr−1) = 1.58 × 10−10 (𝐿UV + 0.46𝐿IR) (𝐿⊙),
+for the Kroupa (2002) IMF. For the dust-undetected galaxies, we
+estimate the lower and upper bounds of their SFR, where the former
+is converted from their 𝐿UV assuming no dust emission (i.e. 𝐿IR = 0),
+whilst the latter accounts for the upper limit of 𝐿IR converted from
+the 3𝜎 upper limit of 𝑆𝜈0.
+In Fig. 8, we show the observed 𝐿[CII]-SFR relation of the rest-UV-
+selected galaxy samples at 𝑧 >∼ 5 (see Table 4 for the details) together
+with the result of the FIRE galaxies at 𝑧 = 4, 𝑧 = 6 and 𝑧 = 8 in the
+two panels. For the observed galaxies having no detection of dust,
+we show the relation between their 𝐿[CII] (for the [CII]-undetected
+galaxies, the 3𝜎 upper limit of their 𝐿[CII]) and the lower and upper
+bound of their SFR, respectively, in the left and right panels of the
+figure. For reference, we also show in Fig. 8 the observed 𝐿[CII]-SFR
+relation of the local star-forming galaxies by L11, L14 and H15.
+It can be seen that the FIRE galaxies at 𝑧 = 4 − 8 lie systematically
+below the observed local 𝐿[CII]-SFR relations (and thus also the FIRE
+galaxies at 𝑧 = 0) over the broad SFR range of ≈ 0.1 − 103 𝑀⊙ yr−1,
+showing a [CII] deficit. This appears to be in agreement with the
+observational data.
+At SFR>∼100 M⊙ yr−1, most of the observed galaxies at 𝑧 >∼5 have
+both [CII] and dust detections and thus their (dust-obscured) SFR
+is more reliably constrained. The mean 𝐿[CII]/SFR ratio of these
+galaxies is lower than the L11 relation (solid green line) by 0.22 dex,
+which is close to the 1𝜎 scatter of the L11 relation (see Table 2).
+The FIRE galaxies at 𝑧 ≥ 4 are about 2𝜎 below the L11 relation in
+the same SFR range, which seem to show a slightly more prominent
+‘deficit’ than the observed samples.
+At SFR <∼ 100 M⊙ yr−1, most of the 𝑧 >∼ 5 galaxies do not have
+confirmed dust detection with the current ALMA observations, and a
+large fraction of them do not have confirmed [CII] detections neither
+(marked by downward arrows). The uncertainty in the SFR estimate
+of these dust-undetected galaxies can be as large as a factor of ∼ 5
+(≈ 20 − 100 𝑀⊙ yr−1, see Fig. 8). Such a large uncertainty is due
+to the high 𝑇eqv of galaxies at 𝑧 >∼ 5 (𝑇eqv >∼ 45 K for 𝛿dzr = 0.4,
+see equation (7)), so that even a low noise level (typically 𝜎 ∼
+10𝜇Jy, see Table 4) of the ALMA observations is converted to a
+relatively high upper bound of 𝐿IR (and hence SFRIR). From Fig. 8,
+it can be seen that the predicted 𝐿[CII]-SFR relation of the FIRE
+galaxies does not conflict with the observational constraints over
+SFR ≈ 10 − 100 𝑀⊙ yr−1. In particular, for the [CII]-undetected
+galaxies, the 3𝜎 upper limit of their 𝐿[CII] (marked by downward
+arrows) appears to be above the data points of the FIRE galaxies
+at similar SFR when their dust emission is insignificant, namely,
+SFR ≈ SFRUV (see the left panel of Fig. 8).
+At SFR <∼ 10 𝑀⊙ yr−1, we lack enough observational data for a
+reliable constraint on the 𝐿[CII]-SFR relation at 𝑧>∼5 because galaxies
+having such low SFR are intrinsically faint. The galaxy having the
+lowest SFR (SFR ≈ 1 𝑀⊙ yr−1) that has had [CII] measurement
+to date at 𝑧 >∼ 5 is MS0451-H (Knudsen et al. 2016), a strongly
+lensed galaxy at 𝑧 = 6.7 with an estimated magnification factor of
+𝜇 = 100 ± 20. MS0451-H has no confirmed [CII] detection yet.
+The upper bound of its 𝐿[CII]/SFR ratio is more than 1.5 dex below
+the L11 relation (even with the most conservative, UV-based SFR,
+see the left panel of Fig. 8), showing a strong [CII] deficit. This
+appears to be in agreement with the FIRE sample. It can be seen
+from the figure that the [CII] deficit of the FIRE galaxies extends to
+SFR <∼ 10 𝑀⊙ yr−1 at 𝑧 >∼ 5, which is even slightly more prominent
+than at higher SFR. Encouragingly, some of the FIRE galaxies at
+𝑧 ≥ 4 show similarly low 𝐿[CII]/SFR ratio as MS0451-H.
+The 𝐿[CII]-SFR relation of the observed galaxies at 𝑧 >∼ 5 reported
+in this work seems to have lower normalization than a number of
+the recent observational studies, including e.g. Schaerer et al. (2020)
+(ALPINE paper), Ferrara et al. (2022) (REBELS paper), Matthee et al.
+(2017, 2019), Carniani et al. (2018a), Harikane et al. (2020) and
+Fujimoto et al. (2021). This is due to the fact that these studies have
+assumed a lower 𝑇eqv than what we use for this study as derived using
+equation (7). As has been mentioned in some of these studies, the
+largest uncertainty of the derived galaxy 𝐿[CII]-SFR relation at 𝑧>∼5 is
+the assumed 𝑇eqv. In Table 5, we explicitly show the difference in the
+mean 𝑇eqv adopted by the ALPINE/REBELS projects and this work
+(for 𝛿dzr = 0.4), as well as the resulting difference in the derived
+mean 𝐿[CII]/SFR ratio (<𝐿[CII]/SFR>) of the galaxies. Note that
+Ferrara et al. (2022) has used very similar 𝑇eqv compared to what
+is used in our work as fiducial (with 𝛿dzr = 0.4), whereas Schaerer
+et al. (2020) has used significantly lower 𝑇eqv (< 𝑇eqv > = 42 K)
+for the ALPINE galaxies than us (< 𝑇eqv > = 52.1 K). Our estimate
+of the 𝐿[CII]-SFR relation of the ALPINE galaxies is therefore about
+0.3 dex below the originally reported result.
+𝐿[CII]/𝐿IR of IR-luminous galaxies
+In addition to the LBGs/LAEs having moderate SFRs, there have
+been studies probing the more extreme systems at 𝑧 >∼ 5, in par-
+ticular, the quasar hosts. These systems are gas/dust-rich and very
+IR-luminous (𝐿IR >∼ 1012 𝐿⊙). They typically are also bright [CII]
+emitters, having 𝐿[CII] that spans across the range of ≈ 108−1010 𝐿⊙.
+We summarize the properties of the quasar hosts at 𝑧 >∼ 5 having had
+[CII] line detections to date in Table 6 (> 65 galaxies in total). Ob-
+servations targeting the quasar hosts have a high successful detection
+rate for [CII] line (e.g. Decarli et al. 2017; Venemans et al. 2020).
+MNRAS 000, 1–42 (2022)
+
+20
+Liang et al.
+Observations of galaxies at z > 5
+FIRE galaxies
+z = 4
+z = 6
+z = 8
+REBELS
+ALPINE
+LBGs/LAEs
+Quasar hosts
+Higher 
+ 
+Teqv
+SMGs
+Local observations  
+(same as in fig.6)
+* 
+Figure 9. 𝐿[CII]/𝐿IR vs. 𝐿IR relation of galaxies at high redshifts. Filled
+coloured symbols indicate the data of the FIRE galaxies (magenta circles for
+𝑧 = 4, green diamonds for 𝑧 = 6 and purple downward triangles for 𝑧 = 8).
+Red vertical and blue diagonal crosses represent the observational data of the
+REBELS (<𝑧> ≈ 7) and ALPINE (<𝑧> ≈ 4.5) galaxy samples, respectively.
+Black symbols represent the observational data of the other galaxy samples
+at 𝑧 >∼5. Specifically, black diagonal crosses, black circles (filled and unfilled)
+and black stars correspond to the UV-selected galaxies, SMGs and quasar
+hosts, respectively. For the galaxies whose dust continuum is measured at
+only single ALMA band, 𝐿IR is derived using 𝑇eqv that follows equation (7)
+assuming 𝛿dzr = 0.4 except for the REBELS galaxies, for which we show two
+different sets of data that are produced by using 𝛿dzr = 0.4 (semi-transparent
+red crosses) and 𝛿dzr = 0.1 (non-transparent red crosses). The lower 𝛿dzr
+yields higher 𝑇eqv (and hence 𝐿IR) estimates for the galaxies. The black arrow
+indicates the direction along which the data points of these galaxies move
+on the diagram with increasing 𝑇eqv. For the SMGs, filled circles indicate
+the galaxies that are either confirmed as un-lensed or have observationally
+determined lensing magnification factor 𝜇, whereas unfilled circles indicate
+the lensed SPT galaxies having no determined 𝜇 yet (see Section 4.2). Grey
+symbols in the background represent the observational data of the local 𝑧 = 0
+galaxy samples, as is shown in Fig. 6 (right panel). Black horizontal line
+indicates the median 𝐿[CII]/𝐿IR ratio (<𝐿[CII]/𝐿IR> = 0.002) of the local
+galaxies at 𝐿IR < 1011 𝐿⊙. Galaxies at 𝑧 > 5 show a trend of declining
+𝐿[CII]/𝐿IR ratio with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙ similar to the local samples.
+The FIRE simulations successfully reproduced the observed [CII] deficit
+at high 𝐿IR at 𝑧 > 5.
+Like most of the LBGs/LAEs at this epoch, the selected quasar
+hosts typically have one or two data points in their dust continuum
+(measured with ALMA band 6 or 7) and their 𝐿IR is converted from
+a single broad-band sub-mm flux density in the literature using the
+standard MBB function with an assumed 𝑇eqv. 𝐿IR has generally
+been considered as a crude estimate of their SFR by the observational
+studies assuming that these quasar hosts are gas and dust-rich and the
+stellar radiation of these galaxies is significantly dust-obscured. It is,
+however, unknown to what degree the radiation from the accreting
+supermassive black hole affects the shape of the IR SED and the
+total IR luminosity of these early galaxies. Observations of galaxies
+at lower redshifts (𝑧 ≈ 0 − 3) demonstrate that the IR SED shape of
+galaxies becomes ‘warmer’ (indicating higher 𝑇eqv) with increasing
+AGN power (Kirkpatrick et al. 2015). A similar conclusion was
+reached in the early study by Younger et al. 2009 with hydrodynamic
+simulations of galaxy mergers that include AGN modelling. Note,
+however, that some recent studies (e.g. Symeonidis 2016; McKinney
+et al. 2021) also suggest that AGN radiation may even dominate the
+cold-dust emission of the host galaxies at high redshifts.
+In Fig. 9, we show the 𝐿[CII]/𝐿IR vs. 𝐿IR relation of the quasar
+hosts, along with other galaxy populations at 𝑧 >∼5, including the few
+SMGs (listed in Table 3), the ALPINE and REBELS galaxies and other
+rest-UV-selected galaxies at 𝑧 >∼ 5 (we only show the galaxies hav-
+ing confirmed dust detection, which have more reliable constraints
+on 𝐿IR than the dust-undetected galaxies). We convert the reported
+single-band sub-mm flux density of all the quasar hosts to 𝐿IR using
+the standard MBB function and 𝑇eqv that follows equation (7) with
+the best-fit parameters derived by Liang et al. (2019). We note that
+for the quasar hosts, this is likely to be an underestimate because
+the best-fit parameters of Liang et al. (2019) are derived using FIRE
+simulations which do not include AGN feedback. Having a higher
+𝑇eqv, the data points of the quasar hosts (black stars) will shift in
+the diagonal direction toward the bottom-right corner of the diagram
+(marked by the black arrow in Fig. 9).
+Looking at the observational data, we can see a clear trend of
+declining 𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR) ratio of the galaxies with 𝐿IR
+([CII] deficit) at 𝐿IR >∼ 1011.5 𝐿⊙ at 𝑧 >∼ 5, similar to the trend seen at
+lower redshifts. The 𝐿[CII]/𝐿IR-𝐿IR relation of these early galaxies
+appears to consistent with the local samples (grey symbols) in the
+overlapping 𝐿IR regime and show similarly large scatter.
+We also show in Fig. 9 the 𝐿[CII]/𝐿IR-𝐿IR relation of the FIRE
+galaxies at 𝑧 = 4 − 8. The result of the FIRE galaxies is in good
+agreement with the observational data in overlapping 𝐿IR range,
+except for the REBELS sample (<𝑧> ≈ 7, indicated by red vertical
+crosses in Fig. 9). Using 𝛿dzr = 0.4, the REBELS galaxies (semi-
+transparent red crosses) show systematically higher 𝐿[CII]/𝐿IR than
+the rest of the observed galaxy samples (blue and black diagonal
+crosses) as well as the FIRE galaxies at similar 𝐿IR (≈ 1012 𝐿⊙)
+by ∼ 0.5 dex. Using 𝛿dzr = 0.1 instead, the expected mean 𝑇eqv of
+the REBELS sample increases by ≈ 20% (from 57 K to 71 K), and
+the derived mean 𝐿IR (𝐿[CII]/𝐿IR ratio) of the galaxies increases
+(decreases) by a factor of ∼ 3. The data of the REBELS sample for
+𝛿dzr = 0.1 (non-transparent red crosses) appears to be consistent with
+the other observed samples as well as the FIRE galaxies.
+The FIRE galaxies at 𝑧 ≥ 4 show a trend of declining 𝐿[CII]/𝐿IR
+ratio with 𝐿IR, which agrees with the observational data. It is also
+clear to see that the 𝐿[CII]/𝐿IR ratio of the FIRE galaxies decreases
+with redshift at fixed 𝐿IR at 𝑧 ≥ 4. The trend of decreasing 𝐿[CII]/𝐿IR
+ratio with both redshift and 𝐿IR persists up to 𝑧 = 8 in the FIRE
+simulations.
+Finally, we note that it is unclear whether AGN activity is directly
+related to the [CII] deficit at high 𝐿IR based on the current data,
+despite the large number of quasar hosts at 𝑧 >∼5 showing strong [CII]
+deficit. This is because most of the selected SMGs in the literature
+(2 <∼ 𝑧 <∼ 7), having similar 𝐿IR to the quasar hosts, have no identified
+AGN feature (see Table 3) but show similarly strong [CII] deficit
+as the quasar hosts. In addition, the FIRE simulations, which do not
+include AGN physics, have also successfully reproduced similarly
+low 𝐿[CII]/𝐿IR ratio at high 𝐿IR.
+5 THE PHYSICS OF THE 𝐿[CII]-SFR SCALING RELATION
+OF GALAXIES
+In the previous section, we have shown that the 𝐿[CII]-SFR relation
+of the FIRE galaxies predicted using our model is in good agreement
+with the observational data of local and high-𝑧 galaxies. In particular,
+our model reproduces the observed [CII] deficit of galaxies at high
+MNRAS 000, 1–42 (2022)
+
+10
+10
+L[CII] /
+10
+10°
+109
+.13
+10
+10
+LIR (Lo).4CII emission as an indicator of galaxy SFR
+21
+Table 6. Characteristics of the high-𝑧 quasar host galaxies.
+Name
+𝑧
+𝑆𝜈 (mJy)∥
+log (𝐿IR/𝐿⊙)§
+log (𝐿[CII]/𝐿⊙) ∥
+References∗
+SDSS J1015+0020
+4.407
+0.60 (ALMA 7)
+12.3
+8.46 (ALMA 7)
+[1]
+BRI 1335-0417
+4.41
+9.03 (ALMA 6)
+14.0
+10.21 (APEX/FLASH)
+[2, 3]
+BR 1202-0725 N
+4.691
+18.8 (ALMA 7)
+13.8
+10.00 (ALMA 7)
+[4, 5]
+BR 1202-0725 S
+4.694
+18.0 (ALMA 7)
+13.8
+9.81 (ALMA 7)
+[4, 5]
+SDSS J0338+0021
+5.027
+2.98 (ALMA 6)
+13.5
+9.76 (ALMA 6)
+[6]
+SDSS J0129-0035
+5.779
+2.61 (ALMA 6)
+13.5
+9.28 (ALMA 6)
+[7, 8, 9]
+SDSS J1044-0125
+5.785
+3.00 (ALMA 6)
+13.5
+9.21 (ALMA 6)
+[7, 8, 9]
+PSO J004+17
+5.817
+0.88 (ALMA 6)
+13.0
+8.31 (ALMA 6)
+[10]
+PSO J352-15
+5.832
+0.34 (ALMA 7)
+12.1
+9.09 (ALMA 7)
+[11]
+HSC J1202-0057
+5.929
+0.25 (ALMA 6)
+12.4
+8.79 (ALMA 7)
+[12]
+PSO J056+16
+5.967
+0.17 (ALMA 6)
+12.3
+7.11 (ALMA 6)
+[10]
+PSO J007+04
+6.001
+2.07 (ALMA 6)
+13.4
+9.20 (ALMA 6)
+[9, 13]
+SDSS J2310+1855†
+6.003
+−
+13.2
+9.94 (ALMA 6)
+[7, 14]
+PSO J009-10
+6.004
+3.66 (ALMA 6)
+13.6
+9.95 (ALMA 6)
+[9, 13]
+CFHQS J0055+0146
+6.006
+0.21 (ALMA 6)
+12.4
+8.92 (ALMA 6)
+[15]
+CFHQS J0216-0455
+6.01
+< 0.04 (ALMA 6)
+< 11.6
+< 7.85 (ALMA 6)
+[16]
+PSO J265+41
+6.026
+3.61 (ALMA 6)
+13.6
+9.96 (ALMA 6)
+[10]
+SDSS J1306+0356
+6.033
+0.74 (ALMA 6)
+12.9
+9.05 (ALMA 6)
+[9, 13]
+ULAS J1207+0630
+6.037
+0.50 (ALMA 6)
+12.7
+9.13 (ALMA 6)
+[13]
+SDSS J2054-0005
+6.039
+3.15 (ALMA 6)
+13.5
+9.49 (ALMA 6)
+[7, 9]
+VDESJ0454-4448
+6.058
+0.71 (ALMA 6)
+12.9
+8.86 (ALMA 6)
+[13]
+PSO J158+14
+6.068
+3.46 (ALMA 6)
+13.6
+9.22 (ALMA 6)
+[10]
+SDSS J0842+1218
+6.075
+0.68 (ALMA 6)
+12.9
+8.88 (ALMA 6)
+[9, 13, 17]
+HSC J2228+0152
+6.081
+< 0.05 (ALMA 6)
+< 11.7
+8.39 (ALMA 6)
+[18]
+CFHQS J2100-1715
+6.081
+0.56 (ALMA 6)
+12.8
+9.12 (ALMA 6)
+[9, 13, 17, 19]
+HSC J2216-0016
+6.096
+0.14 (ALMA 6)
+12.2
+9.01 (ALMA 6)
+[12]
+PSO J239+07
+6.110
+0.23 (ALMA 6)
+12.4
+8.37 (ALMA 6)
+[10]
+HSC J1208-0200
+6.117
+0.09 (ALMA 6)
+12.0
+8.43 (ALMA 6)
+[18]
+CFHQS J1509-1749
+6.123
+1.72 (ALMA 6)
+13.3
+9.37 (ALMA 6)
+[13]
+PSO J065-19
+6.125
+0.46 (ALMA 6)
+12.7
+8.97 (ALMA 6)
+[13]
+CFHQS J0221-0802
+6.13
+0.25 (ALMA 6)
+12.4
+< 8.08 (ALMA 6)
+[16]
+ULAS J1319+0950
+6.135
+5.13 (ALMA 6)
+13.8
+9.61 (ALMA 6)
+[7, 9, 20]
+VIK J2318-3029
+6.146
+3.11 (ALMA 6)
+13.5
+9.35 (ALMA 6)
+[9, 13]
+VIMOS2911
+6.149
+0.77 (ALMA 6)
+12.9
+9.41 (ALMA 6)
+[16]
+PSO J217-16
+6.150
+0.37 (ALMA 6)
+12.6
+9.00 (ALMA 6)
+[13]
+CFHQS J2229+1457
+6.152
+0.05 (ALMA 6)
+11.8
+8.78 (ALMA 6)
+[15]
+PSO J359-06
+6.172
+0.79 (ALMA 6)
+12.9
+9.42 (ALMA 6)
+[9, 10, 13]
+PSO J065-26
+6.187
+1.37 (ALMA 6)
+13.2
+9.23 (ALMA 6)
+[9, 13]
+PSO J308-21
+6.236
+1.18 (ALMA 6)
+13.1
+9.53 (ALMA 6)
+[9, 13, 17]
+HSC J2239+0207
+6.250
+1.11 (ALMA 6)
+13.1
+8.98 (ALMA 6)
+[18]
+SDSS J0100+2802
+6.327
+1.37 (ALMA 6)
+13.2
+9.58 (ALMA 6)
+[21, 22]
+ATLAS J025-33
+6.338
+2.49 (ALMA 6)
+13.4
+9.75 (ALMA 6)
+[9, 13]
+VIK J2211-3206
+6.339
+0.57 (ALMA 6)
+12.8
+8.98 (ALMA 6)
+[13]
+PSO J083+11
+6.340
+5.10 (ALMA 6)
+13.8
+10.02 (ALMA 6)
+[23]
+VIK J1152+0055
+6.364
+0.22 (ALMA 6)
+12.4
+8.81 (ALMA 6)
+[12, 13]
+PSO J159-02
+6.381
+0.65 (ALMA 6)
+12.9
+9.05 (ALMA 6)
+[13]
+HSC J0859+0022
+6.390
+0.16 (ALMA 6)
+12.2
+8.66 (ALMA 6)
+[12]
+J2329-0301
+6.417
+0.04 (ALMA 6)
+11.6
+8.59 (ALMA 6)
+[16]
+SDSS J1148+5251†
+6.42
+−
+13.3
+9.64 (NOEMA)
+[22, 24, 25, 26]
+CFHQS J0210-0456
+6.432
+0.12 (ALMA 6)
+12.1
+8.48 (ALMA 6)
+[27]
+PSO J183+05
+6.439
+4.79 (ALMA 6)
+13.7
+9.85 (ALMA 6)
+[9, 13]
+VIK J2318-3113
+6.443
+0.36 (ALMA 6)
+12.6
+9.20 (ALMA 6)
+[9, 13]
+PSO J011+09
+6.469
+1.20 (ALMA 6)
+13.1
+8.47 (ALMA 6)
+[10]
+PSO J167-13
+6.514
+0.89 (ALMA 6)
+13.0
+9.75 (ALMA 6)
+[9, 13, 16]
+J043947+163415 (lensed‡)
+6.519
+3.27 (ALMA 6)
+13.6
+9.54 (ALMA 6)
+[28, 29]
+PSO J036+03
+6.542
+2.55 (ALMA 6)
+13.5
+9.53 (ALMA 6)
+[9, 30]
+PSO J231-20
+6.587
+4.37 (ALMA 6)
+13.7
+9.55 (ALMA 6)
+[9, 13, 17]
+PSO J323+12
+6.587
+0.23 (ALMA 6)
+12.4
+9.16 (ALMA 6)
+[9, 31]
+PSO J006+39
+6.610
+0.55 (NOEMA)
+12.8
+8.95 (NOEMA)
+[32]
+VIK J030516-315056
+6.614
+5.34 (ALMA 6)
+13.8
+9.77 (ALMA 6)
+[9, 32, 33]
+PSO J338+29
+6.658
+0.97 (NOEMA)
+13.0
+9.30 (NOEMA)
+[31]
+VIK J1048-0109
+6.676
+2.84 (ALMA 6)
+13.5
+9.32 (ALMA 6)
+[9, 13]
+(Continue on next page)
+MNRAS 000, 1–42 (2022)
+
+22
+Liang et al.
+Table 6 – continued
+Name
+𝑧
+𝑆𝜈 (mJy)
+log (𝐿IR/𝐿⊙)§
+log (𝐿[CII]/𝐿⊙)
+References∗
+HSC J1205-0000
+6.723
+1.17 (ALMA 6)
+13.1
+8.58 (ALMA 6)
+[34]
+VIK J0109-3047
+6.791
+0.52 (ALMA 6)
+12.8
+9.38 (ALMA 6)
+[9, 33]
+VIK J2348-3054
+6.901
+2.28 (ALMA 6)
+13.4
+9.25 (ALMA 6)
+[9, 33]
+HSC J1243+0100
+7.075
+1.52 (ALMA 6)
+13.2
+9.40 (ALMA 6)
+[35]
+ULAS J1120+0641
+7.085
+0.64 (ALMA 6)
+12.9
+9.08 (ALMA 6)
+[9, 36]
+ULAS J1342+0928
+7.541
+0.34 (ALMA 6)
+12.6
+9.12 (ALMA 6)
+[9, 37]
+† 𝐿IR of SDSS J2310+1855 and SDSS J1148+5251 are derived by SED fitting (e.g. Casey 2012; Casey et al. 2014) to multiple data points at
+both Wien and Rayleigh-Jeans sides of the dust IR SED.
+‡ J043947+163415 has been confirmed to be gravitationally-lensed, and its luminosities have been de-magnified by 𝜇 = 4.6 ± 2.0, estimated
+based on the lensing configuration from HST imaging by Fan et al. (2019).
+∥ NOEMA: NOrthern Extended Millimeter Array
+(Website: https://www.iram-institute.org/EN/content-page-235-3-235-0-0-0.html).
+§ 𝐿IR (or its upper 3𝜎 limit) is converted from 𝑆 (its 3𝜎 upper limit) using the standard MBB function and with 𝑇eqv that follows equation (7)
+(assuming 𝛽dust = 2.0 and 𝛿dzr = 0.4), except for SDSS J2310+1855 and SDSS J1148+5251.
+∗ References: [1]: Bischetti et al. (2018), [2]: Wagg et al. (2010), [3]: Lu et al. (2018), [4]: Wagg et al. (2012), [5]: Iono et al. (2006), [6]:
+Leipski et al. (2014), [7]: Wang et al. (2013), [8]: Wang et al. (2019), [9]: Venemans et al. (2020), [10]: Eilers et al. (2020): [11]: Rojas-Ruiz
+et al. (2021), [12]: Izumi et al. (2018), [13]: Decarli et al. (2018), [14]: Shao et al. (2019), [15]: Willott et al. (2015a), [16]: Willott et al.
+(2017), [17]: Decarli et al. (2017), [18]: Izumi et al. (2019), [19]: Walter et al. (2018), [20]: Shao et al. (2017), [21]: Wang et al. (2016),
+[22]: Leipski et al. (2013), [23]: Andika et al. (2020), [24]: Walter et al. (2009), [25]: Maiolino et al. (2005), [26]: Meyer et al. (2022), [27]:
+Willott et al. (2013b), [28]: Yang et al. (2019b), [29]: Yue et al. (2021), [30]: Bañados et al. (2015), [31]: Mazzucchelli et al. (2017), [32]:
+Venemans et al. (2019) [33]: Venemans et al. (2016), [34]: Izumi et al. (2021a), [35]: Izumi et al. (2021b), [36]: Venemans et al. (2012),
+[37]: Venemans et al. (2017).
+𝐿IR and high redshifts. In this section, we explore the origin(s) of the
+[CII] deficit of galaxies using the FIRE galaxy sample.
+In Section 5.1, we present the analytic solution of [CII] line flux
+emerging from a plane-parallel gas slab. The toy model provides
+useful insights for understanding the [CII] emission of galaxies.
+In Section 5.2, we derive an important scaling relation of galaxies
+between their 𝐿[CII]/SFR ratio and other physical properties. Based
+on this scaling relation, we investigate the cause of the [CII] deficit of
+galaxies in Section 5.3. Finally, in Section 5.4, we show the presence
+of two distinct physical regimes where the main reason for the [CII]
+deficit of galaxies is different.
+5.1 Insights from the plane parallel slab model
+The [CII] line flux emerging from a plane-parallel slab that is ir-
+radiated by an external radiation field has recently been studied by
+Ferrara et al. (2019, hereafter F19). In this section, we summarize
+the key points of the F19 model. We refer interested readers to F19
+for the details.
+The plane-parallel slab can be characterized by three distinct zones
+based on the ionization structures of gas, as has been discussed in
+Section 3.1. Right beneath the surface of the slab, ionizing radiation
+(𝐸𝛾 > 13.6 eV) creates a HII region extending to a gas column density
+𝑁s (Zone I), where both hydrogen and carbon are ionized. Beyond 𝑁s,
+hydrogen becomes neutral but LW (11.2 < 𝐸𝛾 < 13.6 eV) photons
+maintain carbon in the singly ionized state (Zone II). The LW photons
+become fully absorbed by dust and H2 at a column density 𝑁F, beyond
+which hydrogen turns into H2 and carbon becomes neutral (Zone III).
+We have shown in Fig. 2 the ionization structures of a plane-parallel
+slab calculated by CLOUDY as an example (see also Fig. 1 of F19 for
+a schematic plot).
+𝑁s can be estimated by equating the photo-ionization rate to the
+recombination rate of hydrogen inside the HII region (Zone I) as-
+suming that dust extinction is negligible, which can be expressed as
+(see Appendix C for the details)
+𝑁s = 𝑛H𝑙s = 𝑈𝑐
+𝛼B
+≈ 1023𝑈 cm−2,
+(8)
+where 𝑙s is the distance from the surface of the slab to the end of
+Zone I, 𝑈 parameter represents the ionizing photon-to-gas density
+ratio, i.e.
+𝑈 = 𝑛𝛾
+𝑛H
+,
+(9)
+𝑐 represents the speed of light, and 𝛼B = 2.6 × 10−13 cm3 s−1 is
+the Case-B recombination coefficient at gas temperature 𝑇 ≈ 104 K
+(Ferland et al. 1992). For a slab with density 𝑛H = 50 cm−3 that
+is exposed to a radiation field having 𝐺 = 200 𝐺0, we obtain 𝑈 =
+𝑛𝛾/𝑛H ≈ 1.3 × 10−3 at and near the surface of the slab. Using
+equation (8), we obtain 𝑁s ≈ 1.3 × 1020 cm−2. We can see from
+Fig. 2 that this estimated 𝑁s is in good agreement with the result
+computed by CLOUDY, in particular, for the metal-poor model (with
+𝑍gas = 0.1 𝑍⊙; right panels of Fig. 2), where dust extinction in the
+HII (Zone I) region is negligible. 𝑁s of the metal-rich model (with
+𝑍gas = 𝑍⊙; left panels of Fig. 2) is smaller by about 1/4 due to higher
+absorption of ionizing photons by dust.
+𝑁F can be estimated using
+𝑁F = 𝑛H𝑙F = ¯𝜎−1
+d
+ln(1 + 105𝜔𝑈),
+(10)
+which is obtained by performing a RT calculation (Sternberg et al.
+2014) that accounts for the absorption of LW photons by dust grains
+and H2 as light propagates through the slab. In equation (10), 𝑙F
+represents the distance between the surface of the slab and the end
+of Zone II,
+¯𝜎d = 5.9 × 10−22
+�
+𝛿dgr
+𝛿dgr, MW
+�
+cm2
+(11)
+represents the flux-weighted dust extinction cross section per H-atom,
+and
+𝜔 =
+1
+1 + 0.9(𝛿dgr/𝛿dgr, MW)1/2 ,
+(12)
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+23
+where 𝛿dgr, MW = 10−2 represents the Galactic dust-to-gas ratio
+(see e.g. Gilmore et al. 1989; Sodroski et al. 1997; Zubko et al.
+2004; Rémy-Ruyer et al. 2014; McKinnon et al. 2016; Li et al.
+2019). For the two models where 𝑍gas = 𝑍⊙ and 𝑍gas = 0.1𝑍⊙,
+𝑁F is expected to be ∼ 1021 cm−2 and ∼ 1022 cm−2 (according to
+equation 10), respectively. This result is again in good agreement
+with the prediction of CLOUDY as shown in Fig. 2.
+Now we can derive the [CII] line flux (𝐹[CII]) emerging from
+a plane-parallel slab following the three-zone model. 𝐹[CII] can be
+calculated using
+𝐹[CII] = Λ(1)
+[CII] 𝑙s + Λ(2)
+[CII] (𝑙F − 𝑙s),
+(13)
+where the first and second terms correspond to the contribution of
+[CII] line flux by Zone I and Zone II, respectively. Λ(1)
+[CII] (Λ(2)
+[CII]) in
+the above equation represents the [CII] cooling rate (erg s−1 cm−3)
+of gas in Zone I (II). In the above and the following equations, the
+superscript “(1)" (“(2)") indicates the properties of gas in Zone I (II).
+We neglect the [CII] emission from the H2 region (Zone III).
+Equation (13) can be rewritten as (see Appendix D for the details)
+𝐹[CII] ≈ ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+𝑅e
+ul(𝑇 (1))𝑛(1)
+CII 𝑛(1)
+e
+𝑙s
++ 2
+5 ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+𝑅HI
+ul (𝑇 (2))𝑛(2)
+CII 𝑛(2)
+HI (𝑙F − 𝑙s),
+(14)
+where ℎP is the Planck constant, 𝜈[CII] = 1900.5 GHz is the rest-
+frame frequency of the [CII] line, 𝑔u = 4 (𝑔l = 2) is the statistical
+weight of the 2𝑃3/2 (2𝑃1/2) state, 𝑅e
+ul (𝑅HI
+ul ) is the downward rate
+coefficient (s−1) for CII +𝑒− (CII +H0) collision, and 𝑛(1)
+CII (and 𝑛(2)
+CII ),
+𝑛(1)
+e
+and 𝑛(2)
+HI represent the number density of CII ion, electron and
+H atom, respectively. Equation (14) implies that in Zone I (II), the
+main collision partner of CII ion is electron (H atom). Knowing that
+𝑛(1)
+e
+≈ 𝑛H and 𝑛(2)
+HI ≈ 𝑛H (see the upper panels of Fig. 2), we can
+rewrite equation (14) to be
+𝐹[CII] = ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+� �
+𝑅e
+ul𝑛(1)
+CII 𝑁s + 2
+5 𝑅HI
+ul 𝑛(2)
+CII (𝑁F − 𝑁s)
+�
+,
+(15)
+where 𝑁F = 𝑛H 𝑙F and 𝑁s = 𝑛H 𝑙s. Furthermore, 𝑛(1)
+CII and 𝑛(2)
+CII in the
+above equation can be rewritten as
+𝑛(1)
+CII = 𝑛H𝑥(1)
+CII AC
+and
+𝑛(2)
+CII = 𝑛H𝑥(2)
+CII AC,
+(16)
+where
+AC = 2.5 × 10−4
+� 𝑍gas
+𝑍⊙
+�
+(17)
+represents the abundance of carbon. The numerical factor 2.5×10−4
+in equation (17) is the abundance of carbon in the solar photosphere
+(Asplund et al. 2009). 𝑥(1)
+CII (𝑥(2)
+CII ) in equation (16) represents the
+fraction of carbon in CII form in Zone I (II). 𝑥(1)
+CII is roughly inversely
+proportional to𝑈 (see Appendix E), whereas 𝑥(2)
+CII ≈ 1 (see the middle
+panels of Fig. 2). By inputting equation (16) to equation (15), we get
+𝐹[CII] = 𝑛HAC𝑁FℎP𝜈[CII]
+� 𝑔u
+𝑔l
+� �
+𝑅e
+ul𝑥(1)
+CII
+� 𝑁s
+𝑁F
+�
++ 2
+5 𝑅HI
+ul
+� 𝑁F − 𝑁s
+𝑁F
+��
+= 𝑛HAC𝑁F ¯𝜖[CII], slab,
+(18)
+where we define
+¯𝜖[CII], slab = ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+� �
+𝑅e
+ul𝑥(1)
+CII
+� 𝑁s
+𝑁F
+�
++ 2
+5 𝑅HI
+ul
+� 𝑁F − 𝑁s
+𝑁F
+��
+≡ 𝛼 𝑥(1)
+CII
+� 𝑁s
+𝑁F
+�
++ 𝛾
+� 𝑁F − 𝑁s
+𝑁F
+�
+(19)
+as the specific [CII] cooling rate of the slab (erg s−1 cm3). It can be
+shown that (see Appendix D for the details)
+𝛼 ≡ ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+𝑅e
+ul(𝑇 (1))
+≈ 10−21 erg s−1 cm3 (𝑇 (1) ≈ 104 K)
+(20)
+and
+𝛾 ≡ 2
+5 ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+𝑅HI
+ul (𝑇 (2))
+≈ 10−23 erg s−1 cm3 (𝑇 (2) ≈ 102 K)
+(21)
+From equation (19), we see that ¯𝜖[CII], slab depends on 𝑥(1)
+CII , 𝑁s and
+𝑁F, and varies typically within the range 10−23 −10−21 erg s−1 cm3.
+Likewise, we can derive the [CII] luminosity of a spherical uniform
+gas cloud (𝐿[CII], cl). 𝐿[CII], cl can be expressed as
+𝐿[CII], cl =
+����������
+����������
+4𝜋
+∫ 𝑅cl
+0
+Λ(1)
+[CII]𝑟2d𝑟
+(if 𝑙s ≥ 𝑅cl)
+4𝜋
+�∫ 𝑅cl
+𝑅cl−𝑙s
+Λ(1)
+[CII]𝑟2d𝑟 +
+∫ 𝑅cl−𝑙s
+𝑅cl−min(𝑙F,𝑅cl) Λ(2)
+[CII]𝑟2d𝑟
+�
+.
+(if 𝑙s < 𝑅cl)
+(22)
+The first condition of equation (22) (i.e. 𝑙s ≥ 𝑅cl) corresponds to
+when the cloud is fully ionized, while the second condition (i.e. 𝑙s <
+𝑅cl) corresponds to when neutral hydrogen region (Zone II) forms in
+the cloud. Through simple re-arrangement, 𝐿[CII], cl can be expressed
+as
+𝐿[CII], cl = 𝑓[CII], cl
+� 𝑀cl
+𝜇H𝑚H
+�
+𝑛HAC ¯𝜖[CII], cl,
+(23)
+where 𝑓[CII], cl represents the fraction of the gas mass that is in
+HII or HI phases (Zone I and Zone II), 𝑀cl indicates the mass of
+the gas cloud, 𝜇H is the mean molecular weight of the gas and 𝑚H
+represents the proton mass. By definition, 𝑓[CII], cl = 1 when 𝑙F > 𝑅cl
+and the cloud becomes H2-free. ¯𝜖[CII], cl in equation (22) represents
+the specific [CII] cooling rate of the spherical uniform cloud, which
+accounts for the relative contribution of the [CII] emission from HII
+and HI regions (10−23<∼ ¯𝜖[CII], cl<∼10−21 erg s−1 cm3). Like ¯𝜖[CII], slab
+for the plane-parallel slab (equation 19), ¯𝜖[CII], cl depends on 𝑥(1)
+CII , 𝑁s
+and 𝑁F but have different functional relation with these parameters
+due to the difference in geometry. We refer the readers to Appendix F,
+where we present the derivation for ¯𝜖[CII], cl.
+Note that we do not take into account the effects of the CMB
+background on the [CII] cooling rate of gas in the analytic solution
+for the toy models presented in this section. While the CMB sets
+a floor for the excitation (or spin) temperature of gas and boosts
+the upper level (2𝑃3/2) population of the [CII] transition (‘CMB
+heating’), it acts as a background against which the [CII] line is
+measured (‘CMB attenuation’). The CMB effects (both heating and
+attenuation) can be important for the [CII] emission from the low-
+density and low-temperature gas in galaxies at high redshifts (𝑧 >∼ 6)
+(see Appendix D). We find, however, that the total [CII] luminosity
+of the FIRE sample is not significantly affected by the CMB (in
+agreement with Lagache et al. 2018). This is due to the fact that the
+bulk of the [CII] luminosity of the high-𝑧 (𝑧 ≥ 6) galaxies in our
+sample originates from the gas of densities in excess of the densities
+where the CMB effects become important.
+MNRAS 000, 1–42 (2022)
+
+24
+Liang et al.
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+z = 6
+z = 8
+Herrara-Camus et al. 2015 (
+)
+z ∼ 0
+Pearson correlation coefficient ρ = 0.96
+Figure
+10.
+The
+relation
+between
+the
+𝐿[CII]/SFR
+ratio
+and
+𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII]
+of
+the
+FIRE
+galaxies
+at
+different
+redshifts
+(cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2,
+blue squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6
+and purple downward triangles for 𝑧 = 8). The orange shaded area indicates
+the 𝐿[CII]/SFR ratio of the local star-forming galaxy sample measured by
+Herrera-Camus et al. (2015). The solid black line shows the best linear fit
+to the data of the FIRE galaxies. The FIRE galaxies show a strong linear
+correlation (Pearson correlation coefficient 𝜌 = 0.96) between 𝐿[CII]/SFR
+and 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII].
+5.2 A scaling relation for the 𝐿[CII]/SFR ratio of galaxies
+We have summarized the key points of the F19 model for the struc-
+tures of a plane-parallel gas slab that is exposed to an external radia-
+tion field. We then derive the [CII] luminosity of a uniform spherical
+gas cloud (equation 23). Following the results of the toy models, we
+now present a scaling relation for the [CII] luminosity of galaxies,
+based on which we will explore the origins of the [CII] deficit of
+galaxies.
+From equation (23), one would expect that the [CII] luminosity
+(𝐿[CII]) of galaxy has a similar expression, i.e.
+𝐿[CII] ∼ 𝑓[CII]
+� 𝑀gas
+𝜇𝑚H
+�
+¯𝑛gas ¯
+AC ¯𝜖[CII],
+(24)
+where we have replaced 𝑀cl in equation (23) by 𝑀gas, i.e. the gas
+mass of galaxy19. 𝑓[CII] (= 1 − 𝑓H2) in the above equation represents
+the fraction of the total gas mass in ionized or neutral atomic hydrogen
+forms (Zone I and Zone II), and ¯𝑛gas,
+¯
+AC and ¯𝜖[CII] represent the
+statistical average of gas density, carbon abundance and specific
+[CII] cooling rate of the galaxy, respectively. We can then divide the
+two sides of equation (24) by galaxy SFR, and obtain
+𝐿[CII]
+SFR ∼ 𝑓[CII]𝑡dep ¯𝑛gas ¯
+AC ¯𝜖[CII] (𝜇𝑚H)−1
+(25)
+where
+𝑡dep ≡ 𝑀gas
+SFR
+(26)
+19 We calculate the gas mass of galaxy using the gas particles within 0.1𝑅vir
+around the DM halo centre having 𝑇 < 105 K.
+¯ngas = 0.9 cm−3
+FIRE galaxy z = 0
+¯ngas = 79.4 cm−3
+FIRE galaxy z = 6
+¯nHI, MW = 60.3 cm−3
+¯nHII, MW = 6.2 cm−3
+¯nH2, MW = 794.3 cm−3
+PDF =
+d log M (Mgas)
+d log nH
+or
+d log L[CII]
+d log nH
+PDF =
+d log M (Mgas)
+d log nH
+or
+d log L[CII]
+d log nH
+(luminosity-weighted)
+(luminosity-weighted)
+¯nHI, MW = 1.1 cm−3
+¯nHII, MW = 0.2 cm−3
+¯nH2, MW = 15.1 cm−3
+(mass-weighted)
+(mass-weighted)
+Figure 11. The gas density PDFs of two selected FIRE galaxies at 𝑧 = 0
+(upper panel) and 𝑧 = 6 (lower panel). The 𝑧 = 6 galaxy has a relatively
+denser ISM. In the two panels, magenta lines indicate the luminosity-weighted
+PDFs. Solid, dotted and dashed magenta lines represent the result of the total
+gas, HII gas (Zone I) and HI gas (Zone II) in the ISM, respectively. In the two
+panels, shaded areas show the mass-weighted gas density PDFs. Grey, red,
+green and blue areas represent the result of total gas, HII gas (Zone I), HI gas
+(Zone II) and H2 gas (Zone III), respectively.
+is the gas depletion time of the galaxy (e.g., Genzel et al. 2015;
+Tacchella et al. 2016; Semenov et al. 2017; Scoville et al. 2017; Tac-
+coni et al. 2018; Feldmann 2020). Through further re-arrangement,
+equation (25) can be expressed as
+𝐿[CII]/𝐿⊙
+SFR/(𝑀⊙ yr−1) ∼ 4 × 106 𝑓[CII]
+� ¯𝑍gas
+𝑍⊙
+�
+×
+� 𝑡dep
+Gyr
+� � ¯𝑛gas
+cm−3
+� �
+¯𝜖[CII]
+10−22 erg s−1 cm3
+�
+(27)
+∝ 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII],
+(28)
+where we have replaced the carbon abundance
+¯
+AC in equation (25)
+by metallicity ¯𝑍gas using equation (17).
+Equation (27) indicates that the 𝐿[CII]/SFR ratio of galaxy is
+determined by five physical parameters, 𝑓[CII], ¯𝑍gas, 𝑡dep, ¯𝑛gas and
+¯𝜖[CII]. Whilst 𝑓[CII] and 𝑡dep are global properties of galaxy, which
+are well defined, the other three parameters are the statistical average
+of the corresponding physical properties of all different ‘gas clouds’
+in the ISM. This contrasts with the toy models (uniform plane-parallel
+slab or spherical cloud), where each of these properties (gas density,
+gas metallicity, and the specific [CII] cooling rate) has a single,
+definite value.
+In Fig. 10, we show the relation between the 𝐿[CII]/SFR ratio
+MNRAS 000, 1–42 (2022)
+
+10
+X
+yr)
+10
+10
+10-1
+100
+101
+fcu (Zgas /Zo)(tdep/Gyr)(nH/cm-3)(EiCul/10-22 erg cm3 s1090.7
+0.6
+0.5
+0.4
+0.3
+0.2
+0.1
+0
+-2
+-1
+0
+1
+2
+3
+log (nH/cm-3)0.7
+0.6
+0.5
+0.4
+0.3
+0.2
+0.1
+0
+-1
+0
+1
+2
+3
+4
+log (nH/cm-3)CII emission as an indicator of galaxy SFR
+25
+¯ngas vs . ¯nH2, MW
+¯ngas vs . ¯nHI, MW
+¯ngas vs . ¯nHII, MW
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+Figure 12. The relation between the [CII] luminosity-weighted gas density
+( ¯𝑛gas) and the mass-weighted density of the HII ( ¯𝑛HII, MW), HI ( ¯𝑛HI, MW) and
+H2 gas ( ¯𝑛H2, MW) of the FIRE galaxies at 𝑧 = 0 − 8. Filled, empty and semi-
+transparent symbols correspond to the ¯𝑛HI, MW vs. ¯𝑛gas, the ¯𝑛HII, MW vs. ¯𝑛gas
+and the ¯𝑛H2, MW vs. ¯𝑛gas relations, respectively. The diagonal line indicates
+the one-to-one relationship. It can be seen that ¯𝑛gas appears to be close to
+¯𝑛HI, MW, both being systematically lower (higher) than ¯𝑛H2, MW ( ¯𝑛HII, MW).
+of the FIRE sample at 𝑧 = 0 − 8 and their 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII],
+where ¯𝑛gas, ¯𝑍gas and ¯𝜖[CII] are the luminosity-weighted gas density
+20, gas metallicity21 and specific [CII] cooling rate of the galaxies,
+respectively. Our FIRE sample follows a clear linear scaling relation
+on the diagram (Pearson correlation coefficient 𝜌 = 0.96), which is
+in agreement with equation (27).
+One important question is which part of the ISM contributes the
+most [CII] emission of a galaxy. The ISM of a galaxy spans a wide
+range of density over several orders of magnitude, with the dense
+(diffuse) regions being dominated by H2 (HII) gas. In Fig. 11, we
+show the [CII] luminosity-weighted (magenta lines) and gas mass-
+weighted (grey and coloured shaded areas) probability density func-
+tions (PDFs) of 𝑛H for two selected FIRE galaxies at 𝑧 = 0 (upper
+panel) and 𝑧 = 6 (lower panel). It can be seen in the figure that
+the [CII] emission of FIRE galaxies originates from gas spanning
+20 Note that we use the ‘luminosity-weighted median gas density’, i.e. the gas
+density at the 50th percentile of [CII] luminosity, instead of the ‘luminosity-
+weighted mean gas density’. This is because the gas density PDF of galaxy
+resembles a lognormal function, exhibiting an elongated tail at the high den-
+sity end. Under certain circumstances, the ‘mean gas density’ can be strongly
+biased by the [CII]-emitting gas at the highest density (𝑛H >∼ 103 cm−3, see
+the lower panel of Fig. 11), and hence is not statistically representative for
+the part of the gas that contributes the bulk of the [CII] emission of galaxy.
+Throughout this paper, we use the term ‘luminosity-weighted’ for simplicity
+when we refer to ‘luminosity-weighted median’. Similarly, ‘mass-weighted’
+in this paper refers to ‘mass-weighted median’, i.e. value at the 50th per-
+centile of mass. In Appendix G, we show explicitly the difference between
+the ‘luminosity-weighted median gas density’ and the ‘luminosity-weighted
+mean gas density’ of the FIRE galaxy sample. The former is higher by a factor
+of ∼ 5 on average.
+21 Unlike the gas densities, the luminosity-weighted mean and the
+luminosity-weighted median gas metallicity are similar. Both are close to
+the mass-weighted gas metallicity (see Appendix H).
+a wide range of density across several orders of magnitude. Inter-
+estingly, we find that the luminosity-weighted gas density (¯𝑛gas) of
+FIRE galaxies is close to the mass-weighted density of the HI gas
+(¯𝑛HI, MW) of the ISM, both of which are much higher (lower) than
+the mass-weighted density of the HII (H2) gas. This can be more
+clearly seen from Fig. 12, where we show the relation between ¯𝑛gas
+and the mass-weighted gas density of the HII, HI and H2 gas for the
+FIRE sample at 𝑧 = 0 − 8.
+This can be understood as follows. The bulk of the diffuse, ionized
+HII gas is inefficient at producing [CII] emission due to the low gas
+density (𝐿[CII], cl/𝑀cl ∝ 𝑛H, see equation 23). On the other hand,
+in the densest regions of the ISM, where gas becomes mostly in
+molecular hydrogen form (Zone III), not much [CII] emission is
+produced due to the scarcity of the amount of ionized carbon (which
+exists mostly in Zone I and Zone II) in those regions. As a result,
+the bulk of the [CII] luminosity of the FIRE galaxies at 𝑧 = 0 − 8
+originates from the gas at the intermediate gas density range.
+It should be noted, however, that though the luminosity-weighted
+gas density of the FIRE galaxies coincide with ¯𝑛HI and is system-
+atically higher than ¯𝑛HII, more of the [CII] emission of the FIRE
+galaxies actually originates from the HII gas (Zone I) instead of the
+HI gas (Zone II). Specifically, it is the HII gas layer at the surface
+of the HI-rich clouds having 𝑛 ≈ ¯𝑛gas that contributes most of the
+[CII] emission of the galaxies. In Fig. 13, we show the fraction of
+the total [CII] luminosity of the FIRE galaxies produced by the HII
+gas, i.e. 𝐿[CII], HII/𝐿[CII] (note: 𝐿[CII], HII is the sum of the [CII] lu-
+minosity originating from Zone I in each ‘gas cloud’), as a function
+of the galaxy SFR. It can be seen that the HII gas contributes about
+60% − 80% of the total luminosity of the galaxies, except for the
+few massive starburst galaxies at SFR >∼ 100 𝑀⊙ yr−1, which show a
+reduced fractional contribution by the HII gas down to ∼ 50%. The
+remaining fraction of the [CII] luminosity originates mainly from
+the HI gas. The contribution of the [CII] luminosity by the H2 gas
+(Zone III) is negligible (< 2% of the total luminosity for all the FIRE
+galaxies).
+The relatively high [CII] cooling rate in the HII phase (note:
+𝛼 ≈ 100 𝛾, see equation 20 and 21) explains why a relatively small
+amount of HII gas at 𝑛H ≈ ¯𝑛gas can produce a larger fraction of the
+[CII] luminosity of the galaxies than the HI gas. Also, one would
+expect a correlation between the fractional contribution of the [CII]
+luminosity by the HII gas (Zone I) and the effective [CII] line cooling
+rate (luminosity-weighted), ¯𝜖[CII], of the galaxies. This is indeed the
+case, as is shown in the right panel of Fig. 13.
+5.3 The physical origins of [CII] deficit of galaxies
+In the previous section, we have presented a simple analytic expres-
+sion for the 𝐿[CII]/SFR ratio of galaxies (equation 27) found with
+the FIRE galaxy sample. Based on this result, we will probe in this
+section the origins of the observed [CII] deficit of galaxies.
+Equation (27) indicates that the 𝐿[CII]/SFR ratio of the galaxies
+depends on five parameters: the fraction of gas in the [CII]-emitting
+regions (Zone I and Zone II), the depletion time (i.e. gas mass per
+unit SFR), gas density, gas metallicity and the specific [CII] cooling
+rate. Hence, the [CII] deficit of the galaxies can, in principle, be due
+to a strong deficit of one or few of the five parameters with respect
+to the observed local star-forming samples (e.g., L11, L14 and H15).
+It should be noted that the observed [CII] deficit in the two regimes,
+high redshifts and high 𝐿IR, may not be due to the same reason. We
+will separately discuss the origin of the [CII] deficit in these two
+regimes in this section.
+To
+reveal
+what
+parameters
+drive
+the
+[CII]
+deficit
+of
+MNRAS 000, 1–42 (2022)
+
+10
+10°
+100
+102
+103
+10-
+(cm-
+as26
+Liang et al.
+10-1
+100
+101
+102
+103
+10
+20
+30
+40
+50
+60
+70
+80
+90
+100
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+z = 6
+z = 8
+10-1
+100
+101
+102
+103
+10
+20
+30
+40
+50
+60
+70
+80
+90
+100
+-22.6
+-22.4
+-22.2
+-22
+-21.8
+-21.6
+-21.4
+-21.2
+log ¯ϵ[CII] (erg cm3 s−1)
+Figure 13. The fraction of the total [CII] luminosity of the FIRE galaxy sample that originates from the HII gas region (Zone I) as a function of their SFR. In
+the left and right panels, the data points are colour-coded by the redshift and the effective [CII] cooling rate ( ¯𝜖[CII]) of the galaxies, respectively.
+the
+FIRE
+sample,
+we
+divide
+𝐿[CII]/SFR
+by
+each
+of
+these parameters and check whether in the new parameter
+spaces (i.e. 𝐿[CII]SFR−1 𝑓 −1
+[CII], 𝐿[CII]SFR−1 ¯𝑍−1
+gas, 𝐿[CII]SFR−1 ¯𝑛−1
+gas,
+𝐿[CII]SFR−1𝑡−1
+dep and 𝐿[CII]SFR−1𝜖−1
+[CII]), the [CII] deficit becomes
+alleviated (or even vanishes). We show in Fig. 14 the relation between
+the new parameters and the SFR for the galaxies in our sample at
+different redshifts. In Fig. 15, we also show how 𝐿[CII]/SFR of the
+FIRE sample depends on 𝑓[CII], ¯𝑍gas, ¯𝑛gas, 𝑡dep and ¯𝜖[CII] in separate
+panels. Readers can find the mean of 𝑓[CII], ¯𝑍gas, ¯𝑛gas, 𝑡dep and ¯𝜖[CII]
+and the five new parameters of the FIRE sample at each redshift in
+Table 8 and Table 7, respectively.
+[CII] deficit at high redshifts
+The normalization of the 𝐿[CII]-SFR relation of the FIRE sample
+decreases monotonically with redshift. The mean 𝐿[CII]/SFR ratio
+of the galaxies decreases by 1.2 dex (a factor of ∼ 15) from 𝑧 = 0 to
+𝑧 = 8 (see col. 2 of Table 7).
+It can be seen from Table 7 (and also Fig. 14) that the redshift evo-
+lution of the 𝐿[CII]/SFR ratio of the galaxies is mainly driven by ¯𝑍gas
+and 𝑡dep since the [CII] deficit is significantly alleviated (or even van-
+ishes at some redshifts) in the parameter space of (𝐿[CII]/SFR)𝑡−1
+dep
+and (𝐿[CII]/SFR) ¯𝑍−1
+gas. This result indicates that the [CII] deficit of
+galaxies at high redshifts is due to either low gas metallicity or a
+deficiency of gas (that is able to produce [CII] emission) per unit
+SFR.
+Looking into the details, we see from Table 7 that while 𝑡dep is
+the key parameter driving the evolution of the 𝐿[CII]-SFR relation
+at 𝑧 <∼ 2, ¯𝑍gas plays a more important role at 𝑧 >∼ 4. This is because
+𝑡dep of the FIRE sample decreases more at 𝑧 = 0 − 2 (from 6.30 to
+1.02 Gyr, by a factor of ∼ 6) than at 𝑧 = 2 − 8 (from 1.02 to 0.72
+Gyr, by only ∼ 30%) (see Table 8). At 𝑧 = 2 − 8, ¯𝑍gas of the FIRE
+sample decreases sharply with redshift (from 0.56 𝑍⊙ to 0.09 𝑍⊙, by
+a factor of ∼ 6) and it thus has a stronger impact on the evolution of
+𝐿[CII]/SFR of the FIRE galaxies than 𝑡dep.
+Unlike 𝑡dep and ¯𝑍gas, ¯𝜖[CII] has only a mild impact on the redshift
+evolution of 𝐿[CII]/SFR. From 𝑧 = 0 to 𝑧 = 8, the mean ¯𝜖[CII] of the
+FIRE sample has a slight decrease with redshift by less than a factor
+of 3 (Table 8). The [CII] deficit persists at high redshifts in the space
+of (𝐿[CII]/SFR) ¯𝜖−1
+[CII] (Table 7).
+The other two parameters, ¯𝑛gas and 𝑓[CII], have completely no
+contribution to the [CII] deficit at high redshifts since both increase
+with redshift instead of decreasing. The increase of ¯𝑛gas indicates
+that earlier galaxies have a more compact ISM. Naively, because
+𝐿[CII], cl/𝑀cl ∝ 𝑛H (equation 23), an increase of gas density would
+result in a rise of 𝐿[CII]/SFR with redshift. This effect, however, is
+overwhelmed by the combined effect of 𝑡dep and ¯𝑍gas on 𝐿[CII]/SFR.
+The increase of 𝑓[CII] with redshift indicates that our sample in-
+cludes more H2 gas-poor galaxies at higher redshift where a larger
+fraction of carbon in the ISM gas becomes ionized. Nonetheless, the
+impact of 𝑓[CII] on the evolution of 𝐿[CII]/SFR is negligible since
+𝑓[CII] of the galaxies in our sample differs by no more than a factor
+of 2 (ranging between ≈ 60% and unity, see the lower middle panel
+of Fig. 15).
+To summarize, the decrease of 𝐿[CII]/SFR of the FIRE sample
+with redshift is mainly driven by the decrease of their 𝑡dep and gas
+metallicity. While 𝑡dep plays a more important role at 𝑧 ≤ 2, gas
+metallicity becomes the key parameter driving the [CII] deficit of
+the galaxies at higher redshifts. The redshift evolution of ¯𝑛gas, 𝑓[CII]
+and ¯𝜖[CII] have no or limited contribution.
+[CII] deficit at high 𝐿IR
+The FIRE sample exhibits a trend of declining 𝐿[CII]/𝐿IR ratio with
+𝐿IR at each redshift. To find the main driver of the [CII] deficit at
+high 𝐿IR, we check how each of the five physical parameters ( 𝑓[CII],
+𝑡dep, ¯𝑛gas, ¯𝑍gas and ¯𝜖[CII]) depends on 𝐿IR.
+In Table 8, we explicitly show the mean of 𝑓[CII], 𝑡dep, ¯𝑛gas, ¯𝑍gas
+and ¯𝜖[CII] of the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (where galaxies are
+observed to show [CII] deficit) in our sample at different redshifts,
+in addition to the mean of the five parameters of the entire sample
+(including fainter galaxies). We can see from the table (also Fig. 15)
+that the IR-luminous galaxies (𝐿IR ≥ 1011 𝐿⊙) have lower 𝑡dep, 𝑓[CII]
+and ¯𝜖[CII] but higher ¯𝑍gas and ¯𝑛gas than the rest of the sample — they
+are relatively metal and H2 gas-rich, and have more compact ISM
+and shorter depletion time than the normal SFGs having lower SFR.
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+27
+10-1
+100
+101
+102
+103
+10-4
+10-3
+10-2
+10-1
+10-1
+100
+101
+102
+103
+106
+107
+108
+109
+L[CII]/SFR t−1
+dep (L⊙ M−1
+⊙ )
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 1
+z = 2
+z = 3
+z = 4
+z = 6
+z = 8
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+10-1
+100
+101
+102
+103
+104
+105
+106
+107
+108
+L[CII]/SFR (¯ngas/cm−3)−1 (L⊙ M−1
+⊙ yr)
+10-1
+100
+101
+102
+103
+104
+105
+106
+107
+108
+10-1
+100
+101
+102
+103
+104
+105
+106
+107
+108
+SFR (M⊙ yr−1)
+SFR (M⊙ yr−1)
+SFR (M⊙ yr−1)
+L[CII]/SFR f −1
+[CII] (L⊙ M−1
+⊙ yr)
+L[CII]/SFR (¯ϵ[CII]/10−22 erg s−1 cm3)−1 (L⊙ M−1
+⊙ yr)
+Figure 14. The relation between 𝐿[CII]/SFR 𝑡−1
+dep (upper left), 𝐿[CII]/SFR ¯𝑍−1
+gas (upper right), 𝐿[CII]/SFR ¯𝑛−1
+gas (lower left), 𝐿[CII]/SFR 𝑓 −1
+[CII] (lower middle)
+and 𝐿[CII]/SFR ¯𝜖 −1
+[CII] (lower right) against SFR of the FIRE galaxies at different redshifts (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for
+𝑧 = 2, blue squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6 and purple downward triangles for 𝑧 = 8). In each panel, large (small)
+symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙). The [CII] deficit at high 𝐿IR (at redshift 𝑧 > 5) vanishes in the parameter space of
+𝐿[CII]/SFR 𝑡−1
+dep (𝐿[CII]/SFR ¯𝑍−1
+gas), indicating that low 𝑡dep (low gas metallicity) is the main driver of the [CII] deficit at high 𝐿IR (at high redshifts).
+Table 7. The change of the mean 𝐿[CII]/SFR, 𝐿[CII]/SFR 𝑡−1
+dep, 𝐿[CII]/SFR ¯𝑍−1
+gas, 𝐿[CII]/SFR ¯𝑛−1
+gas, 𝐿[CII]/SFR 𝑓 −1
+[CII] and 𝐿[CII]/SFR ¯𝜖 −1
+[CII] of the FIRE sample
+from redshift 𝑧 to 𝑧 = 0.
+𝑧
+Δ log
+�
+𝐿[CII ]
+SFR
+�
+Δ log
+�
+𝐿[CII ]
+SFR 𝑡−1
+dep
+�
+Δ log
+�
+𝐿[CII ]
+SFR
+¯𝑍−1
+gas
+�
+Δ log
+�
+𝐿[CII ]
+SFR ¯𝑛−1
+gas
+�
+Δ log
+�
+𝐿[CII ]
+SFR 𝑓 −1
+[CII]
+�
+Δ log
+�
+𝐿[CII ]
+SFR
+¯𝜖 −1
+[CII]
+�
+(dex)
+(dex)
+(dex)
+(dex)
+(dex)
+(dex)
+0
+/
+/
+/
+/
+/
+/
+1
+−0.38
+0.13
+−0.16
+−0.78
+−0.38
+−0.35
+2
+−0.67
+0.14
+−0.19
+−1.37
+−0.67
+−0.48
+3
+−0.78
+−0.08
+−0.08
+−1.64
+−0.79
+−0.55
+4
+−0.92
+−0.19
+−0.08
+−1.95
+−0.93
+−0.74
+6
+−1.12
+−0.32
+0.07
+−2.33
+−1.12
+−0.75
+8
+−1.21
+−0.40
+−0.02
+−2.62
+−1.21
+−0.83
+The fact that they have a reduced ¯𝜖[CII] is associated with a stronger
+ISRF in these galaxies (we will discuss this more in Section 6.2).
+Hence, the [CII] deficit at high 𝐿IR is driven by the com-
+bined effect of 𝑡dep, 𝑓[CII] and ¯𝜖[CII]. We see from Fig. 14 that
+the [CII] deficit of the FIRE sample at high 𝐿IR vanishes only in
+the space of (𝐿[CII]/SFR) 𝑡−1
+dep (upper left panel) but not in that
+of (𝐿[CII]/SFR) 𝑓 −1
+[CII] (lower middle panel) or (𝐿[CII]/SFR) ¯𝜖−1
+[CII]
+(lower right panel). This indicates that 𝑡dep plays a major role in
+driving the [CII] deficit at high 𝐿IR. That is, the [CII] deficit of the
+IR-luminous galaxies in our sample is mainly due to the reduced
+amount of gas that is available for producing [CII] emission per unit
+SFR of the galaxies.
+MNRAS 000, 1–42 (2022)
+
+28
+Liang et al.
+10-2
+10-1
+100
+101
+102
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+10-1
+100
+101
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+¯Zgas (Z⊙)
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 1
+z = 2
+z = 3
+z = 4
+z = 6
+z = 8
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+f[CII] ( % )
+100
+101
+102
+103
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+55
+60
+65
+70
+75
+80
+85
+90
+95
+100
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+¯ngas (cm−3)
+10-24
+10-23
+10-22
+10-21
+10-20
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+¯ϵ[CII] (erg cm3 s−1)
+Δlog L[CII] (dex)
+Δlog L[CII] (dex)
+Δlog L[CII] (dex)
+Figure 15. Δ(log 𝐿[CII]) as a function of 𝑡dep (upper left), ¯𝑍gas (upper right), ¯𝑛gas (lower left), 𝑓[CII] (lower middle) and ¯𝜖[CII] (lower right) of the FIRE galaxies
+at different redshifts, where Δ(log 𝐿[CII]) represents the offset between the 𝐿[CII]/SFR ratio of the galaxies and the observed mean value of the local star-forming
+sample of H15 (4.3 × 107 𝐿⊙ 𝑀−1
+⊙ yr). In each panel, large (small) symbols correspond to the FIRE galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).
+Table 8. The mean of 𝑡dep, ¯𝑍gas, ¯𝑛−1
+gas, 𝑓[CII] and ¯𝜖[CII] of the FIRE galaxy
+sample at different redshifts.
+𝑧
+<
+𝑡dep
+Gyr >
+<
+¯𝑍gas
+𝑍⊙ >
+< ¯𝑛gas
+cm−3 >
+< 𝑓[CII]>
+<
+¯𝜖[CII ]
+10−22 erg s−1 cm3 >
+Total
+0
+6.30
+1.69
+0.76
+0.93
+3.2
+1
+2.02
+1.08
+2.29
+0.96
+2.6
+2
+1.02
+0.56
+4.17
+0.98
+2.0
+3
+1.10
+0.43
+5.75
+0.99
+2.1
+4
+1.14
+0.24
+7.59
+1.00
+1.8
+6
+0.86
+0.12
+11.75
+1.00
+1.5
+8
+0.72
+0.09
+16.26
+1.00
+1.2
+𝐿IR ≥ 1011 𝐿⊙
+0
+1.88
+2.40
+1.32
+0.88
+2.5
+1
+1.32
+1.45
+2.89
+0.90
+2.1
+2
+0.52
+1.07
+4.37
+0.95
+1.9
+3
+0.83
+0.54
+7.59
+0.99
+1.7
+4
+0.69
+0.36
+10.97
+1.00
+1.5
+6
+0.51
+0.32
+22.87
+1.00
+0.9
+8
+0.09
+0.59
+41.34
+0.94
+0.5
+5.4 The two regimes of [CII] emission of galaxies
+In the previous section, we have shown with the FIRE sample that
+the main driver of the [CII] deficit at high redshifts and high 𝐿IR
+is different. The observed [CII] deficit of the galaxies at 𝑧 >∼ 4 (at
+𝐿IR >∼1011 𝐿⊙) may be due to their low gas metallicity (gas depletion
+time). In this section, we explore the fundamental reason for galaxies
+having different origin of [CII] deficit in the two regimes.
+We at first discuss the 𝐿[CII]/SFR vs. 𝑡dep relation of the FIRE
+galaxies (Section 5.4.1). We subsequently explore the reason for
+galaxies showing two distinct regimes on the Δ (log 𝐿[CII]) vs. 𝑡dep
+diagram (Section 5.4.2). Finally, we discuss how this is related to
+the distinct origin of [CII] deficit at high redshifts and high 𝐿IR
+(Section 5.4.3).
+5.4.1 The 𝐿[CII]/SFR vs. 𝑡dep relation
+The FIRE galaxies exhibit two distinct regimes on the Δ (log 𝐿[CII])
+vs. 𝑡dep diagram. While a considerable number of the galaxies
+show a tight linear correlation between their log (𝑡dep/Gyr) and
+Δ (log 𝐿[CII]), exhibiting a linear sequence (we hereafter refer to
+it as the ‘deficit-depletion time sequence’, or DDS), others show
+larger scatter on the diagram and fall systematically below the DDS.
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+29
+10-2
+10-1
+100
+101
+102
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+1 
+5 
+10
+20
+30
+40
+L[CII]/SFR ∝ t0.71
+dep
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+The deficit-depletion time sequence
+Figure 16. The relation between 𝑡dep and Δ (log 𝐿[CII]) of the FIRE sample
+at 𝑧 = 0 − 8 (same as the upper left panel of Fig. 15 except for the colour).
+The data points are coloured-coded by 𝑓H2 of the galaxies. The large (small)
+symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).
+The H2 gas-rich galaxies ( 𝑓H2 >∼ 10%) exhibit a linear correlation between
+log (𝑡dep/Gyr) and Δ (log 𝐿[CII]) (indicated by the black dashed line), which
+can be converted to a power-law relation 𝐿[CII]/SFR ∝ 𝑡0.71
+dep (equation 30).
+The galaxies on the DDS appear to be more H2 gas-rich. In Fig. 16,
+we show the same 𝐿[CII]/SFR vs. 𝑡dep relation of the FIRE sample as
+in Fig. 15 (upper left panel), but colour-code the data points by the
+H2 gas mass fraction, 𝑓H2, of the galaxies instead of their redshift. It
+can be seen from Fig. 16 that the galaxies along the DDS tend to be
+more H2 gas-rich, having 𝑓H2 >∼ 10% (equivalent to 𝑓[CII] <∼ 90%).
+Besides, we see from the two figures that the majority of the low-
+redshift (𝑧 = 0 − 2, shown by cyan stars, yellow hexagons and red
+triangles in Fig. 15) and IR-luminous (𝐿IR >∼ 1011 𝐿⊙, indicated by
+large symbols in Fig. 15 and Fig. 16) galaxies locate on or close to
+the DDS.
+We
+derive
+the
+best-fit
+linear
+scaling
+relation
+between
+log (𝑡dep/Gyr) and Δ (log 𝐿[CII]) for the H2 gas-rich galaxies in our
+sample having 𝑓H2 >∼ 10%, i.e.
+Δ(log 𝐿[CII]) = (−0.38 ± 0.01) + (0.71 ± 0.03) log
+� 𝑡dep
+Gyr
+�
+,
+(29)
+which can be rewritten as
+𝐿[CII]/𝐿⊙
+SFR/(𝑀⊙ yr−1) = 1.78 × 107
+� 𝑡dep
+Gyr
+�0.71
+.
+(30)
+The coefficient of determination is 𝑅2 = 0.936.
+5.4.2 The two regimes on the Δ (log 𝐿[CII]) vs. 𝑡dep diagram
+The reasons for the H2 gas-rich galaxies ( 𝑓H2 >∼ 10%) showing a
+linear sequence on the Δ (log 𝐿[CII]) vs. 𝑡dep diagram are threefolds:
+i) Their 𝑓[CII] ¯𝑍gas ‘saturates’, meaning that it becomes almost like
+a constant and hence 𝐿[CII]/SFR of the galaxies simply scales to
+𝑡dep ¯𝑛gas, ii) their 𝑡dep and ¯𝑛gas anti-correlate with each other, and iii)
+¯𝜖[CII] has relatively small variation among different galaxies.
+Let us at first understand the 𝑓[CII] vs. ¯𝑍gas relation. In Fig. 17,
+10-1
+100
+101
+55
+60
+65
+70
+75
+80
+85
+90
+95
+100
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+z = 6
+z = 8
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+f[CII] ¯Zgas = 0.02
+f[CII] ¯Zgas = 0.1
+1
+2
+4
+0.5
+fCII ¯Zgas ∝ ¯Zgas
+(Eq. 32)
+f[CII] ¯Zgas = const . (Eq. 34)
+f[CII] ( % )
+Figure 17. The relation between ¯𝑍gas and 𝑓[CII] of the FIRE sampleat different
+redshifts. The large (small) symbols represent the galaxies having 𝐿IR ≥
+1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙). The black dotted lines indicate the relation of
+𝑓[CII] ¯𝑍gas = 0.02, 0.1, 0.5, 1, 2 and 4 (from left to right). At ¯𝑍gas <∼ 𝑍⊙, where
+galaxies are H2 gas-poor, 𝑓[CII] ≈ 1 and 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas (c.f. equation 32).
+At larger ¯𝑍gas, 𝑓[CII] scales roughly inversely with ¯𝑍gas and hence 𝑓[CII] ¯𝑍gas ≈
+constant (c.f. equation 34).
+we show the 𝑓[CII] vs. ¯𝑍gas relation for the FIRE sample. It can be
+seen that at ¯𝑍gas <∼ 𝑍⊙, 𝑓[CII] barely declines from unity ( 𝑓[CII] ≈ 1)
+with increasing ¯𝑍gas, whereas at higher ¯𝑍gas, 𝑓[CII] declines sharply
+and 𝑓[CII] ¯𝑍gas becomes approximately a constant (‘saturates’) with
+increasing ¯𝑍gas (or decreasing 𝑓[CII]).
+The shape of the 𝑓[CII] vs. ¯𝑍gas relation of the FIRE galaxies can be
+understood as follows. Consider a spherical gas cloud having a radius
+𝑅cl and a surface-to-centre column density 𝑁cl (= 𝑛H𝑅cl). When the
+cloud is metal and dust-poor (having very low 𝑍gas and 𝛿dgr), the
+LW photons from the radiation field can penetrate the entire cloud
+(i.e. 𝑙F > 𝑅cl) and dissociate all the molecular hydrogen (H2) and
+neutral carbon (CI and CO) in the cloud. In such a low-metallicity
+(or 𝛿dgr) regime, we have
+𝑓[CII], cl ≈ 1
+(31)
+and
+𝑓[CII], cl 𝑍gas ∝ 𝑍gas.
+(32)
+Since 𝑁F ∝ 𝑙F ∝ 𝛿−1
+dgr ∝ 𝑍−1
+gas (equation 10 and 11), indicating
+stronger dust absorption of UV photons with increasing gas metal-
+licity, 𝑙F decreases with 𝑍gas and will become equal or less than 𝑅cl
+when 𝑍gas becomes sufficiently large. Through simple mathematics,
+it can be derived that for a spherical geometry, 𝑓[CII]𝑍gas increases
+sub-linearly with 𝑍gas until when 𝑙F ≪ 𝑅cl, we have
+𝑓[CII], cl ∝ 𝑁F
+𝑁cl
+∝ (𝑍gas𝑁cl)−1
+(33)
+or
+𝑓[CII], cl 𝑍gas = constant.
+(34)
+It is not surprising to find similar scaling relations with the FIRE
+galaxies, 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas at low ¯𝑍gas and 𝑓[CII] ¯𝑍gas ≈ const. at
+MNRAS 000, 1–42 (2022)
+
+30
+Liang et al.
+10-1
+100
+101
+102
+10-2
+10-1
+100
+101
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+FIRE galaxies
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+z = 1
+z = 2
+z = 3
+z = 4
+z = 0
+z = 6
+z = 8
+LIR ≥ 1011 L⊙
+LIR < 1011 L⊙
+Figure 18. The relation between ¯𝑛gas and 𝑡dep of the FIRE sample at different redshifts. The data points in the left (right) panel are colour-coded by the redshift
+( 𝑓H2) of the galaxies. Large (small) symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙). The FIRE galaxies show a clear anti-correlation
+between 𝑡dep and ¯𝑛gas, in particular, the H2 gas-rich galaxies in the sample.
+high ¯𝑍gas (as shown in Fig. 17), given that the ISM of the galaxies
+can be viewed as being made up of numerous such idealized gas
+‘clouds’. The ‘saturation’ of 𝑓[CII] ¯𝑍gas at high ¯𝑍gas indicates that
+the [CII] cooling rate of the galaxies does not increase much with
+gas metallicity due to the shrinking of the size of the [CII]-emitting
+region (Zone I + Zone II).
+Another important reason for the H2 gas-rich galaxies showing
+a clear sequence on the Δ (log 𝐿[CII]) vs. 𝑡dep diagram is that their
+𝑡dep and ¯𝑛gas have clear anti-correlation. In Fig. 18, we show the
+𝑡dep vs. ¯𝑛gas relation of the FIRE sample. This anti-correlation is due
+to the fact that the local free-fall timescale of star-forming clouds
+decreases with gas density (𝑡ff ∝ 𝜌−1/2), and hence gas is converted
+into stars more rapidly in the galaxies having denser ISM. It also
+accounts for the sub-linearity (power law index 𝑛 = 0.71) of the
+𝐿[CII]/SFR vs. 𝑡dep scaling relation of the H2 gas-rich galaxies on
+the DDS (equation 30).
+For the H2 gas-poor galaxies, the fact that they lie below the DDS
+on the Δ (log 𝐿[CII]) vs. 𝑡dep diagram (Fig. 16) is because of their
+low gas metallicity (and hence low 𝑓[CII] ¯𝑍gas). From equation (27),
+we see that at fixed 𝐿[CII]/SFR (equivalently, at fixed Δ log 𝐿[CII]),
+their 𝑡dep has to be higher than that of the galaxies on the DDS so
+as to compensate for their having lower 𝑓[CII] ¯𝑍gas. Besides, the fact
+that the H2 gas-poor galaxies show a larger scatter of 𝑡dep at given
+Δ(log 𝐿[CII]) (Fig. 16) than the H2 gas-rich galaxies is due to the
+non-trivial scatter of 𝑓[CII] ¯𝑍gas among these galaxies, as opposed to
+𝑓[CII] ¯𝑍gas being like a constant for the H2 gas-rich galaxies (Fig. 17).
+5.4.3 The physical origins of [CII] deficit of galaxies (a revisit)
+The important consequence of 𝑓[CII] ¯𝑍gas being ‘saturated’ for the
+H2 gas-rich galaxies is that the overall 𝐿[CII]/SFR ratio of the galax-
+ies shows a tight and steep dependence on 𝑡dep (equation 30). As a
+result, 𝑡dep becomes the dominating parameter that determines the
+𝐿[CII]/SFR ratio of these galaxies. Their 𝐿[CII]/SFR, in contrast,
+does not shows a clear correlation with any of the other four param-
+eters ( 𝑓[CII], ¯𝑍gas, ¯𝑛gas or ¯𝜖[CII]).
+Now we should be able to understand the fundamental reason for
+𝑡dep being the main driver of the [CII] deficit at high 𝐿IR. The IR-
+luminous galaxies are H2 gas-rich (due both to their being dust-rich
+and having high gas column density). Hence, they are in the regime
+where the 𝐿[CII]/SFR ratio of galaxies is determined primarily by
+𝑡dep (i.e. they lie on the DDS in the Δ (log 𝐿[CII]) vs. 𝑡dep diagram)
+and their [CII] deficit is due to their low 𝑡dep.
+Besides, we can now understand the redshift evolution of the
+𝐿[CII]/SFR ratio of the FIRE sample at 𝑧 = 0 − 2. At these low
+redshifts, our sample includes more galaxies that are H2 gas-rich
+as a result of their being more metal and dust-rich than the galax-
+ies at higher redshifts. The 𝐿[CII]/SFR ratio of these low-𝑧 galaxies
+therefore depends more sensitively on 𝑡dep.
+At higher redshifts, in contrast, our sample includes a large fraction
+of metal and dust-poor galaxies that are also H2 gas-poor. They
+are off the DDS in the Δ (log 𝐿[CII]) vs. 𝑡dep diagram. For these
+galaxies, 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas (Fig. 17) and hence 𝐿[CII]/SFR of the
+galaxies depends more sensitively on ¯𝑍gas. As a result, gas metallicity
+becomes the main driver of the [CII] deficit of the high-𝑧 galaxies in
+our sample.
+6 DISCUSSIONS
+6.1 The effect of mass resolution
+The fact that the ISM is treated as an aggregate of spherical gas
+‘clouds’ in our model (and in those of the previous studies like
+e.g. Vallini et al. 2015, 2018; Olsen et al. 2017; Narayanan &
+Krumholz 2017; Lagache et al. 2018; Li et al. 2018; Pallottini et al.
+2019; Leung et al. 2020; Yang et al. 2021) is certainly an idealization
+— the ISM in real galaxies is a continuous medium, and has com-
+plex spatial configurations at and below the scale of these idealized
+‘clouds’. Nonetheless, such treatment offers a (crude) sampling of
+MNRAS 000, 1–42 (2022)
+
+30
+10
+20
+10
+(Gyr)
+.0
+tdep
+10
+10
+101
+10-1
+100
+ngas (cm-3)fH240CII emission as an indicator of galaxy SFR
+31
+the column density of gas in the ISM, enabling us to capture the
+essential physics causing the [CII] deficit of galaxies.
+We note that the predicted [CII] luminosity of galaxies can depend
+on the mass resolution of the simulations (mass of the ‘gas clouds’)
+in this model. To assess this dependency, we adopt two additional
+models (‘HighRes’ and ‘LowRes’) in post-processing, where we in-
+crease and decrease the mass of each individual ‘cloud’ by a factor of
+23 = 8 (equivalent to increasing and reducing the surface-to-centre
+column density by a factor of 2). For the HighRes model, we simply
+split each ‘cloud’ in the fiducial model into 8 with equal mass, and
+assume that the 8 HighRes ‘clouds’ have the same density and metal-
+licity and are exposed to the same radiation field as the parent ‘cloud’.
+For the LowRes model, we calculate the luminosity of each ‘cloud’
+assuming as if the ‘cloud’ is 8 times more massive than it is in the
+fiducial model. The total [CII] luminosity of galaxy is calculated by
+summing the luminosity of each massive ‘cloud’ and then dividing
+the sum by 8 (equivalent to having 8 times lower number of ‘clouds’,
+each being 8 times more massive than that in the fiducial model).
+The predicted [CII] luminosity of the HighRes (LowRes) model
+appears to be higher (lower) than that of our fiducial model by 0.13
+dex on average (see Fig. 19). This is because with decreasing (in-
+creasing) gas column density, a higher (lower) fraction of the gas
+becomes in the [CII]-emitting phase (Zone I + Zone II) and besides,
+an increased (reduced) fraction of the [CII]-emitting gas becomes in
+the HII phase (note: HII gas has on average higher [CII] emissivity
+than HI gas). Overall, by changing the mass resolution by about a
+decade results in a difference in the predicted [CII] luminosity of
+the galaxies by <∼0.15 dex. The difference does not show a strong
+dependence on redshift or SFR of the galaxies (see the lower panel
+of Fig. 19).
+Comparing to the observations, it is clear that the 𝐿[CII]-SFR
+relation of the FIRE galaxies at 𝑧 = 0 predicted by the HighRes model
+becomes systematically offset from the data of L14 and H15 (see the
+upper panel of Fig. 19), indicating a too low mean gas column density
+of the galaxies in the HighRes model. The 𝐿[CII]-SFR relation of the
+LowRes model is below that of the fiducial model, but still appears
+to be within the scatter of the L14 and H15 data. The LowRes model
+predicts a slightly stronger (by ∼ 0.13 dex) [CII] deficit of galaxies
+at high redshifts than the fiducial model.
+Nonetheless, our conclusions regarding the causes of [CII] deficit
+of galaxies at high 𝐿IR (low 𝑡dep) and at high redshifts (low gas
+metallicity) does not change with the chosen mass resolution of
+the [CII] model, despite that the predicted 𝐿[CII] of galaxies shows
+moderate dependence on it.
+6.2 Comparison with the previous studies
+Here we discuss the relation between the findings of the previous
+studies to this from this work. Specifically, we will discuss the con-
+clusions regarding the origin of the [CII] deficit at high 𝐿IR in Sec-
+tion 6.1, whereas in Section 6.2, we will compare the predictions of
+the 𝐿[CII]- SFR relation of galaxies at redshift 𝑧 >∼ 5 from the recent
+studies with ours.
+6.2.1 The [CII] deficit at high 𝐿IR
+[CII] deficit due to a strong ISRF
+A number of studies suggest that the observed [CII] deficit at high
+𝐿IR is due to a strong ISRF in IR-luminous galaxies. This can lead
+to large positive grain charge and thus inefficient heating of gas via
+photo-electric processes in the neutral galactic medium (Tielens &
+HighRes
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+Herrera-Camus et al. 2015
+Local observations
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+LowRes
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+Herrera-Camus et al. 2015
+Local observations
+De Looze et al. 2011
+De Looze et al. 2014 (dwarf)
+10-1
+100
+101
+102
+103
+104
+0.5
+1
+2
+3
+4
+5
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+L[CII], HighRes
+L[CII], fiducial
+Unfilled 
+Filled symbols:
+L[CII], LowRes
+L[CII], fiducial
+Unfilled symbols:
+Figure 19. The effect of mass resolution on the predicted [CII] luminosity
+of galaxies. The upper (middle) panel shows the 𝐿[CII]-SFR relation of the
+FIRE sample at 𝑧 = 0 − 8 predicted by the HighRes (LowRes) model (see
+Section 6.1 for details). For reference, we also show in the two panels the
+observed 𝐿[CII]-SFR relation of local galaxies by L11, L14 and H15. In the
+lower panel, we explicitly show the difference between the [CII] luminosity
+predicted by the HighRes (unfilled symbols) and LowRes (filled symbols)
+models and that predicted by the fiducial model as a function of galaxy SFR.
+The shaded grey area indicates a factor of two difference.
+MNRAS 000, 1–42 (2022)
+
+10
+L(CI) (Lo)
+10
+106
+100
+101
+102
+103
+10
+10-
+SFR(Mo yr-1410
+108
+10
+106
+10-1
+101
+102
+103
+100
+10
+SFR(Mo yr-1432
+Liang et al.
+Hollenbach 1985; Kaufman et al. 1999). Consequently, the rate of
+gas cooling via [CII] line drops. Apart from that, a strong ISRF
+(and hence high 𝑈) may also lead to “dust-bounded" HII regions
+near the newly formed young stars (Bottorff et al. 1998; Abel et al.
+2009), i.e. 𝑁s ≈ 𝑁F (note: 𝑁s increases about linearly with 𝑈 until
+𝑁s ≈ 𝑁F). In this case, gas cooling via [CII] can become inefficient
+due to a lack of CII ions in the HII regions — a significant fraction of
+carbon can be ionized further to CIII ions when 𝑈 is large (In Zone I,
+𝑥(1)
+CII ≈ 1 − 𝑥(1)
+CIII ∝ 𝑈−1, see Appendix E). Overall, both mechanisms
+can lead to a reduced ¯𝜖[CII] in galaxies.
+Looking at the FIRE sample, we notice that the few massive star-
+burst galaxies (SFR>∼100 𝑀⊙ yr−1) in our sample do show noticeably
+lower ¯𝜖[CII] than the normal star-forming galaxies having lower SFR
+(see the right panel of Fig. 13 and the bottom right panel of Fig. 15),
+which can be associated with a strong ISRF (and high 𝑈) in these
+galaxies. Note that CLOUDY (version 17.01) takes into account grain
+charging physics (Baldwin et al. 1991; van Hoof et al. 2004; Abel
+et al. 2005) and our approach of performing dust RT calculation with
+SKIRT provides an improved estimate of the ISRF (and hence 𝑈)
+distribution in galaxies than the previous studies. Our result suggests
+that the [CII] deficit at high 𝐿IR may in part be driven by a strong
+ISRF in the massive starburst galaxies, and yet its impact does not
+seem to be as prominent as 𝑡dep.
+[CII] deficit due to high gas density
+It has also been suggested that the [CII] deficit in IR-luminous galax-
+ies can be driven by the high density of the star-forming gas in
+these galaxies (e.g. Narayanan & Krumholz 2017). With increasing
+density, ISM gas becomes more shielded from ionizing radiation of
+massive young stars and more carbon in the ISM gas becomes neutral
+(in CO or CI). The [CII] deficit is thus due to a lack of CII ions in
+the ISM gas in this scenario (i.e. due to a low 𝑓[CII]).
+This, however, does not seem to be exactly like what we find
+with the FIRE simulations. The ISM of the FIRE galaxies spans a
+very wide range of density (see Fig. 11), and even for the most
+massive starburst galaxies in our sample, a large fraction of their
+[CII] luminosity originates from the gas having intermediate density
+(¯𝑛gas ≈ ¯𝑛HI, MW, see Fig. 11). Overall, the luminosity-weighted gas
+density (¯𝑛gas) of the IR-luminous galaxies (𝐿IR ≥ 1011 𝐿⊙) is not
+significantly higher than that of the IR-fainter galaxies in our sample
+at any given redshift (see Table 8), and the difference is not as strong
+as that in 𝑡dep. Hence, the [CII] deficit of the IR-luminous galaxies
+in FIRE simulations doe not appear to be mainly due to their having
+too dense ISM gas.
+6.2.2 The 𝐿[CII]-SFR relation at redshift 𝑧 >∼ 5
+As mentioned in the Introduction, several planned ground-based
+[CII] line intensity mapping (LIM) experiments will target the emit-
+ting sources at redshift 𝑧 >∼ 5 (Kovetz et al. 2017), including CCAT-
+prime, CONCERTO and TIME. Predicting the 𝐿[CII]-SFR relation of
+galaxies at this early epoch has thus become extremely important for
+interpreting the upcoming data of these experiments (see e.g. Vis-
+bal et al. 2011; Gong et al. 2012; Serra et al. 2016; Fonseca et al.
+2017; Padmanabhan 2019; Yue & Ferrara 2019; Chung et al. 2020;
+Padmanabhan et al. 2022; Sun et al. 2022; ?; Murmu et al. 2023).
+In Fig. 20, we present the results from a number of recent studies.
+These include the ones using SAMs (Lagache et al. 2018; Yang et al.
+2021) as well as those using hydrodynamic simulations (Olsen et al.
+2017; Pallottini et al. 2019; Leung et al. 2020; Kannan et al. 2022).
+It can be seen that different studies have generally predicted a clear
+Herrera-Camus et al. 2015
+De Looze et al. 2011
+Local observations
+FIRE galaxies
+z = 4
+z = 6
+z = 8
+Yang et al. 2021 ( 
+ )
+4.5 < z < 6
+Kannan et al. 2022 ( 
+ )
+6 < z < 10
+Leung et al. 2020 ( 
+ )
+z = 6
+Lagache et al. 2018 ( 
+ )
+z ≈ 6
+Lagache et al. 2018 ( 
+ )
+z ≈ 8
+Pallottini et al. 2019 ( 
+ )
+z = 8
+Olsen et al. 2017 ( 
+ )
+z = 6
+Other predictions for early galaxies
+Figure 20. The 𝐿[CII]-SFR relation at 𝑧 >∼ 5 predicted by different simulation
+groups. Red, yellow, blue and cyan lines indicate the mean result of Yang
+et al. (2021) (4.5 < 𝑧 < 6), Leung et al. (2020) (𝑧 = 6), Lagache et al. (2018)
+(dashed blue line for 𝑧 ≈ 6 and dotted blue line for 𝑧 ≈ 8), and Kannan
+et al. (2022) (6 < 𝑧 < 10). These studies use statistically significant samples.
+The corresponding coloured shaded areas represent the 1𝜎 dispersion of the
+data around the mean relation of each sample. In addition, we also show the
+data of individual galaxies of the Olsen et al. (2017) (𝑧 = 6) and Pallottini
+et al. (2019) (𝑧 = 8) samples by grey diamonds and grey downward triangles,
+respectively. For reference, we show the observed 𝐿[CII]-SFR relation of the
+local star-forming samples of H15 (solid orange line) and L11 (solid green
+line) as well as the the data of the FIRE sample at 𝑧 = 4 (magenta circles),
+𝑧 = 6 (green diamonds) and 𝑧 = 8 (purple downward triangles). A [CII]
+deficit at 𝑧 >∼ 5 is generally predicted by various simulation groups.
+[CII] deficit at 𝑧 >∼ 5 with respect to the local samples of L11 and
+H15, similar to this work using the FIRE simulations. Some have also
+predicted a mild trend of growing deficit with increasing redshift
+(e.g. Lagache et al. 2018; Kannan et al. 2022). The predicted 1𝜎
+scatter of the 𝐿[CII]-SFR relation at a given redshift of these studies
+is typically as large as 0.3−0.5 dex (except Kannan et al. 2022, which
+shows noticeably smaller scatter than the others).
+There is, however, a clear difference in the normalization and
+slope of the 𝐿[CII]-SFR relation predicted by the different groups.
+In particular, Yang et al. (2021) (Kannan et al. 2022) produce the
+highest (lowest) normalization among all different groups at SFR ≈
+1 − 100 𝑀⊙ yr−1. Note that both also produce a considerably steeper
+power-law slope (≈ 1.5) than the others. Interestingly, our prediction
+with the FIRE galaxies appears to be in good agreement with the
+result of Lagache et al. (2018) (in both normalization and slope).
+The difference in the 𝐿[CII]-SFR relation indicates that the pre-
+dicted ISM properties (e.g. ¯𝑍gas, 𝑡dep) of the galaxies at 𝑧 >∼ 5 are
+not well converged between the current simulations. We highlight
+that the data of the upcoming LIM experiments may provide useful
+constraints on the ISM properties of the galaxies in this early epoch,
+given that direct measurement of these properties is very challenging
+using the current techniques.
+MNRAS 000, 1–42 (2022)
+
+1010
+二
+L(CI (Lo)
+108
+10°
+V
+106
+11
+105
+101
+10-1
+100
+102
+103
+10
+SFR(M。 yr-1)4CII emission as an indicator of galaxy SFR
+33
+7 SUMMARY AND CONCLUSIONS
+The 158 𝜇m fine structure line of singly ionized carbon ([CII])
+has been considered as a SFR indicator since observations of
+nearby star-forming galaxies found a linear correlation between their
+𝐿[CII] and SFR. There is, however, evidence showing that IR-bright
+(𝐿IR >∼ 1011 𝐿⊙), starburst galaxies as well as early galaxies at 𝑧 >∼ 5
+have reduced 𝐿[CII]/SFR with respect to the local star-forming sam-
+ples (so-called ‘[CII] deficit’ problem). Different models have been
+posited to explain the origin of the [CII] deficit of galaxies at high
+𝐿IR or at high redshifts and yet no consensus has been reached at
+both regimes.
+In this work, we present a comprehensive analysis on the 𝐿[CII]-
+SFR relation of galaxies using a galaxy sample at 𝑧 = 0 − 8
+(𝑀∗ = 107 − 5 × 1011 𝑀⊙) extracted from the cosmological hy-
+drodynamic simulations, which are part of the FIRE project (Hop-
+kins et al. 2014, 2018; Hopkins et al. 2022), coupled with CLOUDY
+(Ferland et al. 1998, 2017) models. The sample consists mainly of
+galaxies (𝑁gal ∼ 500) from FIREbox (Feldmann et al. 2022), a high-
+resolution cosmological-volume hydrodynamic simulation run with
+FIRE-2 physics, and is supplemented with a few dozen of high-𝑧
+massive galaxies from the cosmological ‘zoom-in’ simulations of the
+MassiveFIRE suite (Feldmann et al. 2016, 2017; Anglés-Alcázar et al.
+2017). The sample covers an unprecedentedly broad dynamic range
+among all studies on [CII], including normal star-forming galaxies,
+(U)LIRG and SMG candidates as well as UV-bright galaxies at EoR,
+which can be used to study the full range of the observational data
+on [CII] currently available.
+The predicted 𝐿[CII]-SFR relation of the FIRE sample agrees well
+with the observational data. In particular, we successfully reproduce
+the observed linear correlation of the local star-forming samples over
+the SFR range ≈ 0.1−10 𝑀⊙ yr−1 (Fig. 4 and Fig. 6). Apart from that,
+we also reproduce the sharp decline of 𝐿[CII]/SFR with 𝐿IR (∼ SFR)
+at 𝐿IR >∼ 1011 𝐿⊙ at low and high redshifts, which is consistent with
+the data of the (U)LIRGs and SMGs in this 𝐿IR regime (Fig. 7 and
+Fig. 9).
+Our sample shows a general decline of 𝐿[CII]/SFR with redshift, in
+particular, at low SFR (Fig. 8). The mean 𝐿[CII]/SFR ratio of the early
+EoR galaxies at 𝑧 > 5 in our sample is about one order of magnitude
+below the local galaxies, showing a clear [CII] deficit, similar to what
+has been previously found with other simulations (Section 6.2.2).
+Observations of galaxies at EoR have drawn divergent conclusions
+on their 𝐿[CII]-SFR relation, which is largely due to the uncertainty
+in the dust SED shape (or ‘dust temperature’) of the galaxies at
+these high redshifts. We analyze the sub-mm data of all the observed
+EoR galaxies and derive their dust-obscured SFR using the ‘dust
+temperature’ estimated from the SED templates of the FIRE samples
+self-consistently. We conclude that the 𝐿[CII]-SFR relation of the
+FIRE galaxies at 𝑧 > 5 is in no conflict with the current observational
+constraints, including those placed by the recent ALPINE and REBELS
+surveys.
+The 𝐿[CII]/SFR ratio of the FIRE sample roughly follows a simple
+linear scaling relationship (equation 27)
+𝐿[CII]
+SFR ∝ 𝑓[CII] ¯𝑍gas𝑡dep ¯𝑛gas,
+where 𝑓[CII] is the mass fraction of ionized or neutral atomic hydro-
+gen gas in the ISM, 𝑡dep is the gas depletion time (= 𝑀gas/SFR), and
+¯𝑍gas and ¯𝑛gas indicate the gas metallicity and gas density that are
+weighted by [CII] luminosity. Following this scaling relationship,
+we find that the key driver of the [CII] deficit is different at high
+𝐿IR and high redshifts (Section 5.3). At high 𝐿IR, the [CII] deficit is
+mainly due to the low 𝑡dep of galaxies, indicating that IR-luminous,
+starburst galaxies have less amount of gas that is able to produce
+[CII] emission per unit SFR than the normal star-forming galaxies
+with moderate SFR. The [CII] deficit at 𝑧 >∼ 5, in contrast, is mainly
+driven by the low gas metallicity of galaxies at this epoch.
+The underlying reason for [CII] deficit being driven by different
+physical parameters at high 𝐿IR and high redshifts is as follows.
+In the low-metallicity regime (corresponding to high-𝑧 galaxies),
+𝐿[CII] of galaxies depends sensitively on metallicity because line
+emissivity scales linearly with metallicity. In the high-metallicity
+regime (corresponding to low-𝑧, massive and starburst galaxies),
+however, such dependence can become weak. This is because dust-
+to-gas ratio (𝛿dgr) in the ISM increases with metallicity, which leads
+to the shrinking of the size of [CII]-emitting region (Section 5.4).
+The shrinking of its size almost cancels out the effect of increasing
+emissivity with metallicity (in this case, 𝑓[CII] ¯𝑍gas ≈ constant). As a
+result, 𝐿[CII]/SFR of galaxies does not depend much on metallicity
+— but instead, on 𝑡dep = 𝑀gas/SFR, see equation (30) — for massive,
+metal (dust) and H2 gas-rich starburst galaxies at low redshifts.
+Our study shows that [CII] deficit may be a common phenomenon
+of galaxies. This would be particularly important for interpreting the
+observational data from several major upcoming [CII] line intensity
+mapping experiments, such as EXCLAIM (Ade et al. 2020), TIME (Sun
+et al. 2021), CCAT-prime (CCAT-Prime collaboration et al. 2021) and
+CONCERTO (CONCERTO Collaboration et al. 2020; Gkogkou et al.
+2022). Our result suggests that by using a constant linear 𝐿[CII]-SFR
+relation derived using nearby star-forming galaxies (e.g. De Looze
+et al. 2011, 2014; Herrera-Camus et al. 2015) may lead to systematic
+overestimate of the cosmic star formation rate density of the high-𝑧
+Universe.
+ACKNOWLEDGEMENTS
+LL acknowledges financial support from the Swiss National Science
+Foundation (hereafter SNSF) (grant no P2ZHP2_199729) and the
+University of Toronto Faculty of Arts and Science. RF acknowl-
+edges financial support from the SNSF (grant no PP00P2_194814,
+200021_188552). DN acknowledges funding from the NSF via AST-
+1909153. DAA acknowledges support by NSF grants AST-2009687
+and AST-2108944, CXO grant TM2-23006X, and Simons Founda-
+tion award CCA-1018464. CAFG was supported by NSF through
+grants AST-1715216, AST-2108230, and CAREER award AST-
+1652522; by NASA through grants 17-ATP17-0067 and 21-ATP21-
+0036; by STScI through grants HST-AR-16124.001-A and HST-
+GO-16730.016-A; by CXO through grant TM2-23005X; and by the
+Research Corporation for Science Advancement through a Cottrell
+Scholar Award. LB acknowledge financial support from the SNSF
+(grant no PP00P2_194814). The Flatiron Institute is supported by
+the Simons Foundation.
+We acknowledge PRACE for awarding us access to MareNostrum
+at the Barcelona Supercomputing Center (BSC), Spain. This research
+was partly carried out via the Frontera computing project at the Texas
+Advanced Computing Center. Frontera is made possible by National
+Science Foundation award OAC-1818253. This work was supported
+in part by a grant from the Swiss National Supercomputing Centre
+(CSCS) under project IDs s697 and s698. We acknowledge access to
+Piz Daint at the Swiss National Supercomputing Centre, Switzerland
+under the University of Zurich’s share with the project ID uzh18.
+This work made use of infrastructure services provided by S3IT
+(www.s3it.uzh.ch), the Service and Support for Science IT
+team at the University of Zurich.
+MNRAS 000, 1–42 (2022)
+
+34
+Liang et al.
+DATA AVAILABILITY STATEMENT
+The data underlying this article will be shared on reasonable request
+to the corresponding author.
+REFERENCES
+Abel N. P., Ferland G. J., Shaw G., van Hoof P. A. M., 2005, ApJS, 161, 65
+Abel N. P., van Hoof P. A. M., Shaw G., Ferland G. J., Elwert T., 2008, ApJ,
+686, 1125
+Abel N. P., Dudley C., Fischer J., Satyapal S., van Hoof P. A. M., 2009, ApJ,
+701, 1147
+Ade P. A. R., et al., 2020, Journal of Low Temperature Physics, 199, 1027
+Andika I. T., et al., 2020, ApJ, 903, 34
+Anglés-Alcázar D., Faucher-Giguère C.-A., Quataert E., Hopkins P. F., Feld-
+mann R., Torrey P., Wetzel A., Kereš D., 2017, MNRAS, 472, L109
+Aravena M., et al., 2016, ApJ, 833, 68
+Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A, 47, 481
+Baes M., Camps P., 2015, Astronomy and Computing, 12, 33
+Baes M., Verstappen J., Looze I. D., Fritz J., Saftly W., Pérez E. V., Stalevski
+M., Valcke S., 2011, ApJS, 196, 22
+Bakx T. J. L. C., et al., 2020, MNRAS, 493, 4294
+Baldwin J. A., Ferland G. J., Martin P. G., Corbin M. R., Cota S. A., Peterson
+B. M., Slettebak A., 1991, ApJ, 374, 580
+Bañados E., Decarli R., Walter F., Venemans B. P., Farina E. P., Fan X., 2015,
+ApJ, 805, L8
+Bañados E., et al., 2016, ApJS, 227, 11
+Barisic I., et al., 2017, ApJ, 845, 41
+Bassini L., Feldmann R., Gensior J., Hayward C. C., Faucher-Giguère
+C. A., Cenci E., Liang L., Bernardini M., 2022, arXiv e-prints, p.
+arXiv:2211.08423
+Behrens C., Pallottini A., Ferrara A., Gallerani S., Vallini L., 2018, MNRAS,
+477, 552
+Bernal J. L., Kovetz E. D., 2022, A&AR, 30
+Béthermin M., et al., 2020, A&A, 643, A2
+Bisbas T. G., et al., 2022, ApJ, 934, 115
+Bischetti M., et al., 2018, A&A, 617, A82
+Blain A. W., 1999, MNRAS, 304, 669
+Boselli A., Gavazzi G., Lequeux J., Pierini D., 2002, A&A, 385, 454
+Bottorff M., LaMothe J., Momjian E., Verner E., Vinković D., Ferland G.,
+1998, PASP, 110, 1040
+Bouwens R. J., Illingworth G. D., Franx M., Ford H., 2007, ApJ, 670, 928
+Bouwens R. J., et al., 2011, ApJ, 737, 90
+Bouwens R. J., et al., 2015, ApJ, 803, 34
+Bouwens R. J., et al., 2016, ApJ, 833, 72
+Bouwens R. J., Stefanon M., Oesch P. A., Illingworth G. D., Nanayakkara T.,
+Roberts-Borsani G., Labbé I., Smit R., 2019, ApJ, 880, 25
+Bouwens R. J., et al., 2022, ApJ, 931, 160
+Bowler R. A. A., Bourne N., Dunlop J. S., McLure R. J., McLeod D. J., 2018,
+MNRAS, 481, 1631
+Bowler R. A. A., Jarvis M. J., Dunlop J. S., McLure R. J., McLeod D. J.,
+Adams N. J., Milvang-Jensen B., McCracken H. J., 2020, MNRAS, 493,
+2059
+Bradač M., et al., 2017, ApJ, 836, L2
+Brauher J. R., Dale D. A., Helou G., 2008, ApJS, 178, 280
+Breuck C. D., et al., 2014, A&A, 565, A59
+Brisbin D., Ferkinhoff C., Nikola T., Parshley S., Stacey G. J., Spoon H.,
+Hailey-Dunsheath S., Verma A., 2015, ApJ, 799, 13
+Burgarella D., et al., 2013, A&A, 554, A70
+CCAT-Prime collaboration et al., 2021, arXiv e-prints, p. arXiv:2107.10364
+CONCERTO Collaboration et al., 2020, A&A, 642, A60
+Calzetti D., et al., 2007, ApJ, 666, 870
+Camps P., Baes M., 2015, Astronomy and Computing, 9, 20
+Camps P., Trayford J. W., Baes M., Theuns T., Schaller M., Schaye J., 2016,
+MNRAS, 462, 1057
+Camps P., et al., 2018, ApJS, 234, 20
+Cañameras R., et al., 2018, A&A, 620, A61
+Capak P. L., et al., 2015, Nature, 522, 455
+Carilli C., Walter F., 2013, ARA&A, 51, 105
+Carlstrom J. E., et al., 2011, PASP, 123, 568
+Carniani S., et al., 2017, A&A, 605, A42
+Carniani S., et al., 2018a, MNRAS, 478, 1170
+Carniani S., Maiolino R., Smit R., Amorín R., 2018b, ApJ, 854, L7
+Carniani S., et al., 2020, MNRAS, 499, 5136
+Casey C. M., 2012, MNRAS, 425, 3094
+Casey C. M., Narayanan D., Cooray A., 2014, Physics Reports, 541, 45
+Casey C. M., et al., 2018a, ApJ, 862, 77
+Casey C. M., Hodge J., Zavala J. A., Spilker J., da Cunha E., Staguhn J.,
+Finkelstein S. L., Drew P., 2018b, ApJ, 862, 78
+Çatmabacak O., Feldmann R., Anglés-Alcázar D., Faucher-Giguère C.-A.,
+Hopkins P. F., Kereš D., 2022, MNRAS, 511, 506
+Chung D. T., Viero M. P., Church S. E., Wechsler R. H., 2020, ApJ, 892, 51
+Cochrane R. K., et al., 2019, MNRAS, 488, 1779
+Cochrane R. K., Hayward C. C., Anglés-Alcázar D., 2022, ApJ, 939, L27
+Contursi A., et al., 2017, A&A, 606, A86
+Cooke E. A., et al., 2018, ApJ, 861, 100
+Cooray A., et al., 2014, ApJ, 790, 40
+Cormier D., et al., 2015, A&A, 578, A53
+Cox P., et al., 2011, ApJ, 740, 63
+Crites A. T., et al., 2014, Millimeter, Submillimeter, and Far-Infrared Detec-
+tors and Instrumentation for Astronomy VII
+Curti M., et al., 2022, arXiv e-prints, p. arXiv:2207.12375
+Davé R., Thompson R., Hopkins P. F., 2016, MNRAS, 462, 3265
+Dayal P., Ferrara A., 2018, Physics Reports, 780-782, 1
+De Looze I., Baes M., Bendo G. J., Cortese L., Fritz J., 2011, MNRAS, 416,
+2712
+De Looze I., et al., 2014, A&A, 568, A62
+Decarli R., et al., 2017, Nature, 545, 457
+Decarli R., et al., 2018, ApJ, 854, 97
+Dey A., et al., 2008, ApJ, 677, 943
+Díaz-Santos T., et al., 2013, ApJ, 774, 68
+Díaz-Santos T., et al., 2015, ApJ, 816, L6
+Díaz-Santos T., et al., 2017, ApJ, 846, 32
+Dole H., et al., 2006, A&A, 451, 417
+Donnan C. T., et al., 2022, arXiv e-prints, p. arXiv:2207.12356
+Draine B. T., Salpeter E. E., 1979, ApJ, 231, 438
+Draine B. T., et al., 2007, ApJ, 663, 866
+Dullemond C. P., Juhasz A., Pohl A., Sereshti F., Shetty R., Peters T., Com-
+mercon B., Flock M., 2012, RADMC-3D: A multi-purpose radiative
+transfer tool, Astrophysics Source Code Library, record ascl:1202.015
+(ascl:1202.015)
+Dunne L., Eales S., Edmunds M., Ivison R., Alexander P., Clements D. L.,
+2000, MNRAS, 315, 115
+Dwek E., 1998, ApJ, 501, 643
+Eilers A.-C., et al., 2020, ApJ, 900, 37
+Eisenhardt P. R. M., et al., 2012, ApJ, 755, 173
+Elbaz D., et al., 2011, A&A, 533, A119
+Ellis R. S., et al., 2013, ApJ, 763, L7
+Faisst A. L., et al., 2017, ApJ, 847, 21
+Faisst A. L., et al., 2020a, ApJS, 247, 61
+Faisst A. L., Fudamoto Y., Oesch P. A., Scoville N., Riechers D. A., Pavesi
+R., Capak P., 2020b, MNRAS, 498, 4192
+Fan X., et al., 2019, ApJ, 870, L11
+Farrah D., et al., 2013, ApJ, 776, 38
+Faucher-Giguère C.-A., Lidz A., Zaldarriaga M., Hernquist L., 2009, ApJ,
+703, 1416
+Feldmann R., 2017, MNRAS: Letters, 470, L59
+Feldmann R., 2020, Communications Physics, 3
+Feldmann R., Hopkins P. F., Quataert E., Faucher-Giguère C.-A., Kereš D.,
+2016, MNRAS:Letters, 458, L14
+Feldmann R., Quataert E., Hopkins P. F., Faucher-Giguère C.-A., Kereš D.,
+2017, MNRAS, 470, 1050
+Feldmann R., et al., 2022, arXiv e-prints, p. arXiv:2205.15325
+Ferland G. J., Peterson B. M., Horne K., Welsh W. F., Nahar S. N., 1992, ApJ,
+387, 95
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+35
+Ferland G. J., Korista K. T., Verner D. A., Ferguson J. W., Kingdon J. B.,
+Verner E. M., 1998, PASP, 110, 761
+Ferland G. J., et al., 2013, Rev. Mex. Astron. Astrofis., 49, 137
+Ferland G. J., et al., 2017, Rev. Mex. Astron. Astrofis., 53, 385
+Ferrara A., Vallini L., Pallottini A., Gallerani S., Carniani S., Kohandel M.,
+Decataldo D., Behrens C., 2019, MNRAS, 489, 1
+Ferrara A., et al., 2022, arXiv e-prints, p. arXiv:2202.07666
+Finkelstein S. L., et al., 2013, Nature, 502, 524
+Finkelstein S. L., et al., 2015, ApJ, 810, 71
+Fixsen D. J., Dwek E., Mather J. C., Bennett C. L., Shafer R. A., 1998, ApJ,
+508, 123
+Fonseca J., Silva M. B., Santos M. G., Cooray A., 2017, MNRAS, 464, 1948
+Fudamoto Y., et al., 2021, Nature, 597, 489
+Fudamoto Y., et al., 2022, ApJ, 934, 144
+Fujimoto S., Ouchi M., Ono Y., Shibuya T., Ishigaki M., Nagai H., Momose
+R., 2016, ApJS, 222, 1
+Fujimoto S., et al., 2019, ApJ, 887, 107
+Fujimoto S., et al., 2020, ApJ, 900, 1
+Fujimoto S., et al., 2021, ApJ, 911, 99
+Fujimoto S., et al., 2022, arXiv e-prints, p. arXiv:2212.06863
+Geach J. E., et al., 2016, ApJ, 832, 37
+Genzel R., Cesarsky C. J., 2000, ARA&A, 38, 761
+Genzel R., et al., 2015, ApJ, 800, 20
+Gill S. P. D., Knebe A., Gibson B. K., 2004, MNRAS, 351, 399
+Gilmore G., Wyse R. F. G., Kuijken K., 1989, ARA&A, 27, 555
+Ginolfi M., et al., 2020, A&A, 633, A90
+Gkogkou A., et al., 2022, arXiv e-prints, p. arXiv:2212.02235
+Goldsmith P. F., Langer W. D., Pineda J. L., Velusamy T., 2012, ApJS, 203,
+13
+Gong Y., Cooray A., Silva M., Santos M. G., Bock J., Bradford C. M., Zemcov
+M., 2012, ApJ, 745, 49
+Graciá-Carpio J., et al., 2011, ApJ, 728, L7
+Griffin M. J., et al., 2010, A&A, 518, L3
+Gruppioni C., et al., 2013, MNRAS, 432, 23
+Guilloteau S., et al., 1992, A&A, 262, 624
+Gullberg B., et al., 2015, MNRAS, 449, 2883
+Gullberg B., et al., 2018, ApJ, 859, 12
+Habing H. J., 1968, Bull. Astron. Inst. Netherlands, 19, 421
+Hahn O., Abel T., 2011, MNRAS, 415, 2101
+Hailey-Dunsheath S., 2009, PhD thesis, Cornell University, United States
+Hao C.-N., Kennicutt R. C., Johnson B. D., Calzetti D., Dale D. A., Moustakas
+J., 2011, ApJ, 741, 124
+Harikane Y., et al., 2020, ApJ, 896, 93
+Harikane Y., et al., 2022, arXiv e-prints, p. arXiv:2208.01612
+Harrington K. C., et al., 2021, ApJ, 908, 95
+Hashimoto T., et al., 2018, Nature, 557, 392
+Hashimoto T., et al., 2019a, PASJ, 71
+Hashimoto T., et al., 2019b, MNRAS, 488, 5029
+Hayward C. C., Kereš D., Jonsson P., Narayanan D., Cox T. J., Hernquist L.,
+2011, ApJ, 743, 159
+Hayward C. C., et al., 2014, MNRAS, 445, 1598
+Heintz K. E., et al., 2022a, arXiv e-prints, p. arXiv:2212.02890
+Heintz K. E., et al., 2022b, arXiv e-prints, p. arXiv:2212.06877
+Helou G., Malhotra S., Hollenbach D. J., Dale D. A., Contursi A., 2001, ApJ,
+548, L73
+Herrera-Camus R., et al., 2015, ApJ, 800, 1
+Herrera-Camus R., et al., 2018, ApJ, 861, 95
+Heyminck S., Kasemann C., Güsten R., de Lange G., Graf U. U., 2006, A&A,
+454, L21
+Hezaveh Y. D., Marrone D. P., Holder G. P., 2012, ApJ, 761, 20
+Hezaveh Y. D., et al., 2013, ApJ, 767, 132
+Hildebrand R. H., 1983, QJRAS, 24, 267
+Ho P. T. P., Moran J. M., Lo K. Y., 2004, ApJ, 616, L1
+Hodge J. A., da Cunha E., 2020, Royal Society Open Science, 7, 200556
+Hollenbach D. J., Tielens A. G. G. M., 1999, Reviews of Modern Physics,
+71, 173
+Hollenbach D. J., Takahashi T., Tielens A. G. G. M., 1991, ApJ, 377, 192
+Hopkins P. F., Kereš D., Oñorbe J., Faucher-Giguère C.-A., Quataert E.,
+Murray N., Bullock J. S., 2014, MNRAS, 445, 581
+Hopkins P. F., et al., 2018, MNRAS, 480, 800
+Hopkins P. F., et al., 2022, arXiv e-prints, p. arXiv:2203.00040
+Hopwood R., et al., 2011, ApJ, 728, L4
+Hu E. M., Cowie L. L., McMahon R. G., Capak P., Iwamuro F., Kneib J.-P.,
+Maihara T., Motohara K., 2002, ApJ, 568, L75
+Hughes T. M., et al., 2017, A&A, 602, A49
+Indriolo N., McCall B. J., 2012, ApJ, 745, 91
+Indriolo N., Geballe T. R., Oka T., McCall B. J., 2007, ApJ, 671, 1736
+Inoue A. K., et al., 2016, Science, 352, 1559
+Iono D., et al., 2006, ApJ, 645, L97
+Ivison R. J., et al., 2010, A&A, 518, L35
+Izumi T., et al., 2018, PASJ, 70
+Izumi T., et al., 2019, PASJ, 71
+Izumi T., et al., 2021a, ApJ, 908, 235
+Izumi T., et al., 2021b, ApJ, 914, 36
+Jones T. A., Swinbank A. M., Ellis R. S., Richard J., Stark D. P., 2010,
+MNRAS
+Kanekar N., Wagg J., Chary R. R., Carilli C. L., 2013, ApJ, 771, L20
+Kannan R., Smith A., Garaldi E., Shen X., Vogelsberger M., Pakmor R.,
+Springel V., Hernquist L., 2022, MNRAS, 514, 3857
+Katz H., Kimm T., Sijacki D., Haehnelt M. G., 2017, MNRAS, 468, 4831
+Katz H., et al., 2019, MNRAS, 487, 5902
+Kaufman M. J., Wolfire M. G., Hollenbach D. J., Luhman M. L., 1999, ApJ,
+527, 795
+Kawamata R., Oguri M., Ishigaki M., Shimasaku K., Ouchi M., 2016, ApJ,
+819, 114
+Kennicutt R. C., 1998, ApJ, 498, 541
+Kennicutt R. C., et al., 2011, PASP, 123, 1347
+Kessler M. F., et al., 1996, A&A, 500, 493
+Khusanova Y., et al., 2021, A&A, 649, A152
+Kirkpatrick A., Pope A., Sajina A., Roebuck E., Yan L., Armus L., Díaz-
+Santos T., Stierwalt S., 2015, ApJ, 814, 9
+Knollmann S. R., Knebe A., 2009, ApJS, 182, 608
+Knudsen K. K., Richard J., Kneib J.-P., Jauzac M., Clément B., Drouart G.,
+Egami E., Lindroos L., 2016, MNRAS, 462, L6
+Knudsen K. K., Watson D., Frayer D., Christensen L., Gallazzi A.,
+Michałowski M. J., Richard J., Zavala J., 2017, MNRAS, 466, 138
+Kohandel M., Pallottini A., Ferrara A., Zanella A., Behrens C., Carniani S.,
+Gallerani S., Vallini L., 2019, MNRAS, 487, 3007
+Kovetz E. D., et al., 2017, arXiv e-prints, p. arXiv:1709.09066
+Kovetz E., et al., 2019, BAAS, 51, 101
+Kroupa P., 2002, Science, 295, 82
+Krumholz M. R., 2014, MNRAS, 437, 1662
+Lagache G., Cousin M., Chatzikos M., 2018, A&A, 609, A130
+Laporte N., et al., 2017, ApJ, 837, L21
+Laporte N., et al., 2019, MNRAS, 487, L81
+Le Fèvre O., et al., 2020, A&A, 643, A1
+Leech K. J., et al., 1999, MNRAS, 310, 317
+Leethochawalit N., Roberts-Borsani G., Morishita T., Trenti M., Treu T.,
+2022a, arXiv e-prints, p. arXiv:2205.15388
+Leethochawalit N., et al., 2022b, arXiv e-prints, p. arXiv:2207.11135
+Lehar J., et al., 2000, ApJ, 536, 584
+Leipski C., et al., 2013, ApJ, 772, 103
+Leipski C., et al., 2014, ApJ, 785, 154
+Leitherer C., Heckman T. M., 1995, ApJS, 96, 9
+Leitherer C., et al., 1999, ApJS, 123, 3
+Leroy A. K., Walter F., Brinks E., Bigiel F., de Blok W. J. G., Madore B.,
+Thornley M. D., 2008, ApJ, 136, 2782
+Leung T. K. D., Olsen K. P., Somerville R. S., Davé R., Greve T. R., Hayward
+C. C., Narayanan D., Popping G., 2020, ApJ, 905, 102
+Li Q., Narayanan D., Davè R., Krumholz M. R., 2018, ApJ, 869, 73
+Li Q., Narayanan D., Davé R., 2019, MNRAS, 490, 1425
+Liang L., Feldmann R., Faucher-Giguère C.-A., Kereš D., Hopkins P. F.,
+Hayward C. C., Quataert E., Scoville N. Z., 2018, MNRAS:Letters, 478,
+L83
+Liang L., et al., 2019, MNRAS, 489, 1397
+MNRAS 000, 1–42 (2022)
+
+36
+Liang et al.
+Liang L., Feldmann R., Hayward C. C., Narayanan D., Çatmabacak O., Kereš
+D., Faucher-Giguère C.-A., Hopkins P. F., 2021, MNRAS, 502, 3210
+Lu N., et al., 2018, ApJ, 864, 38
+Luhman M. L., et al., 1998, ApJ, 504, L11
+Luhman M. L., Satyapal S., Fischer J., Wolfire M. G., Sturm E., Dudley C. C.,
+Lutz D., Genzel R., 2003, ApJ, 594, 758
+Lupi A., Bovino S., 2020, MNRAS, 492, 2818
+Lupi A., Pallottini A., Ferrara A., Bovino S., Carniani S., Vallini L., 2020,
+MNRAS, 496, 5160
+Ma X., Hopkins P. F., Faucher-Giguère C.-A., Zolman N., Muratov A. L.,
+Kereš D., Quataert E., 2016, MNRAS, 456, 2140
+Ma X., et al., 2019, MNRAS, 487, 1844
+Madau P., Dickinson M., 2014, ARA&A, 52, 415
+Madden S. C., et al., 2013, PASP, 125, 600
+Magdis G. E., et al., 2014, ApJ, 796, 63
+Magnelli B., Elbaz D., Chary R. R., Dickinson M., Borgne D. L., Frayer D. T.,
+Willmer C. N. A., 2009, A&A, 496, 57
+Maiolino R., et al., 2005, A&A, 440, L51
+Maiolino R., Caselli P., Nagao T., Walmsley M., Breuck C. D., Meneghetti
+M., 2009, A&A, 500, L1
+Maiolino R., et al., 2015, MNRAS, 452, 54
+Malhotra S., et al., 1997, ApJ, 491, L27
+Malhotra S., et al., 2001, ApJ, 561, 766
+Marrone D. P., et al., 2018, Nature, 553, 51
+Matthee J., et al., 2017, ApJ, 851, 145
+Matthee J., et al., 2019, ApJ, 881, 124
+Mazzucchelli C., et al., 2017, ApJ, 849, 91
+McKinney J., Pope A., Armus L., Chary R.-R., Díaz-Santos T., Dickinson
+M. E., Kirkpatrick A., 2020, ApJ, 892, 119
+McKinney J., Hayward C. C., Rosenthal L. J., Martínez-Galarza J. R., Pope
+A., Sajina A., Smith H. A., 2021, ApJ, 921, 55
+McKinnon R., Torrey P., Vogelsberger M., 2016, MNRAS, 457, 3775
+McLeod D. J., McLure R. J., Dunlop J. S., Robertson B. E., Ellis R. S., Targett
+T. A., 2015, MNRAS, 450, 3032
+McLure R. J., et al., 2013, MNRAS, 432, 2696
+Meyer R. A., et al., 2022, ApJ, 927, 152
+Miettinen O., et al., 2017, A&A, 606, A17
+Molyneux S. J., et al., 2022, MNRAS, 512, 535
+Muñoz J. A., Oh S. P., 2016, MNRAS, 463, 2085
+Murmu C. S., et al., 2023, MNRAS, 518, 3074
+Nahar S. N., Pradhan A. K., 1997, ApJS, 111, 339
+Naidu R. P., et al., 2022, arXiv e-prints, p. arXiv:2207.09434
+Narayanan D., Krumholz M. R., 2017, MNRAS, 467, 50
+Narayanan D., et al., 2015, Nature, 525, 496
+Neri R., Downes D., Cox P., Walter F., 2014, A&A, 562, A35
+Neufeld D. A., Wolfire M. G., 2017, ApJ, 845, 163
+Novak M., et al., 2020, ApJ, 904, 131
+Oesch P. A., et al., 2012, ApJ, 745, 110
+Oesch P. A., et al., 2016, ApJ, 819, 129
+Oesch P. A., Bouwens R. J., Illingworth G. D., Labbé I., Stefanon M., 2018,
+ApJ, 855, 105
+Olsen K. P., Greve T. R., Narayanan D., Thompson R., Toft S., Brinch C.,
+2015, ApJ, 814, 76
+Olsen K., Greve T. R., Narayanan D., Thompson R., Davé R., Rios L. N.,
+Stawinski S., 2017, ApJ, 846, 105
+Olsen K., Greve T. R., Narayanan D., Thompson R., Davé R., Rios L. N.,
+Stawinski S., 2018, ApJ, 857, 148
+Ota K., et al., 2014, ApJ, 792, 34
+Oteo I., et al., 2016, ApJ, 827, 34
+Ouchi M., et al., 2013, ApJ, 778, 102
+Padmanabhan H., 2019, MNRAS, 488, 3014
+Padmanabhan H., Breysse P., Lidz A., Switzer E. R., 2022, MNRAS, 515,
+5813
+Pallottini A., Ferrara A., Bovino S., Vallini L., Gallerani S., Maiolino R.,
+Salvadori S., 2017, MNRAS, 471, 4128
+Pallottini A., et al., 2019, MNRAS, 487, 1689
+Pentericci L., et al., 2016, ApJ, 829, L11
+Pilbratt G. L., et al., 2010, A&A, 518, L1
+Pillepich A., et al., 2018a, MNRAS, 473, 4077
+Pillepich A., et al., 2018b, MNRAS, 475, 648
+Planck Collaboration et al., 2016, A&A, 594, A1
+Popping G., Pérez-Beaupuits J. P., Spaans M., Trager S. C., Somerville R. S.,
+2014, MNRAS, 444, 1301
+Popping G., van Kampen E., Decarli R., Spaans M., Somerville R. S., Trager
+S. C., 2016, MNRAS, 461, 93
+Popping G., Narayanan D., Somerville R. S., Faisst A. L., Krumholz M. R.,
+2019, MNRAS, 482, 4906
+Priddey R. S., McMahon R. G., 2001, MNRAS, 324, L17
+Rawle T. D., et al., 2014, ApJ, 783, 59
+Rémy-Ruyer A., et al., 2014, A&A, 563, A31
+Rhoads J. E., et al., 2022, arXiv e-prints, p. arXiv:2207.13020
+Richings A. J., Schaye J., Oppenheimer B. D., 2014a, MNRAS, 440, 3349
+Richings A. J., Schaye J., Oppenheimer B. D., 2014b, MNRAS, 442, 2780
+Richings A. J., Faucher-Giguère C.-A., Gurvich A. B., Schaye J., Hayward
+C. C., 2022, MNRAS, 517, 1557
+Riechers D. A., et al., 2013, Nature, 496, 329
+Rigopoulou D., Pereira-Santaella M., Magdis G. E., Cooray A., Farrah D.,
+Marques-Chaves R., Perez-Fournon I., Riechers D., 2018, MNRAS, 473,
+20
+Rojas-Ruiz S., et al., 2021, ApJ, 920, 150
+Rybak M., et al., 2019, ApJ, 876, 112
+Safarzadeh M., Hayward C. C., Ferguson H. C., Somerville R. S., 2016, ApJ,
+818, 62
+Salim S., Narayanan D., 2020, ARA&A, 58, 529
+Sanders D. B., Mazzarella J. M., Kim D.-C., Surace J. A., Soifer B. T., 2003,
+AJ, 126, 1607
+Sargsyan L., et al., 2012, ApJ, 755, 171
+Schaerer D., Boone F., Zamojski M., Staguhn J., Dessauges-Zavadsky M.,
+Finkelstein S., Combes F., 2015a, A&A, 574, A19
+Schaerer D., et al., 2015b, A&A, 576, L2
+Schaerer D., et al., 2020, A&A, 643, A3
+Schaerer D., Marques-Chaves R., Barrufet L., Oesch P., Izotov Y. I., Naidu
+R., Guseva N. G., Brammer G., 2022, A&A, 665, L4
+Schouws S., et al., 2022a, arXiv e-prints, p. arXiv:2202.04080
+Schouws S., et al., 2022b, ApJ, 928, 31
+Scoville N. Z., 2013, in Falcón-Barroso J., Knapen J. H., eds, Secular Evolu-
+tion of Galaxies. Cambridge University Press, Cambridge, UK, p. 491
+Scoville N., et al., 2017, ApJ, 837, 150
+Semenov V. A., Kravtsov A. V., Gnedin N. Y., 2017, ApJ, 845, 133
+Serjeant S., 2012, MNRAS, 424, 2429
+Serra P., Doré O., Lagache G., 2016, ApJ, 833, 153
+Shao Y., et al., 2017, ApJ, 845, 138
+Shao Y., et al., 2019, ApJ, 876, 99
+Shen X., Vogelsberger M., Nelson D., Tacchella S., Hernquist L., Springel
+V., Marinacci F., Torrey P., 2022, MNRAS, 510, 5560
+Silva M., Santos M. G., Cooray A., Gong Y., 2015, ApJ, 806, 209
+Sklias P., et al., 2014, A&A, 561, A149
+Smit R., et al., 2018, Nature, 553, 178
+Sobral D., Matthee J., Darvish B., Schaerer D., Mobasher B., Röttgering H.
+J. A., Santos S., Hemmati S., 2015, ApJ, 808, 139
+Sodroski T. J., Odegard N., Arendt R. G., Dwek E., Weiland J. L., Hauser
+M. G., Kelsall T., 1997, ApJ, 480, 173
+Somerville R. S., Davé R., 2015, ARA&A, 53, 51
+Somerville R. S., Primack J. R., 1999, MNRAS, 310, 1087
+Somerville R. S., Popping G., Trager S. C., 2015, MNRAS, 453, 4338
+Sommovigo L., Ferrara A., Pallottini A., Carniani S., Gallerani S., Decataldo
+D., 2020, MNRAS, 497, 956
+Sommovigo L., Ferrara A., Carniani S., Zanella A., Pallottini A., Gallerani
+S., Vallini L., 2021, MNRAS, 503, 4878
+Sommovigo L., et al., 2022, MNRAS
+Sparre M., Hayward C. C., Feldmann R., Faucher-Giguère C.-A., Muratov
+A. L., Kereš D., Hopkins P. F., 2017, MNRAS, 466, 88
+Spilker J. S., et al., 2016, ApJ, 826, 112
+Spitzer L., 1998, Physical Processes in the Interstellar Medium. Wi-
+ley, doi:10.1002/9783527617722, https://doi.org/10.1002%
+2F9783527617722
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+37
+Stacey G. J., Geis N., Genzel R., Lugten J. B., Poglitsch A., Sternberg A.,
+Townes C. H., 1991, ApJ, 373, 423
+Stacey G. J., et al., 2007, in Baker A. J., Glenn J., Harris A. I., Mangum J. G.,
+Yun M. S., eds, Astronomical Society of the Pacific Conference Series
+Vol. 375, From Z-Machines to ALMA: (Sub)Millimeter Spectroscopy of
+Galaxies. p. 52
+Stacey G. J., Hailey-Dunsheath S., Ferkinhoff C., Nikola T., Parshley S. C.,
+Benford D. J., Staguhn J. G., Fiolet N., 2010, ApJ, 724, 957
+Sternberg A., Le Petit F., Roueff E., Le Bourlot J., 2014, ApJ, 790, 10
+Suginohara M., Suginohara T., Spergel D. N., 1999, ApJ, 512, 547
+Sun G., et al., 2021, ApJ, 915, 33
+Sun G., Mas-Ribas L., Chang T.-C., Furlanetto S. R., Mebane R. H., Gonzalez
+M. O., Parsons J., Trapp A. C., 2022, arXiv e-prints, p. arXiv:2206.14186
+Swinbank A. M., et al., 2010, Nature, 464, 733
+Swinbank A. M., et al., 2012, MNRAS, 427, 1066
+Swinbank A. M., et al., 2014, MNRAS, 438, 1267
+Symeonidis M., 2016, MNRAS, 465, 1401
+Tacchella S., Dekel A., Carollo C. M., Ceverino D., DeGraf C., Lapiner S.,
+Mandelker N., Joel R. P., 2016, MNRAS, 457, 2790
+Tacconi L. J., et al., 2018, ApJ, 853, 179
+Tadaki K., et al., 2018, Nature, 560, 613
+Tadaki K., et al., 2020, ApJ, 889, 141
+Takeuchi T. T., Buat V., Burgarella D., 2005, A&A, 440, L17
+Tamura Y., et al., 2019, ApJ, 874, 27
+Tielens A. G. G. M., Hollenbach D., 1985, ApJ, 291, 722
+Tielens A. G. G. M., McKee C. F., Seab C. G., Hollenbach D. J., 1994, ApJ,
+431, 321
+Trayford J. W., et al., 2017, MNRAS, 470, 771
+Trump J. R., et al., 2022, arXiv e-prints, p. arXiv:2207.12388
+Umehata H., et al., 2017, ApJ, 834, L16
+Vallini L., Gallerani S., Ferrara A., Baek S., 2013, MNRAS, 433, 1567
+Vallini L., Gallerani S., Ferrara A., Pallottini A., Yue B., 2015, ApJ, 813, 36
+Vallini L., Pallottini A., Ferrara A., Gallerani S., Sobacchi E., Behrens C.,
+2018, MNRAS, 473, 271
+Vallini L., Ferrara A., Pallottini A., Carniani S., Gallerani S., 2021, MNRAS,
+505, 5543
+Valtchanov I., et al., 2011, MNRAS, 415, 3473
+Vazquez G. A., Leitherer C., 2005, ApJ, 621, 695
+Venemans B. P., et al., 2012, ApJ, 751, L25
+Venemans B. P., Walter F., Zschaechner L., Decarli R., Rosa G. D., Findlay
+J. R., McMahon R. G., Sutherland W. J., 2016, ApJ, 816, 37
+Venemans B. P., et al., 2017, ApJ, 851, L8
+Venemans B. P., Neeleman M., Walter F., Novak M., Decarli R., Hennawi
+J. F., Rix H.-W., 2019, ApJ, 874, L30
+Venemans B. P., et al., 2020, ApJ, 904, 130
+Vieira J. D., et al., 2010, ApJ, 719, 763
+Visbal E., Trac H., Loeb A., 2011, J. Cosmology Astropart. Phys., 2011, 010
+Vogelsberger M., et al., 2020, MNRAS, 492, 5167
+Wagg J., Carilli C. L., Wilner D. J., Cox P., Breuck C. D., Menten K., Riechers
+D. A., Walter F., 2010, A&A, 519, L1
+Wagg J., et al., 2012, ApJ, 752, L30
+Walter F., Riechers D., Cox P., Neri R., Carilli C., Bertoldi F., Weiss A.,
+Maiolino R., 2009, Nature, 457, 699
+Walter F., et al., 2012, Nature, 486, 233
+Walter F., et al., 2018, ApJ, 869, L22
+Wang R., et al., 2013, ApJ, 773, 44
+Wang R., et al., 2016, ApJ, 830, 53
+Wang R., et al., 2019, ApJ, 887, 40
+Wardlow J. L., et al., 2018, MNRAS, 479, 3879
+Watson D., 2011, A&A, 533, A16
+Watson D., Christensen L., Knudsen K. K., Richard J., Gallazzi A.,
+Michałowski M. J., 2015, Nature, 519, 327
+Weingartner J. C., Draine B. T., 2001a, ApJS, 134, 263
+Weingartner J. C., Draine B. T., 2001b, ApJ, 548, 296
+Weiß A., et al., 2013, ApJ, 767, 88
+Whitaker K. E., Pope A., Cybulski R., Casey C. M., Popping G., Yun M. S.,
+2017, ApJ, 850, 208
+Willott C. J., et al., 2013a, ApJ, 145, 4
+Willott C. J., Omont A., Bergeron J., 2013b, ApJ, 770, 13
+Willott C. J., Bergeron J., Omont A., 2015a, ApJ, 801, 123
+Willott C. J., Carilli C. L., Wagg J., Wang R., 2015b, ApJ, 807, 180
+Willott C. J., Bergeron J., Omont A., 2017, ApJ, 850, 108
+Wolfire M. G., McKee C. F., Hollenbach D., Tielens A. G. G. M., 2003, ApJ,
+587, 278
+Wong Y. H. V., et al., 2022, arXiv e-prints, p. arXiv:2202.13613
+Woody D. P., et al., 2004, in Zmuidzinas J., Holland W. S., Withing-
+ton S., eds, Millimeter and Submillimeter Detectors for Astronomy
+II. SPIE, doi:10.1117/12.552446, https://doi.org/10.1117%
+2F12.552446
+Wootten A., Thompson A., 2009, Proceedings of the IEEE, 97, 1463
+Yang C., et al., 2019a, A&A, 624, A138
+Yang J., et al., 2019b, ApJ, 880, 153
+Yang S., Somerville R. S., Pullen A. R., Popping G., Breysse P. C., Maniyar
+A. S., 2021, ApJ, 911, 132
+Yang S., Popping G., Somerville R. S., Pullen A. R., Breysse P. C., Maniyar
+A. S., 2022, ApJ, 929, 140
+Younger J. D., Hayward C. C., Narayanan D., Cox T. J., Hernquist L., Jonsson
+P., 2009, MNRAS: Letters, 396, L66
+Yue B., Ferrara A., 2019, MNRAS, 490, 1928
+Yue M., et al., 2021, ApJ, 917, 99
+Zanella A., et al., 2018, MNRAS, 481, 1976
+Zavala J. A., et al., 2021, ApJ, 909, 165
+Zhu Y.-N., Wu H., Cao C., Li H.-N., 2008, ApJ, 686, 155
+Zubko V., Dwek E., Arendt R. G., 2004, ApJS, 152, 211
+da Cunha E., et al., 2013, ApJ, 766, 13
+da Cunha E., et al., 2021, arXiv e-prints, p. arXiv:2106.08566
+van Hoof P. A. M., Weingartner J. C., Martin P. G., Volk K., Ferland G. J.,
+2004, MNRAS, 350, 1330
+APPENDIX A: THE RADIATIVE COOLING RATE OF GAS
+FROM THE [CII] FINE STRUCTURE TRANSITION — I.
+THE GENERAL CASE
+The CII ion has two fine structure levels in the ground electronic
+state. The radiative cooling rate of gas from the [CII] transition
+can therefore be calculated by solving a classical two-level problem
+(Goldsmith et al. 2012).
+The cooling rate in erg s−1 cm−3 can be written as
+Λ[CII] = [𝐴ul𝑛u + 𝐵ul𝑛u𝑈(𝑇b) − 𝐵lu𝑛l𝑈(𝑇b)]𝐸ul
+(A1)
+where 𝑛u and 𝑛l represent the densities of the upper (2𝑃3/2) and
+lower level (2𝑃1/2) CII ions (cm−3) that result from the combina-
+tion of collisional and radiative processes. 𝐴ul, 𝐵ul and 𝐵lu in the
+above equation represent the Einstein coefficients for spontaneous
+emission (s−1), stimulated emission (erg−1 s−2 cm3) and stimulated
+absorption (erg−1 s−2 cm3), respectively. 𝐸ul (≡ ℎP𝜈[CII], where
+𝜈[CII] = 1900.5 GHz) represents the transition energy of the [CII]
+line. 𝑈(𝑇b) indicates the radiative energy density at 𝜈[CII] and 𝑇b
+is the brightness temperature of the background radiation field. The
+source of the background radiation may be the CMB and/or the
+thermal emission of warm dust.
+Λ[CII] can be rewritten as a function of the excitation (or spin)
+temperature for the transition (𝑇ex) and the temperature of the back-
+ground radiation field (𝑇b). The excitation temperature is defined by
+the relative populations of the upper and lower levels through
+𝑛u
+𝑛l
+≡ 𝑔u
+𝑔l
+𝑒−𝑇 ∗/𝑇 ex,
+(A2)
+where 𝑇∗ = ℎP𝜈[CII]/𝑘B = 91.8 K is the equivalent temperature of
+the [CII] transition, and 𝑔u = 4 (𝑔l = 2) is the statistical weight
+MNRAS 000, 1–42 (2022)
+
+38
+Liang et al.
+of the upper (lower)-level state. Given the relationships between the
+Einstein coefficients, i.e.
+𝐵lu = (𝑔u/𝑔l)𝐵ul
+(A3)
+and
+𝐴ul
+𝐵ul
+=
+8𝜋ℎP𝜈3
+[CII]
+𝑐3
+,
+(A4)
+and substituting equation (A2) into equation (A1), we obtain
+Λ[CII] = 𝑛u𝐴ulℎP𝜈[CII]
+�
+1 − e(𝑇 ∗/𝑇 ex) − 1
+e(𝑇 ∗/𝑇 b) − 1
+�
+.
+(A5)
+Neglecting background radiation (i.e. 𝑇b ≃ 0), we get
+Λ[CII] = 𝑛u𝐴ulℎP𝜈[CII],
+(A6)
+which is the usual expression for the cooling rate. The term in the
+square brackets in equation (A5) is the background correction term
+for attenuation (see da Cunha et al. 2013 for the details). From equa-
+tion (A2), we have
+𝑛u = 𝑛CII
+�
+1 +
+� 𝑔l
+𝑔u
+�
+e𝑇 ∗/𝑇 ex�−1
+.
+(A7)
+By substituting equation (A7) into equation (A5), we then obtain the
+analytic expression for the [CII] cooling rate when a background is
+included,
+Λ[CII] = 𝑛CII 𝐴ulℎP𝜈[CII]Ψ(𝑇ex,𝑇b),
+(A8)
+where
+Ψ(𝑇ex,𝑇b) =
+�
+1 − e(𝑇 ∗/𝑇 ex) − 1
+e(𝑇 ∗/𝑇 b) − 1
+� �
+1 +
+� 𝑔l
+𝑔u
+�
+e𝑇 ∗/𝑇 ex�−1
+.
+(A9)
+Equations (A8)-(A9) indicates that one can derive Λ[CII] by solving
+for 𝑇ex.
+APPENDIX B: EXCITATION TEMPERATURE FOR THE
+[CII] TRANSITION
+Here we present the analytic expression for the excitation temperature
+(𝑇ex) for the [CII] transition.
+The rate equation that determines the upper and lower level CII
+densities, 𝑛u and 𝑛l, includes both collisional and radiative processes,
+and is
+𝑛u[𝐴ul + 𝐵ul𝑈(𝑇b) + 𝐶ul] = 𝑛l[𝐵lu𝑈(𝑇b) + 𝐶lu],
+(B1)
+where 𝐶ul (𝐶lu) represents the collisional de-excitation (excitation)
+rate (s−1). The Einstein coefficients, 𝐴ul, 𝐵ul and 𝐵lu, are related by
+equations (A3) and (A4). For a single collision partner, the collision
+rates are equal to the rate coefficients (cm3 s−1) times the density 𝑛X
+of that collision partner (X = 𝑒−, H0 or H2), i.e.
+𝐶ul = 𝑅X
+ul 𝑛X
+and
+𝐶lu = 𝑅X
+lu 𝑛X,
+(B2)
+where 𝑅X
+ul (𝑅X
+lu) is the downward (upward) rate coefficient for col-
+lision partner X. The two rate coefficients are related by detailed
+balance
+𝑅X
+lu/𝑅X
+ul = (𝑔u/𝑔l)e−𝑇 ∗/𝑇 ,
+(B3)
+where 𝑇 is the kinetic temperature of gas. By substituting equa-
+tions (A2)-(A4), (B1)-(B3) into equation (B1) and through rearrange-
+ment, we obtain the analytic expression for the excitation temperature
+e𝑇 ∗/𝑇 ex =
+(1 + 𝐺)𝐴ul + 𝑛X 𝑅X
+ul
+𝐺𝐴ul + 𝑛X 𝑅X
+ule−𝑇 ∗/𝑇
+(B4)
+where we define
+𝐺 =
+1
+e𝑇 ∗/𝑇 b − 1
+(B5)
+following Goldsmith et al. (2012). For the [CII] transition, we have
+(see e.g. Suginohara et al. 1999; Goldsmith et al. 2012)
+𝐴ul = 2.36 × 10−6 s−1,
+(B6)
+𝑅e
+ul(𝑇) = 8.7 × 10−8(𝑇/2000)−0.37 cm3 s−1,
+(B7)
+𝑅HI
+ul (𝑇) = 4.0 × 10−11(16 + 0.35𝑇0.5 + 48𝑇−1) cm3 s−1,
+(B8)
+and
+𝑅H2
+ul (𝑇) = 3.8 × 10−10(𝑇/100)0.14 cm3 s−1.
+(B9)
+We can see from equations (B4) and (B5) that for no background
+radiation (i.e. 𝑇b ≃ 0) and high gas density (i.e. 𝑛X ≫ 𝐴ul/𝑅X
+ul),
+𝐺 → 0 and 𝑇ex → 𝑇. In this case, 𝑇ex (and hence the CII level
+populations) is set totally by the kinetic temperature of gas. The
+impact of background radiation on 𝑇ex can be important in low-
+density environments (i.e. 𝑛X ≪ 𝐴ul/𝑅X
+ul).
+APPENDIX C: THE STRÖMGREN DEPTH OF A
+PLANE-PARALLEL SLAB
+The Strömgren depth (𝑙s) can be derived by equating the ionizing
+photon rate ( �𝑁ion) to the hydrogen recombination rate ( �𝑁rec) in the
+HII region. �𝑁ion can be expressed as
+�𝑁ion = 𝐹ion𝐴,
+(C1)
+where
+𝐹ion =
+∫ ∞
+𝜈L
+𝐹𝜈
+ℎP𝜈 d𝜈,
+(C2)
+is the ionizing photon flux (cm−2 s−1) and 𝐴 is the surface area of
+the slab. 𝐹𝜈 indicates the specific energy flux (cm−2 s−1 Hz−1) at
+frequency 𝜈 and 𝜈L = 3.2 × 106 GHz is the frequency corresponding
+to the ionization energy of hydrogen, i.e. ℎP𝜈L = 13.6 eV. �𝑁rec can
+be expressed as
+�𝑁rec = 𝑛e𝑛p𝛼B𝑙sd𝐴 ≈ 𝑛2
+H𝛼B𝑙s𝐴,
+(C3)
+where 𝛼B = 2.6 × 10−13 cm3 s−1 is the Case-B recombination co-
+efficient at temperature 𝑇 ≈ 104 K. Combining equation (C1) and
+equation (C3), we have
+𝑙s = 𝐹ion
+𝑛2
+H𝛼B
+.
+(C4)
+Hence, the gas column density at the Strömgren depth is
+𝑁s = 𝑛H𝑙s = 𝐹ion
+𝑛H𝛼B
+= 𝑈𝑐
+𝛼B
+≈ 1023𝑈 cm−2,
+(C5)
+where
+𝑈 = 𝐹ion
+𝑛H𝑐 = 𝑛𝛾
+𝑛H
+(C6)
+is the ionizing photon-to-gas density ratio.
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+39
+APPENDIX D: THE RADIATIVE COOLING RATE OF GAS
+FROM THE [CII] FINE STRUCTURE TRANSITION — II.
+THE PLANE-PARALLEL SLAB MODEL
+Following Appendix A, we present specifically here an analytic ex-
+pression for the gas cooling rate via [CII] line in the HII (Zone I) and
+HI regions (Zone II) of a plane-parallel slab. The superscript “(1)"
+and “(2)" in the following equations indicate the properties of gas in
+Zone I and II, respectively.
+HII region
+For HII region (Zone I), where 𝑇 (1) ≈ 104 K (hence e−𝑇 ∗/𝑇 (1) ≈ 1)
+and the main collision partner of CII ions is 𝑒−, we can rewrite
+equation (B4) to be
+e𝑇 ∗/𝑇 ex =
+𝐴ul + 𝑛(1)
+e
+𝑅e
+ul(𝑇 (1))
+𝑛(1)
+e
+𝑅e
+ul(𝑇 (1))
+,
+(D1)
+where we neglect the effect of background field. For densities below
+the critical one (i.e. 𝑛(1)
+e
+<∼ 𝐴ul/𝑅e
+ul),
+e𝑇 ∗/𝑇 ex ≈
+𝐴ul
+𝑛(1)
+e
+𝑅e
+ul(𝑇 (1))
+.
+(D2)
+Given 𝐴ul = 2.36 × 10−6 s−1 and 𝑅e
+ul(𝑇 (1)) ≈ 5 × 10−8 cm3 s−1
+(equation (B7)), equation (D2) can be rewritten as
+e𝑇 ∗/𝑇 ex ≈ 50
+𝑛(1)
+e
+.
+(D3)
+Substituting equation (D3) into equation (A9) gives
+Ψ(1) ≈
+�
+1 +
+� 𝑔l
+𝑔u
+�
+e𝑇 ∗/𝑇 ex�−1
+≈ 𝑛(1)
+e
+25 .
+(D4)
+Finally, by substituting equation (D4) into equation (A8), we obtain
+the expression for the [CII] cooling rate in HII region
+Λ(1)
+[CII] = 𝑛(1)
+CII 𝐴ulℎP𝜈[CII]Ψ(1)
+=
+�
+𝐴ulℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+e−𝑇 ∗/𝑇 ex�
+𝑛(1)
+CII
+≈ 10−21 𝑛(1)
+CII 𝑛(1)
+e
+erg s−1 cm−3.
+(D5)
+HI region
+Now consider the [CII] cooling rate in HI region (Zone II), where
+𝑇 (2) ≈ 100 K (hence e−𝑇 ∗/𝑇 (2) ≈ 2
+5) and the main collision partner
+of CII ions is H0. In this case, equation (B5) can be rewritten as
+e𝑇 ∗/𝑇 ex =
+(1 + 𝐺)𝐴ul + 𝑛(2)
+HI 𝑅HI
+ul
+𝐺𝐴ul + 𝑛(2)
+HI 𝑅HI
+ul e−𝑇 ∗/𝑇 (2)
+≈
+1
+𝐺 + 2
+5𝑛(2)
+HI (𝑅HI
+ul /𝐴ul)
+.
+(D6)
+Given 𝑅HI
+ul (𝑇 (2)) ≈ 8 × 10−10 cm3 s−1 (equation (B8)), we have
+e𝑇 ∗/𝑇 ex ≈
+1
+𝐺 + 𝑛(2)
+HI /7400
+.
+(D7)
+For the case when background radiation is unimportant (e.g. low-𝑧
+CMB), 𝑇b → 0 and thus 𝐺 → 0, we get
+e𝑇 ∗/𝑇 ex ≈ 7400/𝑛(2)
+HI .
+(D8)
+10-1
+100
+101
+102
+103
+10-5
+10-4
+10-3
+10-2
+10-1
+100
+z = 8
+z = 6
+z = 4
+z = 3
+z = 2
+z = 1
+z = 0
+Figure D1. The relation between Ψ (equation D12) and gas density for HI
+gas (𝑇 = 100 K) at different redshifts. Ψ is unaffected by the CMB at redshift
+0 ≤ 𝑧 ≤ 4. At 𝑧 = 6 − 8, Ψ (and hence the [CII] cooling rate) can be much
+affected by the CMB in low-density gas.
+10-1
+100
+101
+102
+103
+10-2
+10-1
+100
+101
+102
+103
+nu/nC+
+ηb
+z = 8
+z = 6
+z = 4
+z = 3
+z = 2
+z = 1
+z = 0
+Figure D2. Solid (dotted) lines indicate the relation between 𝜂b (𝑛u/𝑛CII)
+and gas density for HI gas (𝑇 = 100 K) at different redshifts. At a given
+redshift, both the effects of CMB heating and attenuation increases with
+decreasing gas density.
+Substituting equation (D8) into equation (A9) and equation (A8)
+gives
+Ψ(2) (𝑇b = 0) ≈
+�
+1 +
+� 𝑔l
+𝑔u
+�
+e𝑇 ∗/𝑇 ex�−1
+≈ 2.7 × 10−4 𝑛(2)
+HI
+(D9)
+and
+Λ(2)
+[CII] (𝑇b = 0) = 𝑛(2)
+CII 𝐴ulℎP𝜈[CII] Ψ(2) (𝑇b = 0)
+=
+�
+𝐴ulℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+e−𝑇 ∗/𝑇 ex�
+𝑛(2)
+CII
+≈ 10−23 𝑛(2)
+CII 𝑛(2)
+HI
+erg s−1 cm−3.
+(D10)
+Equation (D10) is the expression for the [CII] cooling rate in HI
+region when background radiation is neglected.
+MNRAS 000, 1–42 (2022)
+
+40
+Liang et al.
+Taking into account background radiation, equation (A9) can be
+expressed as
+Ψ(2) = 𝜂𝑏 (𝑛u/𝑛CII),
+(D11)
+where
+𝜂𝑏 ≡ 1 − e(𝑇 ∗/𝑇 ex) − 1
+e(𝑇 ∗/𝑇 b) − 1
+≈
+𝐺 + 𝑛(2)
+HI /(7400 𝐺)
+1 + 𝑛(2)
+HI /(7400 𝐺)
+(D12)
+is the background attenuation term and
+𝑛u
+𝑛CII
+=
+�
+1 +
+� 𝑔l
+𝑔u
+�
+e𝑇 ∗/𝑇 ex�−1
+≈
+������
+1 +
+1
+2 (𝐺 + 𝑛(2)
+HI /7400)
+������
+−1
+.
+(D13)
+Equation (D13) indicates that background radiation (e.g. the CMB)
+leads to increased upper level (2𝑃3/2) population of the [CII] tran-
+sition (‘background heating’). Using the above equations, we obtain
+the level of change of the [CII] cooling rate by the CMB at redshift
+𝑧,
+R ≡
+Λ(2)
+[CII] (𝑇CMB(𝑧))
+Λ(2)
+[CII] (𝑇b = 0)
+= Ψ(2) (𝑇CMB(𝑧))
+Ψ(2) (𝑇b = 0)
+≈
+������
+𝐺 + 𝑛(2)
+HI /(7400 𝐺)
+1 + 𝑛(2)
+HI /(7400 𝐺)
+������
+������
+2
+7400𝑛(2)
+HI +
+1
+7400 𝐺/𝑛(2)
+HI + 1
+������
+−1
+.
+(D14)
+We show in Fig. D1 the relation between Ψ(2) (equation D11) and
+gas density for HI gas (𝑇 (2) ≈ 100 K) at different redshifts (𝑧 = 0−8),
+where we account for the effects of the CMB background. It can be
+seen that Ψ(2) shows almost no redshift evolution at 𝑧 = 0 − 4 over
+the wide density range being considered. At higher redshifts, Ψ(2)
+(and hence Λ(2)
+[CII]) is raised by the CMB in low-density gas. At 𝑧 = 6
+(𝑧 = 8), for example, Ψ(2) appears to be much higher than that of the
+lower redshifts at densities below ∼ 1 cm−3 (∼ 10 cm−3).
+It should be noted, however, that although the net effect of CMB
+heating and attenuation on the [CII] cooling rate is negligible except
+for the low-density gas at 𝑧 >∼ 6, their own effect can be prominent
+at various densities and at lower redshifts. This can be seen from
+Fig. D2, where we explicitly show how 𝑛u/𝑛CII (indicating heating)
+and 𝜂b (indicating attenuation) depend on gas density for HI gas
+(𝑇 (2) ≈ 100 K) at different redshifts (c.f. Kohandel et al. 2019). Both
+the effects of CMB heating and attenuation increase with decreasing
+gas density, but they almost cancel out each other at above 0.1 cm−3
+at 𝑧 = 0−4 (and at higher densities at 𝑧 = 6−8). As a result, the [CII]
+cooling rate becomes almost unaffected by the CMB in that regime.
+APPENDIX E: CARBON IONIZATION IN THE HII REGION
+Here we present the analytic expression for the abundance of CII
+ions in the HII region. Consider the carbon ionization equilibrium
+equation:
+ΓC𝑛CII = 𝛼C𝑛CIII𝑛e,
+(E1)
+where we only account for the CII ⇔ CIII equilibrium. ΓC is the
+optically thin carbon photo-ionization rate (s−1) and 𝛼C = 6.02 ×
+10−12 cm3 s−1 is the recombination coefficient (Nahar & Pradhan
+1997). Given 𝑛CII = 𝑥CII𝑛C and 𝑛CIII = (1 − 𝑥CII)𝑛C, we can rewrite
+equation (E1) to be
+𝑥CII =
+�
+1 +
+ΓC
+𝑛e𝛼C
+�−1
+≈ 𝑛e𝛼C
+ΓC
+.
+(E2)
+Following Ferrara et al. (2019), we have
+ΓC = 𝐹ion ¯𝜎C = 𝑈𝑛H𝑐 ¯𝜎C,
+(E3)
+where ¯𝜎C ≈ 4 × 10−18 cm2 is the flux-weighted carbon photo-
+ionization cross section (Spitzer 1998). Substituting equation (E3)
+into equation (E2) and given 𝑛e ≈ 𝑛H for the HII region, we then get
+𝑥CII ≈
+𝛼C
+𝑈𝑐 ¯𝜎C
+∝ 𝑈−1.
+(E4)
+Hence, xCII is inversely proportional to 𝑈.
+APPENDIX F: [CII] LUMINOSITY OF A UNIFORM
+SPHERICAL GAS CLOUD
+Here we derive the specific [CII] cooling rate (erg cm3 s−1) for a
+spherical uniform cloud ( ¯𝜖[CII], cl). For the case where the cloud is
+fully photo-ionized by the external UV radiation (i.e. 𝑙s ≥ 𝑅cl), the
+luminosity of the cloud (𝐿[CII], cl) can be expressed as
+𝐿[CII], cl = 4𝜋
+∫ 𝑅cl
+0
+Λ(1)
+[CII]𝑟2d𝑟.
+(F1)
+Substituting equation (D5) into the above equation, we get
+𝐿[CII], cl =
+� 4𝜋
+3 𝑛H𝑅3
+cl
+�
+𝑛HAC
+�
+ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+𝑅e
+ul(𝑇 (1))𝑥(1)
+CII
+�
+.
+(F2)
+For the case where HI region forms in the cloud (i.e. 𝑙s < 𝑅cl),
+𝐿[CII], cl can be expressed as
+𝐿[CII], cl = 4𝜋
+�∫ 𝑅cl
+𝑅cl−𝑙s
+Λ(1)
+[CII]𝑟2d𝑟 +
+∫ 𝑅cl−𝑙s
+max(0, 𝑅cl−𝑙F)
+Λ(2)
+[CII]𝑟2d𝑟
+�
+,
+(F3)
+where the first and second terms on the right-hand side of the equation
+correspond to the [CII] emission from HII (Zone I) and HI regions
+(Zone II), respectively. By substituting equation (D5) into the first
+term and equation (D13) into the second term, we can rewrite the
+above equation to be
+𝐿[CII], cl = 𝑓[CII], cl
+� 4𝜋
+3 𝑛H𝑅3
+cl
+�
+𝑛HAC
+× ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+∫ 𝑅cl
+𝑅cl−𝑙s
+𝑥(1)
+CII 𝑅e
+ul𝑟2d𝑟 +
+∫ 𝑅cl−𝑙s
+max(0, 𝑅cl−𝑙F) (2/5)𝑅HI
+ul 𝑟2d𝑟
+∫ 𝑅cl
+max(0, 𝑅cl−𝑙F) 𝑟2d𝑟
+,
+(F4)
+where 𝑓[CII], cl represents the total fraction of gas mass in HII or
+HI regions (Zone I + Zone II). Combining equation (F2) and equa-
+tion (F4), and substituting 𝑀cl = 4
+3 𝜋𝑅3
+cl(𝜇H𝑚H𝑛H) into the equa-
+tions, we obtain
+𝐿[CII], cl = 𝑓CII, cl
+� 𝑀cl
+𝜇H𝑚H
+�
+𝑛HAC ¯𝜖[CII], cl,
+(F5)
+MNRAS 000, 1–42 (2022)
+
+CII emission as an indicator of galaxy SFR
+41
+10-1
+100
+101
+102
+100
+101
+102
+103
+FIRE galaxies
+z = 0
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+× 10
+˜ngas (cm−3)
+Figure G1. The relation between the [CII] luminosity-weighted median gas
+density ( ¯𝑛gas) and the [CII] luminosity-weighted mean gas density ( ˜𝑛gas)
+of the FIRE galaxy sample at 𝑧 = 0 − 8. The solid black line indicates the
+one-to-one relationship, whilst the dashed black line indicates the relation
+˜𝑛gas = 10 ¯𝑛gas. ˜𝑛gas is systematically higher than ¯𝑛gas.
+where
+𝑓[CII], cl =
+����
+����
+1
+(if 𝑙F ≥ 𝑅cl)
+3
+∫ 𝑅cl
+𝑅cl−𝑙s
+(𝑟/𝑅cl)2d(𝑟/𝑅cl) (if 𝑙F < 𝑅cl)
+(F6)
+and
+¯𝜖[CII], cl = ℎP𝜈[CII]
+� 𝑔u
+𝑔l
+�
+×
+����������
+����������
+𝑅e
+ul(𝑇 (1))𝑥(1)
+CII
+(if 𝑙s ≥ 𝑅cl)
+∫ 𝑅cl
+𝑅cl−𝑙s
+𝑥(1)
+CII 𝑅e
+ul𝑟2d𝑟 +
+∫ 𝑅cl−𝑙s
+max(0, 𝑅cl−𝑙F)
+�
+2
+5
+�
+𝑅HI
+ul 𝑟2d𝑟
+∫ 𝑅cl
+max(0, 𝑅cl−𝑙F) 𝑟2d𝑟
+(if 𝑙s < 𝑅cl)
+(F7)
+Equation (F7) is the analytic expression for the specific [CII] cooling
+rate for a uniform spherical gas cloud.
+APPENDIX G: LUMINOSITY-WEIGHTED GAS DENSITY
+OF GALAXIES
+In Fig. G1, we show the relation between the [CII] luminosity-
+weighted median gas density (¯𝑛gas) and the [CII] luminosity-
+weighted mean gas density (˜𝑛gas) of the FIRE sample at different
+redshifts (𝑧 = 0 − 8). It can be seen from the figure that the latter is
+systematically higher.
+The reason for this result is that the [CII] luminosity-weighted PDF
+of gas density (𝑛H) of the galaxies resembles a lognormal function
+(see Fig. G2 for an example), showing an elongated tail at high
+density end. Consider a lognormal function with two parameters 𝜇
+and 𝜎, i.e.
+𝑃(𝑛H; 𝜇, 𝜎) =
+1
+𝑛H
+√
+2𝜋𝜎
+e− (ln(𝑛H)−𝜇)2
+2𝜎2
+.
+(G1)
+FIRE galaxy z = 0
+FIRE galaxy z = 6
+μ = − 0.11
+μ = 4.45
+μ + σ2
+2 = 1.43
+μ + σ2
+2 = 6.61
+(50%)
+(50%)
+(19.0%)
+(14.9%)
+Figure G2. The [CII]-luminosity-weighted PDF of gas density of two se-
+lected FIRE galaxies at 𝑧 = 0 (upper panel) and 𝑧 = 6 (lower panel) and the
+best-fit lognormal function (equation G1) to the PDF. In each panel, shaded
+grey area represents the original PDF whereas solid red line indicates the
+best-fit lognormal function. The luminosity-weighted mean gas density ( ¯𝑛H;
+marked by the vertical dashed line on the right) of the galaxies is higher than
+the luminosity-weighted median density ( ˜𝑛H; marked by the vertical dashed
+line on the left).
+The cumulative distribution function (CDF) for a lognormal distri-
+bution is
+𝐶(𝑛H; 𝜇, 𝜎) ≡
+∫ 𝑛H
+−∞
+𝑃(𝑥; 𝜇, 𝜎)d𝑥
+= 1
+2
+�
+1 + erf
+� ln(𝑛H) − 𝜇
+√
+2𝜎
+��
+,
+(G2)
+where erf is the error function. It is easy to show that the mean density
+(˜𝑛H) of a lognormal distribution is
+˜𝑛H =
+∫ ∞
+−∞
+𝑥𝑃(𝑥; 𝜇, 𝜎)d𝑥 =
+∫ ∞
+−∞
+1
+√
+2𝜋𝜎
+e− (ln(𝑥)−𝜇)2
+2𝜎2
+d𝑥
+=e𝜇+ 𝜎2
+2 ,
+(G3)
+whereas the median density (¯𝑛H), i.e. the density at which
+𝐶(𝑛H; 𝜇, 𝜎) = 1
+2, is
+¯𝑛H = e𝜇.
+(G4)
+Hence, ˜𝑛H is higher than ¯𝑛H by a factor of ˜𝑛H/¯𝑛H = 𝑒
+𝜎2
+2 .
+In Fig. G2, we show the luminosity-weighted density PDF of two
+selected FIRE galaxies at 𝑧 = 6 (lower panel) and 𝑧 = 0 (upper panel)
+as well as the best-fit lognormal function to their PDF (note: the same
+galaxies as for Fig. 11) as an example. The luminosity-weighted
+MNRAS 000, 1–42 (2022)
+
+0.25
+0.2
+0.15
+0.1
+d
+0.05
+0
+0
+2
+4
+6
+8
+10
+ln (nH/cm-3)0.3
+0.25
+Hu
+/d ln
+0.2
+ M (Mg
+0.15
+d
+0.1
+0.05
+0
+-4
+-2
+0
+2
+4
+6
+ln (nH/cm-3)42
+Liang et al.
+10-2
+10-1
+100
+101
+10-2
+10-1
+100
+101
+FIRE galaxies
+10-1
+100
+101
+102
+106
+107
+108
+109
+1010
+z = 0
+z = 2
+z = 3
+z = 1
+z = 4
+z = 6
+z = 8
+¯Zgas vs . ˜Zgas
+¯Zgas vs . ¯Zgas, MW
+Figure H1. The ¯𝑍gas vs. ˜𝑍gas relation and the ¯𝑍gas (filled coloured symbols)
+vs. ˜𝑍gas, MW (empty symbols) relation of the FIRE sample at 𝑧 = 0 − 8,
+where ¯𝑍gas, ˜𝑍gas and ˜𝑍gas, MW represent the luminosity-weighted median,
+luminosity-weighted mean and mass-weighted median gas metallicity, re-
+spectively. The solid black line indicates the one-to-one relationship. ¯𝑍gas,
+˜𝑍gas and ˜𝑍gas, MW of the galaxies are very similar to each other.
+median gas density ¯𝑛gas of the 𝑧 = 0 (𝑧 = 6) galaxy is 0.9 cm−3
+(79.4 cm−3), whereas its luminosity-weighted mean density ˜𝑛gas is
+4.2 cm−3 (754.4 cm−3). For the 𝑧 = 6 (𝑧 = 0) galaxy, only 19.0%
+(14.9%) of the total [CII] luminosity originates from the gas at
+density above ˜𝑛gas. It is therefore not statistically representative for
+the bulk of the gas in galaxies emitting [CII].
+APPENDIX H: LUMINOSITY-WEIGHTED GAS
+METALLICITY OF GALAXIES
+In Fig. H1, we show the relation between the luminosity-weighted
+median ( ¯𝑍gas) and the luminosity-weighted mean gas metallicity
+( ˜𝑍gas) of the FIRE galaxy sample at 𝑧 = 0 − 8. ˜𝑍gas and ¯𝑍gas are very
+close to each other. The former is higher by only 0.02 dex (4%) on
+average.
+Both ˜𝑍gas and ¯𝑍gas of the galaxies are similar to their mass-
+weighted gas metallicity ( ¯𝑍gas, MW). In the same figure, we show
+the ¯𝑍gas vs. ¯𝑍gas, MW relation for the FIRE sample. ¯𝑍gas is on average
+higher than ¯𝑍gas, MW by 0.10 dex (20%).
+This paper has been typeset from a TEX/LATEX file prepared by the author.
+MNRAS 000, 1–42 (2022)
+
diff --git a/r9E2T4oBgHgl3EQf1Qhf/content/tmp_files/load_file.txt b/r9E2T4oBgHgl3EQf1Qhf/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2d2b1584654712427737f31bbd85a9e66df7cb58
--- /dev/null
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+page_content='0  [CII] 158 𝜇m emission as an indicator of galaxy star formation rate  Lichen Liang1,2★ , Robert Feldmann2 , Norman Murray1,3 , Desika Narayanan4,5,6 ,  Christopher C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content=' University of Zurich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content=' 211 Bryant Space Sciences Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content=' 432 Newell Drive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content=' USA  6Cosmic Dawn Center at the Niels Bohr Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' University of Copenhagen and DTU-Space,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Technical University of Denmark,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Denmark  7Center for Computational Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Flatiron Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 162 Fifth Avenue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' New York,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' NY 10010,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' USA  8Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' University of Connecticut,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 196 Auditorium Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' U-3046,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Storrs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CT 06269-3046,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' USA  9E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Milne Centre for Astrophysics, University of Hull, Cottingham Road, Hull, HU6 7RX, UK  10DAIM, University of Hull, Cottingham Road, Hull, HU6 7RX, UK  11Department of Physics and Astronomy and CIERA, Northwestern University, Evanston, IL 60208, USA  12Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' George Street, Toronto, ON M5S 3H4, Canada  13Department of Physics, Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093, USA  14TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA  Accepted 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Received 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' in original form 2022  ABSTRACT  Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity  (𝐿 [CII]) and star formation rate (SFR), suggesting that 𝐿 [CII] may be a useful SFR tracer for galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Some other galaxy  populations, however, are found to have lower 𝐿 [CII]/SFR than the local SFGs, including the infrared-luminous, starburst  galaxies at low and high redshifts, as well as some moderately star-forming galaxies at the epoch of re-ionization (EoR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  origin of this ‘[CII] deficit’ is unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this work, we study the 𝐿 [CII]-SFR relation of galaxies using a sample of 𝑧 = 0−8 galaxies  with 𝑀∗ ≈ 107 − 5 × 1011 𝑀⊙ extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic  Environments (FIRE) project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We find a simple analytic expression for 𝐿 [CII]/SFR of galaxies in terms of the following parameters:  mass fraction of [CII]-emitting gas ( 𝑓[CII]), gas metallicity (𝑍gas), gas density (𝑛gas) and gas depletion time (𝑡dep = 𝑀gas/SFR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We find two distinct physical regimes, where 𝑡dep (𝑍gas) is the main driver of the [CII] deficit in H2-rich (H2-poor) galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The observed [CII] deficit of IR-luminous galaxies and early EoR galaxies, corresponding to the two different regimes, is due to  short gas depletion time and low gas metallicity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Our result indicates that [CII] deficit is a common phenomenon  of galaxies, and caution needs to be taken when applying a constant 𝐿 [CII]-to-SFR conversion factor derived from local SFGs to  estimate cosmic SFR density at high redshifts and interpret data from upcoming [CII] line intensity mapping experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Key words: evolution — galaxies: high-redshift — galaxies: ISM — infrared: galaxies  1 INTRODUCTION  The census of cosmic star formation from the present day to the  highest redshifts imposes a key constraint on galaxy evolution theory  and physical cosmology (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Madau & Dickinson 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dayal  & Ferrara 2018, and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The rest-frame ultra-violet  (UV) luminosity (𝐿UV) of galaxies, tracing the young, massive stars,  is a common star formation rate (SFR) indicator of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' How-  ever, a large fraction of the UV light from galaxies in the Universe  is absorbed by interstellar dust and gets re-emitted as thermal ra-  diation at far-infrared (far-IR) wavelength (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fixsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ★ Email: lliang@cita.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='utoronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='ca  Takeuchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dole et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Magnelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gruppi-  oni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Burgarella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Whitaker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Salim  & Narayanan 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Therefore, an accurate estimate of the cosmic  SF history depends on a multi-wavelength, UV-to-millimetre (mm)  analysis that accounts for both the direct, unobscured stellar light and  the dust thermal emission of galaxies over cosmic time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In practice, however, our capability of constraining the two com-  ponents of stellar radiation is largely imbalanced (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While the rest-frame UV-based, unobscured component has  been constrained to as early as redshift 𝑧 ∼ 15 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bouwens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2007, 2011, 2015, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Oesch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012, 2016, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ellis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McLure et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Finkelstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McLeod et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Bowler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leethochawalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Naidu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  © 2022 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04149v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='GA]  10 Jan 2023  2  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Donnan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Harikane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) through deep imaging with  the Hubble and the James Webb Space Telescopes, the obscured com-  ponent is still not well constrained beyond 𝑧 ∼ 3 due to the lack of  statistically-representative, unbiased galaxy samples in that regime  (Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dayal & Ferrara 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Zavala  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is therefore important to have other SFR diagnostics  in addition to UV+IR for early galaxies (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Khusanova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2021, and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The 158 𝜇m (1900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 GHz) fine structure transition (2𝑃3/2 →  2𝑃1/2) of singly ionized carbon ([CII]) has been thought as a promis-  ing alternative SFR indicator, particularly for high-𝑧 galaxies (Hodge  & da Cunha 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is a major coolant of the neutral atomic gas of  the interstellar medium (ISM) and the strongest emission line of star-  forming galaxies at rest-frame far-IR wavelength (Carilli & Walter  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] line of galaxies is usually not much affected by dust  extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  To first order, a correlation between 𝐿[CII] and global SFR of  galaxies is expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Much of the [CII] emission of galaxy originates  from the neutral atomic gas regions (Hollenbach & Tielens 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Wolfire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019), where the far-UV (FUV)  photons produced by the young O and B-type stars heat the gas via the  photoelectric (PE) effect on small dust grains and polycyclic aromatic  hydrocarbon (PAH) molecules (Tielens & Hollenbach 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hollen-  bach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Weingartner & Draine 2001a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The photo-electrons ejected from the dust grains/PAH molecules  collisionally couple to and heat the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Since the PE heating rate  ( �𝐸PE) traces galaxy SFR, and 𝐿[CII] balances �𝐸PE given that [CII]  line is the dominant coolant in those regions (assuming a thermal  equilibrium), 𝐿[CII] should therefore be correlated to SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Obser-  vations of local star-forming galaxies (SFGs) have indeed found a  linear correlation between 𝐿[CII] and SFR over the broad SFR range  of ≈ 10−4 − 10 𝑀⊙ yr−1 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leech et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Boselli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These observations suggest that the [CII] line can be a useful  SFR indicator for galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  There is evidence, however, showing that this scaling relation-  ship does not hold on all occasions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For instance, observations find  that local ultra-luminous infrared galaxies (ULIRGs, galaxies having  𝐿IR >∼ 1012 𝐿⊙) show a significant lower 𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR)  ratio than normal star-forming galaxies by up to an order of magni-  tude (Malhotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1997, 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Luhman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Brauher  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Farrah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Magdis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014), the so-called ‘[CII]  deficit’ problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This result was at first revealed with the Infrared  Space Observatory (ISO;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kessler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1996) and later confirmed  by observations with the Herschel Space Observatory (hereafter  Herschel;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pilbratt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010) that has improved far-IR observing  capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Subsequent observations with Herschel also show that  the [CII] deficit extends to lower 𝐿IR and that the 𝐿[CII]/𝐿IR ratio  of galaxies exhibits a continuous decrease with increasing 𝐿IR at  𝐿IR >∼ 1011 𝐿⊙ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Graciá-Carpio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sargsyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Díaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cormier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2015, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Díaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Contursi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Studies have investigated the 𝐿[CII]-SFR relation of galaxies at  higher redshifts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Brisbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Spilker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Zanella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cooke  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Rybak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McKinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At 𝑧 ≈ 1−5, the  selected galaxies are mostly uncovered by sub-mm surveys, which are  traditionally classified as ‘sub-millimetre-bright galaxies (SMGs1)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  1 In the literature, ‘SMGs’ typically refer to the galaxies detectable by single-  These are heavily dust-obscured systems having 𝐿IR >∼1012 𝐿⊙ (cor-  responding to SFR >∼ 100 𝑀⊙ yr−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kennicutt 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In general, it is  found that [CII] deficit persists at high 𝐿IR at high redshifts, although  the high-𝑧 populations appear to show larger scatter of 𝐿[CII]/SFR  at given 𝐿IR than the local ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The advent of the Atacama Large Millimetre/submillimetre Array  (ALMA) Telescope (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Wootten & Thompson 2009) has triggered  particular interest in searching for [CII] emitters at 𝑧 >∼ 5, and accu-  mulating efforts have been made to constrain the 𝐿[CII]-SFR relation  of galaxies at this epoch (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ouchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Capak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Penter-  icci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Smit  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schouws et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ALMA observational programs are  often designed to target the Lyman-𝛼 emitters (LAEs), Lyman-break  galaxies (LBGs) and the quasar host galaxies (hereafter quasar hosts  for simplicity) having pre-determined redshift (Hodge & da Cunha  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Though the earliest attempts targeting the bright LAEs were  mostly unsuccessful (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ouchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Inoue et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016), follow-up programs targeting the  LBGs and quasar hosts generally have had much higher success rate  of [CII] line detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Overall, there have been > 200 galaxies at  𝑧 >∼ 5 that have confirmed detection of [CII] line to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While the  quasar hosts are typically very luminous and have substantial SFR  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bañados et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Decarli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020),  many of the selected LBGs/LAEs at 𝑧 >∼ 5 are normal star-forming  galaxies having moderate SFR (≈ 10 𝑀⊙ yr−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, the  ALMA Large Program to INvestigate [CII] at Early times (ALPINE)  survey (Le Fèvre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Béthermin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Faisst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2020a) in Cycle-5, targeting a sample of 118 star-forming galaxies at  𝑧 ≈ 5 − 6, has contributed more than a third (∼ 75/200) of the total  number of successful detections at 𝑧 >∼ 5 (Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' More  recently, the ALMA Reionization Era Bright Emission Line Survey  (REBELS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bouwens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) in Cycle-7 has targeted a sample of  40 UV-bright, star-forming galaxies at 𝑧 ≈ 7 and confirmed [CII]  line detection for 18 galaxies in their sample (Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Observations have drawn divergent conclusions on the 𝐿[CII]-SFR  relation at 𝑧 >∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While some have argued a clear [CII] deficit of  galaxies at 𝑧 >∼ 5 with respect to the local normal SFGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ouchi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Inoue et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Knudsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pentericci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bradač et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Laporte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022), others have argued that they follow the same linear scaling  relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schaerer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schouws et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It should be noted, however, that the SFR estimates at such  high redshifts can be highly uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Galaxies at 𝑧 >∼ 5 typically  have very few reliable photometric data points in the dust thermal  continuum that are measured with ALMA (at band 6 or 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A number  of recent studies, both observational (Capak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bouwens  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Faisst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020b) and theoretical  (Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sommovigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020,  2021), have pointed out that based on the ALMA broad-band flux(es)  alone, 𝐿IR (and hence the obscured SFR) of galaxies at 𝑧 >∼5 is likely  to be poorly constrained due to the large variation in the shape of  the spectral energy distribution (SED) of their dust emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  reported (in)consistencies of the 𝐿[CII]-SFR relation at 𝑧 >∼5 with the  dish sub-mm telescopes, of which the observed sub-mm flux density is above  ∼ 1 mJy (Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hodge & da Cunha 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  3  local SFGs by the observations therefore need to be more carefully  assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Much effort has been made to model [CII] emission of galaxies  and explain the origins of the observed [CII] deficit over the last  two decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A broad variety of different methods are used by dif-  ferent studies, including pure analytic approaches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Muñoz & Oh  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019), numerical models of idealized gas clouds  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Narayanan & Krumholz 2017), semi-analytic  galaxy models (SAMs, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Popping et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014, 2016, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lagache  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021, 2022) and cosmological hydrodynamic  galaxy simulations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vallini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015,  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Katz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Lupi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lupi & Bovino 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Richings  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bisbas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A pure analytic approach and/or a  simplified cloud model can capture the key physical mechanisms that  determine 𝐿[CII] of galaxies and provide useful insights at low com-  putational cost, but does not provide the necessary galaxy statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  SAMs can produce statistically significant galaxy samples probing a  very wide dynamic range (in stellar mass, SFR, redshift and etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=') and  are computationally efficient (Somerville & Davé 2015), but they do  not provide any information of structures on the sub-galactic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Hydrodynamic simulations, in contrast, can calculate the detailed  sub-galactic structures and thus provide more accurate prediction  for the [CII] emission properties of galaxies, at the cost of more  computational expense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Different explanations for the [CII] deficit in the high 𝐿IR regime  have been proposed by the theory groups (see also e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Narayanan & Krumholz 2017, for a summary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For instance,  some studies argue that the deficit is due to a strong UV radiative  intensity (𝐺) in the IR luminous galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Malhotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Luhman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Genzel & Cesarsky 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Luhman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Graciá-  Carpio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can have two important  effects on the thermal balance of [CII]-emitting gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' First of all, a  high 𝐺 leads to large positive grain charges, thereby reducing the  kinetic energy of the ejected photo-electrons and hence the rate of  PE heating ( �𝐸PE) of gas (Tielens & Hollenbach 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kaufman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a result, [CII] cooling rate drops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Besides, HII regions in  those galaxies may become ‘dust bounded’ rather than ‘ionization  bounded’ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bottorff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' see also Ferrara  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this scenario, most of the UV radiation from young  stars is absorbed by dust in the HII regions, leading to both an excess  of IR emission in the HII regions and a reduced �𝐸PE (and hence  𝐿[CII]) in gas outside the HII regions due to a starvation of UV  photons there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Alternatively, Narayanan & Krumholz (2017) suggest that a high  gas density can lead to a [CII] deficit of galaxy in addition to having  a high 𝐺.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Using a stratified gas cloud model, the authors demonstrate  that with increasing gas density, a larger fraction of carbon in gas  turns into neutral (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' in CO and CI) and 𝐿[CII] decreases due to a  reduced mass fraction of [CII]-emitting gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Apart from these studies, Muñoz & Oh (2016) posit an analytic  model where [CII] deficit is due to thermal saturation of the upper fine  structure transition state (2𝑃3/2) of CII ions2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At above 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 K (note:  𝑇∗ = 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 K is the equivalent temperature of the [CII] transition),  𝐿[CII] does not increase much with gas kinetic temperature and this  has been suggested to be the reason for 𝐿[CII] not increasing much  2 Throughout this paper, we use ‘[CII]’ when referring to the observable  emission line, and ‘CII’ when discussing ionized carbon under the context of  chemical abundances of gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  with SFR at high 𝐿IR (∼ SFR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note, however, that the Muñoz & Oh  (2016) model assumes that the bulk of the [CII] emission of galaxies  originates from the gas having density in excess of the critical density  for the [CII] transition (Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  With the recent success of the ALMA programs in searching for  [CII]-emitters, there has been an increasing amount of effort to pre-  dict [CII] emission properties of galaxies at 𝑧 >∼ 5 by coupling cos-  mological hydrodynamic simulations or SAMs with photo-ionization  codes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CLOUDY, Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' DESPOTIC, Krumholz  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' RADMC-3D, Dullemond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The predicted 𝐿[CII]-SFR  relation for galaxies, however, shows non-trivial discrepancy between  different groups in both normalization and slope (see summary in  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Katz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020), which can be ascribed to  the differences in the simulation methodology and [CII] modelling  techniques adopted by the different groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Despite the discrepancy,  many have predicted a [CII] deficit of galaxies at 𝑧 >∼5 with respect to  the local normal star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For instance, Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2018) couple a sample of ∼ 20 K SAM galaxies at 4 ≤ 𝑧 ≤ 8  with CLOUDY and report a [CII] deficit of > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex and a trend of  decreasing normalization of the relation with redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2017) post-process 30 star-forming galaxies at 𝑧 = 6 extracted from  the MUFASA ‘zoom-in’ simulations (Davé et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016) using CLOUDY  and predict a [CII] deficit of about one decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A similarly strong  [CII] deficit is reported by Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017, 2019) using the  SERRA ‘zoom-in’ simulations that include more sophisticated chem-  ical networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' More recently, Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022) predict an even  more prominent [CII] deficit at 𝑧 ≥ 5 than the above-mentioned ear-  lier studies, especially at low SFR, using a galaxy sample produced  by the THESAN ‘zoom-in’ suite, which includes the Illustris-TNG  galaxy formation model (Pillepich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It has been generally thought that gas metallicity (𝑍gas) is the key  factor in determining the [CII] luminosity of the early galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Vallini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019) since [CII]  emissivity is linearly scaled with 𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The early work by Vallini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2015) shows that the 𝐿[CII]-SFR relation of EoR galaxies depends  sensitively on 𝑍gas, and the significant [CII] deficit found with the  LAEs at 𝑧 ≈ 5−7, such as Himiko (Ouchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014)  and IOK-1 (Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014), can be well accounted for by assigning  a very low gas metallicity (𝑍gas < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 𝑍⊙) to the simulated galaxy  in an ad hoc manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] deficit of galaxies at 𝑧 >∼ 5 commonly  found in the recent simulations, as mentioned above, is likely due to  the much lower 𝑍gas of the early galaxies than the 𝑧 = 0 ones predicted  by these simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Observationally, however, direct measurement  of 𝑍gas at 𝑧 >∼ 5 is still very challenging, though some preliminary  attempts have been made recently (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Rigopoulou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Curti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Heintz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Rhoads et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Trump et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  A few recent studies have predicted [CII] emission of galaxies at  lower redshifts using simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For instance, Popping et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019)  and Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021) predict the 𝐿[CII]-SFR relation for the catalog  derived from the ‘Santa Cruz’ semi-analytic models (Somerville &  Primack 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Somerville et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015) using DESPOTIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Their result  is in good agreement with the observational data at 𝑧 ≈ 2, except  that at high SFR (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR >∼ 10 𝑀⊙ yr−1), they produce a noticeably  weaker [CII] deficit than is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' More recently, Richings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2022) ran a set of hydrodynamic simulations of isolated (dwarf  and Milky Way-mass) galaxies implemented with the CHIMES non-  equilibrium chemistry module (Richings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014a,b) (including a  dust-depletion model) and predict the [CII] emission of their galaxy  sample using RADMC-3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Despite having a small sample size, the  predicted 𝐿[CII] of their galaxies appears to be in agreement with  the observational result of local galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011,  MNRAS 000, 1–42 (2022)  4  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015) at similar SFR (see also another  recent work by Bisbas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022 using isolated dwarf simulations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Apart from these studies, there has been limited effort to predict  the 𝐿[CII]-SFR relation of galaxies at 𝑧 = 0 − 5 using statistically  representative galaxy samples and compare the result to the fruitful  observational data in this regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, the origin of the [CII]  deficit of the IR-luminous galaxies has not yet been studied in detail  using cosmological hydrodynamic simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is largely be-  cause producing a statistically representative sample in this regime  with well-resolved ISM is computationally demanding, which is pos-  sible only for a few large simulation consortiums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is, however, of  critical importance that a robust [CII] model should be able to simul-  taneously reproduce the data of different galaxy populations over the  entire SFR and redshift ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In this study, we conduct a comprehensive analysis of the galaxy  𝐿[CII]-SFR relation using a simulated sample spanning an unprece-  dentedly broad redshift range of 𝑧 = 0−8 extracted from the Massive-  FIRE (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Anglés-Alcázar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017) and  FIREbox (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) cosmological hydrodynamic simu-  lations from the Feedback in Realistic Environments (FIRE) project3  (Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sample cov-  ers a very broad range of galaxy stellar mass and SFR, allowing  us to make direct comparison with the observational data in differ-  ent regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, the sample includes local normal SFGs  (having SFR ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 − 10 𝑀⊙ yr−1) that can be compared with the  observations where a linear 𝐿[CII]-SFR correlation has been found  by the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It also includes IR-luminous (𝐿IR > 1011 𝐿⊙)  galaxies at 𝑧 = 0 − 5 that are candidates for (U)LIRGs and SMGs,  where observations have shown to have [CII] deficit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Moreover, the  sample includes early galaxies at above 𝑧 = 5 spanning a broad SFR  range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Many of these galaxies have similar mass and SFR to the  samples of the ALPINE and REBELS projects and therefore can be  used to provide useful interpretations for a variety of their recent  observational results (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ginolfi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fudamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Sommovigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The main goal of this work is to predict the 𝐿[CII]-SFR relation  for the FIRE galaxy sample (spanning 𝑧 = 0 − 8 and SFR ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 −  103 𝑀⊙ yr−1) and to understand what physical parameters of galaxies  determine their overall 𝐿[CII]-to-SFR ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This will then help us  find the origin of the observed [CII] deficit of galaxies at both high  𝐿IR and high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Note that the results from this work will be useful for interpreting  the data of several upcoming [CII] line intensity mapping (LIM)  experiments (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kovetz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bernal & Kovetz  2022, and references therein), such as TIME4 (Crites et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sun  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021), CCAT-prime5 (CCAT-Prime collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021),  CONCERTO6 (CONCERTO Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gkogkou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022) and EXCLAIM (Ade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The LIM experiments have  been designed to measure the emission from spectral lines originat-  ing from galaxies at all luminosities, including the ones that cannot be  resolved by the current surveys (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' with ALMA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The experiments  that will target [CII] emission, in particular, will be useful for con-  straining the cosmic star-formation history (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Silva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fonseca et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Padmanabhan  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yue & Ferrara 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Chung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Padmanabhan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  3 FIRE project website: http://fire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='northwestern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='edu  4 https://cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='edu/projects/TIME  5 http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='ccatobservatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='org  6 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='apex-telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='org/ns/concerto/  2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is, however, not yet certain whether the  [CII] line always acts as a reliable SFR tracer for galaxies of all types  and at all redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  This paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We describe in Section 2 the  simulation methodology and in Section 3, the method used to simu-  late [CII] emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 4, we compare the predicted 𝐿[CII]-  SFR relation of the FIRE galaxy sample with the observational data at  different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 5, we investigate the origin of the tight  𝐿[CII]-SFR linear scaling relation of normal star-forming galaxies  at 𝑧 = 0 and the causes of the [CII] deficit of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We discuss  our results in Section 6 and finally summarize and conclude this  study in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Throughout this paper, we adopt the cosmologi-  cal parameters of the Planck 2015 Cosmology (Planck Collaboration  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016), specifically Ωm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='309, ΩΛ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='691, Ωb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='049,  𝜎8 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='816, and 𝐻0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='74 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2 SIMULATION METHODOLOGY  In this section, we introduce the simulation suites (FIREbox and  MassiveFIRE) from which we extract the galaxy sample used for this  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 Simulation set-up and galaxy catalogue  We adopt a sample that spans the wide redshift range 𝑧 = 0−8, stellar  mass (𝑀∗) range 𝑀∗ ≈ 107−5×1011 𝑀⊙ and SFR range SFR ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1−  103 𝑀⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sample consists primarily of galaxies at 𝑧 = 0 − 8  produced by FIREbox (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), the new-generation  simulation suite of FIRE run with full cosmological volume boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It  is supplemented by a number of high-𝑧 (𝑧 = 1 − 8) massive galaxies  (𝑀∗ >∼ 1010 𝑀⊙) extracted from the ‘zoom-in’ suite, MassiveFIRE  (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016, 2017), rerun with FIRE-2 physics (Anglés-  Alcázar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Çatmabacak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bassini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Many of the MassiveFIRE galaxies have the 𝐿IR close to that of the  SMGs (Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cochrane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019) that are used by the  observational studies on the 𝐿[CII]-SFR relation at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' All  simulations used for this study are run with the same FIRE-2 physics  and numerics (Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  FIREbox simulations  FIREbox (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) is a new-generation simulation suite  using FIRE physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Different from all previous simulations of FIRE,  FIREbox simulates full cosmological volumes instead of using ‘zoom-  in’ set-up to study galaxy evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' FIREbox simulations are run  in cubic boxes with periodic boundary conditions, and with initial  conditions at redshift 𝑧 = 120 generated using the MUSIC (Multi-  Scale Initial Conditions) code (Hahn & Abel 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The simulations  use the Planck 2015 Cosmology (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  All FIREbox simulations use the same initial conditions and cos-  mology but differ in numerical resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For this study, we extract  galaxies from the fiducial FIREbox hydrodynamic simulation, which  is run with a box length of 15 ℎ−1 cMpc and with the following  number of dark matter (DM) and baryonic particles: 𝑁DM = 10243  and 𝑁b = 10243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mass resolution of DM and baryon particles  are 𝑚DM = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 105 and 𝑚b = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 104 𝑀⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The gravitational  softening lengths are kept fixed in proper (comoving) coordinates at  𝑧 ≤ 9 (𝑧 ≥ 9) and are set to ℎDM = 80 pc for DM particles and  ℎ∗ = 12 pc for star particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The softening length for gas particles  (ℎgas) is fully adaptive and is set equal to their kernel smoothing  length down to a minimum of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 proper pc, which is reached in the  densest parts of the ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' FIREbox is evolved down to 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  5  SFR > 10 M⊙ yr−1  Total  z = 8  FIREBox galaxies  z = 6  z = 4  z = 2  z = 1  z = 0  z = 3  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Histograms of the stellar mass distribution of the FIREbox sample  at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Violet, green, magenta, blue, red, yellow and cyan  histograms correspond to 𝑧 = 8, 𝑧 = 6, 𝑧 = 4, 𝑧 = 3, 𝑧 = 2, 𝑧 = 1 and 𝑧 = 0,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For each redshift, the unfilled histograms indicate the result of  the entire galaxy sample, whereas the filled histograms indicate specifically  the result of the galaxies having SFR ≥ 10 𝑀⊙ yr−1 (corresponding to 𝐿IR >∼  1011 𝐿⊙ based on the Kennicutt 1998 relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note: [CII] deficit is observed  at 𝐿IR >∼ 1011 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For clarity of presentation, we separately show the result  of the 7 snapshots in 3 separate panels (top panel for 𝑧 = 8 and 𝑧 = 6, middle  panel for 𝑧 = 3 and 𝑧 = 4 and bottom panel for 𝑧 = 0, 𝑧 = 1 and 𝑧 = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We identify galaxies in different snapshots of the FIREbox simula-  tion using the AMIGA Halo Finder7 (AHF;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Knollmann  & Knebe 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We use the galaxies extracted from 7 snapshots cor-  responding to redshift 𝑧 = 0, 1, 2, 3, 4, 6 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For each snapshot,  we include the central galaxy of the 30 most massive halos iden-  tified by AHF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To enlarge our sample, we also include the central  galaxy of a number of additional, randomly chosen halos having  log (𝑀vir/𝑀⊙) > 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1 the histograms of the 𝑀∗  distribution of the selected FIREbox galaxies at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The number of galaxies selected at 𝑧 = 0, 1, 2, 3, 4, 6, and 8 are  113, 84, 80, 75, 64, 61 and 30, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1,  all but a few selected galaxies have stellar mass greater than 107 𝑀⊙  (corresponding to ∼ 160 times of the mass resolution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The most  7 Code available at: popia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='ft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='uam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='es/AHF/Download.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='html  massive galaxy of the FIREbox sample has 𝑀∗ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 1011 𝑀⊙ (at  𝑧 = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In the same figure, we also show the 𝑀∗ distribution of the galaxies  having SFR >∼ 10 𝑀⊙ yr−1 (filled histograms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These galaxies have  𝐿IR ≥ 1011 𝐿⊙, the regime where a [CII] deficit is observed (see  Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' They apparently are more massive than the galaxies hav-  ing SFR < 10 𝑀⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In our catalogue, we find most galaxies with  SFR ≥ 10 𝑀⊙ yr−1 at 𝑧 = 2 (red histogram, 𝑁 = 29) and 𝑧 = 3  (blue histogram, 𝑁 = 28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These redshifts are at the ‘cosmic noon’,  where massive galaxies start to form and they are more gas-rich and  actively star-forming than galaxies at lower redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Since the  FIREbox simulation is run with a volume of  (15 ℎ−1cMpc)3, it does not produce enough galaxies at high redshifts  that are as massive and luminous as the galaxy samples selected by  the observational studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We therefore supplement our sample with a  handful of more massive galaxies (𝑀∗ ≈ 109−5×1011 𝑀⊙) extracted  from the MassiveFIRE ‘zoom-in’ simulations (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MassiveFIRE simulations  MassiveFIRE (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016, 2017) is a set of simulations  of massive galaxies at high redshifts using the ‘zoom-in’ method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A  number of low-resolution (LR) DM-only simulations were run with  the initial conditions generated using the MUSIC code within periodic  boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From the outputs of these LR DM-runs, we then select a  number of model haloes to re-simulate at much higher resolution and  with baryons included (HR runs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The selected haloes have a variety  of masses, accretion history, and environmental over-densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For this study, we use the galaxies produced by 10 MassiveFIRE  simulations, which are from the A (Anglés-Alcázar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017), D and  E Series (Çatmabacak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bassini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The A, D and  E Series were run in the periodic boxes with size of (100 ℎ−1 Mpc)3,  (400 ℎ−1 Mpc)3 and (762 ℎ−1 Mpc)3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The model haloes  of the A Series are selected from the snapshot of 𝑧final = 1, those  of the D and E Series are selected from the snapshot of 𝑧final = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  All the HR runs were run down to 𝑧final except D7, where the HR  run is evolved to only 𝑧 = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because part of the ISM in  D7 became too compact so that the gas particles with the highest  densities were evolved at extremely small time-steps and it became  infeasible to run the simulation down to the target redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Initial conditions for the HR runs are set up using a convex hull  surrounding all particles within 3𝑅vir at 𝑧final of the chosen halo  defining the Lagrangian HR region following the method of Hahn &  Abel (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mass resolutions and force softening lengths of the  HR runs are similar to those of the FIREbox simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically,  𝑚DM and 𝑚b are set to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 × 105 𝑀⊙, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 104 𝑀⊙, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Both ℎDM and ℎ∗ are fixed in proper (comoving) coordinates at 𝑧 ≤ 9  (𝑧 ≥ 9) and are set equal to 57 pc and 7 pc, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ℎgas is set  equal to the smoothing length of the gas particles down to a minimum  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 proper pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We include the central galaxy of the chosen haloes at 𝑧final except  for that of the D7 run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In addition, we also include the most massive  progenitors (MMPs) of the central galaxies at higher redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Specifically, for the 4 A Series runs, we include the MMPs at 𝑧 = 2,  𝑧 = 3 and 𝑧 = 4, while for the D and E Series, we include the MMPs  at 𝑧 = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The galaxies are identified in the simulation snapshots  using AHF (Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Knollmann & Knebe 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Table 1,  we summarize the information8 of the 10 MassiveFIRE simulations  8 Physical properties, including e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑀∗ , SFR, 𝐿IR and 𝐿[CII], of the FIRE  galaxies reported in this paper are estimated using a radial kernel of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1𝑅vir  MNRAS 000, 1–42 (2022)  25  20  10  5 6  8  9  10  11  7  12  log (Mstar/Mo)2025  20  10  5  8  9  10  11  6  12  log (Mstar/Mo)25  20  gal  10  5  6  8  9  10  11  12  log (Mstar/Mo)6  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' List of MassiveFIRE simulations used for this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Sim ID †  Box Size  𝑧final  𝑀vir ‡  𝑀∗ (𝑀⊙)  (ℎ−1 Mpc)  (1012 𝑀⊙)  𝑧 = 1  𝑧 = 2  𝑧 = 3  𝑧 = 4  𝑧 = 6  𝑧 = 8  A1  100  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 × 1011  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 × 1010  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 109  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 × 109  /  /  A2  100  1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 × 1011  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 × 1011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 1011  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 × 1010  /  /  A4  100  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 1011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 1011  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 × 1010  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 × 109  /  /  A8  100  1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 1011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 1011  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 1010  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 × 1010  /  /  D3  400  6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  /  /  /  /  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 × 1011  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 × 1010  D7§  400  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  /  /  /  /  /  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 1010  D9  400  6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  /  /  /  /  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 × 1010  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 109  E1  762  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  /  /  /  /  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 1010  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 × 109  E2  762  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  /  /  /  /  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 × 109  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 109  E3  762  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  /  /  /  /  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 109  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 × 109  † The A (D and E) Series of MassiveFIRE were published in Anglés-Alcázar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017) (Çatmabacak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡ Virial mass at 𝑧final.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  § The HR simulation of D7 has been run only down to 𝑧 = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  used for this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Both the MassiveFIRE and FIREbox simulations used in this work  are run using the N-body+hydrodynamics code GIZMO (FIRE-2 ver-  sion) in the Meshless-Finite-Mass (MFM) mode (Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The simulations incorporate various gas cooling processes  (free-free, photoionization/recombination, Compton, photoelectric,  metal-line, molecular and fine structure processes) and a uniform  UV background following the FG09 prescription (Faucher-Giguère  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009), Star formation occurs in dense, self-gravitating and self-  shielding molecular gas based on a sink-particle prescription.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  simulations explicitly incorporate several different stellar feedback  channels (but not feedback from supermassive black holes) includ-  ing 1) local and long-range momentum flux from radiative pressure,  2) energy, momentum, mass and metal injection from supernovae  (Types Ia and II), 3) stellar mass loss (both OB and AGB stars)  and 4) photo-ionization and photo-electric heating processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We re-  fer the reader to Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014, 2018) for details of the star  formation and feedback prescriptions of FIRE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  FIRE has demonstrated success at reproducing a variety of key  galaxy properties that are relevant to this work, such as the stellar-to-  halo mass relation (Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017), the  specific SFR (sSFR) of galaxies at the cosmic noon (𝑧 ∼ 2) (Hopkins  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sparre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Feldmann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), the galaxy molecular (atomic) hydrogen gas mass and  stellar mass relations at 𝑧 = 0 (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), the gas-phase  and stellar mass-metallicity relation at 𝑧 = 0 − 2 (Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), the observational effective dust temperatures  at 𝑧 = 2−4 (Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019) as well as the UV luminosity functions  and UV-based cosmic star formation rate density (CSFRD) at 𝑧 > 5  (Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  3 SIMULATING OBSERVATIONAL PROPERTIES  In this section, we describe the method used to predict the observa-  tional properties for the FIRE galaxy sample, which we compare to  the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1, we describe our [CII] emission  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2, we describe the prescription for the dust RT  modelling of the FIRE galaxies using SKIRT code, based on which we  around the DM halo centre, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the maximum density centre provided by  AHF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  derive the multi-wavelength SED and the distribution of the interstel-  lar radiation field (ISRF) for the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ISRF distribution is  essential for predicting the [CII] emission properties of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 Predicting [CII] emission using CLOUDY  We predict the [CII] line luminosity for the FIRE sample using the  spectral synthesis code CLOUDY version 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01 (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  CLOUDY is a plasma simulation code designed to simulate the ion-  ization, level populations, molecular state and thermal state of gas  over a wide range of density and temperature in different astrophys-  ical environments (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' black hole accretion disks, PDRs, molecular  clouds, etc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It solves for the ionization structure for all stages of  ionization for the lightest 30 elements (Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We treat each gas particle of the galaxies as an idealized spher-  ical uniform ‘gas cloud’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] luminosity of each ‘cloud’ is  calculated based on its physical conditions, including ‘cloud’ (or  gas particle) mass (𝑀cl), gas density9 (𝑛H), gas metallicity (𝑍gas),  gas turbulent velocity dispersion (𝜎) and local UV ISRF strength  (𝐺10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑀cl, 𝑛H, 𝑍gas of each ‘cloud’ are known directly from the  FIRE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜎 is the mass-weighted standard deviation of the  velocities in gas at the location of the ‘cloud’, which is calculated  in post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Finally, 𝐺 at the location of each ‘cloud’ in the  galaxy is calculated using the dust RT code SKIRT (Baes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Baes & Camps 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Camps & Baes 2015) in post-processing (see  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We calculate the [CII] luminosity for each ‘cloud’ (𝐿[CII], cl) by  integrating the [CII] line cooling rate, Λ[CII] (erg s−1 cm−3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' see Ap-  pendix A for its analytic expression), obtained from the output of the  CLOUDY simulations, over the volume of the cloud:  𝐿[CII], cl = 4𝜋  ∫ 𝑅cl  0  Λ[CII] (𝑥) 𝑥2d𝑥,  (1)  9 ‘Gas density’ here refers to H nuclei number density of gas, 𝑛H ≡  𝑋 (𝜌gas/𝑚H), where 𝑋 and 𝑚H represent the mass fraction of hydrogen  in gas and the proton mass, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CLOUDY uses 𝑛H as input instead  of mass density 𝜌gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this paper, we constantly use ‘gas density’ to refer to  𝑛H for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10 Conventionally, 𝐺 is used to denote the mean ISRF in the Habing band  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 − 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is indicated in units of 𝐺0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 10−3 erg s−1 cm−2, the  observed value in the solar neighbourhood (Habing 1968).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  7  where  𝑅cl =  � 3  4𝜋  �1/3 �  𝑀cl  𝜇H𝑚H𝑛H  �1/3  (2)  represents the radius of the cloud11 and 𝜇H in equation (2) represents  the mean molecular weight of the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] luminosity of the  galaxy (𝐿[CII]) is then derived by summing over 𝐿[CII], cl of all gas  clouds calculated using equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We treat the [CII] emission of  our galaxy sample as being optically thin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In practice, to run CLOUDY simulations for every gas particle  for the whole FIRE sample (> 400 galaxies in total) is computa-  tionally formidable: a CLOUDY simulation is typically completed  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' when iterative convergence is reached) in 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 CPU hour,  depending on the gas column density, and hence to analyze one sin-  gle galaxy snapshot that contains ∼ 1 million gas particles would  cost 100 − 500 K CPU hours in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We therefore use a lookup-  table method similar to the previous studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vallini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015,  2018, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Katz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lupi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lupi & Bovino 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically,  for each of the 7 snapshots, we build a grid of CLOUDY models  that covers a gas density range −1 < log (𝑛H/cm−3) < 5, a gas  metallicity range −2 < log (𝑍gas/𝑍⊙) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8, a turbulent velocity  dispersion range 0 < log (𝜎/km s−1) < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 and a UV ISRF range  −1 < log (𝐺/𝐺0) < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The grid spacing is set 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex for 𝑛H and 𝐺,  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 dex for 𝑍gas and 𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In total, the default look-up table that we  use for calculating the [CII] luminosity of our galaxy sample consists  of 8,008 (13 × 8 × 7 × 11) models for each redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We include the  CMB background in the CLOUDY simulations for each redshift and  the predicted [CII] luminosity is corrected for the CMB attenuation  effect (da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cosmic-ray (CR) hydrogen ionization  rate in these models is fixed to the fiducial value of 2 × 10−16 s−1,  the observed value in the Milky Way (Indriolo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Indriolo  & McCall 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Neufeld & Wolfire 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We assume a constant  dust-to-metal mass ratio 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 (Dwek 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Draine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Watson 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019) and adopt the default interstellar medium  metal abundances (abundance ISM) stored in CLOUDY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The simula-  tions are run till sufficiently large distance from the surface of the  slab is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Given 𝑛H, 𝑍gas, 𝐺 and 𝑁H of each gas cloud, we  interpolate [CII] luminosity of the cloud from the values found in  the computed grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  CLOUDY simulation: an example  Here we show the conditions of a plane-parallel gas slab calculated by  CLOUDY (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The slab has a uniform gas density 𝑛H = 50 cm−3  and is illuminated by an external radiation field having 𝐺 = 200 𝐺0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We present CLOUDY simulations for two different models, where 𝑍gas  is set to 𝑍⊙ and 1/10 𝑍⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We include the 𝑧 = 0 CMB background  and the CR hydrogen ionization rate is set to the default value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We  show the results of the dust-rich and dust-poor models in the left and  right panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The slab is characterized by three distinct zones based on the ion-  ization state of hydrogen gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the upper panels, we show the abun-  dance profiles for ionized hydrogen (HII;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' dashed red line), atomic  hydrogen (HI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' solid green line) and molecular hydrogen (H2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' dotted  11 Note that we do not derive 𝐿[CII], cl using the ‘emergent intensity’ (𝐼em,  with physical unit erg s−1 cm−2) output by CLOUDY because 𝐼em is calculated  for a plane-parallel geometry instead of a spherical geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The conversion  factor between the two geometries is not simply a constant but depends on  the profile of [CII] emissivity (Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  blue line), as well as the profile for gas temperature (solid black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We can see that a HII region (Zone I) is created near the surface of  the slab by the ionizing photons (𝐸𝛾 > 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV) of the incident radi-  ation field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gas in this region is heated to high temperature (𝑇 ≈ 104  K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The slab then transits to a HI-dominating region (Zone II) at a  distance where ionizing radiation gets fully absorbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The photons  in the Lyman-Werner (LW) band (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 < 𝐸𝛾 < 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV) dissociate  H2 in this region, while maintaining gas temperature at about 102 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Finally, the slab transits to a H2-dominating region (Zone III) at some  larger distance, beyond which the LW radiation becomes sufficiently  absorbed and the majority of hydrogen turns into H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Like hydrogen, carbon has a very different ionization state in the  three zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can be seen from the middle panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2, where  we explicitly show the abundance profiles for atomic carbon (CI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  dotted blue line), singly ionized carbon (CII;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' solid green line) and  doubly ionized carbon (CIII;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' dashed red line) for the two models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Carbon is mostly ionized in Zone I and II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, in Zone I, it  gets excited to CII level as well as higher ionization levels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CIII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Zone II, on the contrary, carbon is singly ionized by LW photons  but not excited to higher levels since ionizing photons are shielded  from the region12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Finally, in Zone III, carbon turns into CI since the  region is UV-dark13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  [CII] emission originates mostly from the ionized (Zone I) and  atomic hydrogen (Zone II) phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We show in the middle panels  the profile for [CII] cooling rate (erg s−1 cm−3), Λ[CII], for the two  models (solid magenta line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is clear that Λ[CII] drops sharply in  Zone III, which is due to the very low abundance of CII ions (solid  green line) in this region (note: most carbon is in CI state in Zone III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For the chosen models, Λ[CII] appears to be similar in the ionized  and atomic hydrogen phases, varying by less than a factor of few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Comparing the metal-rich (left panel) and metal-poor (right panel)  models, it can be seen that Λ[CII] of the metal-rich model is about  a factor of ten higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is due to the fact that Λ[CII] is linearly  scaled to 𝑍gas and 𝑍gas of the metal-rich model is set as ten times  that of the metal-poor model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Using the Λ[CII] profile output by CLOUDY, we subsequently de-  rive the [CII] luminosity profile (cumulative [CII] luminosity as a  function of column depth from the surface) for a uniform spherical  cloud having 𝑛H = 50 cm−3 (same as the gas slab) and 𝑀cl = 105 𝑀⊙  that is irradiated by an external field having 𝐺 = 200 𝐺0 (same as the  gas slab) following equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We calculate the result for the metal-  rich (𝑍gas = 𝑍⊙) and metal-poor (𝑍gas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1𝑍⊙) models, which are  shown in the lower left and lower right panels of the figure, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen that about 30% (20%) of the total [CII]  luminosity of the cloud is produced by the HII region for the metal-  rich (poor) model, while the remainder originates almost totally from  the HI region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The H2 region contributes very limited fraction of the  [CII] luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that the Λ[CII] profile, the size of the different  zones, and their relatively contribution to the total [CII] luminosity  of the cloud depends on 𝐺, 𝑛H and 𝑍gas (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 for a detailed  discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  One major difference between the two models (metal-rich vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  metal-poor) is whether or not the gas cloud has an H2 region in  the core, as can be seen from the bottom panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the metal-poor  model (bottom right panel), because dust column density is small,  12 Note: the ionization energy of CIII is 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='39 eV, which is above the ioniza-  tion energy of hydrogen atom (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  13 Note: the first ionization energy of carbon is 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='26 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This coincides with  the lower frequency limit of the LW band (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, carbon is neutral  in the H2 region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  8  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  1019  1020  1021  1022  10-2  10-1  100  1019  1020  1021  1022  10-3  10-2  10-1  100  1019  1020  1021  1022  10-2  10-1  100  T / 104K  HII /H  H2/H  HI /H  ZONE I  ZONE III  Z = Z⊙  L[CII] ( < NH) / L[CII]  V ( < NH) / Vtot  Spherical gas cloud  ZONE II  T / 104K  CIII /C  CI /C  CII /C  Λ[CII]  10−22 ergs s−1 cm−3  1019  1020  1021  1022  10-3  10-2  10-1  100 1019  1020  1021  1022  10-2  10-1  100  1019  1020  1021  1022  10-2  10-1  100  T / 104K  HII /H  H2/H  HI /H  Z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1Z⊙  T / 104K  CIII /C  CI /C  CII /C  Λ[CII]  10−22 ergs s−1 cm−3  ZONE I  ZONE II  L[CII] ( < NH) / L[CII]  V ( < NH) / Vtot  Spherical gas cloud  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Top and middle panels: Ionization structures of a plane-parallel gas slab (𝑛H = 50 cm−3) irradiated by an external radiation field (𝐺 = 200 𝐺0)  incident from the left in the figure predicted by the CLOUDY code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dashed red, solid green and dotted blue lines in the top (middle) panels represent the  abundance profiles for HII (CIII), HI (CII) and H2 (CI), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Solid black line in the top and middle panels shows the profile of gas kinetic temperature  (normalized by 104 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Solid magenta line in the middle panels indicates the profile of [CII] cooling rate (normalized by 10−22 erg s−1 cm−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Bottom panels:  Cumulative fraction of [CII] luminosity (thick orange line) and volume (thin blue) as a function of gas column density (from the surface) of a spherical gas  cloud (𝑀cl = 105 𝑀⊙, 𝑛H = 50 cm−3) irradiated by an external radiation field (𝐺 = 200 𝐺0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Red dotted line marks the surface-to-centre column density of the  cloud (𝑁H = 4 × 1021 cm−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The left and right columns correspond to the metal-rich and metal-poor models where gas metallicity of the slab (cloud) is set to  𝑍⊙ and 1/10 𝑍⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the metal-poor model, the dust-to-gas mass ratio (𝛿dgr) becomes lower and therefore Lyman-Werner photons can penetrate deeper into the  slab (cloud), resulting in larger [CII]-emitting region (Zone I + Zone II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  LW photons are able to penetrate the entire cloud, making it H2-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The metal-rich model (bottom left panel), in contrast, has an H2 core  owing to the high dust column density, which accounts for nearly half  of 𝑀cl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The two cloud models correspond to the two distinct regimes  where 𝐿[CII] ,cl has different scaling with 𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' When the cloud has  no H2 core, 𝐿[CII] ,cl scales linearly with 𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As 𝑍gas (and hence  the dust-to-gas mass ratio, 𝛿dgr) increases, the depth of Zone I+Zone  II decreases (Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' When 𝑍gas is high enough that H2  becomes abundant (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' , Zone III forms), 𝐿[CII] ,cl saturates and no  longer depends sensitively on 𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 5, we will discuss in  detail how the 𝐿[CII]/SFR ratio of the FIRE galaxies depends on gas  metallicity, and interpret the results using the insights obtained from  the toy models presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 Calculating ISRF distribution and multi-wavelength SEDs  of galaxies using SKIRT  To predict the [CII] luminosity of the ISM, it is essential to know  the local UV ISRF strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We calculate the ISRF distribution for  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  9  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  7  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  7  UVJ  z = 0  z = 6  Σ[CII]  G  10 pkpc  5 pkpc  5 pkpc  10 pkpc  10 pkpc  5 pkpc  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  7  -2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  log (G/G0)  log (G/G0)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The UVJ false-colour image (left), [CII] surface brightness (middle) and the distribution of UV ISRF strength (𝐺) (right) of selected FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The upper panels show the results of a 𝑧 = 0 disc galaxy from FIREbox (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 of Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), while the lower panels correspond to a galaxy  undergoing multiple mergers at 𝑧 = 6 extracted from the MassiveFIRE ‘zoom-in’ suite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  the FIRE galaxies using the open-source14 3D Monte Carlo dust RT  code SKIRT (Baes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Baes & Camps 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Camps & Baes  2015) (version 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SKIRT provides full treatment of absorption and  anisotropic scattering by dust, and self-consistently computes dust  thermal re-emission and dust temperature distribution for various  astrophysical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  To prepare the galaxy snapshots as RT input models for SKIRT,  we follow the prescription of Camps et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016) (see also Trayford  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Camps et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We summarize the key points of the  prescription here, and refer interested readers to the above-mentioned  papers for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For the analysis, each star particle of the galaxy is treated as a  ‘single stellar population’ (SSP), and a spectrum of stellar emission  is assigned to each particle using the STARBURST99 (Leitherer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vazquez & Leitherer 2005) SED libraries according to the  age, metallicity and initial mass of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The RT calculations  are performed on an equally spaced logarithmic wavelength grid  consisting of 250 wavelength points spanning the wavelength range  𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 − 1000 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We launch 106 photon packages for each of the  250 point in the wavelength grid and for each of the stellar emission  14 Code repository: https://skirt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='ugent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='be/version8/  and following dust emission stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The calculation iterates until  convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To produce mock images and SEDs for the galaxies, we  place mock detectors at an arbitrary ‘local’ distance of 10 Mpc from  galaxy along multiple viewing angles to accumulate both spatially  resolved as well as integrated fluxes at each wavelength grid point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We assume that dust mass traces metal mass in galaxies (Hayward  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Narayanan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Camps et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Trayford  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018, 2019, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cochrane  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vogelsberger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Shen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) and  adopt a constant dust-to-metal mass ratio 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 in gas cooler  than 106 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hotter gas is assumed to be dust-free due to thermal  sputtering (Draine & Salpeter 1979;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Tielens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We adopt  the Weingartner & Draine (2001b) dust model with Milky-Way size  distribution for the case of 𝑅V = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We discretize the spatial domain  using an octree grid and keep subdividing grid cells until the cell  contains less than 𝑓 = 3×10−6 of the total dust mass and the 𝑉-band  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='55 𝜇m) optical depth in each cell is less than unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The highest  grid level corresponds to a cell width of ∼ 20 pc, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' about twice  the minimal SPH smoothing length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We self-consistently calculate  the self-absorption of dust emission and include the transient heating  function to calculate non-local thermal equilibrium dust emission  by transiently heated small grains and PAH molecules (Baes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Camps & Baes 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To account for the heating of dust by  MNRAS 000, 1–42 (2022)  10  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  the cosmic microwave background, we adopt a correction to the dust  temperature using equation (12) of da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The final output of the SKIRT simulations includes the ISRF, 𝐽𝜆  (W cm−3 sr−1), of each adaptive grid cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We calculate the UV ISRF  strength (𝐺) for each cell by integrating 𝐽𝜆 over the Habing band  (6 − 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV) and solid angle (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐺 is assigned to every gas particle  (‘cloud’) inside the cell for predicting its [CII] luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 3, we show the UVJ composite image (left panels), [CII]  surface brightness (middle panels), and 𝐺 distribution (right panels)  for the two selected FIRE galaxies calculated using CLOUDY and  SKIRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The upper panels show the results of a disc galaxy at 𝑧 = 0  extracted from FIREbox, whilst the lower panels show the results of  a galaxy undergoing multiple mergers at 𝑧 = 6 extracted from the  MassiveFIRE simulation (Sim ID: D9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝑧 = 6 galaxy system  has much stronger strength of ISRF (right panels) due to its higher  SFR (220 𝑀⊙ yr−1 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 𝑀⊙ yr−1) and shows higher [CII] surface  brightness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII] of the 𝑧 = 6 system and the 𝑧 = 0 galaxy are  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 108 𝐿⊙ and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 108 𝐿⊙, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  4 COMPARISON WITH OBSERVATIONS  In this section, we compare the 𝐿[CII]-SFR relation of the FIRE  galaxies predicted by our model with the observational data at various  redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We separately discuss the results for three redshift regimes,  𝑧 = 0 (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1), 1 <∼ 𝑧 <∼ 5 (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2) and 𝑧 >∼ 5 (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We make this distinction because observations use different sample  selection methods and the SFR of galaxies is estimated by different  means of calibration in the three different regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 Local Universe (redshift 𝑧 = 0)  Observations of the 𝐿[CII]-SFR relation at 𝑧 = 0 probe a very wide  SFR range across several orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The selected sam-  ples include low-SFR systems such as dwarf galaxies as well as the  extreme IR-luminous starbursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  There are three main samples of nearby galaxies that have been  used for calibrating the 𝐿[CII]-SFR relation of normal star-forming  galaxies (SFR ≈ 10−5−10 𝑀⊙ yr−1): De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011, hereafter  L11), De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014, hereafter L14) and Herrera-Camus  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015, hereafter H15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The L11 sample consists of 24 star-  forming galaxies selected from the early compilation by Brauher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2008) that have measurements at both the Galaxy Evolution Explorer  (GALEX) FUV and the Multiband Imaging Photometer for Spitzer  (MIPS) 24 𝜇m bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sample of L14 includes 48 nearby low-  metallicity (𝑍gas ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='55 𝑍⊙) dwarf galaxies extracted from the  Dwarf Galaxy Survey (DGS, Madden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013) catalogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lastly,  H15 study a sample consisting of 46 local star-forming galaxies  chosen from the KINGFISH catalogue (Kennicutt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011), having  very diverse integrated galaxy properties and ISM environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' All  these studies have excluded the sources with AGN features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Both L11 and L14 derive the SFR of their sample using GALEX  FUV and MIPS 24 𝜇m fluxes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR = 𝛽 (𝐿FUV, obs +𝛼 × 𝐿24 𝜇m))  but with different calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, L11 and L14 use the  calibration by Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2008) (𝛼 = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='31) and Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011)  (𝛼 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='89), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H15, on the other hand, derive the SFR  of their sample using a hybrid of different methods: for 27 galaxies  in their sample, SFR is derived using the H𝛼+24 𝜇m calibration by  Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2007) (equation 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the other 8 galaxies, they  use the FUV+24 𝜇m calibration by Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2008) (equations  D10 and D11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' And lastly, for the remaining 11 galaxies having  no measurement of either H𝛼 nor FUV flux, SFR is derived based  solely on their 24 𝜇m flux using the calibration by Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2007) (equation 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Table 2, we show the SFR range as well as  the median SFR of the three samples (L11, L14 and H15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We also  show in the table the best-fit parameter values for the scaling relation  log(𝐿[CII]/𝐿⊙) = 𝐴 + 𝐵 log(SFR/𝑀⊙ yr−1)  (3)  for the three samples as well as the 1𝜎 scatter (in dex) of the data  around the best-fit relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that for the galaxies of the L11 and  H15 samples whose SFR is derived using the FUV+24 𝜇m fluxes,  we have re-calibrated their SFR following Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011) as has  been done by L14 for a fair comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' All the SFR calibrations are  based on the Kroupa (2002) initial mass function (IMF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  From Table 2, we can see that the three samples all exhibit an  almost linear correlation between 𝐿[CII] and SFR, though having  noticeable difference in the normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The H15 sample has the  highest normalization among the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is higher than that  of the L11 sample by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='32 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This offset may partly be due to the  difference in sample selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Another potential cause is that H15  adopt different SFR indicators and calibration methods compared  with L11 for a large fraction of the galaxies in their sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  offset between the L11 and L14 samples (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21 dex), on the other  hand, is mainly due to the difference in sample selection since L11  and L14 adopt the same SFR indicators (FUV+24 𝜇m fluxes) for  their entire samples and we have re-calibrated their results following  the same method of Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The lower normalization of  the L14 relation is very likely due to the relatively lower 𝑍gas of the  dwarf galaxies they use for the study, as has been explicitly stated in  L14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 4, we show the 𝐿[CII]-SFR relation of the three samples  (L11, L14 and H15) in the left panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To more clearly show the differ-  ence in the normalization of these scaling relations, we present the  𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR relation of the same samples in the right panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In both panels, we also present the results for the FIRE sample15  𝑧 = 0 (filled cyan stars) for comparison with the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Note that for the L11 and H15 samples, we show both the data of  the individual sources as well as the best-fit scaling relation for each  sample, whereas for the L14 sample, we only present the best-fit scal-  ing relation (purple dashed line) for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The L14 sample has  systematically lower gas metallicity than the other two observational  samples as well as the FIRE galaxy sample at 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE simulations, combined with our line model, produce the  𝐿[CII]-SFR relation at 𝑧 = 0 (cyan stars) that is in good agreement  with the local star-forming samples of L11 (black diamonds) and  H15 (black triangles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The best-fit parameter values for the FIRE  galaxies (over the SFR range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 − 100 𝑀⊙ yr−1) are 𝐴 = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='70 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 and 𝐵 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03, and the 1𝜎 scatter of the data points  around the best-fit relation is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21 dex, similar to the L11 and H15  samples (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that we have excluded the galaxies having  SFR < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 𝑀⊙ yr−1 for the fitting to avoid the regime where galaxy  statistics can be contaminated by the shot noise due to the resolution  limit of the simulation (Feldmann 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE galaxies exhibit a sub-linear relation between 𝐿[CII]  and SFR, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII] ∝ SFR0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sub-linearity is due to the  galaxies having SFR>∼3 𝑀⊙ yr−1, which have lower 𝐿[CII]/SFR ratio  on average than the galaxies having lower SFR (see the right panel of  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Such a trend of reduced 𝐿[CII]/SFR ratio at high SFR ([CII]  deficit) is not clearly present in any of the three (L11, L14 and H15)  15 We calculate the SFR of the FIRE galaxies by averaging over a timescale  of the last 100 Myrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  11  FIRE galaxies  z = 0  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  Local observations  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  FIRE galaxies  z = 0  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  Local observations  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR (left panel) and 𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR (right panel) relations of the 𝑧 = 0 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The filled cyan stars in the two panels show  the result of the FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Black triangles and diamonds show the observational data of Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015) (H15) and De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011)  (L11), and the orange and green lines indicate the best-fit linear relation of the H15 and L11 samples, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The coloured shaded regions indicate the 1𝜎  scatter of the data around the best-fit linear relation of the observed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Purple dashed line in the two panels represents the best-fit linear relation to the  low-metallicity dwarf galaxy sample of De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014) (L14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The result of the FIRE galaxies at 𝑧 = 0 is in good agreement with the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Observed scaling relations between SFR and 𝐿[CII] of local galaxies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII]/𝐿⊙ = 𝐴(SFR/𝑀⊙ yr−1) 𝐵.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Galaxy  sample  SFR range (𝑀⊙ yr−1)  Median SFR (𝑀⊙ yr−1)  𝐴  𝐵  1𝜎 scatter  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 − 88  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='75  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='26 dex  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014)  6 × 10−4 − 56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='43 dex  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015)  10−3 − 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='34  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='63 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21 dex  observational samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We note, however, that these samples do not  contain statistically large number of galaxies at SFR >∼ 3 𝑀⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Some other studies probing the local LIRGs and ULIRGs have found  clear evidence of [CII] deficit at high 𝐿IR (∼ SFR) (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR relation of 𝑧 = 0 galaxies  A number of observational studies have probed the relation between  𝐿[CII] and 𝐿IR (or 𝐿FIR16) of local galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐿IR (or 𝐿FIR) can be a good proxy for galaxy SFR when the stellar  light of a galaxy is heavily absorbed by dust (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kennicutt 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Salim & Narayanan 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Galaxies having higher SFR tend to be  more gas/dust-rich and have higher gas density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Therefore, they tend  to have higher dust opacity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Whitaker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We show  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 5 the 𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR relation of the FIRE galaxies at different  redshifts, where 𝐿IR is calculated using their SEDs produced by  SKIRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen that at 𝑧 = 0, the FIRE galaxies (cyan stars)  16 In the literature, ‘𝐿IR’ is used to denote the bolometric IR luminosity of  galaxy that is integrated over the wavelength range 8 − 1000 𝜇m, whereas  ‘𝐿FIR’ represents the FIR luminosity of galaxy (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 𝜇m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Both 𝐿IR  and 𝐿FIR are commonly adopted as SFR indicators for heavily dust-obscured  galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  well follow the Kennicutt (1998, hereafter K98) relation17, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐿IR (𝐿⊙) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36 × 1010 SFR (𝑀⊙ yr−1)  (4)  at SFR >∼ 1 M⊙ yr−1 (or 𝐿IR >∼ 1010 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The K98 relation is derived  assuming that all radiative energy of the young stars is absorbed  and re-emitted by dust and AGN radiation does not contribute to dust  heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At SFR < 1 M⊙ yr−1, however, the 𝑧 = 0 FIRE galaxies show  larger scatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Some of these galaxies are below the K98 relation by  over 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 dex (indicating that less than half of the radiative energy of  the young stars gets re-emitted at FIR by dust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These are the galaxies  having relatively low dust opacity18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Nonetheless, 𝐿IR appears to be  17 We adopt the K98 relation for the Kroupa (2002) IMF using the stellar  population synthesis (SPS) model STARBURST99, assuming a constant star  formation history lasting for 1 Gyr (see Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  original relation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 𝐿IR/𝐿⊙ = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 109 SFR/(𝑀⊙ yr−1)) was derived for  the Salpeter IMF based on the older SPS model of Leitherer & Heckman  (1995), and for a shorter starburst period (𝑡age = 10 − 100 Myrs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  18 It can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 5 that some of the simulated galaxies (particularly  those having low SFR) lie above the K98 relation, which seem to break  the energy conservation law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These are in fact the galaxies that are recently  quenched after a strong starburst whose dust is heated mainly by the stars  older than 100 Myrs (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hayward et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  10  L(CI) (Lo)  106  10-1  100  101  102  SFR(Mo yr-1)LicIm /SFR(Lo M1  10  10  10-1  100  101  102  SFR(Mo yr-1)12  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-2  10-1  100  101  102  103  108  109  1010  1011  1012  1013  Kennicutt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998 (K98) relation  K98 relation × 1/2  K98 relation × 1/10  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR relation of FIRE galaxies at different redshifts  (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2, blue  squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6 and  purple downward diamonds for 𝑧 = 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The diagonal solid black line indicates  the K98 relation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (𝐿⊙) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36 × 1010 SFR (𝑀⊙ yr−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The dashed  and dotted lines indicate the modified K98 relations where the normalization  is lower than the solid black line by a factor of 2 and 10, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  K98 relation (solid black line) fits well to the galaxies at high SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  a good SFR tracer for the 𝑧 = 0 galaxies at SFR >∼ 1 M⊙ yr−1 in the  FIRE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 6 the observed 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (left panel) and  the 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (right panel) relations of the local galaxy  samples of Malhotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2001), Brauher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2008), Sargsyan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012), Farrah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), Díaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), Magdis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), Cormier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015),  Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017) and Contursi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that for those  having used 𝐿FIR as SFR indicator, we convert the reported 𝐿FIR of  the galaxies to 𝐿IR by multiplying it with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 (Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For comparison, we also show in the same figure the data of the 𝑧 = 0  FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR of the FIRE galaxies is computed by integrating  the SKIRT-produced SED over the wavelength range 8 − 1000 𝜇m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The observed samples contain a large number of galaxies that are  IR-luminous (𝐿IR >∼ 1011 𝐿⊙, corresponding to SFR >∼ 10 𝑀⊙ yr−1  following equation 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' With these statistically large samples, the  𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR) ratio of the 𝑧 = 0 galaxies appear to  show a clear decline with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙ ([CII] deficit), albeit  with a large scatter (1𝜎 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 dex) at given 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From 𝐿IR = 1011 to  1013 𝐿⊙, 𝐿[CII]/𝐿IR decreases from 2×10−3 to 10−4, over a factor of  ten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At 𝐿IR <∼1011 𝐿⊙, on the other hand, 𝐿[CII]/𝐿IR of the observed  galaxies is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Overall, the observational and the simulated  data agree well with each other (on both the mean value and level of  scatter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, the FIRE sample exhibits a mild [CII] deficit at  𝐿IR >∼1011 𝐿⊙ at 𝑧 = 0, which is in agreement with the observational  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note, however, that our FIRE sample at 𝑧 = 0 does not include  any ULIRGs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR >∼ 1012 𝐿⊙) at 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 High redshifts (1 <∼ 𝑧 <∼ 5)  Observational studies have investigated the 𝐿[CII]-SFR relation of  galaxies at 1 <∼ 𝑧 <∼ 5, including e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Stacey  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Valtchanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Brisbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gullberg  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015, 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Umehata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Zanella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McKinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Their samples consist of roughly 80 galaxies in total (see  Table 3 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Most of these galaxies have substantial SFR  (SFR >∼ 100 𝑀⊙ yr−1) and are IR-luminous (𝐿IR >∼ 1012 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is  in stark contrast with the local observations (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1), which  probe the galaxies having much lower SFR (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that  a large fraction of the selected galaxies in this redshift regime are  uncovered by wide-field sub-mm galaxy surveys, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the South Pole  Telescope (SPT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vieira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Carlstrom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011) survey  (Weiß et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We derive the SFR of the selected galaxies from their measured  𝐿IR (see Table 3) using the K98 relation (equation 4) assuming that  the galaxies are heavily dust-obscured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that at high redshifts,  the K98 relation may only apply to the more massive and starburst  galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' High-𝑧 galaxies are metal and dust-poorer than the 𝑧 =  0 galaxies at given mass (or SFR), and therefore only the more  massive and gas-rich systems have high enough dust opacity leading  to total obscuration of stellar light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We can see from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 5 that the  K98 relation (solid black line) fits well the high-𝑧 FIRE galaxies at  SFR >∼ 100 𝑀⊙ yr−1 (or 𝐿IR >∼ 1012 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note: For the 𝑧 = 1 galaxies,  the K98 relation fits well to the data down to 𝐿IR ≈ 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At  lower SFR, the high-𝑧 galaxies exhibit larger scatter and they, on the  average, have lower 𝐿IR at given SFR than the 𝑧 = 0 galaxies due to  their reduced dust opacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The galaxies selected at 1 <∼ 𝑧 <∼ 5 typically have a good sampling  of photometric data points in the dust continuum, which are ob-  tained by observations with multiple IR and millimetre instruments  (Spitzer, Herschel, ALMA and etc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The shape of the dust SED of  these galaxies is therefore well constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This results in relatively  small uncertainty in the estimate of their 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The [CII] line of these galaxies is measured with different instru-  ments (see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For instance, Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010) and Brisbin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015) measure the [CII] line of the 20 galaxies at 𝑧 ≈ 1 − 2  of their samples using the redshift (𝑧) and Early Universe Spec-  trometer (ZEUS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hailey-Dunsheath 2009) on the  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 m Caltech Submillimeter Observatory (CSO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2015) measure the [CII] line of the 16 SMGs selected from the  SPT catalogue (Weiß et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013) using the SPIRE Fourier Transform  Spectrometer (FTS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Griffin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010) onboard Herschel (for the  galaxies at 𝑧 < 3) and the First Light APEX Sub-millimetre Het-  erodyne receiver (FLASH;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Heyminck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2006) (for the galaxies  at 𝑧 > 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the remaining galaxies (∼ 40), their [CII] line is  measured with ALMA (at Band 7, 8 and 9 for the galaxies at 𝑧 ∼ 4,  𝑧 ∼ 3 and 𝑧 ∼ 2, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ALMA observations often marginally  resolve a galaxy spatially in [CII], whereas observations with ZEUS,  APEX/FLASH and SPIRE FTS do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It should be particularly noted that a large number (26) of the  selected galaxies (mostly SMGs) in this regime are gravitationally-  lensed systems (see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, one important source of un-  certainty in the estimates of their intrinsic 𝐿[CII] and 𝐿IR (∼SFR) is  the lensing magnification factor 𝜇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To observationally determine 𝜇  of a lensed source requires spatially resolved imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that 16  of the selected SPT galaxies in this regime, however, are not spatially  resolved by the observations and their 𝜇 is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2015) adopt a constant 𝜇 = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 to de-magnify the luminosities of  all the 16 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is the mean of the 𝜇 of the only 4 galaxies  in their selected SPT sample, which is determined using the spatially  resolved ALMA 860 𝜇m broadband imaging of dust continuum by  Hezaveh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' we show the 𝐿[CII]-SFR relation (left panel) of the  MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1–42 (2022)  CII emission as an indicator of galaxy SFR  13  FIRE galaxies  z = 0  FIRE galaxies  z = 0  Local observations  Sargsyan + 2012  Malhotra + 2001  Brauher + 2008  Farrah + 2013  Diaz-Santos + 2013  Hughes + 2017  Coutursi + 2017  Madgis + 2014  Cormier + 2015 Herrara-Camus + 2015  Local observations  Sargsyan + 2012  Malhotra + 2001  Brauher + 2008  Farrah + 2013  Diaz-Santos + 2013  Hughes + 2017  Coutursi + 2017  Madgis + 2014  Cormier + 2015 Herrara-Camus + 2015  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (left panel) and the 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (right panel) relations of 𝑧 = 0 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the two panels, cyan stars show the result  of the FIRE galaxies, whereas black symbols indicate the observational data from different studies, including Malhotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2001) (diamond), Brauher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2008) (vertical crosses), Sargsyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012) (filled squares), Farrah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013) (empty squares), Díaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013) (filled circles), Magdis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2014) (diagonal crosses), Cormier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015) (empty stars), Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015) (asterisks), Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017) (triangles) and Contursi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017)  (empty circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Observations show that 𝐿[CII]/𝐿IR ratio of galaxies is nearly a constant at 109 <∼ 𝐿IR <∼ 1011 𝐿⊙, but declines with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In  the two panels, black line (solid at 𝐿IR < 1011 𝐿⊙ and dotted at 𝐿IR ≥ 1011 𝐿⊙) indicates the median 𝐿[CII]/𝐿IR ratio (≈ 2 × 10−3) of the galaxies having  𝐿IR < 1011 𝐿⊙ and grey shaded bar (dark grey at 𝐿IR < 1011 𝐿⊙ and light grey at 𝐿IR ≥ 1011 𝐿⊙) indicates the 1𝜎 scatter of the 𝐿[CII]/𝐿IR ratio of the same  galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' FIREbox successfully reproduces the observed 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (and the 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR) relation at 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  FIRE galaxies  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  Local observations  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='109  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1010  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Observational data at 1 < z < 5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Star-forming galaxies  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SMGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='(un-lensed or  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='determined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='μ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SMGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='(lensed but  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='undetermined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='μ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Observations by ZEUS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1010  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1011  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1012  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1013  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1014  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='FIRE galaxies  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='109  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1010  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Observational data at 1 < z < 5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Star-forming galaxies  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SMGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='(un-lensed or  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='determined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='μ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SMGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='(lensed but  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='undetermined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='μ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Observations by ZEUS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Local observations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='(same as in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6) Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR (left panel) and the 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR (right panel) relations of galaxies at 𝑧 = 0 and high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In both panels, filled coloured  symbols represent the FIRE galaxies (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2, blue squares for 𝑧 = 3 and magenta circles for  𝑧 = 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Black symbols (filled and empty) show the observational data of galaxies at 1 <∼ 𝑧 <∼ 5 (see Table 3 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, black circles and black  triangles correspond to SMGs and other star-forming galaxies, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the gravitationally-lensed galaxies, their [CII] and IR luminosities have been  corrected by the lensing magnification factor 𝜇 reported in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Those having direct measurement of 𝜇 as well as the un-lensed galaxies are marked  by filled symbols (triangles and circles), whereas the 16 lensed SPT galaxies whose 𝜇 is extrapolated (𝜇 has been assumed to be 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 by Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015)  are shown by empty circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The two grey empty squares represent the stacked result of the galaxy samples of Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010) and Brisbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The [CII] line of the two samples is measured with the redshift and Early Universe Spectrometer (ZEUS) and their data systematically offsets from that of the  other galaxy samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show in the left (right) panel the observational results of the local galaxy samples as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 4 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Both  observations and FIRE simulations show that high-𝑧 (1 <∼ 𝑧 <∼ 5) galaxies exhibit a [CII] deficit at high 𝐿IR similar to local galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  10  中  () [I  8  10  10  10  109  10  LIR (Lo)3101010  LIR  10  [CII  L  0  10  109  10  LIR (Lo)10-110  10  10  () [I  108  10  10  101  100  102  103  10  SFR(Mo yr-14101114  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The observed 𝐿[CII]-SFR relation of galaxies at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Name†  𝑧  log (𝐿IR/𝐿⊙)§  log (𝐿[CII]/𝐿⊙)‡, §, ∥  Galaxy type#  AGN  𝜇  References∗  ID 7118  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7290  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01  < 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='70 (ALMA 9)  MS  No  −  [1, 2]  GS IRS61  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='759  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13  < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='31 (ALMA 9)  SB  No  −  [3, 4]  ID 9834  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7644  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07 (ALMA 9)  MS  No  −  [1, 2]  ID 2910  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7686  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  < 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 (ALMA 9)  MS  No  −  [1, 2]  ID 2861  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8102  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  < 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58 (ALMA 9)  MS  No  −  [1, 2]  ID 6515  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8438  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12 (ALMA 9)  MS  No  −  [1, 2]  ID 9347  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8505  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14 (ALMA 9)  MS  No  −  [1, 2]  ID 9681  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8852  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='20 (ALMA 9)  MS  No  −  [1, 2]  ID 8490  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9056  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='20 (ALMA 9)  MS  No  −  [1, 2]  ID 10049  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9200  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='78 (ALMA 9)  MS  Yes  −  [1, 2]  GS IRS20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='923  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01 (ALMA 9)  SB  Yes  −  [3, 4]  ID 10076  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9462  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14 (ALMA 9)  MS  No  −  [1, 2]  MACS J0451+0006  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='013  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04 (ALMA 9)  MS  No  49 ± 5  [5, 6, 7]  GRB 080207  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0865  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='05  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='89 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12 (ALMA 9)  MS  No  −  [8]  SPT 0551-50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='33 (SPIRE FTS)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0512-59  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='234  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 (SPIRE FTS)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SMM J2135  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3259  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 (SPIRE FTS)  SMG  No  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  [12, 13]  SDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='130  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='625  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  < 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14 (SPIRE FTS)  SMG  No  6 ± 1  [14, 15]  SPT 0538-50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='782  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  < 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='95 (SPIRE FTS)  SMG  No  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  [9, 10]  ALESS 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12 (ALMA 8)  SMG  No  −  [16, 17, 18]  ALESS 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='943  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='17 (ALMA 8)  SMG  No  −  [16, 17, 18]  SDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='81  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='042  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01 (SPIRE FTS)  SMG  No  25 ± 7  [14, 15]  SPT 0103-45  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='090  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  LAB1-ALMA3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0993  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='76  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (ALMA 8)  MS  No  −  [19, 20]  LAB1-ALMA1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='54  < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 (ALMA 8)  MS  No  −  [19, 20]  LAB1-ALMA2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='60  < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 (ALMA 8)  MS  No  −  [19, 20]  SPT 0550-53  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='129  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0529-54  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='369  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04 (APEX/FLASH)  SMG  No  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  [9, 10]  SPT 0532-50  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='399  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0300-46  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='596  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 2147-50  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='761  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='06  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0418-47  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='224  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03 (APEX/FLASH)  SMG  No  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  [9, 10]  SPT 0113-46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='232  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='141  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='24  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07 (APEX/FLASH)  SMG  No  10 − 30  [11]  SPT 2311-54  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='281  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0345-47  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='296  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='37 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  COSMOS-AzTEC-1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='342  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04 (ALMA 7)  SMG  No  −  [21, 22]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0568.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='404  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 (ALMA 7)  SMG  No  −  [23, 24]  ALESS 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4189  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='17 (ALMA 7)  SMG  No  −  [24, 25, 26]  UDS 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4201  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12 (ALMA 7)  SMG  No  −  [24, 26]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0051.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='05 (ALMA 7)  SMG  No  −  [23, 24]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='05 (ALMA 7)  SMG  No  −  [23, 24]  SGP 38326 (SMG1)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 (ALMA 7)  SMG (SB)  No  −  [27]  SGP 38326 (SMG2)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 (ALMA 7)  SMG (SB)  No  −  [27]  BRI 0952-0115  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4337  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='25  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='25 (APEX/FLASH)  SMG (SB)  No  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  [28, 29, 30]  SPT 2103-60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='435  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 (ALMA 7)  SMG  No  −  [23, 24]  ALESS 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 (ALMA 7)  SMG  No  −  [24, 25, 26]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03 (ALMA 7)  SMG  No  −  [23, 24]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='90 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 (ALMA 7)  SMG  No  <∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 2  [23, 24]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0643.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='95 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15 (ALMA 7)  SMG  No  <∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 2  [23, 24]  AS2UDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4615  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (ALMA 7)  SMG  No  <∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 2  [23, 24]  SPT 0441-46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='477  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 2146-55  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='567  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  W2246–0526  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='601  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03 (ALMA 7)  DOG  Yes  −  [31]  ALESS 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7555  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='69 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14 (ALMA 7)  SMG (SB)  Yes  −  [24, 26, 32]  SPT 2132-58  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='768  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  HDF850.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='185  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05 (IRAM/PdBI)  SMG  No  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7  [33, 34]  HLSJ091828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6+514223 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='24  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01 (SMA)  SMG  No  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9  [35]  SPT 2319-55  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='293  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  SPT 0346-52  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='656  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (APEX/FLASH)  SMG  No  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  [9, 10]  SPT 0243-49  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='699  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04  < 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40 (APEX/FLASH)  SMG  No  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8)  [9, 10]  (Continue on next page)  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  15  Table 3 – continued The observed 𝐿[CII]-SFR relation of galaxies at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Name†  𝑧  log (𝐿IR/𝐿⊙)§  log (𝐿[CII]/𝐿⊙)‡, §, ∥  Galaxy type#  AGN  𝜇  References∗  HerMESFLS3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3369  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10 (CARMA)  SMG  No  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  [36, 37]  SPT 0311-58-E  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='900  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (ALMA 6)  SMG  No  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  [38]  SPT 0311-58-W  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='900  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06 (ALMA 6)  SMG  No  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  [38]  † The table does not include the 20 galaxies (𝑧 ≈ 2) in the samples of Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010) and Brisbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), of which the [CII] line is  measured by ZEUS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII]/𝐿IR vs 𝐿IR relation of these two samples systematically offsets from the others that use different instrument to  measure [CII] line (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  § For the gravitationally-lensed galaxies, 𝐿[CII] and 𝐿IR have been de-magnified by the reported lensing magnification factor 𝜇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For those SPT  galaxies having no direct measurement of 𝜇 (galaxies are not spatially resolved by any observation), we adopt a constant 𝜇 = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 as is done by  Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), which is the mean of the four galaxies (SPT 0538-50, SPT 0529-54, SPT 0418-47 and SPT 0346-52) in the same sample  that is observationally determined via lensing modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡ For the [CII]-undetected galaxies, we show the 3𝜎 upper confidence limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∥ IRAM/PdBI: the IRAM Plateau de Bure Interferometer (Guilloteau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1992);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SMA: the Submillimeter Array (Ho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2004);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CARMA: the  Combined Array for Research in Millimeter-wave Astronomy (Woody et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that the three telescopes have produced spatially resolved  line emission maps of [CII] for high-𝑧 SMGs (HDF850.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1, HLSJ091828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6+514223 and HerMESFLS3) as ALMA does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  # SMG: sub-mm galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' MS: ‘main-sequence’ galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SB: starburst galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' DOG: hot dust-obscured galaxies (galaxies uncovered by surveys  at near-infrared wavelengths, which have strong IR emission from warm dust, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Eisenhardt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∗ References: (1): Zanella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [2]: Elbaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011), [3]: McKinney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [4]: Kirkpatrick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [5]:Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015b),  [6]: Sklias et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [7]: Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010), [8]: Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019b), [9]: Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [10]: Weiß et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [11]: Cox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2011), [12]: Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010), [13]: Swinbank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010), [14]: Valtchanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011), [15]: Hopwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011), [16]: Rybak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2019), [17]: Wardlow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [18]: da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021), [19]: Umehata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [20]: Geach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [21]: Tadaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018),  [22]: Tadaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [23]: Cooke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [24]: Swinbank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [25]: Swinbank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012), [26]: Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [27]:  Oteo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [28]: Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2009), [29]: Priddey & McMahon (2001), [30]: Lehar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2000), [31]: Díaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [32]:  Breuck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [33]: Neri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [34]: Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012), [35]: Rawle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [36]: Riechers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [37]: Cooray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2014), [38]: Marrone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  observed samples at 1 <∼ 𝑧 <∼ 5, where we have converted the SFR  of all galaxies from their 𝐿IR using the K98 relation following the  observational studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We show the stacked result for the samples  of Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010) and Brisbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015) by grey empty  squares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Both studies measure [CII] line with ZEUS, and both obtain  systematically higher 𝐿[CII]/SFR ratio of galaxies than the other  studies using different instruments (by about one dex) at similar  SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the other studies, we explicitly show the data of each  individual source in their samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, we show the result  of the SMGs by black circles (empty and filled), whilst the other star-  forming galaxies are denoted by black triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For all the lensed  galaxies, both 𝐿[CII] and 𝐿IR are de-magnified by the observationally  determined 𝜇 when available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the 16 SPT galaxies having no  determined 𝜇 (indicated by empty black circles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7), we correct  their luminosities by an assumed 𝜇 = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 following Gullberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show the 𝐿[CII]-SFR relation of local  galaxies by L11, L14 and H15 in the same (left) panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The bulk of the selected samples at 1 <∼ 𝑧 <∼ 5 have higher SFR  than the local samples of L11, L14 and H15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Only the few galaxies  at 𝑧 ≈ 1 − 2 of the Zanella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018) sample overlap with the  SFR range of the most actively star-forming galaxies of the L11  sample, and they appear to follow the same 𝐿[CII]-SFR relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At higher SFR (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR >∼ 100 𝑀⊙ yr−1), the high-𝑧 galaxy samples  show a larger scatter in the 𝐿[CII]-SFR relation compared to the local  samples (L11, L14 and H15) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Apart from that, the high-𝑧 samples  show a decline of 𝐿[CII]/SFR ratio with increasing SFR at above  100 𝑀⊙ yr−1 (corresponding to 𝐿IR >∼ 1012 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This trend can be  more clearly seen in the right panel, where we show the 𝐿[CII]/𝐿IR  (≈ 𝐿[CII]/SFR at high SFR) ratio of the same high-𝑧 galaxy samples  as a function of their 𝐿IR (∼SFR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From 𝐿IR = 1012 𝐿⊙ to 1013 𝐿⊙,  the 𝐿[CII]/𝐿IR (or 𝐿[CII]/SFR) ratio of the high-𝑧 samples decreases  by roughly a factor of 50 (excluding the Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2010 and Brisbin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015 samples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This [CII] deficit at high 𝐿IR is similar to what  has been found with the local galaxy samples (indicated by the filled  grey symbols in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In the same figure, we also show the results of the FIRE galaxies  at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, we show the 𝐿[CII]-SFR (left panel)  and the 𝐿[CII]/𝐿IR-𝐿IR (right panel) relations of the FIRE galaxies at  𝑧 = 1 (yellow hexagons), 𝑧 = 2 (red triangles), 𝑧 = 3 (blue squares)  and 𝑧 = 4 (magenta circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show in the two  panels the results of the FIRE sample at 𝑧 = 0 (cyan stars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE galaxies follow a roughly linear 𝐿[CII]-SFR scaling rela-  tion over the SFR range of ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05−100 𝑀⊙ yr−1 at each redshift (left  panel), though having considerable scatter (1𝜎 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='35 dex).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The normalization of the relation, however, shows clear redshift evo-  lution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From 𝑧 = 0 to 𝑧 = 4, the mean 𝐿[CII]/SFR ratio of the FIRE  sample declines by about one dex (see the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This  indicates that using the 𝐿[CII]-SFR relation derived by L11 or H15  will lead to a systematic underestimate of SFR of galaxies at high  redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  On the other hand, the 𝐿[CII]/𝐿IR ratio of the FIRE galaxies does  not evolve as much with redshift between 𝑧 = 0−4 (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From  𝑧 = 0 to 𝑧 = 4, the mean 𝐿[CII]/𝐿IR ratio of the FIRE galaxies de-  creases by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex, which is less than the decrease of the 𝐿[CII]/SFR  ratio (∼ 1 dex).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Obviously, the reason for the discrepancy in the red-  shift evolution of the two ratios (𝐿[CII]/SFR and 𝐿[CII]/𝐿IR) is the  redshift evolution of the 𝐿IR-SFR relation of the galaxies (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 5  for the result of the FIRE galaxies, and also the observational data of  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Whitaker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017) — at fixed SFR, galaxies at higher red-  shift have on average lower dust opacity and thus a smaller fraction  of stellar radiation is absorbed and re-emitted at far-IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean  𝐿IR/SFR ratio of galaxies therefore decreases with redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Apart from that, it is clear from the right panel that the FIRE  galaxies at 𝑧 = 1 − 4 show a similar decrease of 𝐿[CII]/𝐿IR ratio  with 𝐿IR like the local 𝑧 = 0 FIRE galaxies (cyan stars), and the  decrease appears to be more significant at 𝐿IR >∼ 5 × 1011 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  MNRAS 000, 1–42 (2022)  16  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  sharp decrease of 𝐿[CII]/𝐿IR at the high 𝐿IR end is in line with the  trend in the observational data at similar redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Section 5, we  will examine in detail the origin of this ‘[CII] deficit’ at high 𝐿IR  and we will show that it is mainly driven by the decrease of gas mass  per unit SFR, or depletion timescale (𝑡dep ≡ 𝑀gas/SFR), of galaxies  with SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Note that at 𝐿IR ≈ 1012 𝐿⊙, the observed 𝐿[CII]/𝐿IR ratio of the  galaxies at high redshifts (black symbols) appears to be higher than  that of the observed 𝑧 = 0 galaxy samples (grey symbols) as well  as the FIRE galaxies (coloured symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean 𝐿[CII]/𝐿IR ratio  is roughly in agreement with the upper bound of the FIRE galaxies  at similar 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can possibly be due to selection effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Those  galaxies at 𝐿IR ≈ 1012 𝐿⊙ are mostly the ‘main-sequence’ (MS)  galaxies at 𝑧 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 − 2 selected by Zanella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), which are  expected to have longer 𝑡dep (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' gas mass per unit SFR) than starburst  galaxies at the same redshift (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Genzel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Aravena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Miettinen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Tacconi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Feldmann 2020)  and hence higher 𝐿[CII]/𝐿IR (note: 𝐿[CII]/SFR ∝ 𝑡0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7  dep, equation 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE sample as well as the local observed galaxy samples, on  the contrary, consist of galaxies across the star-forming MS as well  as starburst galaxies, exhibiting a wide range of 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Finally, we note that the observational data in this redshift regime  has large uncertainties due to the large fraction of gravitationally-  lensed galaxies included in the samples (see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' First of all,  as mentioned above, many of the lensed galaxies do not have deter-  mined magnification factor 𝜇 (marked by empty circles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Even for those whose 𝜇 is derived from either the rest-UV (with  Hubble Space Telescope) or dust continuum imaging (with ALMA),  it is not yet certain whether their [CII] luminosity is magnified by the  same level, given that the [CII] and stellar/dust emission of galaxies  may have different spatial configuration (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cochrane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Novak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fu-  damoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) and thus the different emission components may  have different 𝜇 due to the effect of differential lensing (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Blain  1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hezaveh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Serjeant 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cañameras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Harrington et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, it is important  to obtain spatially resolved imaging of both [CII] and dust emission  for lensed galaxies and re-examine the intrinsic 𝐿[CII]/𝐿IR ratio of  these galaxies (note: most of the lensed SMGs do not have spatially  resolved [CII] imaging, see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 Early galaxies (redshift 𝑧 >∼ 5)  Observational studies on the 𝐿[CII]-SFR relation at 𝑧 >∼ 5 depend  mainly on the rest-frame UV-selected galaxies whose redshift has  previously been confirmed either spectroscopically or via the Ly-  man break ‘drop-out’ technique (Hodge & da Cunha 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Their  [CII] and dust emission are constrained in follow-up observational  campaigns with ALMA, which has the power to spatially resolve the  distant galaxies down to the scale of ∼ 1 physical kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The majority  of the UV-selected galaxies at this epoch are unlensed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  There have been two major observational campaigns for searching  for [CII] line of galaxies at 𝑧 >∼5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ALPINE ALMA Large Program  (Le Fèvre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Béthermin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020) in cycle-5 targeted a  sample of 118 UV-selected star-forming galaxies at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 < 𝑧 < 6 with  𝑀UV, AB < −20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 and identified [CII] emission (at > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5𝜎 level) in  75 galaxies of them (Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' More recently, the REBELS  Large Program (Bouwens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) in Cycle-7 studied a sample  of 40 UV-bright (𝑀UV, AB < −21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4) galaxies at 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 < 𝑧 < 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 and  confirmed [CII] detection (at > 7𝜎) in 18 galaxies in their sample  (Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Other observations targeting the LBGs/LAEs  at 𝑧 >∼ 5 have identified [CII] emission in another > 35 sources in  total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The most distant galaxy that has a [CII] detection to date is  MACS1149-JD1 (Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018), a gravitationally-lensed  (𝜇 = 10) galaxy at 𝑧 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11 (Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' see also Inoue  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016 and Laporte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We provide a summary of the  star-forming galaxies at 𝑧 >∼ 5 having confirmed [CII] detection in  Table 4 (excluding quasar host galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The SFR of these UV-selected galaxies has been derived based on  their 𝐿UV and 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Because the galaxies at 𝑧>∼5 typically do not have  good photometric sampling of the dust continuum (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2018b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Faisst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020b), 𝐿IR has frequently been  converted from the ALMA broad-band flux density (measured at band  6 or 7 for galaxies at 𝑧 >∼ 5) using the standard modified-blackbody  (MBB) function of the form (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hildebrand 1983;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hayward et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2011)  𝑆𝜈0 = (1 + 𝑧)  𝑑2  L  𝜅𝜈𝑀dust𝐵𝜈(𝑇),  (5)  where 𝜈0 is the observing frequency (note: 𝜈0 = 345 GHz for ALMA  band 7 and 𝜈0 = 230 GHz for ALMA band 6), 𝑆𝜈0 is the broad-band  flux density at 𝜈0, 𝜈 = (1 + 𝑧)𝜈0 is the rest-frame frequency, 𝜅𝜈 is  the dust opacity (per unit dust mass) at 𝜈, 𝑀dust is the dust mass of  galaxy, 𝑇 is the ‘dust temperature’, 𝐵𝜈(𝑇) is the Planck function and  𝑑L is the luminosity distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR is then converted from 𝑆𝜈0 using  (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 of Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019 for the details)  𝐿IR =  D𝑑2  L𝑇4+𝛽dust  (1 + 𝑧)𝜅𝜈𝐵𝜈(𝑇) 𝑆𝜈0,  (6)  where 𝛽dust ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 is the dust emissivity spectral index (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Dunne  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Draine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2007) and D is a parameter that depends  on the shape of the dust opacity curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The derived 𝐿IR (and hence  the obscured SFR) therefore depends mainly on the assumed ‘dust  temperature’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It should be noted that recent cosmological simulations  show that the true SED of high-𝑧 galaxies may significantly differ  from the standard MBB function (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2019, and also Casey 2012, Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018b) and 𝑇 does not  faithfully reflect the physical temperature of dust in galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Behrens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019) defines  the ‘dust temperature’ that one would need to obtain the correct  𝐿IR and match the observed 𝑆𝜈0 under the assumption that the SED  has the shape of a standard MBB function (equation 5) to be the  ‘equivalent dust temperature’ (𝑇eqv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Using a sample of high-𝑧 galaxies produced by the MassiveFIRE  suite (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016, 2017), Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019) derived the  best-fitting formula for 𝑇eqv using redshift and dust-to-gas mass ratio  (𝛿dzr) as variables, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑇eqv = 𝑇0 (1 + 𝑧)𝛼(𝛿dzr/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4)𝛾.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (L19)  (7)  For ALMA band 7 (6) fluxes, the best-fitting parameter values are  𝑇0 = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 (24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5) K, 𝛼 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='31 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36) and 𝛾 = − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13 (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  increase of 𝑇eqv with redshift is related to the enhanced level of star  formation activity in galaxies (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' higher specific SFR) (Safarzadeh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sommovigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The anti-correlation with 𝛿dzr, on the other hand, is due to the  fact that an increase of 𝛿dzr leads to a higher dust opacity, which in  turn results in a ‘colder’ dust SED shape of galaxies (Scoville 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Faisst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Observationally, 𝛿dzr of high-𝑧  galaxies has not yet been constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Often, it is easier to detect the [CII] line than the dust continuum  of galaxies at 𝑧 >∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For example, 75 out of the 118 (63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6%) galaxies  in the ALPINE sample have confirmed detection of [CII] emission,  whilst only 21 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8%) of them have confirmed detection of dust  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  17  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Properties of the star-forming galaxies at 𝑧 >∼ 5 targeted for search for [CII] emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Name†  𝑧  SFRUV§, #  (𝑀⊙ yr−1)  𝑆 (𝜇Jy)‡, ¶, #  log (𝐿IR/𝐿⊙) ∥  SFR††  (𝑀⊙ yr−1)  log (𝐿[CII]/𝐿⊙) ¶, #  𝜇  References ∗  HZ7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='306  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 (ALMA 6)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='20 (ALMA 6)  −  [45, 46, 47]  REBELS-12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='349  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 (ALMA 6)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='00 (ALMA 6)  −  [45, 46, 47]  (Continue on next page)  MNRAS 000, 1–42 (2022)  18  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Observations of LBGs/LAEs at z > 5  FIRE galaxies  z = 4  z = 6  z = 8  FIRE galaxies  z = 4  z = 6  z = 8  Observations of LBGs/LAEs at z > 5  and dust-detected  [CII]  detected, but no dust-detection  [CII]  (SFR converted from  )  LUV  undetected  [CII]  REBELS  ALPINE  Others  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  REBELS  ALPINE  Others  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  and dust-detected  [CII]  detected, but no dust-detection  [CII]  (SFR corrected by 3  upper limit of  )  σ  LIR  undetected  [CII]  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Comparison of the 𝐿[CII]-SFR relation of the FIRE galaxies with the observational data at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the two panels, we show the result of the  FIRE galaxies at 𝑧 = 4, 𝑧 = 6 and 𝑧 = 8 by magenta circles, green diamonds and purple downward triangles, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We also show in the two panels the  observational data of the rest-UV-selected star-forming galaxies at 𝑧 >∼ 5, including the ones targeted by the ALPINE (blue symbols) and REBELS (red symbols)  ALMA surveys as well as the others targeted by the other observations (black symbols) (see Table 4 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The galaxies having both confirmed [CII]  and dust continuum detection are indicated by vertical (REBELS) and diagonal (red for ALPINE and black for others) crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The galaxies having no [CII]  detection are shown by downward arrows in both panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The location of the arrows indicate the 3𝜎 upper limit of their 𝐿[CII].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the ones having [CII] but  without dust detection (meaning that their SFRIR is uncertain), we show the relation between their 𝐿[CII] and the lower (upper) SFR limit in the left (right) panel  by rightward (leftward) triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show the result of local (𝑧 = 0) observations of normal star-forming galaxies (SFGs) by L11, L14 and  H15 in the two panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The FIRE sample at 𝑧 = 4 − 8 shows systematically lower 𝐿[CII]/SFR ratio than the local SFGs ([CII] deficit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The observed galaxy  samples at 𝑧 >∼ 5 show similar [CII] deficit if 𝑇eqv follows equation (7) (assuming 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 4 – continued  Name†  𝑧  SFRUV§, #  (𝑀⊙ yr−1)  𝑆 (𝜇Jy)‡, ¶, #  log (𝐿IR/𝐿⊙) ∥  SFR††  (𝑀⊙ yr−1)  log (𝐿[CII]/𝐿⊙) ¶, # 𝜇  References ∗  REBELS-40  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='365  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 (ALMA 6)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='69 (ALMA 6)  −  [43, 44, 45]  REBELS-19  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='369  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 (ALMA 6)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='94 (ALMA 6)  −  [43, 44, 45]  REBELS-18  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='675  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 (ALMA 6)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03 (ALMA 6)  −  [43, 44, 45]  † The table does not include the 118 galaxies (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 <∼ 𝑧 <∼ 6) selected by the ALPINE project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The information of the ALPINE galaxies can be  downloaded from the official webpage of the project: https://cesam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='lam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='fr/a2c2s/data_release.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='php.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ALPINE galaxies  are unlensed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  § SFRUV is converted from 𝐿UV via SFRUV (𝑀⊙ yr−1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58 × 10−10 𝐿UV (𝐿⊙) following Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011) (see Table 3) for the Kroupa  (2002) IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡ The number in the brackets indicates the specific ALMA band at which dust continuum is measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ¶ For the galaxies having no detection of dust thermal continuum ([CII] emission), we show the 3𝜎 upper confidence limit of 𝑆 (𝐿[CII]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  # For the gravitationally-lensed galaxies, 𝐿UV (and hence SFRUV), 𝑆, 𝐿IR and 𝐿[CII] are de-magnified by 𝜇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∥ 𝐿IR (or the upper limit of 𝐿IR for the dust-undetected sources) is converted from 𝑆 (the 3𝜎 upper limit of 𝑆) via the standard MBB function  with 𝑇eqv calculated by equation (4) (assuming 𝛽dust = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 and 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  †† SFR is derived using SFR (𝑀⊙ yr−1) = SFRUV + SFRIR = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58 × 10−10 (𝐿UV + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46𝐿IR) (𝐿⊙) following Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2011) (see Table 3) for  the Kroupa (2002) IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡‡ We only list here the 13 galaxies of the REBELS sample that have confirmed detection of both [CII] and dust continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The information of  the other 5 galaxies having [CII] but no dust detection is not yet publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∗ References: (1): Capak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [2]: Barisic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [3]: Faisst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [4]: Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [5]: Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016),  [6]: Knudsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [7]: Harikane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [8]: Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018a), [9]: Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015b), [10]: Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013a), [11]:  Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021), [12]: Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [13]: Kanekar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [14]: Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2002), [15]: Ouchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [16]: Carniani  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018b), [17]: Sobral et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [18]: Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [19]: Pentericci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [20]: Schouws et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022a), [21]: Schouws  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022b), [22]: Bradač et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [23]: Smit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [24]: Molyneux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022), [25]: Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [26]: Ota et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2014), [27]: Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [28]: Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [29]: Watson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [30]: Knudsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [31]: Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022),  [32]: Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019a), [33]: Bowler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [34]: Inoue et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [35]: Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015a), [36]: Finkelstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013),  [37]: Tamura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [38]: Bakx et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [39]: Kawamata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [40]: Laporte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [41]: Laporte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [42]:  Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022), [43]: Heintz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022b), [44]: Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [45]: Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022), [46]: Sommovigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022),  [47]: Bouwens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  X  10  () I  108  X  10  106  10-1  100  101  102  103  10  SFR(Mo yr-14X  10  108  10  106  100  101  10-1  102  103  10  SFR(Mo yr-1CII emission as an indicator of galaxy SFR  19  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Comparison between the mean ‘equivalent dust temperature’ (<𝑇eqv>) assumed by the ALPINE and REBELS projects and by this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Project name  Reference  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' of galaxies  <𝑧>  <𝑇eqv/K>  <𝑇eqv/K>†  Δ<log(  𝐿[CII ]  SFR )>‡  (literature)  (this work)  (dex)  ALPINE  Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020)  118  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58  42  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='27  REBELS  Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022)  40  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  55  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  † Calculated using equation (7) with 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that with a lower 𝛿dzr, 𝑇eqv is higher than the listed value in this column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡ The resulting difference in the derived mean 𝐿[CII]/SFR ratio (in dex) of the galaxy samples due to the difference in 𝑇eqv used by the previous  studies (Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020 and Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Almost all dust-detected galaxies have detection of [CII]  line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The detection limit of [CII] of the current ALMA observations  is about 108 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We convert the sub-mm broad-band flux density (𝑆𝜈0) of the dust-  detected galaxies (or the 3𝜎 upper limit of 𝑆𝜈0 for the dust-undetected  galaxies) to 𝐿IR (the upper limit of 𝐿IR) consistently using 𝑇eqv that  follows equation (7) (assuming 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4) to make a fair comparison  between different observed samples and our theoretical predictions  using FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We compute the SFR of the observed galaxies  using their measured 𝐿UV and the derived 𝐿IR following Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2011), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SFR (𝑀⊙ yr−1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='58 × 10−10 (𝐿UV + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='46𝐿IR) (𝐿⊙),  for the Kroupa (2002) IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the dust-undetected galaxies, we  estimate the lower and upper bounds of their SFR, where the former  is converted from their 𝐿UV assuming no dust emission (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR = 0),  whilst the latter accounts for the upper limit of 𝐿IR converted from  the 3𝜎 upper limit of 𝑆𝜈0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8, we show the observed 𝐿[CII]-SFR relation of the rest-UV-  selected galaxy samples at 𝑧 >∼ 5 (see Table 4 for the details) together  with the result of the FIRE galaxies at 𝑧 = 4, 𝑧 = 6 and 𝑧 = 8 in the  two panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the observed galaxies having no detection of dust,  we show the relation between their 𝐿[CII] (for the [CII]-undetected  galaxies, the 3𝜎 upper limit of their 𝐿[CII]) and the lower and upper  bound of their SFR, respectively, in the left and right panels of the  figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8 the observed 𝐿[CII]-SFR  relation of the local star-forming galaxies by L11, L14 and H15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It can be seen that the FIRE galaxies at 𝑧 = 4 − 8 lie systematically  below the observed local 𝐿[CII]-SFR relations (and thus also the FIRE  galaxies at 𝑧 = 0) over the broad SFR range of ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 − 103 𝑀⊙ yr−1,  showing a [CII] deficit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This appears to be in agreement with the  observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At SFR>∼100 M⊙ yr−1, most of the observed galaxies at 𝑧 >∼5 have  both [CII] and dust detections and thus their (dust-obscured) SFR  is more reliably constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean 𝐿[CII]/SFR ratio of these  galaxies is lower than the L11 relation (solid green line) by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='22 dex,  which is close to the 1𝜎 scatter of the L11 relation (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE galaxies at 𝑧 ≥ 4 are about 2𝜎 below the L11 relation in  the same SFR range, which seem to show a slightly more prominent  ‘deficit’ than the observed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At SFR <∼ 100 M⊙ yr−1, most of the 𝑧 >∼ 5 galaxies do not have  confirmed dust detection with the current ALMA observations, and a  large fraction of them do not have confirmed [CII] detections neither  (marked by downward arrows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The uncertainty in the SFR estimate  of these dust-undetected galaxies can be as large as a factor of ∼ 5  (≈ 20 − 100 𝑀⊙ yr−1, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Such a large uncertainty is due  to the high 𝑇eqv of galaxies at 𝑧 >∼ 5 (𝑇eqv >∼ 45 K for 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4,  see equation (7)), so that even a low noise level (typically 𝜎 ∼  10𝜇Jy, see Table 4) of the ALMA observations is converted to a  relatively high upper bound of 𝐿IR (and hence SFRIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8,  it can be seen that the predicted 𝐿[CII]-SFR relation of the FIRE  galaxies does not conflict with the observational constraints over  SFR ≈ 10 − 100 𝑀⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, for the [CII]-undetected  galaxies, the 3𝜎 upper limit of their 𝐿[CII] (marked by downward  arrows) appears to be above the data points of the FIRE galaxies  at similar SFR when their dust emission is insignificant, namely,  SFR ≈ SFRUV (see the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At SFR <∼ 10 𝑀⊙ yr−1, we lack enough observational data for a  reliable constraint on the 𝐿[CII]-SFR relation at 𝑧>∼5 because galaxies  having such low SFR are intrinsically faint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The galaxy having the  lowest SFR (SFR ≈ 1 𝑀⊙ yr−1) that has had [CII] measurement  to date at 𝑧 >∼ 5 is MS0451-H (Knudsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016), a strongly  lensed galaxy at 𝑧 = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 with an estimated magnification factor of  𝜇 = 100 ± 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' MS0451-H has no confirmed [CII] detection yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The upper bound of its 𝐿[CII]/SFR ratio is more than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex below  the L11 relation (even with the most conservative, UV-based SFR,  see the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8), showing a strong [CII] deficit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This  appears to be in agreement with the FIRE sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen  from the figure that the [CII] deficit of the FIRE galaxies extends to  SFR <∼ 10 𝑀⊙ yr−1 at 𝑧 >∼ 5, which is even slightly more prominent  than at higher SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Encouragingly, some of the FIRE galaxies at  𝑧 ≥ 4 show similarly low 𝐿[CII]/SFR ratio as MS0451-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The 𝐿[CII]-SFR relation of the observed galaxies at 𝑧 >∼ 5 reported  in this work seems to have lower normalization than a number of  the recent observational studies, including e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Schaerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020)  (ALPINE paper), Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022) (REBELS paper), Matthee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2017, 2019), Carniani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018a), Harikane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020) and  Fujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is due to the fact that these studies have  assumed a lower 𝑇eqv than what we use for this study as derived using  equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As has been mentioned in some of these studies, the  largest uncertainty of the derived galaxy 𝐿[CII]-SFR relation at 𝑧>∼5 is  the assumed 𝑇eqv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Table 5, we explicitly show the difference in the  mean 𝑇eqv adopted by the ALPINE/REBELS projects and this work  (for 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4), as well as the resulting difference in the derived  mean 𝐿[CII]/SFR ratio (<𝐿[CII]/SFR>) of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that  Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022) has used very similar 𝑇eqv compared to what  is used in our work as fiducial (with 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4), whereas Schaerer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020) has used significantly lower 𝑇eqv (< 𝑇eqv > = 42 K)  for the ALPINE galaxies than us (< 𝑇eqv > = 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Our estimate  of the 𝐿[CII]-SFR relation of the ALPINE galaxies is therefore about  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 dex below the originally reported result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐿[CII]/𝐿IR of IR-luminous galaxies  In addition to the LBGs/LAEs having moderate SFRs, there have  been studies probing the more extreme systems at 𝑧 >∼ 5, in par-  ticular, the quasar hosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These systems are gas/dust-rich and very  IR-luminous (𝐿IR >∼ 1012 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' They typically are also bright [CII]  emitters, having 𝐿[CII] that spans across the range of ≈ 108−1010 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We summarize the properties of the quasar hosts at 𝑧 >∼ 5 having had  [CII] line detections to date in Table 6 (> 65 galaxies in total).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ob-  servations targeting the quasar hosts have a high successful detection  rate for [CII] line (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Decarli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  20  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Observations of galaxies at z > 5  FIRE galaxies  z = 4  z = 6  z = 8  REBELS  ALPINE  LBGs/LAEs  Quasar hosts  Higher  Teqv  SMGs  Local observations  (same as in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6) Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR relation of galaxies at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Filled  coloured symbols indicate the data of the FIRE galaxies (magenta circles for  𝑧 = 4, green diamonds for 𝑧 = 6 and purple downward triangles for 𝑧 = 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Red vertical and blue diagonal crosses represent the observational data of the  REBELS (<𝑧> ≈ 7) and ALPINE (<𝑧> ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5) galaxy samples, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Black symbols represent the observational data of the other galaxy samples  at 𝑧 >∼5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, black diagonal crosses, black circles (filled and unfilled)  and black stars correspond to the UV-selected galaxies, SMGs and quasar  hosts, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the galaxies whose dust continuum is measured at  only single ALMA band, 𝐿IR is derived using 𝑇eqv that follows equation (7)  assuming 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 except for the REBELS galaxies, for which we show two  different sets of data that are produced by using 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 (semi-transparent  red crosses) and 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 (non-transparent red crosses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The lower 𝛿dzr  yields higher 𝑇eqv (and hence 𝐿IR) estimates for the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The black arrow  indicates the direction along which the data points of these galaxies move  on the diagram with increasing 𝑇eqv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the SMGs, filled circles indicate  the galaxies that are either confirmed as un-lensed or have observationally  determined lensing magnification factor 𝜇, whereas unfilled circles indicate  the lensed SPT galaxies having no determined 𝜇 yet (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Grey  symbols in the background represent the observational data of the local 𝑧 = 0  galaxy samples, as is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 6 (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Black horizontal line  indicates the median 𝐿[CII]/𝐿IR ratio (<𝐿[CII]/𝐿IR> = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='002) of the local  galaxies at 𝐿IR < 1011 𝐿⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Galaxies at 𝑧 > 5 show a trend of declining  𝐿[CII]/𝐿IR ratio with 𝐿IR at 𝐿IR >∼ 1011 𝐿⊙ similar to the local samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE simulations successfully reproduced the observed [CII] deficit  at high 𝐿IR at 𝑧 > 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Like most of the LBGs/LAEs at this epoch, the selected quasar  hosts typically have one or two data points in their dust continuum  (measured with ALMA band 6 or 7) and their 𝐿IR is converted from  a single broad-band sub-mm flux density in the literature using the  standard MBB function with an assumed 𝑇eqv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR has generally  been considered as a crude estimate of their SFR by the observational  studies assuming that these quasar hosts are gas and dust-rich and the  stellar radiation of these galaxies is significantly dust-obscured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is,  however, unknown to what degree the radiation from the accreting  supermassive black hole affects the shape of the IR SED and the  total IR luminosity of these early galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Observations of galaxies  at lower redshifts (𝑧 ≈ 0 − 3) demonstrate that the IR SED shape of  galaxies becomes ‘warmer’ (indicating higher 𝑇eqv) with increasing  AGN power (Kirkpatrick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A similar conclusion was  reached in the early study by Younger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009 with hydrodynamic  simulations of galaxy mergers that include AGN modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note,  however, that some recent studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Symeonidis 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McKinney  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021) also suggest that AGN radiation may even dominate the  cold-dust emission of the host galaxies at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 9, we show the 𝐿[CII]/𝐿IR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿IR relation of the quasar  hosts, along with other galaxy populations at 𝑧 >∼5, including the few  SMGs (listed in Table 3), the ALPINE and REBELS galaxies and other  rest-UV-selected galaxies at 𝑧 >∼ 5 (we only show the galaxies hav-  ing confirmed dust detection, which have more reliable constraints  on 𝐿IR than the dust-undetected galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We convert the reported  single-band sub-mm flux density of all the quasar hosts to 𝐿IR using  the standard MBB function and 𝑇eqv that follows equation (7) with  the best-fit parameters derived by Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We note that  for the quasar hosts, this is likely to be an underestimate because  the best-fit parameters of Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019) are derived using FIRE  simulations which do not include AGN feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Having a higher  𝑇eqv, the data points of the quasar hosts (black stars) will shift in  the diagonal direction toward the bottom-right corner of the diagram  (marked by the black arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Looking at the observational data, we can see a clear trend of  declining 𝐿[CII]/𝐿IR (∼ 𝐿[CII]/SFR) ratio of the galaxies with 𝐿IR  ([CII] deficit) at 𝐿IR >∼ 1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 𝐿⊙ at 𝑧 >∼ 5, similar to the trend seen at  lower redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII]/𝐿IR-𝐿IR relation of these early galaxies  appears to consistent with the local samples (grey symbols) in the  overlapping 𝐿IR regime and show similarly large scatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We also show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 9 the 𝐿[CII]/𝐿IR-𝐿IR relation of the FIRE  galaxies at 𝑧 = 4 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The result of the FIRE galaxies is in good  agreement with the observational data in overlapping 𝐿IR range,  except for the REBELS sample (<𝑧> ≈ 7, indicated by red vertical  crosses in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Using 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4, the REBELS galaxies (semi-  transparent red crosses) show systematically higher 𝐿[CII]/𝐿IR than  the rest of the observed galaxy samples (blue and black diagonal  crosses) as well as the FIRE galaxies at similar 𝐿IR (≈ 1012 𝐿⊙)  by ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Using 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 instead, the expected mean 𝑇eqv of  the REBELS sample increases by ≈ 20% (from 57 K to 71 K), and  the derived mean 𝐿IR (𝐿[CII]/𝐿IR ratio) of the galaxies increases  (decreases) by a factor of ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The data of the REBELS sample for  𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 (non-transparent red crosses) appears to be consistent with  the other observed samples as well as the FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The FIRE galaxies at 𝑧 ≥ 4 show a trend of declining 𝐿[CII]/𝐿IR  ratio with 𝐿IR, which agrees with the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is also  clear to see that the 𝐿[CII]/𝐿IR ratio of the FIRE galaxies decreases  with redshift at fixed 𝐿IR at 𝑧 ≥ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The trend of decreasing 𝐿[CII]/𝐿IR  ratio with both redshift and 𝐿IR persists up to 𝑧 = 8 in the FIRE  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Finally, we note that it is unclear whether AGN activity is directly  related to the [CII] deficit at high 𝐿IR based on the current data,  despite the large number of quasar hosts at 𝑧 >∼5 showing strong [CII]  deficit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because most of the selected SMGs in the literature  (2 <∼ 𝑧 <∼ 7), having similar 𝐿IR to the quasar hosts, have no identified  AGN feature (see Table 3) but show similarly strong [CII] deficit  as the quasar hosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In addition, the FIRE simulations, which do not  include AGN physics, have also successfully reproduced similarly  low 𝐿[CII]/𝐿IR ratio at high 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5 THE PHYSICS OF THE 𝐿[CII]-SFR SCALING RELATION  OF GALAXIES  In the previous section, we have shown that the 𝐿[CII]-SFR relation  of the FIRE galaxies predicted using our model is in good agreement  with the observational data of local and high-𝑧 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular,  our model reproduces the observed [CII] deficit of galaxies at high  MNRAS 000, 1–42 (2022)  10  10  L[CII] /  10  10°  109  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='30 (NOEMA)  [31]  VIK J1048-0109  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='32 (ALMA 6)  [9, 13]  (Continue on next page)  MNRAS 000, 1–42 (2022)  22  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 6 – continued  Name  𝑧  𝑆𝜈 (mJy)  log (𝐿IR/𝐿⊙)§  log (𝐿[CII]/𝐿⊙)  References∗  HSC J1205-0000  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='58 (ALMA 6)  [34]  VIK J0109-3047  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='25 (ALMA 6)  [9, 33]  HSC J1243+0100  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='075  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='52 (ALMA 6)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='40 (ALMA 6)  [35]  ULAS J1120+0641  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='085  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='64 (ALMA 6)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08 (ALMA 6)  [9, 36]  ULAS J1342+0928  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='541  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='34 (ALMA 6)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12 (ALMA 6)  [9, 37]  † 𝐿IR of SDSS J2310+1855 and SDSS J1148+5251 are derived by SED fitting (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014) to multiple data points at  both Wien and Rayleigh-Jeans sides of the dust IR SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ‡ J043947+163415 has been confirmed to be gravitationally-lensed, and its luminosities have been de-magnified by 𝜇 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0, estimated  based on the lensing configuration from HST imaging by Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∥ NOEMA: NOrthern Extended Millimeter Array  (Website: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='iram-institute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='org/EN/content-page-235-3-235-0-0-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='html).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  § 𝐿IR (or its upper 3𝜎 limit) is converted from 𝑆 (its 3𝜎 upper limit) using the standard MBB function and with 𝑇eqv that follows equation (7)  (assuming 𝛽dust = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 and 𝛿dzr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4), except for SDSS J2310+1855 and SDSS J1148+5251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ∗ References: [1]: Bischetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [2]: Wagg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2010), [3]: Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [4]: Wagg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012), [5]: Iono et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2006), [6]:  Leipski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2014), [7]: Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [8]: Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [9]: Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [10]: Eilers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020): [11]: Rojas-Ruiz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021), [12]: Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [13]: Decarli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [14]: Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [15]: Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015a), [16]: Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (2017), [17]: Decarli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [18]: Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), [19]: Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018), [20]: Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [21]: Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016),  [22]: Leipski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013), [23]: Andika et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020), [24]: Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2009), [25]: Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2005), [26]: Meyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022), [27]:  Willott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2013b), [28]: Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019b), [29]: Yue et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021), [30]: Bañados et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015), [31]: Mazzucchelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017), [32]:  Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019) [33]: Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2016), [34]: Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021a), [35]: Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021b), [36]: Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012),  [37]: Venemans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐿IR and high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this section, we explore the origin(s) of the  [CII] deficit of galaxies using the FIRE galaxy sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1, we present the analytic solution of [CII] line flux  emerging from a plane-parallel gas slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The toy model provides  useful insights for understanding the [CII] emission of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2, we derive an important scaling relation of galaxies  between their 𝐿[CII]/SFR ratio and other physical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Based  on this scaling relation, we investigate the cause of the [CII] deficit of  galaxies in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Finally, in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4, we show the presence  of two distinct physical regimes where the main reason for the [CII]  deficit of galaxies is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 Insights from the plane parallel slab model  The [CII] line flux emerging from a plane-parallel slab that is ir-  radiated by an external radiation field has recently been studied by  Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019, hereafter F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this section, we summarize  the key points of the F19 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We refer interested readers to F19  for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The plane-parallel slab can be characterized by three distinct zones  based on the ionization structures of gas, as has been discussed in  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Right beneath the surface of the slab, ionizing radiation  (𝐸𝛾 > 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV) creates a HII region extending to a gas column density  𝑁s (Zone I), where both hydrogen and carbon are ionized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Beyond 𝑁s,  hydrogen becomes neutral but LW (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 < 𝐸𝛾 < 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV) photons  maintain carbon in the singly ionized state (Zone II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The LW photons  become fully absorbed by dust and H2 at a column density 𝑁F, beyond  which hydrogen turns into H2 and carbon becomes neutral (Zone III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We have shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2 the ionization structures of a plane-parallel  slab calculated by CLOUDY as an example (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1 of F19 for  a schematic plot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑁s can be estimated by equating the photo-ionization rate to the  recombination rate of hydrogen inside the HII region (Zone I) as-  suming that dust extinction is negligible, which can be expressed as  (see Appendix C for the details)  𝑁s = 𝑛H𝑙s = 𝑈𝑐  𝛼B  ≈ 1023𝑈 cm−2,  (8)  where 𝑙s is the distance from the surface of the slab to the end of  Zone I, 𝑈 parameter represents the ionizing photon-to-gas density  ratio, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑈 = 𝑛𝛾  𝑛H  ,  (9)  𝑐 represents the speed of light, and 𝛼B = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 10−13 cm3 s−1 is  the Case-B recombination coefficient at gas temperature 𝑇 ≈ 104 K  (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For a slab with density 𝑛H = 50 cm−3 that  is exposed to a radiation field having 𝐺 = 200 𝐺0, we obtain 𝑈 =  𝑛𝛾/𝑛H ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 10−3 at and near the surface of the slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Using  equation (8), we obtain 𝑁s ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 1020 cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We can see from  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2 that this estimated 𝑁s is in good agreement with the result  computed by CLOUDY, in particular, for the metal-poor model (with  𝑍gas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 𝑍⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' right panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2), where dust extinction in the  HII (Zone I) region is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑁s of the metal-rich model (with  𝑍gas = 𝑍⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' left panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2) is smaller by about 1/4 due to higher  absorption of ionizing photons by dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑁F can be estimated using  𝑁F = 𝑛H𝑙F = ¯𝜎−1  d  ln(1 + 105𝜔𝑈),  (10)  which is obtained by performing a RT calculation (Sternberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2014) that accounts for the absorption of LW photons by dust grains  and H2 as light propagates through the slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In equation (10), 𝑙F  represents the distance between the surface of the slab and the end  of Zone II,  ¯𝜎d = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 × 10−22  �  𝛿dgr  𝛿dgr, MW  �  cm2  (11)  represents the flux-weighted dust extinction cross section per H-atom,  and  𝜔 =  1  1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9(𝛿dgr/𝛿dgr, MW)1/2 ,  (12)  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  23  where 𝛿dgr, MW = 10−2 represents the Galactic dust-to-gas ratio  (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gilmore et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sodroski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Zubko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Rémy-Ruyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' McKinnon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the two models where 𝑍gas = 𝑍⊙ and 𝑍gas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1𝑍⊙,  𝑁F is expected to be ∼ 1021 cm−2 and ∼ 1022 cm−2 (according to  equation 10), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This result is again in good agreement  with the prediction of CLOUDY as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Now we can derive the [CII] line flux (𝐹[CII]) emerging from  a plane-parallel slab following the three-zone model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐹[CII] can be  calculated using  𝐹[CII] = Λ(1)  [CII] 𝑙s + Λ(2)  [CII] (𝑙F − 𝑙s),  (13)  where the first and second terms correspond to the contribution of  [CII] line flux by Zone I and Zone II, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Λ(1)  [CII] (Λ(2)  [CII]) in  the above equation represents the [CII] cooling rate (erg s−1 cm−3)  of gas in Zone I (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the above and the following equations, the  superscript “(1)" (“(2)") indicates the properties of gas in Zone I (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We neglect the [CII] emission from the H2 region (Zone III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Equation (13) can be rewritten as (see Appendix D for the details)  𝐹[CII] ≈ ℎP𝜈[CII]  � 𝑔u  𝑔l  �  𝑅e  ul(𝑇 (1))𝑛(1)  CII 𝑛(1)  e  𝑙s  + 2  5 ℎP𝜈[CII]  � 𝑔u  𝑔l  �  𝑅HI  ul (𝑇 (2))𝑛(2)  CII 𝑛(2)  HI (𝑙F − 𝑙s),  (14)  where ℎP is the Planck constant, 𝜈[CII] = 1900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 GHz is the rest-  frame frequency of the [CII] line, 𝑔u = 4 (𝑔l = 2) is the statistical  weight of the 2𝑃3/2 (2𝑃1/2) state, 𝑅e  ul (𝑅HI  ul ) is the downward rate  coefficient (s−1) for CII +𝑒− (CII +H0) collision, and 𝑛(1)  CII (and 𝑛(2)  CII ),  𝑛(1)  e  and 𝑛(2)  HI represent the number density of CII ion, electron and  H atom, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Equation (14) implies that in Zone I (II), the  main collision partner of CII ion is electron (H atom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Knowing that  𝑛(1)  e  ≈ 𝑛H and 𝑛(2)  HI ≈ 𝑛H (see the upper panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2), we can  rewrite equation (14) to be  𝐹[CII] = ℎP𝜈[CII]  � 𝑔u  𝑔l  � �  𝑅e  ul𝑛(1)  CII 𝑁s + 2  5 𝑅HI  ul 𝑛(2)  CII (𝑁F − 𝑁s)  �  ,  (15)  where 𝑁F = 𝑛H 𝑙F and 𝑁s = 𝑛H 𝑙s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Furthermore, 𝑛(1)  CII and 𝑛(2)  CII in the  above equation can be rewritten as  𝑛(1)  CII = 𝑛H𝑥(1)  CII AC  and  𝑛(2)  CII = 𝑛H𝑥(2)  CII AC,  (16)  where  AC = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 × 10−4  � 𝑍gas  𝑍⊙  �  (17)  represents the abundance of carbon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The numerical factor 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5×10−4  in equation (17) is the abundance of carbon in the solar photosphere  (Asplund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑥(1)  CII (𝑥(2)  CII ) in equation (16) represents the  fraction of carbon in CII form in Zone I (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑥(1)  CII is roughly inversely  proportional to𝑈 (see Appendix E), whereas 𝑥(2)  CII ≈ 1 (see the middle  panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' By inputting equation (16) to equation (15), we get  𝐹[CII] = 𝑛HAC𝑁FℎP𝜈[CII]  � 𝑔u  𝑔l  � �  𝑅e  ul𝑥(1)  CII  � 𝑁s  𝑁F  �  + 2  5 𝑅HI  ul  � 𝑁F − 𝑁s  𝑁F  ��  = 𝑛HAC𝑁F ¯𝜖[CII], slab,  (18)  where we define  ¯𝜖[CII], slab = ℎP𝜈[CII]  � 𝑔u  𝑔l  � �  𝑅e  ul𝑥(1)  CII  � 𝑁s  𝑁F  �  + 2  5 𝑅HI  ul  � 𝑁F − 𝑁s  𝑁F  ��  ≡ 𝛼 𝑥(1)  CII  � 𝑁s  𝑁F  �  + 𝛾  � 𝑁F − 𝑁s  𝑁F  �  (19)  as the specific [CII] cooling rate of the slab (erg s−1 cm3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be  shown that (see Appendix D for the details)  𝛼 ≡ ℎP𝜈[CII]  � 𝑔u  𝑔l  �  𝑅e  ul(𝑇 (1))  ≈ 10−21 erg s−1 cm3 (𝑇 (1) ≈ 104 K)  (20)  and  𝛾 ≡ 2  5 ℎP𝜈[CII]  � 𝑔u  𝑔l  �  𝑅HI  ul (𝑇 (2))  ≈ 10−23 erg s−1 cm3 (𝑇 (2) ≈ 102 K)  (21)  From equation (19), we see that ¯𝜖[CII], slab depends on 𝑥(1)  CII , 𝑁s and  𝑁F, and varies typically within the range 10−23 −10−21 erg s−1 cm3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Likewise, we can derive the [CII] luminosity of a spherical uniform  gas cloud (𝐿[CII], cl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII], cl can be expressed as  𝐿[CII], cl =  ����������  ����������  4𝜋  ∫ 𝑅cl  0  Λ(1)  [CII]𝑟2d𝑟  (if 𝑙s ≥ 𝑅cl)  4𝜋  �∫ 𝑅cl  𝑅cl−𝑙s  Λ(1)  [CII]𝑟2d𝑟 +  ∫ 𝑅cl−𝑙s  𝑅cl−min(𝑙F,𝑅cl) Λ(2)  [CII]𝑟2d𝑟  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (if 𝑙s < 𝑅cl)  (22)  The first condition of equation (22) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑙s ≥ 𝑅cl) corresponds to  when the cloud is fully ionized, while the second condition (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑙s <  𝑅cl) corresponds to when neutral hydrogen region (Zone II) forms in  the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Through simple re-arrangement, 𝐿[CII], cl can be expressed  as  𝐿[CII], cl = 𝑓[CII], cl  � 𝑀cl  𝜇H𝑚H  �  𝑛HAC ¯𝜖[CII], cl,  (23)  where 𝑓[CII], cl represents the fraction of the gas mass that is in  HII or HI phases (Zone I and Zone II), 𝑀cl indicates the mass of  the gas cloud, 𝜇H is the mean molecular weight of the gas and 𝑚H  represents the proton mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' By definition, 𝑓[CII], cl = 1 when 𝑙F > 𝑅cl  and the cloud becomes H2-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝜖[CII], cl in equation (22) represents  the specific [CII] cooling rate of the spherical uniform cloud, which  accounts for the relative contribution of the [CII] emission from HII  and HI regions (10−23<∼ ¯𝜖[CII], cl<∼10−21 erg s−1 cm3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Like ¯𝜖[CII], slab  for the plane-parallel slab (equation 19), ¯𝜖[CII], cl depends on 𝑥(1)  CII , 𝑁s  and 𝑁F but have different functional relation with these parameters  due to the difference in geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We refer the readers to Appendix F,  where we present the derivation for ¯𝜖[CII], cl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Note that we do not take into account the effects of the CMB  background on the [CII] cooling rate of gas in the analytic solution  for the toy models presented in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While the CMB sets  a floor for the excitation (or spin) temperature of gas and boosts  the upper level (2𝑃3/2) population of the [CII] transition (‘CMB  heating’), it acts as a background against which the [CII] line is  measured (‘CMB attenuation’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The CMB effects (both heating and  attenuation) can be important for the [CII] emission from the low-  density and low-temperature gas in galaxies at high redshifts (𝑧 >∼ 6)  (see Appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We find, however, that the total [CII] luminosity  of the FIRE sample is not significantly affected by the CMB (in  agreement with Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is due to the fact that the  bulk of the [CII] luminosity of the high-𝑧 (𝑧 ≥ 6) galaxies in our  sample originates from the gas of densities in excess of the densities  where the CMB effects become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  24  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 1  z = 2  z = 3  z = 4  z = 0  z = 6  z = 8  Herrara-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015 (  )  z ∼ 0  Pearson correlation coefficient ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='96  Figure  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The  relation  between  the  𝐿[CII]/SFR  ratio  and  𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII]  of  the  FIRE  galaxies  at  different  redshifts  (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for 𝑧 = 2,  blue squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6  and purple downward triangles for 𝑧 = 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The orange shaded area indicates  the 𝐿[CII]/SFR ratio of the local star-forming galaxy sample measured by  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The solid black line shows the best linear fit  to the data of the FIRE galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The FIRE galaxies show a strong linear  correlation (Pearson correlation coefficient 𝜌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='96) between 𝐿[CII]/SFR  and 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 A scaling relation for the 𝐿[CII]/SFR ratio of galaxies  We have summarized the key points of the F19 model for the struc-  tures of a plane-parallel gas slab that is exposed to an external radia-  tion field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We then derive the [CII] luminosity of a uniform spherical  gas cloud (equation 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Following the results of the toy models, we  now present a scaling relation for the [CII] luminosity of galaxies,  based on which we will explore the origins of the [CII] deficit of  galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  From equation (23), one would expect that the [CII] luminosity  (𝐿[CII]) of galaxy has a similar expression, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐿[CII] ∼ 𝑓[CII]  � 𝑀gas  𝜇𝑚H  �  ¯𝑛gas ¯  AC ¯𝜖[CII],  (24)  where we have replaced 𝑀cl in equation (23) by 𝑀gas, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the gas  mass of galaxy19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑓[CII] (= 1 − 𝑓H2) in the above equation represents  the fraction of the total gas mass in ionized or neutral atomic hydrogen  forms (Zone I and Zone II), and ¯𝑛gas,  ¯  AC and ¯𝜖[CII] represent the  statistical average of gas density, carbon abundance and specific  [CII] cooling rate of the galaxy, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We can then divide the  two sides of equation (24) by galaxy SFR, and obtain  𝐿[CII]  SFR ∼ 𝑓[CII]𝑡dep ¯𝑛gas ¯  AC ¯𝜖[CII] (𝜇𝑚H)−1  (25)  where  𝑡dep ≡ 𝑀gas  SFR  (26)  19 We calculate the gas mass of galaxy using the gas particles within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1𝑅vir  around the DM halo centre having 𝑇 < 105 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ¯ngas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 cm−3  FIRE galaxy z = 0  ¯ngas = 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 cm−3  FIRE galaxy z = 6  ¯nHI, MW = 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 cm−3  ¯nHII, MW = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 cm−3  ¯nH2, MW = 794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 cm−3  PDF =  d log M (Mgas)  d log nH  or  d log L[CII]  d log nH  PDF =  d log M (Mgas)  d log nH  or  d log L[CII]  d log nH  (luminosity-weighted)  (luminosity-weighted)  ¯nHI, MW = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 cm−3  ¯nHII, MW = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 cm−3  ¯nH2, MW = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 cm−3  (mass-weighted)  (mass-weighted)  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The gas density PDFs of two selected FIRE galaxies at 𝑧 = 0  (upper panel) and 𝑧 = 6 (lower panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝑧 = 6 galaxy has a relatively  denser ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the two panels, magenta lines indicate the luminosity-weighted  PDFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Solid, dotted and dashed magenta lines represent the result of the total  gas, HII gas (Zone I) and HI gas (Zone II) in the ISM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the two  panels, shaded areas show the mass-weighted gas density PDFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Grey, red,  green and blue areas represent the result of total gas, HII gas (Zone I), HI gas  (Zone II) and H2 gas (Zone III), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  is the gas depletion time of the galaxy (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Genzel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Tacchella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Semenov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Scoville et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Tac-  coni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Feldmann 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Through further re-arrangement,  equation (25) can be expressed as  𝐿[CII]/𝐿⊙  SFR/(𝑀⊙ yr−1) ∼ 4 × 106 𝑓[CII]  � ¯𝑍gas  𝑍⊙  �  ×  � 𝑡dep  Gyr  � � ¯𝑛gas  cm−3  � �  ¯𝜖[CII]  10−22 erg s−1 cm3  �  (27)  ∝ 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII],  (28)  where we have replaced the carbon abundance  ¯  AC in equation (25)  by metallicity ¯𝑍gas using equation (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Equation (27) indicates that the 𝐿[CII]/SFR ratio of galaxy is  determined by five physical parameters, 𝑓[CII], ¯𝑍gas, 𝑡dep, ¯𝑛gas and  ¯𝜖[CII].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Whilst 𝑓[CII] and 𝑡dep are global properties of galaxy, which  are well defined, the other three parameters are the statistical average  of the corresponding physical properties of all different ‘gas clouds’  in the ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This contrasts with the toy models (uniform plane-parallel  slab or spherical cloud), where each of these properties (gas density,  gas metallicity, and the specific [CII] cooling rate) has a single,  definite value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 10, we show the relation between the 𝐿[CII]/SFR ratio  MNRAS 000, 1–42 (2022)  10  X  yr)  10  10  10-1  100  101  fcu (Zgas /Zo)(tdep/Gyr)(nH/cm-3)(EiCul/10-22 erg cm3 s1090.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  0  2  1  0  1  2  3  log (nH/cm-3)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  0  1  0  1  2  3  4  log (nH/cm-3)CII emission as an indicator of galaxy SFR  25  ¯ngas vs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯nH2, MW  ¯ngas vs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯nHI, MW  ¯ngas vs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯nHII, MW  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between the [CII] luminosity-weighted gas density  ( ¯𝑛gas) and the mass-weighted density of the HII ( ¯𝑛HII, MW), HI ( ¯𝑛HI, MW) and  H2 gas ( ¯𝑛H2, MW) of the FIRE galaxies at 𝑧 = 0 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Filled, empty and semi-  transparent symbols correspond to the ¯𝑛HI, MW vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑛gas, the ¯𝑛HII, MW vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑛gas  and the ¯𝑛H2, MW vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑛gas relations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The diagonal line indicates  the one-to-one relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen that ¯𝑛gas appears to be close to  ¯𝑛HI, MW, both being systematically lower (higher) than ¯𝑛H2, MW ( ¯𝑛HII, MW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  of the FIRE sample at 𝑧 = 0 − 8 and their 𝑓[CII] ¯𝑍gas 𝑡dep ¯𝑛gas ¯𝜖[CII],  where ¯𝑛gas, ¯𝑍gas and ¯𝜖[CII] are the luminosity-weighted gas density  20, gas metallicity21 and specific [CII] cooling rate of the galaxies,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Our FIRE sample follows a clear linear scaling relation  on the diagram (Pearson correlation coefficient 𝜌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='96), which is  in agreement with equation (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  One important question is which part of the ISM contributes the  most [CII] emission of a galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ISM of a galaxy spans a wide  range of density over several orders of magnitude, with the dense  (diffuse) regions being dominated by H2 (HII) gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 11, we  show the [CII] luminosity-weighted (magenta lines) and gas mass-  weighted (grey and coloured shaded areas) probability density func-  tions (PDFs) of 𝑛H for two selected FIRE galaxies at 𝑧 = 0 (upper  panel) and 𝑧 = 6 (lower panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen in the figure that  the [CII] emission of FIRE galaxies originates from gas spanning  20 Note that we use the ‘luminosity-weighted median gas density’, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the gas  density at the 50th percentile of [CII] luminosity, instead of the ‘luminosity-  weighted mean gas density’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because the gas density PDF of galaxy  resembles a lognormal function, exhibiting an elongated tail at the high den-  sity end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Under certain circumstances, the ‘mean gas density’ can be strongly  biased by the [CII]-emitting gas at the highest density (𝑛H >∼ 103 cm−3, see  the lower panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 11), and hence is not statistically representative for  the part of the gas that contributes the bulk of the [CII] emission of galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Throughout this paper, we use the term ‘luminosity-weighted’ for simplicity  when we refer to ‘luminosity-weighted median’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Similarly, ‘mass-weighted’  in this paper refers to ‘mass-weighted median’, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' value at the 50th per-  centile of mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Appendix G, we show explicitly the difference between  the ‘luminosity-weighted median gas density’ and the ‘luminosity-weighted  mean gas density’ of the FIRE galaxy sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The former is higher by a factor  of ∼ 5 on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  21 Unlike the gas densities, the luminosity-weighted mean and the  luminosity-weighted median gas metallicity are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Both are close to  the mass-weighted gas metallicity (see Appendix H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  a wide range of density across several orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Inter-  estingly, we find that the luminosity-weighted gas density (¯𝑛gas) of  FIRE galaxies is close to the mass-weighted density of the HI gas  (¯𝑛HI, MW) of the ISM, both of which are much higher (lower) than  the mass-weighted density of the HII (H2) gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can be more  clearly seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 12, where we show the relation between ¯𝑛gas  and the mass-weighted gas density of the HII, HI and H2 gas for the  FIRE sample at 𝑧 = 0 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  This can be understood as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The bulk of the diffuse, ionized  HII gas is inefficient at producing [CII] emission due to the low gas  density (𝐿[CII], cl/𝑀cl ∝ 𝑛H, see equation 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' On the other hand,  in the densest regions of the ISM, where gas becomes mostly in  molecular hydrogen form (Zone III), not much [CII] emission is  produced due to the scarcity of the amount of ionized carbon (which  exists mostly in Zone I and Zone II) in those regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a result,  the bulk of the [CII] luminosity of the FIRE galaxies at 𝑧 = 0 − 8  originates from the gas at the intermediate gas density range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It should be noted, however, that though the luminosity-weighted  gas density of the FIRE galaxies coincide with ¯𝑛HI and is system-  atically higher than ¯𝑛HII, more of the [CII] emission of the FIRE  galaxies actually originates from the HII gas (Zone I) instead of the  HI gas (Zone II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, it is the HII gas layer at the surface  of the HI-rich clouds having 𝑛 ≈ ¯𝑛gas that contributes most of the  [CII] emission of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 13, we show the fraction of  the total [CII] luminosity of the FIRE galaxies produced by the HII  gas, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII], HII/𝐿[CII] (note: 𝐿[CII], HII is the sum of the [CII] lu-  minosity originating from Zone I in each ‘gas cloud’), as a function  of the galaxy SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen that the HII gas contributes about  60% − 80% of the total luminosity of the galaxies, except for the  few massive starburst galaxies at SFR >∼ 100 𝑀⊙ yr−1, which show a  reduced fractional contribution by the HII gas down to ∼ 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  remaining fraction of the [CII] luminosity originates mainly from  the HI gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The contribution of the [CII] luminosity by the H2 gas  (Zone III) is negligible (< 2% of the total luminosity for all the FIRE  galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The relatively high [CII] cooling rate in the HII phase (note:  𝛼 ≈ 100 𝛾, see equation 20 and 21) explains why a relatively small  amount of HII gas at 𝑛H ≈ ¯𝑛gas can produce a larger fraction of the  [CII] luminosity of the galaxies than the HI gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Also, one would  expect a correlation between the fractional contribution of the [CII]  luminosity by the HII gas (Zone I) and the effective [CII] line cooling  rate (luminosity-weighted), ¯𝜖[CII], of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is indeed the  case, as is shown in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 The physical origins of [CII] deficit of galaxies  In the previous section, we have presented a simple analytic expres-  sion for the 𝐿[CII]/SFR ratio of galaxies (equation 27) found with  the FIRE galaxy sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Based on this result, we will probe in this  section the origins of the observed [CII] deficit of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Equation (27) indicates that the 𝐿[CII]/SFR ratio of the galaxies  depends on five parameters: the fraction of gas in the [CII]-emitting  regions (Zone I and Zone II), the depletion time (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' gas mass per  unit SFR), gas density, gas metallicity and the specific [CII] cooling  rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, the [CII] deficit of the galaxies can, in principle, be due  to a strong deficit of one or few of the five parameters with respect  to the observed local star-forming samples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', L11, L14 and H15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It should be noted that the observed [CII] deficit in the two regimes,  high redshifts and high 𝐿IR, may not be due to the same reason.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We  will separately discuss the origin of the [CII] deficit in these two  regimes in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  To  reveal  what  parameters  drive  the  [CII]  deficit  of  MNRAS 000, 1–42 (2022)  10  10°  100  102  103  10-  (cm-  as26  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-1  100  101  102  103  10  20  30  40  50  60  70  80  90  100  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 1  z = 2  z = 3  z = 4  z = 0  z = 6  z = 8  10-1  100  101  102  103  10  20  30  40  50  60  70  80  90  100  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  22  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  log ¯ϵ[CII] (erg cm3 s−1)  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The fraction of the total [CII] luminosity of the FIRE galaxy sample that originates from the HII gas region (Zone I) as a function of their SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In  the left and right panels, the data points are colour-coded by the redshift and the effective [CII] cooling rate ( ¯𝜖[CII]) of the galaxies, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  the  FIRE  sample,  we  divide  𝐿[CII]/SFR  by  each  of  these parameters and check whether in the new parameter  spaces (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐿[CII]SFR−1 𝑓 −1  [CII], 𝐿[CII]SFR−1 ¯𝑍−1  gas, 𝐿[CII]SFR−1 ¯𝑛−1  gas,  𝐿[CII]SFR−1𝑡−1  dep and 𝐿[CII]SFR−1𝜖−1  [CII]), the [CII] deficit becomes  alleviated (or even vanishes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 14 the relation between  the new parameters and the SFR for the galaxies in our sample at  different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15, we also show how 𝐿[CII]/SFR of the  FIRE sample depends on 𝑓[CII], ¯𝑍gas, ¯𝑛gas, 𝑡dep and ¯𝜖[CII] in separate  panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Readers can find the mean of 𝑓[CII], ¯𝑍gas, ¯𝑛gas, 𝑡dep and ¯𝜖[CII]  and the five new parameters of the FIRE sample at each redshift in  Table 8 and Table 7, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  [CII] deficit at high redshifts  The normalization of the 𝐿[CII]-SFR relation of the FIRE sample  decreases monotonically with redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean 𝐿[CII]/SFR ratio  of the galaxies decreases by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 dex (a factor of ∼ 15) from 𝑧 = 0 to  𝑧 = 8 (see col.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2 of Table 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It can be seen from Table 7 (and also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 14) that the redshift evo-  lution of the 𝐿[CII]/SFR ratio of the galaxies is mainly driven by ¯𝑍gas  and 𝑡dep since the [CII] deficit is significantly alleviated (or even van-  ishes at some redshifts) in the parameter space of (𝐿[CII]/SFR)𝑡−1  dep  and (𝐿[CII]/SFR) ¯𝑍−1  gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This result indicates that the [CII] deficit of  galaxies at high redshifts is due to either low gas metallicity or a  deficiency of gas (that is able to produce [CII] emission) per unit  SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Looking into the details, we see from Table 7 that while 𝑡dep is  the key parameter driving the evolution of the 𝐿[CII]-SFR relation  at 𝑧 <∼ 2, ¯𝑍gas plays a more important role at 𝑧 >∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because  𝑡dep of the FIRE sample decreases more at 𝑧 = 0 − 2 (from 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='30 to  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 Gyr, by a factor of ∼ 6) than at 𝑧 = 2 − 8 (from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='72  Gyr, by only ∼ 30%) (see Table 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At 𝑧 = 2 − 8, ¯𝑍gas of the FIRE  sample decreases sharply with redshift (from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='56 𝑍⊙ to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09 𝑍⊙, by  a factor of ∼ 6) and it thus has a stronger impact on the evolution of  𝐿[CII]/SFR of the FIRE galaxies than 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Unlike 𝑡dep and ¯𝑍gas, ¯𝜖[CII] has only a mild impact on the redshift  evolution of 𝐿[CII]/SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From 𝑧 = 0 to 𝑧 = 8, the mean ¯𝜖[CII] of the  FIRE sample has a slight decrease with redshift by less than a factor  of 3 (Table 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] deficit persists at high redshifts in the space  of (𝐿[CII]/SFR) ¯𝜖−1  [CII] (Table 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The other two parameters, ¯𝑛gas and 𝑓[CII], have completely no  contribution to the [CII] deficit at high redshifts since both increase  with redshift instead of decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The increase of ¯𝑛gas indicates  that earlier galaxies have a more compact ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Naively, because  𝐿[CII], cl/𝑀cl ∝ 𝑛H (equation 23), an increase of gas density would  result in a rise of 𝐿[CII]/SFR with redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This effect, however, is  overwhelmed by the combined effect of 𝑡dep and ¯𝑍gas on 𝐿[CII]/SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The increase of 𝑓[CII] with redshift indicates that our sample in-  cludes more H2 gas-poor galaxies at higher redshift where a larger  fraction of carbon in the ISM gas becomes ionized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Nonetheless, the  impact of 𝑓[CII] on the evolution of 𝐿[CII]/SFR is negligible since  𝑓[CII] of the galaxies in our sample differs by no more than a factor  of 2 (ranging between ≈ 60% and unity, see the lower middle panel  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  To summarize, the decrease of 𝐿[CII]/SFR of the FIRE sample  with redshift is mainly driven by the decrease of their 𝑡dep and gas  metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While 𝑡dep plays a more important role at 𝑧 ≤ 2, gas  metallicity becomes the key parameter driving the [CII] deficit of  the galaxies at higher redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The redshift evolution of ¯𝑛gas, 𝑓[CII]  and ¯𝜖[CII] have no or limited contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  [CII] deficit at high 𝐿IR  The FIRE sample exhibits a trend of declining 𝐿[CII]/𝐿IR ratio with  𝐿IR at each redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To find the main driver of the [CII] deficit at  high 𝐿IR, we check how each of the five physical parameters ( 𝑓[CII],  𝑡dep, ¯𝑛gas, ¯𝑍gas and ¯𝜖[CII]) depends on 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Table 8, we explicitly show the mean of 𝑓[CII], 𝑡dep, ¯𝑛gas, ¯𝑍gas  and ¯𝜖[CII] of the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (where galaxies are  observed to show [CII] deficit) in our sample at different redshifts,  in addition to the mean of the five parameters of the entire sample  (including fainter galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We can see from the table (also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15)  that the IR-luminous galaxies (𝐿IR ≥ 1011 𝐿⊙) have lower 𝑡dep, 𝑓[CII]  and ¯𝜖[CII] but higher ¯𝑍gas and ¯𝑛gas than the rest of the sample — they  are relatively metal and H2 gas-rich, and have more compact ISM  and shorter depletion time than the normal SFGs having lower SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1–42 (2022)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='CII emission as an indicator of galaxy SFR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='109  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='L[CII]/SFR t−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='dep (L⊙ M−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='⊙ )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='109  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1010  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='z = 8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='LIR ≥ 1011 L⊙  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='LIR < 1011 L⊙  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='L[CII]/SFR (¯ngas/cm−3)−1 (L⊙ M−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='⊙ yr)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='108  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SFR (M⊙ yr−1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SFR (M⊙ yr−1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='SFR (M⊙ yr−1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='L[CII]/SFR f −1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='[CII] (L⊙ M−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='⊙ yr)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='L[CII]/SFR (¯ϵ[CII]/10−22 erg s−1 cm3)−1 (L⊙ M−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='⊙ yr)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between 𝐿[CII]/SFR 𝑡−1  dep (upper left), 𝐿[CII]/SFR ¯𝑍−1  gas (upper right), 𝐿[CII]/SFR ¯𝑛−1  gas (lower left), 𝐿[CII]/SFR 𝑓 −1  [CII] (lower middle)  and 𝐿[CII]/SFR ¯𝜖 −1  [CII] (lower right) against SFR of the FIRE galaxies at different redshifts (cyan stars for 𝑧 = 0, yellow hexagons for 𝑧 = 1, red triangles for  𝑧 = 2, blue squares for 𝑧 = 3, magenta circles for 𝑧 = 4, green diamonds for 𝑧 = 6 and purple downward triangles for 𝑧 = 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In each panel, large (small)  symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] deficit at high 𝐿IR (at redshift 𝑧 > 5) vanishes in the parameter space of  𝐿[CII]/SFR 𝑡−1  dep (𝐿[CII]/SFR ¯𝑍−1  gas), indicating that low 𝑡dep (low gas metallicity) is the main driver of the [CII] deficit at high 𝐿IR (at high redshifts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The change of the mean 𝐿[CII]/SFR, 𝐿[CII]/SFR 𝑡−1  dep, 𝐿[CII]/SFR ¯𝑍−1  gas, 𝐿[CII]/SFR ¯𝑛−1  gas, 𝐿[CII]/SFR 𝑓 −1  [CII] and 𝐿[CII]/SFR ¯𝜖 −1  [CII] of the FIRE sample  from redshift 𝑧 to 𝑧 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑧  Δ log  �  𝐿[CII ]  SFR  �  Δ log  �  𝐿[CII ]  SFR 𝑡−1  dep  �  Δ log  �  𝐿[CII ]  SFR  ¯𝑍−1  gas  �  Δ log  �  𝐿[CII ]  SFR ¯𝑛−1  gas  �  Δ log  �  𝐿[CII ]  SFR 𝑓 −1  [CII]  �  Δ log  �  𝐿[CII ]  SFR  ¯𝜖 −1  [CII]  �  (dex)  (dex)  (dex)  (dex)  (dex)  (dex)  0  /  /  /  /  /  /  1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='16  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='78  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='35  2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='19  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='37  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='67  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='48  3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='78  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='64  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='55  4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='92  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='95  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='93  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='74  6  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='33  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='75  8  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='40  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='62  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='83  The fact that they have a reduced ¯𝜖[CII] is associated with a stronger  ISRF in these galaxies (we will discuss this more in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Hence, the [CII] deficit at high 𝐿IR is driven by the com-  bined effect of 𝑡dep, 𝑓[CII] and ¯𝜖[CII].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We see from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 14 that  the [CII] deficit of the FIRE sample at high 𝐿IR vanishes only in  the space of (𝐿[CII]/SFR) 𝑡−1  dep (upper left panel) but not in that  of (𝐿[CII]/SFR) 𝑓 −1  [CII] (lower middle panel) or (𝐿[CII]/SFR) ¯𝜖−1  [CII]  (lower right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This indicates that 𝑡dep plays a major role in  driving the [CII] deficit at high 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' That is, the [CII] deficit of the  IR-luminous galaxies in our sample is mainly due to the reduced  amount of gas that is available for producing [CII] emission per unit  SFR of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  28  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-2  10-1  100  101  102  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  10-1  100  101  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  ¯Zgas (Z⊙)  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 1  z = 2  z = 3  z = 4  z = 6  z = 8  LIR ≥ 1011 L⊙  LIR < 1011 L⊙  f[CII] ( % )  100  101  102  103  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  55  60  65  70  75  80  85  90  95  100  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  ¯ngas (cm−3)  10-24  10-23  10-22  10-21  10-20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  ¯ϵ[CII] (erg cm3 s−1)  Δlog L[CII] (dex)  Δlog L[CII] (dex)  Δlog L[CII] (dex)  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Δ(log 𝐿[CII]) as a function of 𝑡dep (upper left), ¯𝑍gas (upper right), ¯𝑛gas (lower left), 𝑓[CII] (lower middle) and ¯𝜖[CII] (lower right) of the FIRE galaxies  at different redshifts, where Δ(log 𝐿[CII]) represents the offset between the 𝐿[CII]/SFR ratio of the galaxies and the observed mean value of the local star-forming  sample of H15 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 × 107 𝐿⊙ 𝑀−1  ⊙ yr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In each panel, large (small) symbols correspond to the FIRE galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean of 𝑡dep, ¯𝑍gas, ¯𝑛−1  gas, 𝑓[CII] and ¯𝜖[CII] of the FIRE galaxy  sample at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑧  <  𝑡dep  Gyr >  <  ¯𝑍gas  𝑍⊙ >  < ¯𝑛gas  cm−3 >  < 𝑓[CII]>  <  ¯𝜖[CII ]  10−22 erg s−1 cm3 >  Total  0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+page_content='4 The two regimes of [CII] emission of galaxies  In the previous section, we have shown with the FIRE sample that  the main driver of the [CII] deficit at high redshifts and high 𝐿IR  is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The observed [CII] deficit of the galaxies at 𝑧 >∼ 4 (at  𝐿IR >∼1011 𝐿⊙) may be due to their low gas metallicity (gas depletion  time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this section, we explore the fundamental reason for galaxies  having different origin of [CII] deficit in the two regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We at first discuss the 𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep relation of the FIRE  galaxies (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We subsequently explore the reason for  galaxies showing two distinct regimes on the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep  diagram (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Finally, we discuss how this is related to  the distinct origin of [CII] deficit at high redshifts and high 𝐿IR  (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 The 𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep relation  The FIRE galaxies exhibit two distinct regimes on the Δ (log 𝐿[CII])  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' While a considerable number of the galaxies  show a tight linear correlation between their log (𝑡dep/Gyr) and  Δ (log 𝐿[CII]), exhibiting a linear sequence (we hereafter refer to  it as the ‘deficit-depletion time sequence’, or DDS), others show  larger scatter on the diagram and fall systematically below the DDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  29  10-2  10-1  100  101  102  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  5  10  20  30  40  L[CII]/SFR ∝ t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='71  dep  LIR ≥ 1011 L⊙  LIR < 1011 L⊙  The deficit-depletion time sequence  Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between 𝑡dep and Δ (log 𝐿[CII]) of the FIRE sample  at 𝑧 = 0 − 8 (same as the upper left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15 except for the colour).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The data points are coloured-coded by 𝑓H2 of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The large (small)  symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The H2 gas-rich galaxies ( 𝑓H2 >∼ 10%) exhibit a linear correlation between  log (𝑡dep/Gyr) and Δ (log 𝐿[CII]) (indicated by the black dashed line), which  can be converted to a power-law relation 𝐿[CII]/SFR ∝ 𝑡0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='71  dep (equation 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The galaxies on the DDS appear to be more H2 gas-rich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 16,  we show the same 𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep relation of the FIRE sample as  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15 (upper left panel), but colour-code the data points by the  H2 gas mass fraction, 𝑓H2, of the galaxies instead of their redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It  can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 16 that the galaxies along the DDS tend to be  more H2 gas-rich, having 𝑓H2 >∼ 10% (equivalent to 𝑓[CII] <∼ 90%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Besides, we see from the two figures that the majority of the low-  redshift (𝑧 = 0 − 2, shown by cyan stars, yellow hexagons and red  triangles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15) and IR-luminous (𝐿IR >∼ 1011 𝐿⊙, indicated by  large symbols in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 16) galaxies locate on or close to  the DDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We  derive  the  best-fit  linear  scaling  relation  between  log (𝑡dep/Gyr) and Δ (log 𝐿[CII]) for the H2 gas-rich galaxies in our  sample having 𝑓H2 >∼ 10%, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Δ(log 𝐿[CII]) = (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01) + (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='03) log  � 𝑡dep  Gyr  �  ,  (29)  which can be rewritten as  𝐿[CII]/𝐿⊙  SFR/(𝑀⊙ yr−1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='78 × 107  � 𝑡dep  Gyr  �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='71  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (30)  The coefficient of determination is 𝑅2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='936.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 The two regimes on the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram  The reasons for the H2 gas-rich galaxies ( 𝑓H2 >∼ 10%) showing a  linear sequence on the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram are threefolds:  i) Their 𝑓[CII] ¯𝑍gas ‘saturates’, meaning that it becomes almost like  a constant and hence 𝐿[CII]/SFR of the galaxies simply scales to  𝑡dep ¯𝑛gas, ii) their 𝑡dep and ¯𝑛gas anti-correlate with each other, and iii)  ¯𝜖[CII] has relatively small variation among different galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Let us at first understand the 𝑓[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 17,  10-1  100  101  55  60  65  70  75  80  85  90  95  100  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 1  z = 2  z = 3  z = 4  z = 0  z = 6  z = 8  LIR ≥ 1011 L⊙  LIR < 1011 L⊙  f[CII] ¯Zgas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02  f[CII] ¯Zgas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  1  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  fCII ¯Zgas ∝ ¯Zgas  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 32)  f[CII] ¯Zgas = const .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 34)  f[CII] ( % )  Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between ¯𝑍gas and 𝑓[CII] of the FIRE sampleat different  redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The large (small) symbols represent the galaxies having 𝐿IR ≥  1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The black dotted lines indicate the relation of  𝑓[CII] ¯𝑍gas = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5, 1, 2 and 4 (from left to right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At ¯𝑍gas <∼ 𝑍⊙, where  galaxies are H2 gas-poor, 𝑓[CII] ≈ 1 and 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' equation 32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At larger ¯𝑍gas, 𝑓[CII] scales roughly inversely with ¯𝑍gas and hence 𝑓[CII] ¯𝑍gas ≈  constant (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' equation 34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  we show the 𝑓[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas relation for the FIRE sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be  seen that at ¯𝑍gas <∼ 𝑍⊙, 𝑓[CII] barely declines from unity ( 𝑓[CII] ≈ 1)  with increasing ¯𝑍gas, whereas at higher ¯𝑍gas, 𝑓[CII] declines sharply  and 𝑓[CII] ¯𝑍gas becomes approximately a constant (‘saturates’) with  increasing ¯𝑍gas (or decreasing 𝑓[CII]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The shape of the 𝑓[CII] vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas relation of the FIRE galaxies can be  understood as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Consider a spherical gas cloud having a radius  𝑅cl and a surface-to-centre column density 𝑁cl (= 𝑛H𝑅cl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' When the  cloud is metal and dust-poor (having very low 𝑍gas and 𝛿dgr), the  LW photons from the radiation field can penetrate the entire cloud  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑙F > 𝑅cl) and dissociate all the molecular hydrogen (H2) and  neutral carbon (CI and CO) in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In such a low-metallicity  (or 𝛿dgr) regime, we have  𝑓[CII], cl ≈ 1  (31)  and  𝑓[CII], cl 𝑍gas ∝ 𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (32)  Since 𝑁F ∝ 𝑙F ∝ 𝛿−1  dgr ∝ 𝑍−1  gas (equation 10 and 11), indicating  stronger dust absorption of UV photons with increasing gas metal-  licity, 𝑙F decreases with 𝑍gas and will become equal or less than 𝑅cl  when 𝑍gas becomes sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Through simple mathematics,  it can be derived that for a spherical geometry, 𝑓[CII]𝑍gas increases  sub-linearly with 𝑍gas until when 𝑙F ≪ 𝑅cl, we have  𝑓[CII], cl ∝ 𝑁F  𝑁cl  ∝ (𝑍gas𝑁cl)−1  (33)  or  𝑓[CII], cl 𝑍gas = constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (34)  It is not surprising to find similar scaling relations with the FIRE  galaxies, 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas at low ¯𝑍gas and 𝑓[CII] ¯𝑍gas ≈ const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' at  MNRAS 000, 1–42 (2022)  30  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-1  100  101  102  10-2  10-1  100  101  10-1  100  101  102  106  107  108  109  1010  FIRE galaxies  LIR ≥ 1011 L⊙  LIR < 1011 L⊙  z = 1  z = 2  z = 3  z = 4  z = 0  z = 6  z = 8  LIR ≥ 1011 L⊙  LIR < 1011 L⊙  Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between ¯𝑛gas and 𝑡dep of the FIRE sample at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The data points in the left (right) panel are colour-coded by the redshift  ( 𝑓H2) of the galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Large (small) symbols represent the galaxies having 𝐿IR ≥ 1011 𝐿⊙ (𝐿IR < 1011 𝐿⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The FIRE galaxies show a clear anti-correlation  between 𝑡dep and ¯𝑛gas, in particular, the H2 gas-rich galaxies in the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  high ¯𝑍gas (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 17), given that the ISM of the galaxies  can be viewed as being made up of numerous such idealized gas  ‘clouds’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ‘saturation’ of 𝑓[CII] ¯𝑍gas at high ¯𝑍gas indicates that  the [CII] cooling rate of the galaxies does not increase much with  gas metallicity due to the shrinking of the size of the [CII]-emitting  region (Zone I + Zone II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Another important reason for the H2 gas-rich galaxies showing  a clear sequence on the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram is that their  𝑡dep and ¯𝑛gas have clear anti-correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 18, we show the  𝑡dep vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑛gas relation of the FIRE sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This anti-correlation is due  to the fact that the local free-fall timescale of star-forming clouds  decreases with gas density (𝑡ff ∝ 𝜌−1/2), and hence gas is converted  into stars more rapidly in the galaxies having denser ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It also  accounts for the sub-linearity (power law index 𝑛 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='71) of the  𝐿[CII]/SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep scaling relation of the H2 gas-rich galaxies on  the DDS (equation 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For the H2 gas-poor galaxies, the fact that they lie below the DDS  on the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 16) is because of their  low gas metallicity (and hence low 𝑓[CII] ¯𝑍gas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From equation (27),  we see that at fixed 𝐿[CII]/SFR (equivalently, at fixed Δ log 𝐿[CII]),  their 𝑡dep has to be higher than that of the galaxies on the DDS so  as to compensate for their having lower 𝑓[CII] ¯𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Besides, the fact  that the H2 gas-poor galaxies show a larger scatter of 𝑡dep at given  Δ(log 𝐿[CII]) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 16) than the H2 gas-rich galaxies is due to the  non-trivial scatter of 𝑓[CII] ¯𝑍gas among these galaxies, as opposed to  𝑓[CII] ¯𝑍gas being like a constant for the H2 gas-rich galaxies (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3 The physical origins of [CII] deficit of galaxies (a revisit)  The important consequence of 𝑓[CII] ¯𝑍gas being ‘saturated’ for the  H2 gas-rich galaxies is that the overall 𝐿[CII]/SFR ratio of the galax-  ies shows a tight and steep dependence on 𝑡dep (equation 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a  result, 𝑡dep becomes the dominating parameter that determines the  𝐿[CII]/SFR ratio of these galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Their 𝐿[CII]/SFR, in contrast,  does not shows a clear correlation with any of the other four param-  eters ( 𝑓[CII], ¯𝑍gas, ¯𝑛gas or ¯𝜖[CII]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Now we should be able to understand the fundamental reason for  𝑡dep being the main driver of the [CII] deficit at high 𝐿IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The IR-  luminous galaxies are H2 gas-rich (due both to their being dust-rich  and having high gas column density).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, they are in the regime  where the 𝐿[CII]/SFR ratio of galaxies is determined primarily by  𝑡dep (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' they lie on the DDS in the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram)  and their [CII] deficit is due to their low 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Besides, we can now understand the redshift evolution of the  𝐿[CII]/SFR ratio of the FIRE sample at 𝑧 = 0 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At these low  redshifts, our sample includes more galaxies that are H2 gas-rich  as a result of their being more metal and dust-rich than the galax-  ies at higher redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII]/SFR ratio of these low-𝑧 galaxies  therefore depends more sensitively on 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  At higher redshifts, in contrast, our sample includes a large fraction  of metal and dust-poor galaxies that are also H2 gas-poor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' They  are off the DDS in the Δ (log 𝐿[CII]) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑡dep diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For these  galaxies, 𝑓[CII] ¯𝑍gas ≈ ¯𝑍gas (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 17) and hence 𝐿[CII]/SFR of the  galaxies depends more sensitively on ¯𝑍gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a result, gas metallicity  becomes the main driver of the [CII] deficit of the high-𝑧 galaxies in  our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  6 DISCUSSIONS  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 The effect of mass resolution  The fact that the ISM is treated as an aggregate of spherical gas  ‘clouds’ in our model (and in those of the previous studies like  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vallini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Narayanan &  Krumholz 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021) is certainly an idealization  — the ISM in real galaxies is a continuous medium, and has com-  plex spatial configurations at and below the scale of these idealized  ‘clouds’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Nonetheless, such treatment offers a (crude) sampling of  MNRAS 000, 1–42 (2022)  30  10  20  10  (Gyr)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0  tdep  10  10  101  10-1  100  ngas (cm-3)fH240CII emission as an indicator of galaxy SFR  31  the column density of gas in the ISM, enabling us to capture the  essential physics causing the [CII] deficit of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We note that the predicted [CII] luminosity of galaxies can depend  on the mass resolution of the simulations (mass of the ‘gas clouds’)  in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' To assess this dependency, we adopt two additional  models (‘HighRes’ and ‘LowRes’) in post-processing, where we in-  crease and decrease the mass of each individual ‘cloud’ by a factor of  23 = 8 (equivalent to increasing and reducing the surface-to-centre  column density by a factor of 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the HighRes model, we simply  split each ‘cloud’ in the fiducial model into 8 with equal mass, and  assume that the 8 HighRes ‘clouds’ have the same density and metal-  licity and are exposed to the same radiation field as the parent ‘cloud’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  For the LowRes model, we calculate the luminosity of each ‘cloud’  assuming as if the ‘cloud’ is 8 times more massive than it is in the  fiducial model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The total [CII] luminosity of galaxy is calculated by  summing the luminosity of each massive ‘cloud’ and then dividing  the sum by 8 (equivalent to having 8 times lower number of ‘clouds’,  each being 8 times more massive than that in the fiducial model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The predicted [CII] luminosity of the HighRes (LowRes) model  appears to be higher (lower) than that of our fiducial model by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13  dex on average (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because with decreasing (in-  creasing) gas column density, a higher (lower) fraction of the gas  becomes in the [CII]-emitting phase (Zone I + Zone II) and besides,  an increased (reduced) fraction of the [CII]-emitting gas becomes in  the HII phase (note: HII gas has on average higher [CII] emissivity  than HI gas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Overall, by changing the mass resolution by about a  decade results in a difference in the predicted [CII] luminosity of  the galaxies by <∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The difference does not show a strong  dependence on redshift or SFR of the galaxies (see the lower panel  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Comparing to the observations, it is clear that the 𝐿[CII]-SFR  relation of the FIRE galaxies at 𝑧 = 0 predicted by the HighRes model  becomes systematically offset from the data of L14 and H15 (see the  upper panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 19), indicating a too low mean gas column density  of the galaxies in the HighRes model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII]-SFR relation of the  LowRes model is below that of the fiducial model, but still appears  to be within the scatter of the L14 and H15 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The LowRes model  predicts a slightly stronger (by ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13 dex) [CII] deficit of galaxies  at high redshifts than the fiducial model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Nonetheless, our conclusions regarding the causes of [CII] deficit  of galaxies at high 𝐿IR (low 𝑡dep) and at high redshifts (low gas  metallicity) does not change with the chosen mass resolution of  the [CII] model, despite that the predicted 𝐿[CII] of galaxies shows  moderate dependence on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 Comparison with the previous studies  Here we discuss the relation between the findings of the previous  studies to this from this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Specifically, we will discuss the con-  clusions regarding the origin of the [CII] deficit at high 𝐿IR in Sec-  tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1, whereas in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2, we will compare the predictions of  the 𝐿[CII]- SFR relation of galaxies at redshift 𝑧 >∼ 5 from the recent  studies with ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 The [CII] deficit at high 𝐿IR  [CII] deficit due to a strong ISRF  A number of studies suggest that the observed [CII] deficit at high  𝐿IR is due to a strong ISRF in IR-luminous galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can lead  to large positive grain charge and thus inefficient heating of gas via  photo-electric processes in the neutral galactic medium (Tielens &  HighRes  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  Local observations  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  LowRes  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  Local observations  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014 (dwarf)  10-1  100  101  102  103  104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5  1  2  3  4  5  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  L[CII], HighRes  L[CII], fiducial  Unfilled  Filled symbols:  L[CII], LowRes  L[CII], fiducial  Unfilled symbols:  Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The effect of mass resolution on the predicted [CII] luminosity  of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The upper (middle) panel shows the 𝐿[CII]-SFR relation of the  FIRE sample at 𝑧 = 0 − 8 predicted by the HighRes (LowRes) model (see  Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we also show in the two panels the  observed 𝐿[CII]-SFR relation of local galaxies by L11, L14 and H15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the  lower panel, we explicitly show the difference between the [CII] luminosity  predicted by the HighRes (unfilled symbols) and LowRes (filled symbols)  models and that predicted by the fiducial model as a function of galaxy SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The shaded grey area indicates a factor of two difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  10  L(CI) (Lo)  10  106  100  101  102  103  10  10-  SFR(Mo yr-1410  108  10  106  10-1  101  102  103  100  10  SFR(Mo yr-1432  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Hollenbach 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kaufman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Consequently, the rate of  gas cooling via [CII] line drops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Apart from that, a strong ISRF  (and hence high 𝑈) may also lead to “dust-bounded" HII regions  near the newly formed young stars (Bottorff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2009), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑁s ≈ 𝑁F (note: 𝑁s increases about linearly with 𝑈 until  𝑁s ≈ 𝑁F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this case, gas cooling via [CII] can become inefficient  due to a lack of CII ions in the HII regions — a significant fraction of  carbon can be ionized further to CIII ions when 𝑈 is large (In Zone I,  𝑥(1)  CII ≈ 1 − 𝑥(1)  CIII ∝ 𝑈−1, see Appendix E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Overall, both mechanisms  can lead to a reduced ¯𝜖[CII] in galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Looking at the FIRE sample, we notice that the few massive star-  burst galaxies (SFR>∼100 𝑀⊙ yr−1) in our sample do show noticeably  lower ¯𝜖[CII] than the normal star-forming galaxies having lower SFR  (see the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 13 and the bottom right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 15),  which can be associated with a strong ISRF (and high 𝑈) in these  galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that CLOUDY (version 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01) takes into account grain  charging physics (Baldwin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' van Hoof et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Abel  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2005) and our approach of performing dust RT calculation with  SKIRT provides an improved estimate of the ISRF (and hence 𝑈)  distribution in galaxies than the previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Our result suggests  that the [CII] deficit at high 𝐿IR may in part be driven by a strong  ISRF in the massive starburst galaxies, and yet its impact does not  seem to be as prominent as 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  [CII] deficit due to high gas density  It has also been suggested that the [CII] deficit in IR-luminous galax-  ies can be driven by the high density of the star-forming gas in  these galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Narayanan & Krumholz 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' With increasing  density, ISM gas becomes more shielded from ionizing radiation of  massive young stars and more carbon in the ISM gas becomes neutral  (in CO or CI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] deficit is thus due to a lack of CII ions in  the ISM gas in this scenario (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' due to a low 𝑓[CII]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  This, however, does not seem to be exactly like what we find  with the FIRE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ISM of the FIRE galaxies spans a  very wide range of density (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 11), and even for the most  massive starburst galaxies in our sample, a large fraction of their  [CII] luminosity originates from the gas having intermediate density  (¯𝑛gas ≈ ¯𝑛HI, MW, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Overall, the luminosity-weighted gas  density (¯𝑛gas) of the IR-luminous galaxies (𝐿IR ≥ 1011 𝐿⊙) is not  significantly higher than that of the IR-fainter galaxies in our sample  at any given redshift (see Table 8), and the difference is not as strong  as that in 𝑡dep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hence, the [CII] deficit of the IR-luminous galaxies  in FIRE simulations doe not appear to be mainly due to their having  too dense ISM gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 The 𝐿[CII]-SFR relation at redshift 𝑧 >∼ 5  As mentioned in the Introduction, several planned ground-based  [CII] line intensity mapping (LIM) experiments will target the emit-  ting sources at redshift 𝑧 >∼ 5 (Kovetz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017), including CCAT-  prime, CONCERTO and TIME.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Predicting the 𝐿[CII]-SFR relation of  galaxies at this early epoch has thus become extremely important for  interpreting the upcoming data of these experiments (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Vis-  bal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Fonseca et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Padmanabhan 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yue & Ferrara 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Chung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Padmanabhan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Murmu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 20, we present the results from a number of recent studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  These include the ones using SAMs (Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2021) as well as those using hydrodynamic simulations (Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It can be seen that different studies have generally predicted a clear  Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015  De Looze et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011  Local observations  FIRE galaxies  z = 4  z = 6  z = 8  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021 (  )  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 < z < 6  Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022 (  )  6 < z < 10  Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020 (  )  z = 6  Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018 (  )  z ≈ 6  Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018 (  )  z ≈ 8  Pallottini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019 (  )  z = 8  Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2017 (  )  z = 6  Other predictions for early galaxies  Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The 𝐿[CII]-SFR relation at 𝑧 >∼ 5 predicted by different simulation  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Red, yellow, blue and cyan lines indicate the mean result of Yang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021) (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 < 𝑧 < 6), Leung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2020) (𝑧 = 6), Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018)  (dashed blue line for 𝑧 ≈ 6 and dotted blue line for 𝑧 ≈ 8), and Kannan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2022) (6 < 𝑧 < 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' These studies use statistically significant samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The corresponding coloured shaded areas represent the 1𝜎 dispersion of the  data around the mean relation of each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In addition, we also show the  data of individual galaxies of the Olsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2017) (𝑧 = 6) and Pallottini  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019) (𝑧 = 8) samples by grey diamonds and grey downward triangles,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For reference, we show the observed 𝐿[CII]-SFR relation of the  local star-forming samples of H15 (solid orange line) and L11 (solid green  line) as well as the the data of the FIRE sample at 𝑧 = 4 (magenta circles),  𝑧 = 6 (green diamonds) and 𝑧 = 8 (purple downward triangles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A [CII]  deficit at 𝑧 >∼ 5 is generally predicted by various simulation groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  [CII] deficit at 𝑧 >∼ 5 with respect to the local samples of L11 and  H15, similar to this work using the FIRE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Some have also  predicted a mild trend of growing deficit with increasing redshift  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The predicted 1𝜎  scatter of the 𝐿[CII]-SFR relation at a given redshift of these studies  is typically as large as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 dex (except Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022, which  shows noticeably smaller scatter than the others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  There is, however, a clear difference in the normalization and  slope of the 𝐿[CII]-SFR relation predicted by the different groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In particular, Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2021) (Kannan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022) produce the  highest (lowest) normalization among all different groups at SFR ≈  1 − 100 𝑀⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Note that both also produce a considerably steeper  power-law slope (≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5) than the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Interestingly, our prediction  with the FIRE galaxies appears to be in good agreement with the  result of Lagache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2018) (in both normalization and slope).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The difference in the 𝐿[CII]-SFR relation indicates that the pre-  dicted ISM properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas, 𝑡dep) of the galaxies at 𝑧 >∼ 5 are  not well converged between the current simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We highlight  that the data of the upcoming LIM experiments may provide useful  constraints on the ISM properties of the galaxies in this early epoch,  given that direct measurement of these properties is very challenging  using the current techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  1010  二  L(CI (Lo)  108  10°  V  106  11  105  101  10-1  100  102  103  10  SFR(M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' yr-1)4CII emission as an indicator of galaxy SFR  33  7 SUMMARY AND CONCLUSIONS  The 158 𝜇m fine structure line of singly ionized carbon ([CII])  has been considered as a SFR indicator since observations of  nearby star-forming galaxies found a linear correlation between their  𝐿[CII] and SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' There is, however, evidence showing that IR-bright  (𝐿IR >∼ 1011 𝐿⊙), starburst galaxies as well as early galaxies at 𝑧 >∼ 5  have reduced 𝐿[CII]/SFR with respect to the local star-forming sam-  ples (so-called ‘[CII] deficit’ problem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Different models have been  posited to explain the origin of the [CII] deficit of galaxies at high  𝐿IR or at high redshifts and yet no consensus has been reached at  both regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In this work, we present a comprehensive analysis on the 𝐿[CII]-  SFR relation of galaxies using a galaxy sample at 𝑧 = 0 − 8  (𝑀∗ = 107 − 5 × 1011 𝑀⊙) extracted from the cosmological hy-  drodynamic simulations, which are part of the FIRE project (Hop-  kins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2014, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), coupled with CLOUDY  (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1998, 2017) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sample consists mainly of  galaxies (𝑁gal ∼ 500) from FIREbox (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2022), a high-  resolution cosmological-volume hydrodynamic simulation run with  FIRE-2 physics, and is supplemented with a few dozen of high-𝑧  massive galaxies from the cosmological ‘zoom-in’ simulations of the  MassiveFIRE suite (Feldmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2016, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Anglés-Alcázar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The sample covers an unprecedentedly broad dynamic range  among all studies on [CII], including normal star-forming galaxies,  (U)LIRG and SMG candidates as well as UV-bright galaxies at EoR,  which can be used to study the full range of the observational data  on [CII] currently available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The predicted 𝐿[CII]-SFR relation of the FIRE sample agrees well  with the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In particular, we successfully reproduce  the observed linear correlation of the local star-forming samples over  the SFR range ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1−10 𝑀⊙ yr−1 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 4 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Apart from that,  we also reproduce the sharp decline of 𝐿[CII]/SFR with 𝐿IR (∼ SFR)  at 𝐿IR >∼ 1011 𝐿⊙ at low and high redshifts, which is consistent with  the data of the (U)LIRGs and SMGs in this 𝐿IR regime (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 7 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Our sample shows a general decline of 𝐿[CII]/SFR with redshift, in  particular, at low SFR (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The mean 𝐿[CII]/SFR ratio of the early  EoR galaxies at 𝑧 > 5 in our sample is about one order of magnitude  below the local galaxies, showing a clear [CII] deficit, similar to what  has been previously found with other simulations (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Observations of galaxies at EoR have drawn divergent conclusions  on their 𝐿[CII]-SFR relation, which is largely due to the uncertainty  in the dust SED shape (or ‘dust temperature’) of the galaxies at  these high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We analyze the sub-mm data of all the observed  EoR galaxies and derive their dust-obscured SFR using the ‘dust  temperature’ estimated from the SED templates of the FIRE samples  self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We conclude that the 𝐿[CII]-SFR relation of the  FIRE galaxies at 𝑧 > 5 is in no conflict with the current observational  constraints, including those placed by the recent ALPINE and REBELS  surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The 𝐿[CII]/SFR ratio of the FIRE sample roughly follows a simple  linear scaling relationship (equation 27)  𝐿[CII]  SFR ∝ 𝑓[CII] ¯𝑍gas𝑡dep ¯𝑛gas,  where 𝑓[CII] is the mass fraction of ionized or neutral atomic hydro-  gen gas in the ISM, 𝑡dep is the gas depletion time (= 𝑀gas/SFR), and  ¯𝑍gas and ¯𝑛gas indicate the gas metallicity and gas density that are  weighted by [CII] luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Following this scaling relationship,  we find that the key driver of the [CII] deficit is different at high  𝐿IR and high redshifts (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At high 𝐿IR, the [CII] deficit is  mainly due to the low 𝑡dep of galaxies, indicating that IR-luminous,  starburst galaxies have less amount of gas that is able to produce  [CII] emission per unit SFR than the normal star-forming galaxies  with moderate SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII] deficit at 𝑧 >∼ 5, in contrast, is mainly  driven by the low gas metallicity of galaxies at this epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The underlying reason for [CII] deficit being driven by different  physical parameters at high 𝐿IR and high redshifts is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In the low-metallicity regime (corresponding to high-𝑧 galaxies),  𝐿[CII] of galaxies depends sensitively on metallicity because line  emissivity scales linearly with metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the high-metallicity  regime (corresponding to low-𝑧, massive and starburst galaxies),  however, such dependence can become weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This is because dust-  to-gas ratio (𝛿dgr) in the ISM increases with metallicity, which leads  to the shrinking of the size of [CII]-emitting region (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The shrinking of its size almost cancels out the effect of increasing  emissivity with metallicity (in this case, 𝑓[CII] ¯𝑍gas ≈ constant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a  result, 𝐿[CII]/SFR of galaxies does not depend much on metallicity  — but instead, on 𝑡dep = 𝑀gas/SFR, see equation (30) — for massive,  metal (dust) and H2 gas-rich starburst galaxies at low redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Our study shows that [CII] deficit may be a common phenomenon  of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This would be particularly important for interpreting the  observational data from several major upcoming [CII] line intensity  mapping experiments, such as EXCLAIM (Ade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020), TIME (Sun  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021), CCAT-prime (CCAT-Prime collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2021) and  CONCERTO (CONCERTO Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Gkogkou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Our result suggests that by using a constant linear 𝐿[CII]-SFR  relation derived using nearby star-forming galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' De Looze  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2011, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Herrera-Camus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2015) may lead to systematic  overestimate of the cosmic star formation rate density of the high-𝑧  Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  LL acknowledges financial support from the Swiss National Science  Foundation (hereafter SNSF) (grant no P2ZHP2_199729) and the  University of Toronto Faculty of Arts and Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' RF acknowl-  edges financial support from the SNSF (grant no PP00P2_194814,  200021_188552).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' DN acknowledges funding from the NSF via AST-  1909153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' DAA acknowledges support by NSF grants AST-2009687  and AST-2108944, CXO grant TM2-23006X, and Simons Founda-  tion award CCA-1018464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' CAFG was supported by NSF through  grants AST-1715216, AST-2108230, and CAREER award AST-  1652522;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' by NASA through grants 17-ATP17-0067 and 21-ATP21-  0036;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' by STScI through grants HST-AR-16124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='001-A and HST-  GO-16730.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='016-A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' by CXO through grant TM2-23005X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' and by the  Research Corporation for Science Advancement through a Cottrell  Scholar Award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' LB acknowledge financial support from the SNSF  (grant no PP00P2_194814).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The Flatiron Institute is supported by  the Simons Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  We acknowledge PRACE for awarding us access to MareNostrum  at the Barcelona Supercomputing Center (BSC), Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This research  was partly carried out via the Frontera computing project at the Texas  Advanced Computing Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Frontera is made possible by National  Science Foundation award OAC-1818253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This work was supported  in part by a grant from the Swiss National Supercomputing Centre  (CSCS) under project IDs s697 and s698.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' We acknowledge access to  Piz Daint at the Swiss National Supercomputing Centre, Switzerland  under the University of Zurich’s share with the project ID uzh18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  This work made use of infrastructure services provided by S3IT  (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='s3it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='uzh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='ch), the Service and Support for Science IT  team at the University of Zurich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  34  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  DATA AVAILABILITY STATEMENT  The data underlying this article will be shared on reasonable request  to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  REFERENCES  Abel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shaw G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', van Hoof P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2005, ApJS, 161, 65  Abel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', van Hoof P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shaw G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Elwert T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2008, ApJ,  686, 1125  Abel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dudley C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fischer J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Satyapal S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', van Hoof P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, ApJ,  701, 1147  Ade P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, Journal of Low Temperature Physics, 199, 1027  Andika I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 903, 34  Anglés-Alcázar D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feld-  mann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Torrey P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wetzel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 472, L109  Aravena M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 833, 68  Asplund M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Grevesse N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sauval A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Scott P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, ARA&A, 47, 481  Baes M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Camps P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, Astronomy and Computing, 12, 33  Baes M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Verstappen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Looze I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fritz J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Saftly W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pérez E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stalevski  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Valcke S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJS, 196, 22  Bakx T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 493, 4294  Baldwin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Martin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Corbin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cota S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Peterson  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Slettebak A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1991, ApJ, 374, 580  Bañados E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Farina E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fan X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015,  ApJ, 805, L8  Bañados E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJS, 227, 11  Barisic I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 845, 41  Bassini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gensior J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cenci E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Liang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bernardini M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08423  Behrens C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS,  477, 552  Bernal J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kovetz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, A&AR, 30  Béthermin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, A&A, 643, A2  Bisbas T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 934, 115  Bischetti M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, A&A, 617, A82  Blain A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, MNRAS, 304, 669  Boselli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gavazzi G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lequeux J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pierini D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2002, A&A, 385, 454  Bottorff M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', LaMothe J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Momjian E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Verner E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vinković D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  1998, PASP, 110, 1040  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Illingworth G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Franx M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ford H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2007, ApJ, 670, 928  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJ, 737, 90  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 803, 34  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 833, 72  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stefanon M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Illingworth G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nanayakkara T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Roberts-Borsani G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Labbé I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Smit R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 880, 25  Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 931, 160  Bowler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bourne N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dunlop J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McLure R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McLeod D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018,  MNRAS, 481, 1631  Bowler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Jarvis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dunlop J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McLure R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McLeod D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Adams N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Milvang-Jensen B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McCracken H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 493,  2059  Bradač M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 836, L2  Brauher J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dale D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Helou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2008, ApJS, 178, 280  Breuck C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, A&A, 565, A59  Brisbin D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferkinhoff C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nikola T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Parshley S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stacey G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Spoon H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Hailey-Dunsheath S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Verma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 799, 13  Burgarella D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, A&A, 554, A70  CCAT-Prime collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10364  CONCERTO Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, A&A, 642, A60  Calzetti D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2007, ApJ, 666, 870  Camps P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Baes M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, Astronomy and Computing, 9, 20  Camps P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trayford J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Baes M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Theuns T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaller M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaye J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016,  MNRAS, 462, 1057  Camps P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJS, 234, 20  Cañameras R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, A&A, 620, A61  Capak P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, Nature, 522, 455  Carilli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ARA&A, 51, 105  Carlstrom J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, PASP, 123, 568  Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, A&A, 605, A42  Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018a, MNRAS, 478, 1170  Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Smit R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Amorín R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018b, ApJ, 854, L7  Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 499, 5136  Casey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, MNRAS, 425, 3094  Casey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, Physics Reports, 541, 45  Casey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018a, ApJ, 862, 77  Casey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hodge J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zavala J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Spilker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', da Cunha E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Staguhn J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Finkelstein S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Drew P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018b, ApJ, 862, 78  Çatmabacak O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Anglés-Alcázar D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 511, 506  Chung D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Viero M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Church S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wechsler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 892, 51  Cochrane R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 488, 1779  Cochrane R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Anglés-Alcázar D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 939, L27  Contursi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, A&A, 606, A86  Cooke E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 861, 100  Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 790, 40  Cormier D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, A&A, 578, A53  Cox P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJ, 740, 63  Crites A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, Millimeter, Submillimeter, and Far-Infrared Detec-  tors and Instrumentation for Astronomy VII  Curti M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12375  Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Thompson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 462, 3265  Dayal P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, Physics Reports, 780-782, 1  De Looze I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Baes M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bendo G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cortese L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fritz J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, MNRAS, 416,  2712  De Looze I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, A&A, 568, A62  Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, Nature, 545, 457  Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 854, 97  Dey A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2008, ApJ, 677, 943  Díaz-Santos T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 774, 68  Díaz-Santos T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 816, L6  Díaz-Santos T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 846, 32  Dole H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2006, A&A, 451, 417  Donnan C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12356  Draine B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Salpeter E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1979, ApJ, 231, 438  Draine B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2007, ApJ, 663, 866  Dullemond C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Juhasz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pohl A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sereshti F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shetty R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Peters T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Com-  mercon B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Flock M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, RADMC-3D: A multi-purpose radiative  transfer tool, Astrophysics Source Code Library, record ascl:1202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='015  (ascl:1202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='015)  Dunne L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Eales S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Edmunds M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ivison R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Alexander P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Clements D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2000, MNRAS, 315, 115  Dwek E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, ApJ, 501, 643  Eilers A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 900, 37  Eisenhardt P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 755, 173  Elbaz D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, A&A, 533, A119  Ellis R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 763, L7  Faisst A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 847, 21  Faisst A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020a, ApJS, 247, 61  Faisst A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fudamoto Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Scoville N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Riechers D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pavesi  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Capak P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020b, MNRAS, 498, 4192  Fan X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 870, L11  Farrah D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 776, 38  Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lidz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zaldarriaga M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, ApJ,  703, 1416  Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS: Letters, 470, L59  Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, Communications Physics, 3  Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2016, MNRAS:Letters, 458, L14  Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2017, MNRAS, 470, 1050  Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15325  Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Peterson B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Horne K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Welsh W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nahar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1992, ApJ,  387, 95  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  35  Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Korista K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Verner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferguson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kingdon J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Verner E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, PASP, 110, 761  Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Mex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Astrofis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 49, 137  Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Mex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Astrofis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 53, 385  Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kohandel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Decataldo D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Behrens C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 489, 1  Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='07666  Finkelstein S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, Nature, 502, 524  Finkelstein S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 810, 71  Fixsen D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dwek E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mather J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bennett C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shafer R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, ApJ,  508, 123  Fonseca J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Silva M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Santos M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 464, 1948  Fudamoto Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, Nature, 597, 489  Fudamoto Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 934, 144  Fujimoto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ouchi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ono Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shibuya T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ishigaki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nagai H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Momose  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJS, 222, 1  Fujimoto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 887, 107  Fujimoto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 900, 1  Fujimoto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 911, 99  Fujimoto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06863  Geach J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 832, 37  Genzel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cesarsky C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2000, ARA&A, 38, 761  Genzel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 800, 20  Gill S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Knebe A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gibson B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2004, MNRAS, 351, 399  Gilmore G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wyse R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kuijken K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1989, ARA&A, 27, 555  Ginolfi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, A&A, 633, A90  Gkogkou A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02235  Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Langer W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pineda J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Velusamy T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJS, 203,  13  Gong Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Silva M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Santos M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bock J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bradford C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zemcov  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 745, 49  Graciá-Carpio J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJ, 728, L7  Griffin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, A&A, 518, L3  Gruppioni C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, MNRAS, 432, 23  Guilloteau S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1992, A&A, 262, 624  Gullberg B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, MNRAS, 449, 2883  Gullberg B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 859, 12  Habing H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1968, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Netherlands, 19, 421  Hahn O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Abel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, MNRAS, 415, 2101  Hailey-Dunsheath S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, PhD thesis, Cornell University, United States  Hao C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kennicutt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Johnson B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Calzetti D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dale D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Moustakas  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJ, 741, 124  Harikane Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 896, 93  Harikane Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='01612  Harrington K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 908, 95  Hashimoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, Nature, 557, 392  Hashimoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019a, PASJ, 71  Hashimoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019b, MNRAS, 488, 5029  Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Jonsson P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cox T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2011, ApJ, 743, 159  Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, MNRAS, 445, 1598  Heintz K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022a, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02890  Heintz K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022b, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='06877  Helou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Malhotra S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dale D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Contursi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2001, ApJ,  548, L73  Herrera-Camus R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 800, 1  Herrera-Camus R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 861, 95  Heyminck S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kasemann C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Güsten R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', de Lange G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Graf U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2006, A&A,  454, L21  Hezaveh Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Marrone D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Holder G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 761, 20  Hezaveh Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 767, 132  Hildebrand R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1983, QJRAS, 24, 267  Ho P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Moran J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lo K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2004, ApJ, 616, L1  Hodge J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', da Cunha E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, Royal Society Open Science, 7, 200556  Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Tielens A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, Reviews of Modern Physics,  71, 173  Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Takahashi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Tielens A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1991, ApJ, 377, 192  Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oñorbe J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Murray N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bullock J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, MNRAS, 445, 581  Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS, 480, 800  Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='00040  Hopwood R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, ApJ, 728, L4  Hu E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cowie L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McMahon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Capak P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Iwamuro F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kneib J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Maihara T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Motohara K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2002, ApJ, 568, L75  Hughes T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, A&A, 602, A49  Indriolo N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McCall B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 745, 91  Indriolo N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Geballe T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oka T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McCall B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2007, ApJ, 671, 1736  Inoue A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, Science, 352, 1559  Iono D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2006, ApJ, 645, L97  Ivison R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, A&A, 518, L35  Izumi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, PASJ, 70  Izumi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, PASJ, 71  Izumi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021a, ApJ, 908, 235  Izumi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021b, ApJ, 914, 36  Jones T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Swinbank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ellis R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Richard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stark D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010,  MNRAS  Kanekar N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wagg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Chary R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carilli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 771, L20  Kannan R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Smith A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Garaldi E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shen X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pakmor R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 514, 3857  Katz H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kimm T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sijacki D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Haehnelt M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 468, 4831  Katz H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 487, 5902  Kaufman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wolfire M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Luhman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, ApJ,  527, 795  Kawamata R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oguri M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ishigaki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Shimasaku K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ouchi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ,  819, 114  Kennicutt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, ApJ, 498, 541  Kennicutt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, PASP, 123, 1347  Kessler M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1996, A&A, 500, 493  Khusanova Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, A&A, 649, A152  Kirkpatrick A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sajina A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Roebuck E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Yan L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Armus L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Díaz-  Santos T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stierwalt S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 814, 9  Knollmann S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Knebe A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, ApJS, 182, 608  Knudsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Richard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kneib J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Jauzac M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Clément B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Drouart G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Egami E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lindroos L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 462, L6  Knudsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Watson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Frayer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Christensen L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallazzi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Michałowski M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Richard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zavala J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 466, 138  Kohandel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zanella A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Behrens C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 487, 3007  Kovetz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09066  Kovetz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, BAAS, 51, 101  Kroupa P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2002, Science, 295, 82  Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, MNRAS, 437, 1662  Lagache G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cousin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Chatzikos M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, A&A, 609, A130  Laporte N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 837, L21  Laporte N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 487, L81  Le Fèvre O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, A&A, 643, A1  Leech K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, MNRAS, 310, 317  Leethochawalit N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Roberts-Borsani G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Morishita T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trenti M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Treu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2022a, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15388  Leethochawalit N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022b, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11135  Lehar J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2000, ApJ, 536, 584  Leipski C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 772, 103  Leipski C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 785, 154  Leitherer C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Heckman T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1995, ApJS, 96, 9  Leitherer C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, ApJS, 123, 3  Leroy A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Brinks E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bigiel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', de Blok W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Madore B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Thornley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2008, ApJ, 136, 2782  Leung T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Olsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Greve T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 905, 102  Li Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davè R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 869, 73  Li Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 490, 1425  Liang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Scoville N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS:Letters, 478,  L83  Liang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 489, 1397  MNRAS 000, 1–42 (2022)  36  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Liang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Çatmabacak O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, MNRAS, 502, 3210  Lu N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 864, 38  Luhman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, ApJ, 504, L11  Luhman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Satyapal S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fischer J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wolfire M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sturm E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dudley C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Lutz D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Genzel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2003, ApJ, 594, 758  Lupi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bovino S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 492, 2818  Lupi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bovino S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020,  MNRAS, 496, 5160  Ma X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zolman N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Muratov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 456, 2140  Ma X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 487, 1844  Madau P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dickinson M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ARA&A, 52, 415  Madden S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, PASP, 125, 600  Magdis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 796, 63  Magnelli B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Elbaz D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Chary R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dickinson M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Borgne D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Frayer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Willmer C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, A&A, 496, 57  Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2005, A&A, 440, L51  Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Caselli P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nagao T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walmsley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Breuck C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Meneghetti  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, A&A, 500, L1  Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, MNRAS, 452, 54  Malhotra S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1997, ApJ, 491, L27  Malhotra S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2001, ApJ, 561, 766  Marrone D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, Nature, 553, 51  Matthee J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 851, 145  Matthee J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 881, 124  Mazzucchelli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 849, 91  McKinney J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Armus L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Chary R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Díaz-Santos T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dickinson  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kirkpatrick A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 892, 119  McKinney J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Rosenthal L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Martínez-Galarza J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pope  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sajina A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Smith H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 921, 55  McKinnon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Torrey P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 457, 3775  McLeod D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McLure R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dunlop J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Robertson B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ellis R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Targett  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, MNRAS, 450, 3032  McLure R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, MNRAS, 432, 2696  Meyer R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 927, 152  Miettinen O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, A&A, 606, A17  Molyneux S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 512, 535  Muñoz J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oh S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 463, 2085  Murmu C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2023, MNRAS, 518, 3074  Nahar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pradhan A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1997, ApJS, 111, 339  Naidu R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='09434  Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 467, 50  Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, Nature, 525, 496  Neri R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Downes D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cox P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, A&A, 562, A35  Neufeld D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wolfire M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 845, 163  Novak M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 904, 131  Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 745, 110  Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 819, 129  Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bouwens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Illingworth G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Labbé I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Stefanon M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018,  ApJ, 855, 105  Olsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Greve T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Thompson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Toft S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Brinch C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2015, ApJ, 814, 76  Olsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Greve T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Thompson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Rios L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Stawinski S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 846, 105  Olsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Greve T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Thompson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Rios L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Stawinski S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 857, 148  Ota K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 792, 34  Oteo I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 827, 34  Ouchi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 778, 102  Padmanabhan H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 488, 3014  Padmanabhan H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Breysse P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lidz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Switzer E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 515,  5813  Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bovino S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Salvadori S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 471, 4128  Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 487, 1689  Pentericci L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 829, L11  Pilbratt G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, A&A, 518, L1  Pillepich A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018a, MNRAS, 473, 4077  Pillepich A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018b, MNRAS, 475, 648  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, A&A, 594, A1  Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pérez-Beaupuits J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Spaans M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trager S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2014, MNRAS, 444, 1301  Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', van Kampen E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Spaans M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trager  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 461, 93  Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faisst A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2019, MNRAS, 482, 4906  Priddey R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McMahon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2001, MNRAS, 324, L17  Rawle T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 783, 59  Rémy-Ruyer A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, A&A, 563, A31  Rhoads J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13020  Richings A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaye J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oppenheimer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014a, MNRAS, 440, 3349  Richings A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaye J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oppenheimer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014b, MNRAS, 442, 2780  Richings A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gurvich A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaye J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 517, 1557  Riechers D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, Nature, 496, 329  Rigopoulou D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pereira-Santaella M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Magdis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Farrah D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Marques-Chaves R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Perez-Fournon I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Riechers D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS, 473,  20  Rojas-Ruiz S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 920, 150  Rybak M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 876, 112  Safarzadeh M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferguson H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ,  818, 62  Salim S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ARA&A, 58, 529  Sanders D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mazzarella J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kim D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Surace J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Soifer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2003,  AJ, 126, 1607  Sargsyan L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 755, 171  Schaerer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Boone F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zamojski M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Staguhn J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dessauges-Zavadsky M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Finkelstein S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Combes F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015a, A&A, 574, A19  Schaerer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015b, A&A, 576, L2  Schaerer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, A&A, 643, A3  Schaerer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Marques-Chaves R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Barrufet L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Oesch P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Izotov Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Naidu  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Guseva N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Brammer G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, A&A, 665, L4  Schouws S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022a, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='04080  Schouws S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022b, ApJ, 928, 31  Scoville N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, in Falcón-Barroso J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Knapen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', eds, Secular Evolu-  tion of Galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cambridge University Press, Cambridge, UK, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 491  Scoville N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 837, 150  Semenov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kravtsov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gnedin N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 845, 133  Serjeant S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, MNRAS, 424, 2429  Serra P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Doré O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lagache G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 833, 153  Shao Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 845, 138  Shao Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 876, 99  Shen X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nelson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Tacchella S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Springel  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Marinacci F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Torrey P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS, 510, 5560  Silva M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Santos M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gong Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 806, 209  Sklias P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, A&A, 561, A149  Smit R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, Nature, 553, 178  Sobral D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Matthee J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Darvish B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Schaerer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mobasher B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Röttgering H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Santos S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hemmati S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 808, 139  Sodroski T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Odegard N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Arendt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dwek E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Weiland J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hauser  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kelsall T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1997, ApJ, 480, 173  Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Davé R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ARA&A, 53, 51  Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Primack J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, MNRAS, 310, 1087  Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trager S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, MNRAS, 453, 4338  Sommovigo L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Decataldo  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 497, 956  Sommovigo L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zanella A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, MNRAS, 503, 4878  Sommovigo L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, MNRAS  Sparre M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Feldmann R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Faucher-Giguère C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Muratov  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Kereš D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 466, 88  Spilker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 826, 112  Spitzer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1998, Physical Processes in the Interstellar Medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Wi-  ley, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1002/9783527617722, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1002%  2F9783527617722  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  37  Stacey G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Geis N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Genzel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lugten J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Poglitsch A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sternberg A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Townes C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1991, ApJ, 373, 423  Stacey G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2007, in Baker A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Glenn J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Harris A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mangum J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Yun M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', eds, Astronomical Society of the Pacific Conference Series  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 375, From Z-Machines to ALMA: (Sub)Millimeter Spectroscopy of  Galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 52  Stacey G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hailey-Dunsheath S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferkinhoff C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Nikola T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Parshley S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Benford D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Staguhn J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Fiolet N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, ApJ, 724, 957  Sternberg A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Le Petit F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Roueff E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Le Bourlot J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, ApJ, 790, 10  Suginohara M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Suginohara T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Spergel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1999, ApJ, 512, 547  Sun G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 915, 33  Sun G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mas-Ribas L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Chang T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Furlanetto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Mebane R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gonzalez  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Parsons J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trapp A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14186  Swinbank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, Nature, 464, 733  Swinbank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, MNRAS, 427, 1066  Swinbank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2014, MNRAS, 438, 1267  Symeonidis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 465, 1401  Tacchella S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dekel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carollo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ceverino D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', DeGraf C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Lapiner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Mandelker N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Joel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, MNRAS, 457, 2790  Tacconi L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 853, 179  Tadaki K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, Nature, 560, 613  Tadaki K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 889, 141  Takeuchi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Buat V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Burgarella D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2005, A&A, 440, L17  Tamura Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 874, 27  Tielens A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1985, ApJ, 291, 722  Tielens A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McKee C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Seab C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 1994, ApJ,  431, 321  Trayford J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, MNRAS, 470, 771  Trump J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='12388  Umehata H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 834, L16  Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Baek S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, MNRAS, 433, 1567  Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Yue B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, ApJ, 813, 36  Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sobacchi E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Behrens C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2018, MNRAS, 473, 271  Vallini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pallottini A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carniani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallerani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, MNRAS,  505, 5543  Valtchanov I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, MNRAS, 415, 3473  Vazquez G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Leitherer C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2005, ApJ, 621, 695  Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 751, L25  Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Zschaechner L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Rosa G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Findlay  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McMahon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Sutherland W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 816, 37  Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 851, L8  Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Neeleman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Novak M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Decarli R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hennawi  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Rix H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 874, L30  Venemans B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, ApJ, 904, 130  Vieira J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, ApJ, 719, 763  Visbal E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Trac H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Loeb A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, 010  Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2020, MNRAS, 492, 5167  Wagg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carilli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wilner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cox P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Breuck C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Menten K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Riechers  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2010, A&A, 519, L1  Wagg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, ApJ, 752, L30  Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Riechers D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cox P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Neri R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carilli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bertoldi F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Weiss A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Maiolino R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, Nature, 457, 699  Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2012, Nature, 486, 233  Walter F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, ApJ, 869, L22  Wang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 773, 44  Wang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2016, ApJ, 830, 53  Wang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, ApJ, 887, 40  Wardlow J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS, 479, 3879  Watson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2011, A&A, 533, A16  Watson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Christensen L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Knudsen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Richard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Gallazzi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  Michałowski M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015, Nature, 519, 327  Weingartner J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Draine B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2001a, ApJS, 134, 263  Weingartner J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Draine B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2001b, ApJ, 548, 296  Weiß A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 767, 88  Whitaker K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cybulski R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Casey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Yun M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2017, ApJ, 850, 208  Willott C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013a, ApJ, 145, 4  Willott C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Omont A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bergeron J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013b, ApJ, 770, 13  Willott C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bergeron J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Omont A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015a, ApJ, 801, 123  Willott C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Carilli C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wagg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2015b, ApJ, 807, 180  Willott C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Bergeron J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Omont A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2017, ApJ, 850, 108  Wolfire M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', McKee C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hollenbach D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Tielens A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2003, ApJ,  587, 278  Wong Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='13613  Woody D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2004, in Zmuidzinas J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Holland W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Withing-  ton S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', eds, Millimeter and Submillimeter Detectors for Astronomy  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' SPIE, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='552446, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1117%  2F12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='552446  Wootten A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Thompson A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, Proceedings of the IEEE, 97, 1463  Yang C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019a, A&A, 624, A138  Yang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019b, ApJ, 880, 153  Yang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pullen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Breysse P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Maniyar  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 911, 132  Yang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Popping G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Somerville R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Pullen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Breysse P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Maniyar  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2022, ApJ, 929, 140  Younger J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hayward C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Narayanan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cox T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Jonsson  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2009, MNRAS: Letters, 396, L66  Yue B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferrara A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2019, MNRAS, 490, 1928  Yue M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 917, 99  Zanella A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2018, MNRAS, 481, 1976  Zavala J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, ApJ, 909, 165  Zhu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Wu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Cao C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Li H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2008, ApJ, 686, 155  Zubko V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Dwek E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Arendt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2004, ApJS, 152, 211  da Cunha E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2013, ApJ, 766, 13  da Cunha E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='08566  van Hoof P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Weingartner J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Martin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Volk K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=', Ferland G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=',  2004, MNRAS, 350, 1330  APPENDIX A: THE RADIATIVE COOLING RATE OF GAS  FROM THE [CII] FINE STRUCTURE TRANSITION — I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  THE GENERAL CASE  The CII ion has two fine structure levels in the ground electronic  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The radiative cooling rate of gas from the [CII] transition  can therefore be calculated by solving a classical two-level problem  (Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The cooling rate in erg s−1 cm−3 can be written as  Λ[CII] = [𝐴ul𝑛u + 𝐵ul𝑛u𝑈(𝑇b) − 𝐵lu𝑛l𝑈(𝑇b)]𝐸ul  (A1)  where 𝑛u and 𝑛l represent the densities of the upper (2𝑃3/2) and  lower level (2𝑃1/2) CII ions (cm−3) that result from the combina-  tion of collisional and radiative processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐴ul, 𝐵ul and 𝐵lu in the  above equation represent the Einstein coefficients for spontaneous  emission (s−1), stimulated emission (erg−1 s−2 cm3) and stimulated  absorption (erg−1 s−2 cm3), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐸ul (≡ ℎP𝜈[CII], where  𝜈[CII] = 1900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 GHz) represents the transition energy of the [CII]  line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑈(𝑇b) indicates the radiative energy density at 𝜈[CII] and 𝑇b  is the brightness temperature of the background radiation field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  source of the background radiation may be the CMB and/or the  thermal emission of warm dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Λ[CII] can be rewritten as a function of the excitation (or spin)  temperature for the transition (𝑇ex) and the temperature of the back-  ground radiation field (𝑇b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The excitation temperature is defined by  the relative populations of the upper and lower levels through  𝑛u  𝑛l  ≡ 𝑔u  𝑔l  𝑒−𝑇 ∗/𝑇 ex,  (A2)  where 𝑇∗ = ℎP𝜈[CII]/𝑘B = 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 K is the equivalent temperature of  the [CII] transition, and 𝑔u = 4 (𝑔l = 2) is the statistical weight  MNRAS 000, 1–42 (2022)  38  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  of the upper (lower)-level state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Given the relationships between the  Einstein coefficients, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐵lu = (𝑔u/𝑔l)𝐵ul  (A3)  and  𝐴ul  𝐵ul  =  8𝜋ℎP𝜈3  [CII]  𝑐3  ,  (A4)  and substituting equation (A2) into equation (A1), we obtain  Λ[CII] = 𝑛u𝐴ulℎP𝜈[CII]  �  1 − e(𝑇 ∗/𝑇 ex) − 1  e(𝑇 ∗/𝑇 b) − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (A5)  Neglecting background radiation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑇b ≃ 0), we get  Λ[CII] = 𝑛u𝐴ulℎP𝜈[CII],  (A6)  which is the usual expression for the cooling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The term in the  square brackets in equation (A5) is the background correction term  for attenuation (see da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2013 for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' From equa-  tion (A2), we have  𝑛u = 𝑛CII  �  1 +  � 𝑔l  𝑔u  �  e𝑇 ∗/𝑇 ex�−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (A7)  By substituting equation (A7) into equation (A5), we then obtain the  analytic expression for the [CII] cooling rate when a background is  included,  Λ[CII] = 𝑛CII 𝐴ulℎP𝜈[CII]Ψ(𝑇ex,𝑇b),  (A8)  where  Ψ(𝑇ex,𝑇b) =  �  1 − e(𝑇 ∗/𝑇 ex) − 1  e(𝑇 ∗/𝑇 b) − 1  � �  1 +  � 𝑔l  𝑔u  �  e𝑇 ∗/𝑇 ex�−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (A9)  Equations (A8)-(A9) indicates that one can derive Λ[CII] by solving  for 𝑇ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX B: EXCITATION TEMPERATURE FOR THE  [CII] TRANSITION  Here we present the analytic expression for the excitation temperature  (𝑇ex) for the [CII] transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The rate equation that determines the upper and lower level CII  densities, 𝑛u and 𝑛l, includes both collisional and radiative processes,  and is  𝑛u[𝐴ul + 𝐵ul𝑈(𝑇b) + 𝐶ul] = 𝑛l[𝐵lu𝑈(𝑇b) + 𝐶lu],  (B1)  where 𝐶ul (𝐶lu) represents the collisional de-excitation (excitation)  rate (s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The Einstein coefficients, 𝐴ul, 𝐵ul and 𝐵lu, are related by  equations (A3) and (A4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For a single collision partner, the collision  rates are equal to the rate coefficients (cm3 s−1) times the density 𝑛X  of that collision partner (X = 𝑒−, H0 or H2), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝐶ul = 𝑅X  ul 𝑛X  and  𝐶lu = 𝑅X  lu 𝑛X,  (B2)  where 𝑅X  ul (𝑅X  lu) is the downward (upward) rate coefficient for col-  lision partner X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The two rate coefficients are related by detailed  balance  𝑅X  lu/𝑅X  ul = (𝑔u/𝑔l)e−𝑇 ∗/𝑇 ,  (B3)  where 𝑇 is the kinetic temperature of gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' By substituting equa-  tions (A2)-(A4), (B1)-(B3) into equation (B1) and through rearrange-  ment, we obtain the analytic expression for the excitation temperature  e𝑇 ∗/𝑇 ex =  (1 + 𝐺)𝐴ul + 𝑛X 𝑅X  ul  𝐺𝐴ul + 𝑛X 𝑅X  ule−𝑇 ∗/𝑇  (B4)  where we define  𝐺 =  1  e𝑇 ∗/𝑇 b − 1  (B5)  following Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the [CII] transition, we have  (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Suginohara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2012)  𝐴ul = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36 × 10−6 s−1,  (B6)  𝑅e  ul(𝑇) = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 × 10−8(𝑇/2000)−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='37 cm3 s−1,  (B7)  𝑅HI  ul (𝑇) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0 × 10−11(16 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='35𝑇0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='5 + 48𝑇−1) cm3 s−1,  (B8)  and  𝑅H2  ul (𝑇) = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='8 × 10−10(𝑇/100)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='14 cm3 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (B9)  We can see from equations (B4) and (B5) that for no background  radiation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑇b ≃ 0) and high gas density (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑛X ≫ 𝐴ul/𝑅X  ul),  𝐺 → 0 and 𝑇ex → 𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this case, 𝑇ex (and hence the CII level  populations) is set totally by the kinetic temperature of gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The  impact of background radiation on 𝑇ex can be important in low-  density environments (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑛X ≪ 𝐴ul/𝑅X  ul).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX C: THE STRÖMGREN DEPTH OF A  PLANE-PARALLEL SLAB  The Strömgren depth (𝑙s) can be derived by equating the ionizing  photon rate ( �𝑁ion) to the hydrogen recombination rate ( �𝑁rec) in the  HII region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' �𝑁ion can be expressed as  �𝑁ion = 𝐹ion𝐴,  (C1)  where  𝐹ion =  ∫ ∞  𝜈L  𝐹𝜈  ℎP𝜈 d𝜈,  (C2)  is the ionizing photon flux (cm−2 s−1) and 𝐴 is the surface area of  the slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝐹𝜈 indicates the specific energy flux (cm−2 s−1 Hz−1) at  frequency 𝜈 and 𝜈L = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 × 106 GHz is the frequency corresponding  to the ionization energy of hydrogen, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ℎP𝜈L = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' �𝑁rec can  be expressed as  �𝑁rec = 𝑛e𝑛p𝛼B𝑙sd𝐴 ≈ 𝑛2  H𝛼B𝑙s𝐴,  (C3)  where 𝛼B = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='6 × 10−13 cm3 s−1 is the Case-B recombination co-  efficient at temperature 𝑇 ≈ 104 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Combining equation (C1) and  equation (C3), we have  𝑙s = 𝐹ion  𝑛2  H𝛼B  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (C4)  Hence, the gas column density at the Strömgren depth is  𝑁s = 𝑛H𝑙s = 𝐹ion  𝑛H𝛼B  = 𝑈𝑐  𝛼B  ≈ 1023𝑈 cm−2,  (C5)  where  𝑈 = 𝐹ion  𝑛H𝑐 = 𝑛𝛾  𝑛H  (C6)  is the ionizing photon-to-gas density ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  39  APPENDIX D: THE RADIATIVE COOLING RATE OF GAS  FROM THE [CII] FINE STRUCTURE TRANSITION — II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  THE PLANE-PARALLEL SLAB MODEL  Following Appendix A, we present specifically here an analytic ex-  pression for the gas cooling rate via [CII] line in the HII (Zone I) and  HI regions (Zone II) of a plane-parallel slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The superscript “(1)"  and “(2)" in the following equations indicate the properties of gas in  Zone I and II, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  HII region  For HII region (Zone I), where 𝑇 (1) ≈ 104 K (hence e−𝑇 ∗/𝑇 (1) ≈ 1)  and the main collision partner of CII ions is 𝑒−, we can rewrite  equation (B4) to be  e𝑇 ∗/𝑇 ex =  𝐴ul + 𝑛(1)  e  𝑅e  ul(𝑇 (1))  𝑛(1)  e  𝑅e  ul(𝑇 (1))  ,  (D1)  where we neglect the effect of background field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For densities below  the critical one (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑛(1)  e  <∼ 𝐴ul/𝑅e  ul),  e𝑇 ∗/𝑇 ex ≈  𝐴ul  𝑛(1)  e  𝑅e  ul(𝑇 (1))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D2)  Given 𝐴ul = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='36 × 10−6 s−1 and 𝑅e  ul(𝑇 (1)) ≈ 5 × 10−8 cm3 s−1  (equation (B7)), equation (D2) can be rewritten as  e𝑇 ∗/𝑇 ex ≈ 50  𝑛(1)  e  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D3)  Substituting equation (D3) into equation (A9) gives  Ψ(1) ≈  �  1 +  � 𝑔l  𝑔u  �  e𝑇 ∗/𝑇 ex�−1  ≈ 𝑛(1)  e  25 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D4)  Finally, by substituting equation (D4) into equation (A8), we obtain  the expression for the [CII] cooling rate in HII region  Λ(1)  [CII] = 𝑛(1)  CII 𝐴ulℎP𝜈[CII]Ψ(1)  =  �  𝐴ulℎP𝜈[CII]  � 𝑔u  𝑔l  �  e−𝑇 ∗/𝑇 ex�  𝑛(1)  CII  ≈ 10−21 𝑛(1)  CII 𝑛(1)  e  erg s−1 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D5)  HI region  Now consider the [CII] cooling rate in HI region (Zone II), where  𝑇 (2) ≈ 100 K (hence e−𝑇 ∗/𝑇 (2) ≈ 2  5) and the main collision partner  of CII ions is H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In this case, equation (B5) can be rewritten as  e𝑇 ∗/𝑇 ex =  (1 + 𝐺)𝐴ul + 𝑛(2)  HI 𝑅HI  ul  𝐺𝐴ul + 𝑛(2)  HI 𝑅HI  ul e−𝑇 ∗/𝑇 (2)  ≈  1  𝐺 + 2  5𝑛(2)  HI (𝑅HI  ul /𝐴ul)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D6)  Given 𝑅HI  ul (𝑇 (2)) ≈ 8 × 10−10 cm3 s−1 (equation (B8)), we have  e𝑇 ∗/𝑇 ex ≈  1  𝐺 + 𝑛(2)  HI /7400  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D7)  For the case when background radiation is unimportant (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' low-𝑧  CMB), 𝑇b → 0 and thus 𝐺 → 0, we get  e𝑇 ∗/𝑇 ex ≈ 7400/𝑛(2)  HI .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D8)  10-1  100  101  102  103  10-5  10-4  10-3  10-2  10-1  100  z = 8  z = 6  z = 4  z = 3  z = 2  z = 1  z = 0  Figure D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between Ψ (equation D12) and gas density for HI  gas (𝑇 = 100 K) at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Ψ is unaffected by the CMB at redshift  0 ≤ 𝑧 ≤ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At 𝑧 = 6 − 8, Ψ (and hence the [CII] cooling rate) can be much  affected by the CMB in low-density gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-1  100  101  102  103  10-2  10-1  100  101  102  103  nu/nC+  ηb  z = 8  z = 6  z = 4  z = 3  z = 2  z = 1  z = 0  Figure D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Solid (dotted) lines indicate the relation between 𝜂b (𝑛u/𝑛CII)  and gas density for HI gas (𝑇 = 100 K) at different redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At a given  redshift, both the effects of CMB heating and attenuation increases with  decreasing gas density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Substituting equation (D8) into equation (A9) and equation (A8)  gives  Ψ(2) (𝑇b = 0) ≈  �  1 +  � 𝑔l  𝑔u  �  e𝑇 ∗/𝑇 ex�−1  ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='7 × 10−4 𝑛(2)  HI  (D9)  and  Λ(2)  [CII] (𝑇b = 0) = 𝑛(2)  CII 𝐴ulℎP𝜈[CII] Ψ(2) (𝑇b = 0)  =  �  𝐴ulℎP𝜈[CII]  � 𝑔u  𝑔l  �  e−𝑇 ∗/𝑇 ex�  𝑛(2)  CII  ≈ 10−23 𝑛(2)  CII 𝑛(2)  HI  erg s−1 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D10)  Equation (D10) is the expression for the [CII] cooling rate in HI  region when background radiation is neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)  40  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Taking into account background radiation, equation (A9) can be  expressed as  Ψ(2) = 𝜂𝑏 (𝑛u/𝑛CII),  (D11)  where  𝜂𝑏 ≡ 1 − e(𝑇 ∗/𝑇 ex) − 1  e(𝑇 ∗/𝑇 b) − 1  ≈  𝐺 + 𝑛(2)  HI /(7400 𝐺)  1 + 𝑛(2)  HI /(7400 𝐺)  (D12)  is the background attenuation term and  𝑛u  𝑛CII  =  �  1 +  � 𝑔l  𝑔u  �  e𝑇 ∗/𝑇 ex�−1  ≈  ������  1 +  1  2 (𝐺 + 𝑛(2)  HI /7400)  ������  −1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D13)  Equation (D13) indicates that background radiation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the CMB)  leads to increased upper level (2𝑃3/2) population of the [CII] tran-  sition (‘background heating’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Using the above equations, we obtain  the level of change of the [CII] cooling rate by the CMB at redshift  𝑧,  R ≡  Λ(2)  [CII] (𝑇CMB(𝑧))  Λ(2)  [CII] (𝑇b = 0)  = Ψ(2) (𝑇CMB(𝑧))  Ψ(2) (𝑇b = 0)  ≈  ������  𝐺 + 𝑛(2)  HI /(7400 𝐺)  1 + 𝑛(2)  HI /(7400 𝐺)  ������  ������  2  7400𝑛(2)  HI +  1  7400 𝐺/𝑛(2)  HI + 1  ������  −1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (D14)  We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D1 the relation between Ψ(2) (equation D11) and  gas density for HI gas (𝑇 (2) ≈ 100 K) at different redshifts (𝑧 = 0−8),  where we account for the effects of the CMB background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be  seen that Ψ(2) shows almost no redshift evolution at 𝑧 = 0 − 4 over  the wide density range being considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At higher redshifts, Ψ(2)  (and hence Λ(2)  [CII]) is raised by the CMB in low-density gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' At 𝑧 = 6  (𝑧 = 8), for example, Ψ(2) appears to be much higher than that of the  lower redshifts at densities below ∼ 1 cm−3 (∼ 10 cm−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  It should be noted, however, that although the net effect of CMB  heating and attenuation on the [CII] cooling rate is negligible except  for the low-density gas at 𝑧 >∼ 6, their own effect can be prominent  at various densities and at lower redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' This can be seen from  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' D2, where we explicitly show how 𝑛u/𝑛CII (indicating heating)  and 𝜂b (indicating attenuation) depend on gas density for HI gas  (𝑇 (2) ≈ 100 K) at different redshifts (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Kohandel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Both  the effects of CMB heating and attenuation increase with decreasing  gas density, but they almost cancel out each other at above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1 cm−3  at 𝑧 = 0−4 (and at higher densities at 𝑧 = 6−8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' As a result, the [CII]  cooling rate becomes almost unaffected by the CMB in that regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX E: CARBON IONIZATION IN THE HII REGION  Here we present the analytic expression for the abundance of CII  ions in the HII region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Consider the carbon ionization equilibrium  equation:  ΓC𝑛CII = 𝛼C𝑛CIII𝑛e,  (E1)  where we only account for the CII ⇔ CIII equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ΓC is the  optically thin carbon photo-ionization rate (s−1) and 𝛼C = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 ×  10−12 cm3 s−1 is the recombination coefficient (Nahar & Pradhan  1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Given 𝑛CII = 𝑥CII𝑛C and 𝑛CIII = (1 − 𝑥CII)𝑛C, we can rewrite  equation (E1) to be  𝑥CII =  �  1 +  ΓC  𝑛e𝛼C  �−1  ≈ 𝑛e𝛼C  ΓC  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (E2)  Following Ferrara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' (2019), we have  ΓC = 𝐹ion ¯𝜎C = 𝑈𝑛H𝑐 ¯𝜎C,  (E3)  where ¯𝜎C ≈ 4 × 10−18 cm2 is the flux-weighted carbon photo-  ionization cross section (Spitzer 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Substituting equation (E3)  into equation (E2) and given 𝑛e ≈ 𝑛H for the HII region, we then get  𝑥CII ≈  𝛼C  𝑈𝑐 ¯𝜎C  ∝ 𝑈−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (E4)  Hence, xCII is inversely proportional to 𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX F: [CII] LUMINOSITY OF A UNIFORM  SPHERICAL GAS CLOUD  Here we derive the specific [CII] cooling rate (erg cm3 s−1) for a  spherical uniform cloud ( ¯𝜖[CII], cl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the case where the cloud is  fully photo-ionized by the external UV radiation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑙s ≥ 𝑅cl), the  luminosity of the cloud (𝐿[CII], cl) can be expressed as  𝐿[CII], cl = 4𝜋  ∫ 𝑅cl  0  Λ(1)  [CII]𝑟2d𝑟.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (F1)  Substituting equation (D5) into the above equation, we get  𝐿[CII], cl =  � 4𝜋  3 𝑛H𝑅3  cl  �  𝑛HAC  �  ℎP𝜈[CII]  � 𝑔u  𝑔l  �  𝑅e  ul(𝑇 (1))𝑥(1)  CII  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (F2)  For the case where HI region forms in the cloud (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝑙s < 𝑅cl),  𝐿[CII], cl can be expressed as  𝐿[CII], cl = 4𝜋  �∫ 𝑅cl  𝑅cl−𝑙s  Λ(1)  [CII]𝑟2d𝑟 +  ∫ 𝑅cl−𝑙s  max(0, 𝑅cl−𝑙F)  Λ(2)  [CII]𝑟2d𝑟  �  ,  (F3)  where the first and second terms on the right-hand side of the equation  correspond to the [CII] emission from HII (Zone I) and HI regions  (Zone II), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' By substituting equation (D5) into the first  term and equation (D13) into the second term, we can rewrite the  above equation to be  𝐿[CII], cl = 𝑓[CII], cl  � 4𝜋  3 𝑛H𝑅3  cl  �  𝑛HAC  × ℎP𝜈[CII]  � 𝑔u  𝑔l  �  ∫ 𝑅cl  𝑅cl−𝑙s  𝑥(1)  CII 𝑅e  ul𝑟2d𝑟 +  ∫ 𝑅cl−𝑙s  max(0, 𝑅cl−𝑙F) (2/5)𝑅HI  ul 𝑟2d𝑟  ∫ 𝑅cl  max(0, 𝑅cl−𝑙F) 𝑟2d𝑟  ,  (F4)  where 𝑓[CII], cl represents the total fraction of gas mass in HII or  HI regions (Zone I + Zone II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Combining equation (F2) and equa-  tion (F4), and substituting 𝑀cl = 4  3 𝜋𝑅3  cl(𝜇H𝑚H𝑛H) into the equa-  tions, we obtain  𝐿[CII], cl = 𝑓CII, cl  � 𝑀cl  𝜇H𝑚H  �  𝑛HAC ¯𝜖[CII], cl,  (F5)  MNRAS 000, 1–42 (2022)  CII emission as an indicator of galaxy SFR  41  10-1  100  101  102  100  101  102  103  FIRE galaxies  z = 0  10-1  100  101  102  106  107  108  109  1010  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  × 10  ˜ngas (cm−3)  Figure G1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The relation between the [CII] luminosity-weighted median gas  density ( ¯𝑛gas) and the [CII] luminosity-weighted mean gas density ( ˜𝑛gas)  of the FIRE galaxy sample at 𝑧 = 0 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The solid black line indicates the  one-to-one relationship, whilst the dashed black line indicates the relation  ˜𝑛gas = 10 ¯𝑛gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ˜𝑛gas is systematically higher than ¯𝑛gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  where  𝑓[CII], cl =  ����  ����  1  (if 𝑙F ≥ 𝑅cl)  3  ∫ 𝑅cl  𝑅cl−𝑙s  (𝑟/𝑅cl)2d(𝑟/𝑅cl) (if 𝑙F < 𝑅cl)  (F6)  and  ¯𝜖[CII], cl = ℎP𝜈[CII]  � 𝑔u  𝑔l  �  ×  ����������  ����������  𝑅e  ul(𝑇 (1))𝑥(1)  CII  (if 𝑙s ≥ 𝑅cl)  ∫ 𝑅cl  𝑅cl−𝑙s  𝑥(1)  CII 𝑅e  ul𝑟2d𝑟 +  ∫ 𝑅cl−𝑙s  max(0, 𝑅cl−𝑙F)  �  2  5  �  𝑅HI  ul 𝑟2d𝑟  ∫ 𝑅cl  max(0, 𝑅cl−𝑙F) 𝑟2d𝑟  (if 𝑙s < 𝑅cl)  (F7)  Equation (F7) is the analytic expression for the specific [CII] cooling  rate for a uniform spherical gas cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX G: LUMINOSITY-WEIGHTED GAS DENSITY  OF GALAXIES  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G1, we show the relation between the [CII] luminosity-  weighted median gas density (¯𝑛gas) and the [CII] luminosity-  weighted mean gas density (˜𝑛gas) of the FIRE sample at different  redshifts (𝑧 = 0 − 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It can be seen from the figure that the latter is  systematically higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The reason for this result is that the [CII] luminosity-weighted PDF  of gas density (𝑛H) of the galaxies resembles a lognormal function  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G2 for an example), showing an elongated tail at high  density end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' Consider a lognormal function with two parameters 𝜇  and 𝜎, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  𝑃(𝑛H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜇, 𝜎) =  1  𝑛H  √  2𝜋𝜎  e− (ln(𝑛H)−𝜇)2  2𝜎2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (G1)  FIRE galaxy z = 0  FIRE galaxy z = 6  μ = − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='11  μ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='45  μ + σ2  2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='43  μ + σ2  2 = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='61  (50%)  (50%)  (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0%)  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9%)  Figure G2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The [CII]-luminosity-weighted PDF of gas density of two se-  lected FIRE galaxies at 𝑧 = 0 (upper panel) and 𝑧 = 6 (lower panel) and the  best-fit lognormal function (equation G1) to the PDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In each panel, shaded  grey area represents the original PDF whereas solid red line indicates the  best-fit lognormal function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The luminosity-weighted mean gas density ( ¯𝑛H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  marked by the vertical dashed line on the right) of the galaxies is higher than  the luminosity-weighted median density ( ˜𝑛H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' marked by the vertical dashed  line on the left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  The cumulative distribution function (CDF) for a lognormal distri-  bution is  𝐶(𝑛H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜇, 𝜎) ≡  ∫ 𝑛H  −∞  𝑃(𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜇, 𝜎)d𝑥  = 1  2  �  1 + erf  � ln(𝑛H) − 𝜇  √  2𝜎  ��  ,  (G2)  where erf is the error function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is easy to show that the mean density  (˜𝑛H) of a lognormal distribution is  ˜𝑛H =  ∫ ∞  −∞  𝑥𝑃(𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜇, 𝜎)d𝑥 =  ∫ ∞  −∞  1  √  2𝜋𝜎  e− (ln(𝑥)−𝜇)2  2𝜎2  d𝑥  =e𝜇+ 𝜎2  2 ,  (G3)  whereas the median density (¯𝑛H), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' the density at which  𝐶(𝑛H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 𝜇, 𝜎) = 1  2, is  ¯𝑛H = e𝜇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  (G4)  Hence, ˜𝑛H is higher than ¯𝑛H by a factor of ˜𝑛H/¯𝑛H = 𝑒  𝜎2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' G2, we show the luminosity-weighted density PDF of two  selected FIRE galaxies at 𝑧 = 6 (lower panel) and 𝑧 = 0 (upper panel)  as well as the best-fit lognormal function to their PDF (note: the same  galaxies as for Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' 11) as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The luminosity-weighted  MNRAS 000, 1–42 (2022)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05  0  0  2  4  6  8  10  ln (nH/cm-3)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='25  Hu  /d ln  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2  M (Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='15  d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='05  0  4  2  0  2  4  6  ln (nH/cm-3)42  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  10-2  10-1  100  101  10-2  10-1  100  101  FIRE galaxies  10-1  100  101  102  106  107  108  109  1010  z = 0  z = 2  z = 3  z = 1  z = 4  z = 6  z = 8  ¯Zgas vs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ˜Zgas  ¯Zgas vs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯Zgas, MW  Figure H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The ¯𝑍gas vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ˜𝑍gas relation and the ¯𝑍gas (filled coloured symbols)  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ˜𝑍gas, MW (empty symbols) relation of the FIRE sample at 𝑧 = 0 − 8,  where ¯𝑍gas, ˜𝑍gas and ˜𝑍gas, MW represent the luminosity-weighted median,  luminosity-weighted mean and mass-weighted median gas metallicity, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The solid black line indicates the one-to-one relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas,  ˜𝑍gas and ˜𝑍gas, MW of the galaxies are very similar to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  median gas density ¯𝑛gas of the 𝑧 = 0 (𝑧 = 6) galaxy is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9 cm−3  (79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 cm−3), whereas its luminosity-weighted mean density ˜𝑛gas is  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='2 cm−3 (754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='4 cm−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' For the 𝑧 = 6 (𝑧 = 0) galaxy, only 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='0%  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='9%) of the total [CII] luminosity originates from the gas at  density above ˜𝑛gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' It is therefore not statistically representative for  the bulk of the gas in galaxies emitting [CII].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  APPENDIX H: LUMINOSITY-WEIGHTED GAS  METALLICITY OF GALAXIES  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' H1, we show the relation between the luminosity-weighted  median ( ¯𝑍gas) and the luminosity-weighted mean gas metallicity  ( ˜𝑍gas) of the FIRE galaxy sample at 𝑧 = 0 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ˜𝑍gas and ¯𝑍gas are very  close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' The former is higher by only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='02 dex (4%) on  average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  Both ˜𝑍gas and ¯𝑍gas of the galaxies are similar to their mass-  weighted gas metallicity ( ¯𝑍gas, MW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' In the same figure, we show  the ¯𝑍gas vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas, MW relation for the FIRE sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content=' ¯𝑍gas is on average  higher than ¯𝑍gas, MW by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='10 dex (20%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
+page_content='  MNRAS 000, 1–42 (2022)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/r9E2T4oBgHgl3EQf1Qhf/content/2301.04149v1.pdf'}
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+박 사 학 위 논 문
+Ph.D. Dissertation
+KSTAR 플라즈마 평형을 위한
+베이즈 추론 신경망
+Bayesian neural network for plasma equilibria
+in the Korea Superconducting Tokamak Advanced Research
+2022
+정 세 민
+(丁 世 敏 Joung, Semin)
+한 국 과 학 기 술 원
+Korea Advanced Institute of Science and Technology
+arXiv:2301.11555v1  [physics.plasm-ph]  27 Jan 2023
+
+박 사 학 위 논 문
+KSTAR 플라즈마 평형을 위한
+베이즈 추론 신경망
+2022
+정 세 민
+한 국 과 학 기 술 원
+원자력 및 양자공학과
+
+KSTAR 플라즈마 평형을 위한
+베이즈 추론 신경망
+정 세 민
+위 논문은 한국과학기술원 박사학위논문으로
+학위논문 심사위원회의 심사를 통과하였음
+2022년 5월 31일
+심사위원장
+김 영 철
+(인)
+심 사 위 원
+김 현 석
+(인)
+심 사 위 원
+성 충 기
+(인)
+심 사 위 원
+윤 시 우
+(인)
+심 사 위 원
+최 원 호
+(인)
+
+Bayesian neural network for plasma equilibria
+in the Korea Superconducting Tokamak Advanced
+Research
+Semin Joung
+Advisor: Young-chul Ghim
+A dissertation submitted to the faculty of
+Korea Advanced Institute of Science and Technology in
+partial fulfillment of the requirements for the degree of
+Doctor of Philosophy in Nuclear and Quantum Engineering
+Daejeon, Korea
+May 31, 2022
+Approved by
+Young-chul Ghim
+Professor of Nuclear and Quantum Engineering
+The study was conducted in accordance with Code of Research Ethics1.
+1 Declaration of Ethical Conduct in Research: I, as a graduate student of Korea Advanced Institute of Science and
+Technology, hereby declare that I have not committed any act that may damage the credibility of my research.
+This
+includes, but is not limited to, falsification, thesis written by someone else, distortion of research findings, and plagiarism.
+I confirm that my thesis contains honest conclusions based on my own careful research under the guidance of my advisor.
+
+DNQE
+정세민. KSTAR 플라즈마 평형을 위한 베이즈 추론 신경망. 원자
+력 및 양자공학과 . 2022년. 192+vi 쪽. 지도교수: 김영철. (영문
+논문)
+Semin Joung.
+Bayesian neural network for plasma equilibria
+in the Korea Superconducting Tokamak Advanced Research.
+Department of Nuclear and Quantum Engineering .
+2022.
+192+vi pages. Advisor: Young-chul Ghim. (Text in English)
+초 록
+핵융합 플라즈마는 물리적으로 복잡한 시스템 중 하나이기에 핵융합로 제어를 위
+하여 여러 물리 현상에 대한 추가적인 이론 정비가 지속적으로 요구된다. 따라서
+여러 물리 현상에 대한 심층적인 이해가 없어도 장치 제어에 도움을 일조하는 딥
+러닝 (심층 학습 기법) 이용은 과거 수십 년간 핵융합 플라즈마 분야에 큰 화두가
+되어 왔었다. 그러나 다양한 딥러닝 기법들이 핵융합 플라즈마의 여러 분야에 연
+구되어 왔지만 본질적인 물리 현상에 대한 심층적 이해의 부재로 과학적인 사용에
+있어서 딥러닝 기법의 신뢰성 정량화가 지속적으로 요구되어 왔었다. 이러한 요
+구들로 핵융합 플라즈마 분야에서 신뢰성 검증 가능하며 물리 이론까지 만족시킬
+수 있는 딥러닝 개발이 새롭게 대두되었다. 우리는 본 논문에서 지배 방정식을
+만족하며 관측된 물리 현상을 핵융합로 장치 제어 관련 정보로 변환시킬 수 있는
+신경망 개발에 주안점을 둔다. 본 학위 논문에서는 토로이달 및 폴로이달 자기장
+으로 핵융합 플라즈마를 가두는 핵융합로 실험 장치 중 하나인 토카막을 활용한다.
+토카막은 플라즈마를 자기적으로 가두기에 플라즈마 압력과 자기장 및 플라즈마
+전류로 인한 로렌츠 힘의 균형 유지가 필수이다. 플라즈마 평형은 바로 이 균형이
+유지된 상태를 이야기하는 것으로 토카막 외부 자기장 코일 전류에 의해 제어되는
+플라즈마의 형상과 위치를 제공한다. 다만 약 1 억 도의 초고온 환경인 플라즈마로
+인하여 플라즈마 형상을 직접 진단할 수 없기에 간접 및 국소 측정 기기로 진단
+된 플라즈마 물리 정보 활용으로 힘의 균형 및 맥스웰 방정식을 따르는 플라즈마
+형상을 간접적으로 재구성한다. 이 재구성에 사용되는 식이 바로 힘의 균형과 맥
+스웰 방정식으로부터 유도된 Grad-Shafranov (GS) 식이다. 이 식은 2 차원 2 계
+비선형 미분 방정식으로 수치 해석이 반드시 요구되며 수치적인 수렴을 위해 진단
+데이터의 취사 선택과 같은 인간의 선택이 종종 요구된다. 또한 수치 해석의 반복
+계산으로 인한 근본적인 계산 시간 한계로 실시간 토카막 운전에 활용되기 위해
+서는 정확도의 희생 등을 필요로 한다. 과거에 실시간 계산 한계 극복으로 인해
+
+개발된 지도 학습 기반 신경망이 과거 제시 되었지만 결과적으로 인간의 선택을
+바탕으로 한 결과로 훈련된 신경망이란 사실에는 변함이 없었다. 그러므로 이 논
+문은 신경망을 기반으로 하되 기존 수치 해석과 독립적이며 물리 이론을 스스로
+만족함과 동시에 신뢰성의 정량화가 가능한 플라즈마 형상 재구성 방법을 제안
+한다. 즉 신경망을 통해 GS 식의 해를 직접 구하며 베이즈 추론 신경망을 통해
+재구성된 플라즈마 평형의 신뢰성을 평가한다. 또한 자유 경계 문제 중 하나인
+GS 식 해의 탐색을 위해 경계 추적이 가능한 보조 모듈을 고안하였다. 나아가
+베이지안 추론과 가우시안 프로세스 및 기계 학습을 기반으로 하는 진단된 자기장
+신호의 표류 현상, 신호 간의 비 일관성, 진단 신호 손실을 해결하는 방법을 소개하
+여 어떠한 운전 환경에서도 우리의 신경망이 사용될 수 있음을 입증한다. 그리고
+신경망 훈련이 GS 식에 기반할 수 있는지를 검증하기 위해 기존 수치 해석의 데이
+터 및 GS 식을 신경망의 비용 함수로써 사용한 결과를 소개한다. 추가로 우리는
+이 학위 논문에 활용된 원리 및 방법이 여러 딥러닝이 활용될 법한 전통적인 과학
+분야에 충분히 응용될 수 있음을 밝힌다. 그리하여 단순한 딥러닝 사용을 벗어나
+여러 공학 및 물리 분야에 물리적 신뢰성을 획득한 신경망 사용 방안을 제안할 수
+있을 것이라고 우리는 희망한다.
+핵 심 낱 말 케이스타, 플라즈마 평형 재구성, EFIT, 자기 진단법, 톰슨 산란 진단,
+전하 교환 분광계, 가우시안 프로세스, 베이지안 추론, 베이즈 추론 신경망, 비지도
+학습
+Abstract
+Fusion-graded plasmas are one of the physically complex systems, resulting in
+continuous establishment of plasma theories for unclarified physical phenomena
+in order to thoroughly control nuclear fusion reactors. Deep learning has drawn
+vast attention to this field of controlled fusion plasma to link physical phenom-
+ena with control-relevant parameters without a deepened understanding about
+plasma theories. Albeit, quantifying the uncertainty of deep learning models has
+been constantly requested due to their fundamental shortage of physical under-
+standing. Thus, a concept of a reliable deep learning model to be able to present
+their probability distributions is raised as well as a method to inculcate physical
+
+theories in the model is also concerned. These are the main concept focused in
+this thesis with a tokamak experiment, one of the nuclear fusion experiments by
+confining the plasmas via toroidal and poloidal magnetic fields in a torus shape
+device. Since the tokamak confines a plasma magnetically, balancing the Lorentz
+force due to the magnetic field with the plasma pressure is crucial. This bal-
+anced state with equilibrium assumption is called plasma equilibrium, giving us
+the shape and location of the plasma determined and controlled by the exter-
+nal coil currents of the tokamak. However, this plasma shape cannot be directly
+measured due to the harsh environment caused by the plasma itself of 100 million
+degrees Celsius, thus the shape is indirectly reconstructed from the force balance
+and Maxwell’s equations consistent with externally and locally measured plasma
+information. The Grad-Shafranov (GS) equation derived from those equations is
+used to reconstruct the plasma. This equation is a two-dimensional second-order
+differential equation, inherently requiring numerical analysis so that human de-
+cisions such as selecting some of the measured signals arbitrarily for numerical
+convergence are followed. Furthermore, it is likely to sacrifice accuracy of solu-
+tions of the equation for real-time tokamak controls due to multiple iterations
+in numerical analysis which requires intensive computations.
+Although there
+were neural network based real-time approaches via supervised learning with
+databases from numerical algorithms, they were inevitably under the influence
+of human decisions. Hence, this thesis suggests a reconstruction method based
+on deep neural networks which are able to not only estimate their uncertainties
+but also learn the governing equation themselves without depending on previous
+numerical algorithms. Namely, our neural networks solve the GS equation via
+a unsupervised learning algorithm and show probability distributions of their
+solutions based on Bayesian neural networks. Since solving the GS equation is
+a free-boundary problem, our networks are supported by an auxiliary module
+that detects the plasma boundary from the network outputs. Furthermore, we
+introduce preprocessing methods for the network inputs to address the magnetic
+signal drift, the flux loop inconsistency and the magnetic signal impairment based
+on Bayesian inference, Gaussian processes and neural networks. These methods
+
+are developed to guarantee the use of the networks in any circumstance of the
+tokamak experiments. In addition, we also prove that the Grad-Shafranov equa-
+tion can be used as a cost function of the networks with a given equilibrium
+database. The principles and methods applied here are not only acceptable for
+fusion research but also applicable to various engineering and scientific fields.
+Thus, we expect that our proposal which fulfills physical reliability for the use
+of deep learning deserves further studies for various complex physics systems.
+Keywords KSTAR, Grad-Shafranov equation, EFIT, Magnetic diagnostics, Thom-
+son scattering system, Charge exchange spectroscopy, Gaussian processes, Bayesian
+inference, Bayesian neural networks, Unsupervised learning
+
+Contents
+Contents
+. . . . . . . . . . . . . . . . . . . . . . . . .
+i
+List of Tables
+. . . . . . . . . . . . . . . . . . . . . .
+v
+List of Figures
+. . . . . . . . . . . . . . . . . . . . . .
+vi
+Chapter 1.
+Preface: what would we do with a Black
+Box for fusion research?
+1
+Chapter 2.
+Nuclear Fusion
+7
+2.1
+Tokamak . . . . . . . . . . . . . . . . . . . . .
+11
+2.2
+Equilibrium . . . . . . . . . . . . . . . . . . .
+13
+2.2.1
+Biot-Savart Law . . . . . . . . . . . .
+15
+2.3
+Plasma diagnostics . . . . . . . . . . . . . . .
+18
+2.3.1
+Magnetic diagnostics . . . . . . . . .
+19
+2.3.2
+Pressure measurements . . . . . . . .
+20
+2.4
+Deep learning for tokamak equilibrium . . .
+22
+Chapter 3.
+Deep learning and Bayesian Inference
+23
+3.1
+Feedforward Neural Network . . . . . . . . .
+24
+3.1.1
+Bayesian Inference
+. . . . . . . . . .
+27
+3.1.2
+Sine function Regression: Part 1 . .
+29
+3.1.3
+Sine function Regression: Part 2 . .
+31
+3.2
+Advanced topic: GAN . . . . . . . . . . . . .
+33
+3.3
+Outlook
+. . . . . . . . . . . . . . . . . . . . .
+40
+i
+
+CONTENTS
+Chapter 4.
+Bayesian neural network in fusion re-
+search
+42
+4.1
+Article I: Signal drift correction . . . . . . .
+43
+4.1.1
+Introduction
+. . . . . . . . . . . . . .
+45
+4.1.2
+Real-time drift correction based on
+Bayesian inference . . . . . . . . . . .
+47
+4.1.3
+Two-step drift correction method . .
+47
+4.1.4
+Results with KSTAR experimental
+data . . . . . . . . . . . . . . . . . . .
+53
+4.1.5
+Discussions . . . . . . . . . . . . . . .
+61
+4.1.6
+Conclusions . . . . . . . . . . . . . . .
+64
+4.2
+Article II: Imputation . . . . . . . . . . . . .
+65
+4.2.1
+Introduction
+. . . . . . . . . . . . . .
+66
+4.2.2
+Imputation Scheme: Based on Bayes’
+model . . . . . . . . . . . . . . . . . .
+67
+4.2.3
+Based on Gaussian Process
+. . . . .
+70
+4.2.4
+Based on Bayes’ model coupled with
+Gaussian Process
+. . . . . . . . . . .
+73
+4.2.5
+Discussion and Conclusion . . . . . .
+76
+4.3
+Article III: Preprocessing flux loop . . . . .
+78
+4.3.1
+Introduction
+. . . . . . . . . . . . . .
+79
+4.3.2
+Magnetic data collection . . . . . . .
+80
+4.3.3
+Domain knowledge regarding the poloidal
+magnetic field
+. . . . . . . . . . . . .
+80
+4.3.4
+Modelling the network architecture
+82
+ii
+
+CONTENTS
+4.3.5
+Recovering flux loop consistency via
+the deep neural network . . . . . . .
+84
+4.3.6
+Quantitative assessment of the net-
+work . . . . . . . . . . . . . . . . . . .
+85
+4.3.7
+Equilibrium reconstruction using the
+network magnetic flux
+. . . . . . . .
+86
+4.3.8
+Discussion
+. . . . . . . . . . . . . . .
+87
+4.4
+Article IV: Preliminary result under super-
+vised learning . . . . . . . . . . . . . . . . . .
+89
+4.4.1
+Introduction
+. . . . . . . . . . . . . .
+90
+4.4.2
+Collection and real-time preprocess-
+ing of data
+. . . . . . . . . . . . . . .
+94
+4.4.3
+Neural network model and training
+97
+4.4.4
+Performance of the developed neural
+networks: Benchmark tests
+. . . . .
+101
+4.4.5
+Discussions and Conclusions . . . . .
+116
+4.5
+Article V: Plasma reconstruction via unsu-
+pervised learning . . . . . . . . . . . . . . . .
+119
+4.5.1
+Introduction
+. . . . . . . . . . . . . .
+120
+4.5.2
+Modelling Grad-Shafranov Deep Neu-
+ral Networks . . . . . . . . . . . . . .
+122
+4.5.3
+Statistical analysis of GS-DeepNet train-
+ing . . . . . . . . . . . . . . . . . . . .
+129
+4.5.4
+Physical knowledge learned by GS-
+DeepNet
+. . . . . . . . . . . . . . . .
+132
+iii
+
+CONTENTS
+4.5.5
+Final performance of GS-DeepNet with
+the kinetic constraints
+. . . . . . . .
+135
+4.5.6
+Materials and Methods . . . . . . . .
+137
+4.5.7
+Discussion
+. . . . . . . . . . . . . . .
+142
+Chapter 5.
+Conclusions
+144
+Chapter A.
+Bayesian Deep Learning: Model uncer-
+tainty
+147
+Chapter B.
+Neural Network Differentiation
+152
+Bibliography
+159
+Acknowledgments in Korean
+188
+Curriculum Vitae
+190
+iv
+
+List of Tables
+2.1
+Designed ranges of major paramters of KSTAR [1] . . . . . . . . .
+12
+4.1
+Summary of the data samples to train and validate the networks .
+95
+4.2
+The imputation results shown in Figure 4.32 with KSTAR shot
+#20341 at 2.1 sec.
+. . . . . . . . . . . . . . . . . . . . . . . . . . 114
+v
+
+List of Figures
+1.1
+Sine function regressions . . . . . . . . . . . . . . . . . . . . . . .
+3
+2.1
+Fusion reaction rates . . . . . . . . . . . . . . . . . . . . . . . . .
+8
+2.2
+Lawson criterion
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+10
+2.3
+Tokamak configuration . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.4
+Circular wire
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+16
+2.5
+Magnetic diagnostics . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+2.6
+KSTAR TS and CES systems . . . . . . . . . . . . . . . . . . . .
+20
+3.1
+Simple neural network
+. . . . . . . . . . . . . . . . . . . . . . . .
+25
+3.2
+Learning curve
+. . . . . . . . . . . . . . . . . . . . . . . . . . . .
+26
+3.3
+Bayesian neural network regressions . . . . . . . . . . . . . . . . .
+30
+3.4
+Bayesian neural network differentiation . . . . . . . . . . . . . . .
+32
+3.5
+GAN architecture . . . . . . . . . . . . . . . . . . . . . . . . . . .
+33
+3.6
+GAN results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+40
+4.1
+Configuration of magnetic diagnostics on a poloidal cross-section
+of KSTAR at a certain toroidal position. Blue dots show the posi-
+tions of both MPn and MPt, and red open circles for the positions
+of the FLs. The black thick line shows the first wall. Note that we
+only show five FL sensor numbers out of 45 of them for simplicity.
+44
+4.2
+An example of temporal evolutions of (a) currents in the PF coils,
+(b) normal and (c) tangential components of magnetic fields mea-
+sured by an MPn and an MPt, respectively, and (d) magnetic flux
+measured by an FL during the initial magnetization stage, i.e.,
+t < 0, for a typical KSTAR discharge. Information from the time
+interval d1 (d2) is used to estimate am
+i (bm
+i ). . . . . . . . . . . . .
+46
+vi
+
+LIST OF FIGURES
+4.3
+Examples of the proposed two-step drift correction method for
+the MDs of (a) MPn #6, (b) MPt #27 and (c) FL #45. Left
+and middle panels show the posteriors of the slope and the offset
+for each MD where the red dots depict the maximum a posterior.
+Right panel shows both the original magnetic signals with the
+signal drifts (red) and the drift corrected signals (blue). . . . . . .
+48
+4.4
+Histograms of the validation errors for randomly selected 297 KSTAR
+discharges before (left panel) and after (right panel) the two-step
+drift correction for (a) m =MPn measuring Bn, (b) m =MPt mea-
+suring Bt, and (c) m =FL measuring magnetic fluxes. MD # in
+horizontal axes denote the MD sensor numbers, i.e., subscript i in
+ϵm
+i,s. Colors represent the relative occurrence normalized to a unity
+for every sensor. Non-existing magnetic signals are displayed as
+white streaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+49
+4.5
+Averaged validation errors ⟨ϵm
+i ⟩ for 297 KSTAR discharges for (a)
+the normal (MPn) and (b) the tangential (MPt) components of
+magnetic signals, and for (c) the flux loop (FL) measurements.
+Blue circles indicate the validation errors after the two-step drift
+correction method, and red crosses mean the validation errors be-
+fore applying our correction method.
+. . . . . . . . . . . . . . . .
+50
+4.6
+Qualitative comparisons between a typical chi-square linear fitting
+method (blue line) and our proposed two-step method (red line)
+with the raw (before correction) signal (green line) in (a) KSTAR
+shot #17016 and (b) #9387 for the tangential component of mag-
+netic signal MPt #14. (c) and (d) show temporal evolutions of
+currents through KSTAR PF coils, and vertical dotted lines indi-
+cate the time where we expect all the magnetic signals return to
+zeros if there were no signal drifts. Note that the blue line in (b)
+is almost overlapped with the red line, but it is slightly more off
+from the zero compared to the red line. . . . . . . . . . . . . . . .
+53
+vii
+
+LIST OF FIGURES
+4.7
+Histograms of the degree of corrections (DoC’s), where signal drift
+corrections are performed based on a typical chi-square linear fit-
+ting method (left panel) and our proposed two-step drift correction
+method (right panel) for (a) MPn measuring Bn, (b) MPt measur-
+ing Bt, and (c) FL measuring magnetic fluxes. MD # in horizontal
+axes denote the MD sensor numbers. Colors represent the relative
+occurrence normalized to a unity for every sensor. Same sets of
+magnetic signals used to generate Fig. 4.4 are used. Non-existing
+magnetic signals are displayed as white streaks.
+. . . . . . . . . .
+54
+4.8
+Averaged validation errors as in Fig. 4.5 before (red crosses) and
+after the correction (blue circle) for (a) the normal component
+(MPn) and (b) the tangential component (MPt) of magnetic sig-
+nals and for (c) flux loop measurements. Left panels show the re-
+sults for the 286 short pulse discharges (< 40 sec), while the right
+panels show the results for the 11 long pulse discharges (> 40 sec).
+Note the different scales for y-axis.
+. . . . . . . . . . . . . . . . .
+56
+4.9
+Temporal evolutions of the magnetic signals measured by MPn
+#07 (blue) and MPn #36 (red) for (a) KSTAR shot #16051 (ab-
+normal MPn #36) and (b) #16447 (normal MPn #36). These two
+magnetic sensors are located at the up-down symmetric positions
+as shown in Fig. 4.1, and the discrepancy between MPn #07 and
+#36 in (a) are too large compared to (b) to be explained by the
+slight up-down asymmetry of the KSTAR plasmas. Vertical dot-
+ted lines indicate where all the currents through the PF coils are
+returned to zeros. . . . . . . . . . . . . . . . . . . . . . . . . . . .
+57
+4.10 Temporal evolutions of the magnetic signals measured by (a) FL
+#25 (KSTAR shot #14262), (b) FL #27 (KSTAR shot #17320)
+and (c) FL #35 (KSTAR shot #16369). These signals are basi-
+cally noises (see Fig. 4.3(c) as an example of working FL signal).
+Vertical dotted lines indicate where all the currents through the
+PF coils are returned to zeros. . . . . . . . . . . . . . . . . . . . .
+58
+viii
+
+LIST OF FIGURES
+4.11 Temporal evolutions of the magnetic signals measured by (a) FL
+#01 (KSTAR shot #17321), (b) FL #23 (KSTAR shot #13366)
+and (c) FL #34 (KSTAR shot #17039). Blue (green) line is the
+signal after (before) the correction. Vertical dotted lines indicate
+where all the currents through the PF coils are returned to zeros.
+60
+4.12 Schematics of (a) the Amperian loop (blue line connecting blue
+dots) for ∇ × ⃗B = µ0 ⃗J and (b) the pancake-shaped Gaussian
+surface with three surfaces s1, s2 and s3 for ∇ · ⃗B = 0. Blue dots
+with the numbers in (a) indicate the magnetic probes. [2] . . . . .
+67
+4.13 Log-posterior, ln[p(B∗
+⊕|B⊕, Ω⊕)], of the missing magnetic signals
+inferred by the Bayes’ model with the Maxwell’s equations, when
+two tangential components (Bt from MPs #15 and #16) of the
+magnetic signals are missing. Thick black line marks where the
+posterior is maximum indicating that infinite number of solutions
+are possible. Data are inferred for KSTAR shot #9010 at 0.1 sec.
+68
+4.14 Successful GP predictions (red crosses) compared with the actual
+data (blue circles) for (a) Bt and (b) Bn at 3.70 sec of KSTAR
+shot #9010 where we remove nine non-consecutive signals (indi-
+cated by red arrows) simultaneously to examine the proposed GP
+imputation scheme. On the other hand, if the magnetic signals
+are spatially varying fast such as (c) Bt of MPs #15 and #16 and
+(d) Bn of MPs #17 and #18 at 0.10 sec of the same shot, the GP
+imputation scheme fails to infer the correct values. . . . . . . . . .
+71
+ix
+
+LIST OF FIGURES
+4.15 (a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and #18
+from KSTAR shot #9010 at 0.1 sec as shown in Fig. 4.14(c) and
+(d). Green triangles obtained by the Bayes’ mode with the GP
+match the measured values (blue circles) well, while the GP-only
+method (red crosses) fails to do so as has been discussed in Sec.
+4.2.3. Comparisons of temporal evolutions for (c) Bt from MP
+#15 and (d) Bn from MP #17 from KSTAR shot #9427 where
+blue line is the measured values, red line for the GP-only and green
+line for the Baye’s model with the GP. Green lines agree well with
+blue lines well throughout the whole discharge including ramp-up
+and ramp-down phases. . . . . . . . . . . . . . . . . . . . . . . . .
+73
+4.16 Schematic diagram of FL recovery via a deep neural network. (A)
+The positions of magnetic measurements on the KSTAR poloidal
+cross-section where both Bn and Bt exist (blue dots), only Bn
+exists (pink dot), only Bt exists (green dots), and FLs exist (red
+crosses). (B) Schematics of the deep neural network whose output
+stands for the flux function converted into BR and BZ through
+analytic differentiation.
+(C) Temporal evolution of the plasma
+current for KSTAR 24445 shot. (D–G) The network results (blue
+area) at the red dotted lines in (C) are presented compared with
+the measured signals (red dots). First row is for BR, second row
+is for BZ, and the last row is for FL.
+. . . . . . . . . . . . . . . .
+81
+4.17 Statistical analysis of the trained network with test dataset. (A)
+Statistics of the coefficient of determination between the measured
+and the network BR (left) and BZ (right) from the ramp-up phase,
+and (B) from the flat-top phase. (C) Distributions of the plasma
+current measured from the Rogowski coil (purple line) and the
+network (purple area) of the ramp-up phase (top) and the flat-top
+phase (bottom). (D) Using 24445 shot, Statistics on the difference
+between the measured ψ and the network ψa
+rel of the ramp-up
+phase (blue) and the flat-top phase (red). . . . . . . . . . . . . . .
+82
+x
+
+LIST OF FIGURES
+4.18 Comparison of equilibrium reconstructions based on the network
+(black), the expert (green) and the novice (orange).
+(A) Left:
+comparison of the equilibrium results at 498.5 msec of 24445 shot.
+Right: a novice producing equilibrium overlaid with the plasma
+boundaries from the network and the expert (dotted lines). (B)
+Spatial profiles of the plasma current density at Z=0 location.
+(C) Chi-square results of the ψ. (D-F) Same results with (A-C)
+at 2704.3 msec. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+84
+4.19 A poloidal cross-section of KSTAR with the first wall (blue dotted
+line). Green dotted line indicates a Rogowski coil measuring the
+plasma current (Ip). Green open circles and crosses depict loca-
+tions of the magnetic pick-up coils measuring 32 normal (Bn) and
+36 tangential (Bt) magnetic fields, respectively, whereas green tri-
+angles represent 22 flux loops measuring poloidal magnetic fluxes
+(ΨFL). Black asterisks (22 × 13 spatial positions) show locations
+where we obtain the values of ψ from the off-line EFIT results. . .
+91
+4.20 Before (blue) and after (red) the magnetic signal adjustments for
+(a) normal and (b) tangential components of magnetic fields mea-
+sured by the magnetic pick-up coils, and (c) poloidal magnetic
+flux measured by one of the flux loops. The signals return closer
+to zeros after the adjustment when all the external magnetic coils
+(except the toroidal field coils) are turned off at around 30 sec in
+this KSTAR discharge. . . . . . . . . . . . . . . . . . . . . . . . .
+93
+4.21 An example of the two networks’ results trained with the cost func-
+tion (a) ϵ and (b) ϵnew for KSTAR shot# 17939 at 0.950 sec. Both
+networks (red dashed line) reproduce the ψTarget (black line) well
+(left panels), but only the network trained with ϵnew reproduces
+∆∗ψTarget (right panels).
+. . . . . . . . . . . . . . . . . . . . . . .
+97
+4.22 The descending feature of training (blue line) and validation (red
+dashed line) errors as a function of iterations. Shaded areas rep-
+resent standard deviation of the errors. . . . . . . . . . . . . . . .
+99
+xi
+
+LIST OF FIGURES
+4.23 Performance tests of the NN2017,2018 network on the unseen KSTAR
+discharges from (a)(b) 2017 campaign and (c)(d) 2018 campaign.
+The values of R2 and histograms of (a)(c) ψNN vs. ψTarget and
+(b)(d) ∆∗ψNN vs. ∆∗ψTarget with colors representing number of
+counts manifest goodness of the NN2017,2018 network. Red dashed
+line is the y = x line. . . . . . . . . . . . . . . . . . . . . . . . . . 101
+4.24 The actual reconstruction results for the KSTAR shot#18057,
+comparing the network results and off-line EFIT reconstructions
+for ramp-up ((b) and (c)), flat-top ((d) and (e)), ramp-down ((f)
+and (g)) phases following (a) the plasma current evolution. Black
+lines indicate the flux surfaces from the off-line EFIT, overlaid
+with the red dotted lines which stand for the NN reconstructions.
+As a figure of merit, magnitudes of PSNR metric are written on
+each figure.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
+4.25 Same as Figure 4.23 for the the NN2017 network, i.e., trained with
+the data sets from 2017 campaign. . . . . . . . . . . . . . . . . . . 103
+4.26 Same as Figure 4.23 for the the NN2018 network, i.e., trained with
+the data sets from 2018 campaign. . . . . . . . . . . . . . . . . . . 104
+4.27 Histograms of MSSIM (left panel) and PSNR (right panel) for (a)
+NN2017, (b) NN2018 and (c) NN2017,2018. Red (green) line indicates
+the test results on the data sets from 2017 (2018) campaign. In
+each sub-figure, top (bottom) panel show the results for ψ (∆∗ψ).
+The off-line EFIT results are used as reference. . . . . . . . . . . . 106
+4.28 An example of reconstructed ψ (R, Z) (left panel) and ∆∗ψ (R, Z)
+(right panel) for KSTAR shot #17975 at 0.7 sec comparing (a) rt-
+EFIT (green) and off-line EFIT (black) and (b) nn-EFIT (NN2017,2018)
+(red) and off-line EFIT (black). . . . . . . . . . . . . . . . . . . . 108
+xii
+
+LIST OF FIGURES
+4.29 Histograms of MSSIM (left panel) and PSNR (right panel) of ψ
+(top) and ∆∗ψ (bottom) calculated by the nn-EFIT (black) and
+the rt-EFIT (green), where the nn-EFIT is the NN2017,2018. For
+both the nn-EFIT and the rt-EFIT, the off-line EFIT is treated
+as reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
+4.30 Same as Figure 4.29 with the NN2017 as the nn-EFIT where the
+test data sets are obtained from (a) 2017 campaign and (b) 2018
+campaign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
+4.31 Same as Figure 4.29 with the NN2018 as the nn-EFIT where the
+test data sets are obtained from (a) 2017 campaign and (b) 2018
+campaign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
+4.32 Measured (blue open circles) and inferred with the imputation
+method [3] (red crosses with their uncertainties) values for (a)
+Bn and (b) Bt.
+Probe # on the horizontal axis is used as an
+identification index of magnetic pick-up coils. Inferred probes are
+Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn and Probe #4, 6, 8,
+11, 17, 29, 30, 32, 35 for Bt. . . . . . . . . . . . . . . . . . . . . . 112
+4.33 Top panel: nn-EFIT (NN2017,2018 network) reconstructed equilibria
+without any missing values (black line), and with two missing val-
+ues replaced with the inferred values using the imputation method
+(green line) or with the zeros using the zero-padding method (pink
+dashed line), where the missing values are (a) Bn Probe #14 and
+30 (left panel) and (b) Bt Probe #4 and 8 (right panel). Bottom
+panels: histograms of MSSIM and PSNR using the imputation
+method (green) and the zero-padding method (pink) for all the
+equilibria obtained from KSTAR shot #20341, where the refer-
+ence values are those obtained using nn-EFIT without any missing
+values. Note that there are many more counts less than 0.9 for
+MSSIM with the zero-padding method.
+. . . . . . . . . . . . . . 113
+4.34 Same color code as in Figure 4.33. Missing values are (a) eight Bt
+(except only Probe #6) and (b) all nine Bt.
+. . . . . . . . . . . . 115
+xiii
+
+LIST OF FIGURES
+4.35 Same color code as in Figure 4.33. Missing values are (a) eight Bn
+(except only Probe #37), (b) all nine Bn. . . . . . . . . . . . . . . 116
+4.36 Same color code as in Figure 4.33. Combinations of missing Bn
+and Bt are examined: (a) four missing Bn and four mssing Bt case
+and (b) nine missing Bn and nine missing Bt case. . . . . . . . . . 117
+4.37 Self-teaching unsupervised learning scheme in GS-DeepNet . . . . 123
+4.38 Statistical evaluation of GS-DeepNet training
+. . . . . . . . . . . 128
+4.39 Equilibrium knowledge learned by GS-DeepNet
+. . . . . . . . . . 131
+4.40 Performance of GS-DeepNet with local pressure constraints . . . . 132
+B.1 Simple neural network 2 . . . . . . . . . . . . . . . . . . . . . . . 153
+B.2 Simple neural network 3 . . . . . . . . . . . . . . . . . . . . . . . 156
+xiv
+
+Chapter 1
+Preface: what would we do with
+a Black Box for fusion research?
+“No one has ever proved that EL DORADO or
+SKYPIEA doesn’t exist!!”, “Well, Let them laugh!
+That’s what makes it A GREAT ADVENTURE!!”
+— Oda Eiichiro,
+ONE PIECE
+When I started studying nuclear fusion and deep learning for the first time, I
+was totally absorbed in two tasks: (1) surveying the whole history of Neural
+Network used in the field of nuclear fusion; (2) neural network regressions for
+sine functions with various signal-to-noise ratios (SNRs). When it comes to the
+usage of neural networks, in brief, there were two major pedigrees such that one
+wished to control tokamaks accurately via neural networks, and the others tried
+to make neural networks predict tokamak disruptions (violent events undoubtedly
+forcibly terminating tokamak operations).
+Starting with an idea of real-time prediction of plasma positions [4], mapping
+measurement signals of the plasma to the positions of that was extensively studied
+by Ref. [5–11] in the 1990s as well as a review article introducing the studies to
+readers with no previous knowledge of the network [12]. Yet there had been
+no significant change in this research field [13] until advanced neural network
+techniques (deep learning) contributed to the field again [14–16].
+Regarding
+the disruption prediction, in 1994, there was a master’s thesis [17] trying to
+predict disruptions in a tokamak plasma (probably for the first time) by using
+a neural network. Afterward, this disruption prediction field has grown rapidly
+1
+
+CHAPTER 1. Preface: what would we do with a Black Box for fusion research?
+over decades, being able to predict multi-tokamak disruptions based on a single
+neural network [18,19] by taking advantage of previous researches that focused
+on disruptions occurring in a single fusion device [20, 21] as a cornerstone. Of
+course, there is other genealogy of the neural network in fusion community which
+dealt with tokamak transport [22–28], but I would like to spare the details of it
+since I believe that two main start points of the history of the neural network in
+fusion research are definitely tokamak control and disruption prediction.
+In short, the neural networks have been simply used to connect control-
+relevant parameters of the plasma generated from plasma equilibrium (a force-
+balanced state of the plasma) with given diagnostic signals as a viewpoint of
+tokamak control as well as they have been used to let a tokamak discharge be on
+a disruption alert by looking at tokamak measurements in real time in case that
+a disruption is about to occur. However, in either case, all the neural network
+did was merely to link given inputs to certain plasma physically meaningful
+parameters without understanding any physics behind. If the neural network
+doesn’t know physics, how can it be used in the physics field? Thus, the idea
+that I have always had in my mind after finding these results is that the neural
+network just acts as a “good but not great” supporting actor in nuclear fusion
+since the network seems to be such a magical tool that maps any inputs to any
+outputs, which does not require enough physics interpretation. Thus, I thought
+“Isn’t that a limitation of the neural network for nuclear fusion research (but also
+other scientific fields) because its working principle might be hard to be trusted
+(or scrutable)?”
+The ability of the neural network is actually impressive. The neural network
+has the ability to extract relations between two (or more) phenomena in terms
+of basic arithmetic operations. As well as two dimensional data regression in
+multidimensional space [29–31], deep learning is powerful to handle image pro-
+cessing [32,33], which is far beyond human abilities, and able to perform natural
+language understanding [34], video processing [35] and language generation [36].
+These applications show that deep learning is (nearly) close to human level in
+various fields.
+2
+
+CHAPTER 1. Preface: what would we do with a Black Box for fusion research?
+Figure 1.1: The network regression results compared to the sine functions
+with various noise levels, σ. The blue, the orange dots, the red lines and the
+black lines are the training, the validation sets, the network results and the
+noise-free sine functions, respectively.
+This remarkable strength of deep learning can be found even with a simple
+regression analysis. I would like to discuss sine function regressions here which
+I started figuring out when I studied neural networks for the first time. Figure
+1.1 shows the results of neural networks trained with data points generated from
+sine functions, i.e.,
+t(x) = sin 6πx + ϵ
+(1.1)
+where t is the observed data and ϵ stands for the level of Gaussian noise, ϵ =
+N(µ, σ2), whose mean value µ is zero, and standard deviation σ is set arbitrar-
+3
+
+ = 0.05
+ = 0.5
+=3CHAPTER 1. Preface: what would we do with a Black Box for fusion research?
+ily. To train the networks, I divide the dataset into training (blue dots) and
+validation data (orange dots) which are used to train and validate the networks
+during the training procedure, respectively. The black line is the noise-free sine
+function, and the red line is the network results. The data points are prepared
+within the interval of 0 – 1 along the x-axis. From top to bottom of Figure 1.1,
+with one significant figure, the standard deviation σ are 0.05, 0.5 and 3 where
+the SNRs are approximately 200, 2 and 0.05 (20, 3 and -10 in decibel). The de-
+tailed explanation about the network training will be discussed in the following
+chapters.
+As shown in the figure, the first two plots have the relatively less noisy
+observed data which is straightforward to be identified as sinusoidal functions
+even with our bare eyes. Thus, it is quite acceptable that the networks seem to
+be the sine functions since they are matched well with our intuition. However,
+let us take a look at the last figure. Could anyone find any features of the sine
+function from the blue (and orange) dots with the naked eye only? I swear that
+no one can do that. It means that even if the networks tell us the blue dots are
+possibly produced from a sinusoidal function, because our intuition (we indeed
+have our intuition in this case although the intuition is not proper anymore)
+refuses to accept the argument provided by the network since it is difficult to
+determine that the network fits to our intuition or not, therefore we cannot
+believe and trust what the network insists on.
+The result above is quite surprising since the network actually “did not
+know” what the observed data is made from, but “infer” the sine function. This
+process is seemingly “magical” like a black box to those who were not involved
+in the process of generation of the training data, which could be the fact that
+makes us doubt the network’s capabilities. In other words, I would like to argue
+that the sine function can be regarded as physical parameters of interest, and
+similarly the intuition can turn out to be physical theories. Namely, although
+the neural network is able to generate physically reliable outputs, we would not
+depend on the results since we can think the network never fully follows laws of
+physics of interest.
+4
+
+CHAPTER 1. Preface: what would we do with a Black Box for fusion research?
+Then how can the neural network be counted on for scientific uses (or nuclear
+fusion research)? To answer this question, I shall start from defining uncertainty
+in deep learning. First of all, there are situations such that observed (or collected)
+data is too noisy or too sparse to sufficiently cover possible phenomena, which
+leads to the first type of uncertainty, i.e., aleatoric uncertainty. This is yielded by
+the poor quality of observed (or collected) data. The other type of uncertainty
+is caused by a network model itself such that the model is not as complex as
+collected data, or free-parameters of the model is poorly determined.1 These yield
+epistemic uncertainty (also referred to as model uncertainty). Both uncertainties
+result in predictive uncertainty which quantifies how the network is sure about
+its prediction.
+Perhaps, if we have a lot of data which can sufficiently cover all possible
+physical phenomena, then we can possibly give credence to whatever a neural
+network outputs. This is unfortunately almost impossible, and does not always
+guarantee that the neural network follows physics theories. Then, what if we
+train a neural network with physics theories? Does this way quantify (or reduce)
+the network’s epistemic uncertainty (knowledge uncertainty) related to the “the-
+ories”? As a result, does this mean the network truly follows the theories and
+shows how it is confident with respect to given inputs (and given theories)? In
+particular, unlike the past “magic” approaches, can’t that lead us to trust the
+neural network a little more (or further)? Answers to these questions are the
+main gist of this thesis, which will be provided in the following chapters from the
+perspective of tokamak control.
+With the Korea Superconducting Tokamak Advanced Research (KSTAR),
+Article IV has been developed to show that a neural network can learn a plasma
+‘theory’ with the support of a database prepared from a numerical algorithm by
+1The etymology of the word aleatoric is the Latin “aleator”, or “dice player”, meaning that
+aleatoric uncertainty is the “dice player’s uncertainty”. The etymology of the word epistemic is
+the Greek “episteme” known as “knowledge”, meaning that epistemic uncertainty is “knowledge
+uncertainty”. Epistemic uncertainty can be often reducible through having more knowledge,
+while aleatoric uncertainty sometimes cannot be reduced due to the measurement noise or the
+inherent stochasticity.
+5
+
+CHAPTER 1. Preface: what would we do with a Black Box for fusion research?
+reconstructing plasma equilibria based on the Grad-Shafranov (GS) equation.
+This is a preliminary application for the network to provide the possibility of a
+complete unsupervised learning for the reconstruction such that the neural net-
+work can understand the GS equation itself, and the database from the numerical
+algorithm is no longer required. This is described in Article V, providing how
+a principle of the unsupervised learning works, and why this kind of network
+is required for tokamak control. Article I, Article II and Article III have been
+developed to preprocess KSTAR measurements used to inputs of our networks
+since baseline increases of measured signals in time (signal drift), missing signals
+due to mechanical issues and inconsistency between signals should be handled
+to use our networks in any experimental circumstances. From Bayesian neural
+networks, our applications are able to quantify the epistemic uncertainty related
+to the plasma theory by obtaining inference results of the GS equation as well
+as plasma information such as positions and locations of the plasmas (which are
+hard to be measured directly) in the KSTAR. One can find the detailed funda-
+mentals and analyses in the next chapters.
+I have recognized that the neural network is treated as a black box, in-
+scrutable as well as unbelievable. How can this prejudice be resolved? Let me
+leave this here: solving differential equations numerically also faced a tough
+proof back then around 1950. I would say, we are simply taking a look at a novel
+method whose detail is not fully figured out yet, and I hope this thesis corrobo-
+rates it is fine to use a neural network in nuclear fusion research, including the
+controls of the tokamak plasmas in real time.
+6
+
+Chapter 2
+Nuclear Fusion
+나가와 도깨비, 인간, 레콘이 살고 있는 집에서
+누군가가 바닥에 바늘을 떨어뜨렸다. 잘 보이지 않는
+바늘을 찾아내는 방법은?
+답 : 도깨비가 바늘이 뜨거워질 정도의 도깨비불을
+퍼뜨리고 나가가 뜨겁게 달아오른 바늘을 눈으로
+확인하여 집어 올린다. 그리고 인간은 온 힘을 다해
+레콘을 말려야 한다. 설득력이 충분하다면 레콘이
+집을 들어 흔드는 것은 막을 수 있을 것이다.
+— 이영도,
+피를 마시는 새
+What is nuclear fusion?
+It is the morning and the evening star.
+I slightly
+transform a Sinclair Lewis (Harry Sinclair Lewis, February 7, 1885 – January
+10, 1951) quote to start explaining what nuclear fusion is in the less heavy mood.
+The energy from the nucleus can be obtained by combining light nuclei into
+heavier ones. This is called nuclear fusion energy [37], which is a foundation of
+energy generated from the Sun and stars in outer space. Before deepening our
+sight about nuclear fusion, let me consider three very different time scales which
+are involved in climate change or energy sources if one considers either of them.
+The first view is a few months – a few years scale that is a short time scale to
+be required to take temporary solutions such as making an agreement like the
+Kyoto Protocol, issuing carbon credits, limiting the speed limit of automobiles,
+offering tax credits for renewable energy plants, etc. As a relatively longer time
+scale, 10 – 50 years, we can use this to take such solutions like developing new
+clean (or carbon-free) energy sources. The last perspective about the time scales
+7
+
+CHAPTER 2. Nuclear Fusion
+Figure 2.1: Fusion reaction rates of deuterium and tritium (D-T) and
+deuterium and deuterium (D-D) with some well-known cross sections. The D-T
+fusion reaction rate is remarkably higher than the other reaction rates at the
+temperature of the order of 10–100 keV.
+is the longest time scale, 100 – 5000 years, which is the faraway future, so we
+barely know what will happen in the future. The problem is we are already
+facing global warming and sea level rise as well as rising fuel prices. A more
+vicious truth is that we do not have much time to prepare them and, especially,
+the intermediate time scale. (I largely take this information from Ref. [38]).
+In these circumstances, nuclear fusion is a solution as a clean energy source
+which has ideally no blemish to be worried about generating any carbon-like
+byproducts and a vast resource of fusion fuels available from the sea. Although
+fusion power will take time (and money also) to be realized, however, we are
+living in the land and era of taking photos of Pluto, trying to reuse space rockets
+8
+
+T /million K
+15
+150
+1500
+0009
+10-14
+D-T
+D-D
+D _3 He
+p-11 B
+10~15
+T-T
+T _3 He
+3He 3 He
+10-16
+10-17
+(n0)
+10-18
+10~19
+10~20
+10
+100
+1000
+T /keVCHAPTER 2. Nuclear Fusion
+and build AI technology in our daily life, thus, they can be affordable. Over
+decades, we have been trying to build nuclear fusion power plants which are able
+to contain and sustain fusion reactions occurring only in really extreme conditions
+on Earth. The sequence of the fusion reaction of interest is following: two small
+nuclei are given enough kinetic energy to pass over a potential (Coulomb) barrier
+due to their charges, then they fuse together and are transformed into another
+nuclei, and then they produce large energy which is often called fusion energy.
+We often tap deuterium and tritium as the two nuclei since their reaction rate is
+extraordinarily superior to the other famous reaction rates shown in Figure 2.1,
+which is
+2
+1D + 3
+1T −→ 4
+2He (3.5 MeV) + 1
+0n (14.1 MeV)
+(2.1)
+where the goal to crash through the Coulomb barrier is to heat them up to the
+temperature of the order of 10 keV (≈ 108 K), which makes the deuterium and
+the tritium to become plasma, the fourth state of matter. In this state, the
+dynamics of the plasma is governed by a collective behaviour and sensitive to
+externally applied electromagnetic fields. Sensitivity to external fields can be
+interpreted as a way to control the plasma through the fields, allowing us to have
+a fusion reactor confining the plasma magnetically for a sufficiently long time
+to acquire enough fusion reactions. The alpha particles (4
+2He) confined in the
+magnetic cage can heat the plasma through collisions, while the neutrons (1
+0n)
+ignoring magnetic fields can be used for a blanket [39] to capture the neutrons
+and convert their energy into heat.
+From now on, let me consider an actual time scale that we need to have
+in order to see enough fusion reactions in the fusion reactors. There is a rela-
+tion portraying how much time do the reactions require when a certain amount
+of plasma and a certain plasma temperature are given. This is known as the
+Lawson Criterion which describes the relation between plasma density n, ion
+temperature T and confinement time τE as shown below
+nTτE ≥ 3 × 1021 keV s/m3
+(2.2)
+where the confinement time τE is the ratio of the plasma thermal energy density
+9
+
+CHAPTER 2. Nuclear Fusion
+Figure 2.2: Lawson criterion for D-T fusion. The ordinate stands for nτE.
+This figure is taken from [38].
+W to the power Pheat that is needed to keep the plasma at a certain temperature
+as shown below
+τE = W/Pheat.
+(2.3)
+A modified Lawson Criterion is shown in Figure 2.2 where BREAKEVEN
+stands for balances between the fusion energy and the energy needed to sustain
+the plasma, and IGNITION is a condition to ignite a self-sustaining plasma.
+The figure says that we need at least nτE of the order of 1020s/m3 to achieve the
+breakeven condition with τE of the order of 1 sec if we expect that a reasonable
+plasma density is ∼ 1020#/m3. Dramatically speaking, we must hold the plasma
+for 1 sec inside of the fusion reactors, and I develop a neural network to control
+the plasma for the time scale of 1 sec really precisely by reconstructing a better
+plasma equilibrium in real time, which will be introduced out of this thesis.
+Thus, we can probably say that nuclear fusion is figuratively the morning and
+the evening star of which awakens us to reach a future of using the clean and
+carbon-free energy invented by humankind’s knowledge.
+10
+
+1E+16
+Density x time
+1E+15
+IGNITION
+1E+14
+BREAKEVEN
+1E+13
+0
+20
+40
+60
+80
+100
+lon temperature (keV)CHAPTER 2. Nuclear Fusion
+Figure 2.3: (a) A typical tokamak configuration. Image courtesy of
+EUROfusion. (b) Elevation view of ths KSTAR tokamak [40].
+2.1
+Tokamak
+Previously, I mentioned that the plasma responds to the external electromag-
+netic fields sensitively, and this leads us to build the fusion reactor generating
+the magnetic fields to confine and control the plasma. One of the reactors working
+such a way is tokamak whose name comes from the Russian words toroidalnaya
+kamera magnitnaya katushka. These words mean toroidal chamber magnetic
+coils. Although there are various concepts of magnetic confinement devices such
+as stellarator and reversed field pinch device, I would like to consider the tokamak
+solely in this thesis since this thesis is mainly based on tokamak experimental
+results. As shown in Figure 2.3 (a), the tokamak generates two major direc-
+tions of the magnetic fields; toroidal magnetic field and poloidal magnetic field.
+The toroidal field coils represented as the gray structures generate the toroidal
+magnetic field in the direction of the red arrow in the figure. Similarly, The
+poloidal field coils (green) and the central solenoids (blue) produce the poloidal
+magnetic field in the direction of the purple arrows, while purposes of those coils
+are slightly different: the poloidal field coils are generally used to control the
+plasma position; the object of the central solenoids is to induce a current to the
+plasma in order to generate a plasma current in toroidal direction. Therefore,
+the plasma current is the main source of the poloidal magnetic field.
+I would like to note that the tokamak experiments done by the Korea
+11
+
+Outerpoloidal
+A
+field coil
+Cryostat
+B
+Central solenoid
+PF5U
+PF6U
+Toroidal field coil
+X
+PF7U
+PF2U
+Vacuum
+PFIU
+Vessel
+PFIL
+PF2L
+PF3L
+PF4L
+proida
+PF7L
+Central
+PF6L
+Gravity
+Solenoid
+toddns
+PF5L
+Poloidal
+field
+netic
+ConcreteFloorCHAPTER 2. Nuclear Fusion
+Table 2.1: Designed ranges of major paramters of KSTAR [1]
+Symbol
+Parameter
+Baseline
+Upgrade
+BT
+Toroidal field [T]
+3.5
+Ip
+Plasma current [MA]
+2.0
+R0
+Major radius [m]
+1.8
+a
+Minor raidus [m]
+0.5
+κ
+Elongation
+2.0
+δ
+Triangularity
+0.8
+-
+Pulse length [s]
+20
+300
+-
+Neutral beam [MW]
+8.0
+16.0
+-
+Ion cyclotron [MW]
+6.0
+6.0
+-
+Lower hybrid [MW]
+1.5
+3.0
+-
+Electron cyclotron [MW]
+0.5
+1.0
+Superconducting Tokamak Advanced Research (KSTAR) which is one of the
+first research tokamaks with fully superconducting magnets in the world located
+at South Korea have been dedicated to developments of this thesis. The elevation
+view of KSTAR is shown in Figure 2.3 (b). I outline briefly below KSTAR and
+its specifications.
+KSTAR is one of the first fusion experimental reactors using superconducting
+magnets in the world. The typical and designed ranges of the major specifications
+of KSTAR are shown in Table 2.1. It is worth mentioning that KSTAR recently
+sustained the ion (deuterium) temperature up to ∼100 million degree Kelvin at
+the center of the plasma for ∼20 sec for the first time [41]. KSTAR has a major
+radius of 1.8 m and a minor radius of 0.5 m. The central solenoids of KSTAR are
+designed to induce the plasma current of 2.0 MA, and the toroidal field coils are
+capable of generating the toroidal magnetic field of 3.5 T. The application in this
+thesis provides a self-sustained deep learning approach for the plasma equilibrium
+from KSTAR plasma diagnostic data which has been supported from developed
+preprocessors based on Bayesian inference and deep learning respectively. I will
+12
+
+CHAPTER 2. Nuclear Fusion
+introduce what I mean by the plasma equilibrium in the next section.
+2.2
+Equilibrium
+In the field of nuclear fusion, Equilibrium, Tokamak Equilibrium, Plasma Equilib-
+rium and Magnetic Equilibrium all mean the same phenomenon that the Lorentz
+force exerted on the plasma balances the plasma pressure (or pressure gradient)
+in a macroscopic equilibrium state inside the tokamak.
+The basic condition
+for the plasma equilibrium suggest that the force on the plasma be zero at all
+plasma regions. This equilibrium comes from the single fluid magnetohydrody-
+namic (MHD) equations [42] which explain fluid-like, macroscopic behaviors of
+ionized ions and electrons.
+Before explaining equations of the plasma equilibrium, I would like to state
+two fundamental aspects of the equilibrium: (1) the internal balance between the
+two forces as introduced above; (2) there is the shape and position of the plasma
+determined and controlled by the external coil currents.
+From now on, Let us take a look at the MHD equation to arrive at the force
+balance equation and beyond. The MHD momentum is given by,
+ρ
+�∂⃗v
+∂t +
+�
+⃗v · ∇
+�
+⃗v
+�
+= ⃗J × ⃗B − ∇p
+(2.4)
+where ρ is the mass density, ⃗v is the bulk plasma velocity field, ⃗J is the (plasma
+and external) current density, ⃗B is the magnetic field, and p is the plasma pres-
+sure. If the static equilibrium conditions (⃗v = 0 and ∂/∂t = 0) are assumed, the
+equation turns out to be the force balance equation which is
+⃗J × ⃗B = ∇p.
+(2.5)
+From this equation, it is obvious that there is no pressure gradient along the
+magnetic field lines, which is
+⃗B · ∇p = 0
+(2.6)
+13
+
+CHAPTER 2. Nuclear Fusion
+where it also means that the plasma forms magnetic surfaces of constant pressure.
+Likewise, the force balance equation tells us a relation:
+⃗J · ∇p = 0
+(2.7)
+which also imply that the current lines lie in the magnetic surfaces. Furthermore,
+it is convenient to define the poloidal magnetic function ψ. This is a constant
+quantity on each magnetic surface acting as the poloidal flux lying within that
+surface. Thus, there is another relation with the magnetic field:
+⃗B · ∇ψ = 0.
+(2.8)
+Through the force balance equation, based on a cylindrical coordinate and
+an axisymmetric systems with Maxwell’s equations (∇· ⃗B = 0 and ∇× ⃗B = µ0 ⃗J),
+we can now derive a differential equation for the poloidal flux function ψ which
+is called the Grad-Shafranov (GS) equation [43,44] as shown below
+∆∗ψ = R ∂
+∂R
+1
+R
+∂ψ
+∂R + ∂2ψ
+∂Z2
+= −µ0RJt
+= −R2µ0
+∂p
+�
+ψ
+�
+∂ψ
+− F
+�
+ψ
+�∂F
+�
+ψ
+�
+∂ψ
+(2.9)
+where F
+�
+ψ
+�
+is the poloidal current function as a function of ψ, which is related
+with the toroidal magnetic field BT as F
+�
+ψ
+�
+= R BT. The first two lines of the
+equation include effects of Maxwell’s equations, and the second to third lines are
+influenced by the force-balance equation.
+To obtain the solution of the equation, ψ(R, Z), it is required to observe Jt
+over the whole plasma volume. Unfortunately, magnetic measurements externally
+installed from the plasma are generally available, together with local temperature
+and density data of the plasma. Furthermore, the plasma exists in a certain region
+inside the tokamak. A boundary dividing the plasma with a vacuum region is
+called plasma boundary, last closed flux surface and separatrix. This boundary
+is determined after the solution ψ is found. Thus, this leads us to solve a free
+boundary and inverse problem.
+14
+
+CHAPTER 2. Nuclear Fusion
+Usually, a Green function’s formulation is carried out to solve the GS equa-
+tion as follows:
+ψ(R, Z) =
+� �
+G(R, Z; R′, Z′)Jφ(R′, Z′)dR′dZ′
+(2.10)
+where G is the free-space Green’s function, and (R′, Z′) is the position of a current
+source. But, one can raise a question like “Does the GS equation just give us a
+relation between given current densities and structures of the poloidal magnetic
+field (or flux surfaces) after all?”, “If that is true, can we use the Biot-Savart law
+instead of such complex differential equations?” Well, as a conclusion, it turns
+out that the formulation of the Green function and using the Biot-Savart law are
+the same eventually, meaning that using the law is viable. Therefore, I would like
+to introduce how to use the Biot-Savart law in our case and what is insufficient
+if we use the law only in the following subsection.
+2.2.1
+Biot-Savart Law
+In the tokamak, there are four major sources of the poloidal magnetic field,
+i.e., the poloidal field coils, the central solenoids, in-vessel coils [45] and the
+plasma (current). Eddy currents (vessel currents) which are currents induced on
+tokamak vessel structures are ignored for simplicity. As one can find in Ref. [46]
+and Ref. [45], all the external current coils have rectangular cross-sections, and
+they carry constant currents at a certain time. This means that if we assume
+the plasma current as a collection of wires whose cross-sections look rectangular
+shapes, we can use the Biot-Savart law for the vector potential and the magnetic
+field due to an arbitrary three-dimensional volume current with a rectangular
+cross-section (R2−R1)×(Z2−Z1) shown in Figure 2.4 in cylindrical coordinates.
+It is worth to mention that derivations introduced in this subsection are mainly
+based on Ref. [47].
+Let me consider the Biot-Savart law for the vector potential and the magnetic
+field by a volume current:
+⃗A (⃗r) = 1
+4π
+�
+l
+�
+s
+jd⃗l |⃗r − ⃗r′|−1 ds,
+(2.11)
+15
+
+CHAPTER 2. Nuclear Fusion
+Figure 2.4: A segment of the circular wire showing rectangular cross-section
+and carrying toroidal current in cylinder coordinates.
+⃗B (⃗r) = µ0
+4π
+�
+l
+�
+s
+j
+�
+d⃗l × (⃗r − ⃗r′)
+�
+d⃗l |⃗r − ⃗r′|−3 ds,
+(2.12)
+where ⃗r and ⃗r′ are positions of the field and source respectively, j is a constant
+current, ds is a differential element of cross-sectional area perpendicular to d⃗l
+which is a segmented line element along the current. Then, as shown in Figure
+2.4, set the field and source positions as ⃗r = (r, φ, z) and ⃗r′ = (r′, φ′, z′), respec-
+tively, where a current-carrying arc segment has properties such as R1 ≤ r′ ≤ R2,
+Z1 ≤ z′ ≤ Z2 and (φ2 − φ1) as the azimuthal length of the arc segment.
+I can rewrite the above equations as the following simple expressions
+⃗A (⃗r) = J
+4π
+� R2
+R1
+dr′
+� Z2
+Z1
+dz′ ⃗ˆA (⃗r) ,
+(2.13)
+⃗B (⃗r) = µ0J
+4π
+� R2
+R1
+dr′
+� Z2
+Z1
+dz′ ⃗ˆH (⃗r) ,
+(2.14)
+where J is the azimuthal constant current density, and Az = 0 due to the con-
+16
+
+CHAPTER 2. Nuclear Fusion
+ductor structure. Now, I can define the relevant forms as follows:
+ˆAj (⃗r) = 1
+2
+� φ2
+φ1
+dΦ
+�
+γD(Φ) + 2γr cos Φ sinh−1 β1(Φ)
++
+�
+r′2 − r2 cos 2Φ sinh−1 β2(Φ)
+�
+− r2 sin 2Φ tan−1 β3(Φ)
+�
+�
+�
+�
+− sin Φ,
+cos Φ,
+j = r, φ,
+(2.15)
+where the first and the second terms inside the bracket correspond to r and φ
+directions, respectively, and
+ˆHl (⃗r) =
+� φ2
+φ1
+dΦ
+�
+�
+�
+�
+�
+�
+�
+�
+�
+cos Φ
+�
+D(Φ) + r cos Φ sinh−1 β1(Φ)
+�
+,
+sin Φ
+�
+D(Φ) + r cos Φ sinh−1 β1(Φ)
+�
+,
+γ sinh−1 β1(Φ) − r cos Φ sinh−1 β2(Φ) − r sin Φ tan−1 β3(Φ),
+l = r, φ, z,
+(2.16)
+where the components inside the brackets correspond to r, φ and z directions
+from the top. I also define the following expressions as:
+γ = z′ − z,
+Φ = φ′ − φ,
+D2(Φ) = γ2 + B2(Φ),
+B2(Φ) = r′2 + r2 − 2rr′ cos Φ,
+G2(Φ) = γ2 + r2 sin2 (Φ),
+β1(Φ) = (r′ − r cos Φ)/G(Φ),
+β2(Φ) = γ/B(Φ),
+β3(Φ) = γ(r′ − r cos φ)/[r sin φD(Φ)].
+(2.17)
+Therefore, for all the conductors in the tokamak, the only task left is calculating
+the equations above for each conductor with a condition of (φ2 −φ1) = 2π. Now,
+17
+
+CHAPTER 2. Nuclear Fusion
+we finally have the poloidal flux function ψ related to the Biot-Savart law given
+by ψ(R, Z) = 2πRAφ.
+At this moment, it seems that we have a complete formula for a solution
+of the tokamak equilibrium. However, we should remember that our problem is
+a free-boundary and inverse problem. For simplicity, let us consider the inverse
+problem only. Thus, if we assume an arbitrary distribution of the plasma current
+density, then we can obtain a distribution of ψ from the equations above and
+update the plasma current density again using the obtained ψ based on ∇ ×
+⃗B = µ0 ⃗J or the first and second lines of the GS equation to be consistent with
+the external magnetic measurements. If we keep carrying out those sequences
+repeatedly, we may end up with a converged distribution of ψ, i.e., flux surfaces;
+seemingly we finish solving the tokamak equilibrium! However, what we must
+never forget during the sequences is whether or not the result satisfies the force
+balance. In other words, if our result does not meet the second and third lines
+of the GS equation, i.e., Jφ = Jφ(R, ψ), then our result is totally meaningless.
+We fully contemplate this in order to design a neural network that solves the
+GS equation without any support of solutions of the GS equation, which will be
+presented soon.
+2.3
+Plasma diagnostics
+In this section, I briefly introduce plasma diagnostics used in this thesis. The GS
+equation shows that the spatial variation of ψ is related to the current density.
+Namely, if the current density is exactly known, then the solution ψ would be
+obtained through the GS equation. Unfortunately, knowing internal information
+of the plasma is barely straightforward due to the temperature of the plasma
+(∼ 108 K), therefore the current density should be inferred as well by taking ad-
+vantage of externally and locally measured data. From the inferred current, the
+GS equation is iteratively solved until an estimated equilibrium fits the measured
+data reasonably. Here, the external and the local measurements are magnetic
+measurements and plasma pressure measurements, respectively, which are essen-
+18
+
+CHAPTER 2. Nuclear Fusion
+Figure 2.5: A schematic of the magnetic diagnostics. Image courtesy of
+Ref. [48].
+tial to observe the plasma equilibrium and energy transport in nuclear fusion
+experiments.
+2.3.1
+Magnetic diagnostics
+Here, I would like to deal with magnetic diagnostics relevant to the poloidal
+magnetic field since solving the GS equation is highlighted.
+KSTAR has in-
+stalled the magnetic measurements [49] on the KSTAR vessel wall far away from
+the plasma as induction coil-type measurements with analogue integrators [48].
+Among them, I take advantage of 84 magnetic pick-up coils (magnetic probes)
+which measure the poloidal magnetic fields of the normal and the tangential
+directions to the vessel wall and 45 flux loops (FLs) measuring the poloidal mag-
+netic fluxes, respectively [2, 49]. I also use Rogowski coils measuring the total
+plasma current, the poloidal field coil currents and the in-vessel coil currents.
+Basic forms of the diagnostics are shown in Figure 2.5.
+The brief history of the KSTAR magnetic diagnostic system is as follows.
+A schematic design of the diagnostics and how to install it to the KSTAR were
+suggested [49], and performances of the designed magnetic pick-up coils were
+tested in a vacuum chamber [50]. The designs were improved and analyzed in a
+radio-frequency environment [51]. After that, it was reported that some of the
+fabricated magnetic measurements were installed at the KSTAR vessel [52] as
+well as the design of the integrators for the systems was reported [53]. In 2008,
+19
+
+Diamagnetic
+loop
+Magnetic
+Flux loop
+Saddle
+field
+loop
+probe
+Rogowski
+coilCHAPTER 2. Nuclear Fusion
+Figure 2.6: (a) Port allocation of KSTAR TS system. Image courtesy of
+Ref. [65]. (b) KSTAR CES layout composed of a window, mirror, collection
+lens, a spectrometer and a CCD camera. Image courtesy of Ref. [66].
+only some of the poloidal field coils were driven to analyze operation performances
+of the measurements [2] for the first plasma on KSTAR. Diamagnetic loops were
+also designed and installed [54], and their performances were reported in 2011
+[55]. An outline of the first plasma of the KSTAR was published in 2010 [56]
+with measured magnetic data from various measurements.
+In 2017, a study
+about how to improve a plasma operation based on the magnetic diagnostics was
+introduced [57].
+When it comes to the integrator, several hardware designs were introduced
+[53, 58–62] to correct a phenomenon called signal drift, i.e., a baseline of a
+measured signal drifting in time, and software correction approaches were sug-
+gested [58,59,63,64].
+2.3.2
+Pressure measurements
+To solve the GS equation, the plasma pressure on the ψ coordinate is necessary
+over the whole tokamak region.
+Currently, all we can do is measuring local
+thermal pressures of the plasma. These pressures are estimated from the ideal gas
+law, i.e., the pressure p = nT where n and T are the density and the temperature,
+respectively. The reason why I stress the term “thermal” is there is the fast
+ion pressure, pfast, which is contributed by the fast ion (more energetic than a
+thermal ion) populations coming from the Neutral Beam Injection (NBI) system
+20
+
+KSTAR hall
+Diagnostic room
+Beamdumpsystem
+B
+D
+ControlPC
+Optic system &
+Cassette
+CCD
+PhotonMax
+512B
+M
+Wal
+Spectrometer
+A
+Laserinputsystem
+McPherson
+1.33 m
+Tangential Beam
+Nd:YAG
+(1064nm)CHAPTER 2. Nuclear Fusion
+[67] in the KSTAR. Profile measurement systems for this pressure still need to
+be developed further [68–70].
+To estimate the plasma pressure, we need to measure n and T of the elec-
+tron and the ion, respectively. The Thomson Scattering (TS) system is used
+detect the electron density ne and the electron temperature Te simultaneously,
+which is one of the major methods to obtain those information by measuring the
+scattered and Doppler-shifted photons from an interaction between high-power
+laser photons and the plasma electrons. The KSTAR TS system provides 31
+local measurements with a spatial resolution of 6 mm to 13 mm, together with
+a temporal resolution of 50 Hz, as shown in Figure 2.6 (a).
+Regarding the ion density, quasi-neutrality works here, i.e., ni ≈ ne. For
+the ion temperature, the Charge Exchange Spectroscopy (CES) system, which
+obtain local carbon density and flow velocity measurements along the NBI beam
+path by capturing the Doppler line width and deviation of a spectrum emitted
+from an interaction between the neutral beam ions and the carbon ions in the
+tokamak. The KSTAR CES system has 32 local measurements with a spatial
+resolution < 5 mm, together with a temporal resolution < 100 Hz, as shown in
+Figure 2.6 (b).
+Therefore, based on the equation below, we can relate the density and tem-
+perature measurements with the plasma pressure, i.e.,
+ptot = neTe + niTi + pfast + prest
+(2.18)
+where prest is the pressure of impurities in the tokamak whose profile is not
+sufficiently available yet. Thus, we can use this for p(ψ) term in the GS equation,
+which will be dealt with in Article V.
+One can have curiosity about the F(ψ) term in the GS equation. In fact,
+the Motional Stark Effect (MSE) system [71] which measures local magnetic field
+pitch angles along the NBI path from the polarization of the motional Stark effect
+emission signals by the NBI beam. In this thesis, I would like to prove the fact
+whether deep learning can solve the GS equation by only using the equation itself
+or not, and a way of using the MSE measurements is considerably similar with
+21
+
+CHAPTER 2. Nuclear Fusion
+that of the plasma pressure. Thus, I would like to leave this as a future work.
+It is worth to mention that the KSTAR MSE system has 25 local measurements
+with a spatial resolution of 1 cm to 3 cm, together with a temporal resolution of
+100 Hz [72].
+2.4
+Deep learning for tokamak equilibrium
+This thesis addresses reconstructing “tokamak equilibria” in real time in the
+field of magnetically controlled nuclear fusion, from the perspective of solving
+the GS equation by an application of deep learning. As explained before, the GS
+equation gives us two facts: (1) balancing the plasma pressure and the Lorentz
+force and (2) information of plasma positions in the tokamak. Although there
+were previous approaches [73–77] to find a solution of the GS equation, sacrificing
+accuracy or depending on human subjectivity (manually determined complexity
+of the solutions) is still left to be resolved. Thus, we present a deep learning
+method which solves the GS equation by itself with no guess of the GS equation.
+How can we believe that the networks truly understand the GS equation?
+Are they soluble if the network’s outputs are trained with well-calculated toka-
+mak equilibria given by the previous methods? Unfortunately, I do not think
+so.
+The networks may not be able to capture the force balance behind the
+dataset [78], and there is still the human decision regarding numerical conver-
+gence such that some of the measured signal are arbitrarily selected for the re-
+construction, although the network can produce the equilibria outstandingly. To
+answer those questions, I make the networks find the equilibria after they fully
+understand the GS equation without any human selection. Eventually, they can
+generate the equilibria consistent with given measurements. How this is possi-
+ble will be served in Article V in chapter 4. Article IV provides a prototype of
+Article V by trying to learn the GS equation by means of the KSTAR EFIT
+database [79]. Article I, Article II and Article III provides how to preprocess
+inputs of the networks, which guarantees that the networks can be used in any
+circumstance.
+22
+
+Chapter 3
+Deep learning and Bayesian
+Inference
+“황새의 울음을 듣겠느냐?”
+정우는 놀란 얼굴로 새장을 바라보다가 말했다.
+“동백꽃의 향기요?”
+회의장의 사람들은 자신들의 이해력에 도대체 무슨
+문제가 있나 고민했다.
+— 이영도,
+피를 마시는 새
+The human brain is a extremely complex, non-linear and parallel information-
+processing system, which is constituted with neurons, the brain’s structural el-
+ements, performing logical, cognitive and unconscious reasoning relatively effi-
+ciently compared to contemporary digital computers. This ability is purportedly
+built up over time with certain rules called experience. This keeps continuing the
+development of our brain constantly. Artificial neural networks (simply referred
+to as neural networks) are designed to mimic our brain’s functioning by using
+a massive interconnection of simple digital units called neurons, perceptrons or
+nodes. This intuitive structure, i.e., plasticity is an inception of deep learning,
+an enormous pile of the interconnection to perform human-like or superhuman
+capabilities.
+In 1943–1958, the formation of neural networks begins with McCulloch and
+Pitts (1943) [80] suggesting the idea of neural networks as computing machines,
+Hebb (1949) [81] underlying self-organizing learning, and Rosenblatt (1958) [82]
+introducing the perceptron as the first model for supervised learning. Although
+23
+
+CHAPTER 3. Deep learning and Bayesian Inference
+there were critics pointed out by Minsky and Selfridge (1961, 1969, 1988) [83–85]
+that the perceptron is not essentially capable of being globally generalized based
+on locally learned examples, it would not be an overstatement that we are living
+in an era of neural networks and deep learning.
+Then, how can we implement physically reliable deep learning? The methods
+that I propose in this thesis are to develop a Bayesian neural network which is
+capable of perceiving physics theories and quantifying its confidence level with
+given input information. Although the ways are not restricted to the field of
+nuclear fusion, I would like to propose a neural network available for tokamak
+control based on learning with plasma magnetohydrodynamic (MHD) theory [42]
+and Maxwell’s equations. Thus, I would like to prove that there is definitely a
+physically reliable neural network based on the arguments in this thesis.
+From the next section, I will describe a structure of a feedforward neural
+network and a basic notion of supervised learning on the basis of the simple sine
+regression introduced in Chapter 1. Then I will introduce uncertainty in neural
+networks in light of Bayesian neural networks. How networks are taught with
+physics theories will be also given later. Finally, I will convey a short discussion
+about the usage of Generative Adversarial Networks (GANs) in light of tokamak
+control.
+3.1
+Feedforward Neural Network
+Feedforward neural networks basically have an input layer, hidden layers and an
+output layer, and Figure 3.1 shows an example of them with a simple architecture.
+Given arbitrary inputs R and Z, the input information flows through the hidden
+layer toward the output node after going through an activation function in each
+layer. This process is non-linear, which lends the network to resemble any forms
+of data distributions. Each layer has its own bias as well.
+24
+
+CHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.1: A simple neural network having two input nodes (except the input
+bias), a single hidden layer and an output node.
+The formula for the network in Figure 3.1 can be expressed as follows:
+ˆy = v0 + v1f
+�
+w10 + w11R + w21Z
+�
++ v2f
+�
+w20 + w12R + w22Z
+�
++ v3f
+�
+w30 + w13R + w23Z
+�
++ v4f
+�
+w40 + w14R + w24Z
+�
+(3.1)
+where w and v are the weights between the input and the hidden layers, and
+between the hidden and the output layers, respectively. f is an activation func-
+tion originated from the biological activation function where sigmoid, tanh, and
+ReLU functions are popular to be used.
+Among the training methods for the network, here I would like to introduce
+supervised learning whose cost function is a function of observed quantities t and
+the network outputs ˆy as shown below:
+ϵ = (ti − ˆyi)2
+(3.2)
+where i is the feature of a database for training the network. With the sine
+function regression mentioned in Chapter 1, we can define ti ∼ 0 at xi = 0 as an
+instance. This makes the network be almost zero when the input is zero if the
+25
+
+W11
+V1
+W-
+R
+W12
+W13
+V2
+W14
+y
+Z
+W10
+b1
+W30
+VA
+WA
+W40
+Vo
+b2CHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.2: Training (blue) and validation (orange) costs versus epochs.
+network has a single input node by taking advantage of the well-known gradient
+descent method.
+In general, there are features involved in training set and validation set
+separately.
+With the sine example again, I create (observe) a total of 1024
+features (data points) in interval (0, 1) along x-axis. 90 percent of these features
+are used to build the training set, while the remaining features form the validation
+set. The training set indeed takes part in the training process, i.e., updating
+weights of the network. Conversely, the validation set does not contribute to the
+update process, while it is used to stop the training early to avoid over-fitting
+issue. The over-fitting is a problem that the network try to follow all the sporadic
+data points exactly, deteriorating the network’s prediction ability, i.e., network
+generality.
+Figure 3.2 shows the training (blue) and validation (orange) costs calculated
+based on Equation 3.2 over epochs (a single loop of the update procedure). The
+epoch is identical to an iteration if we use whole features to update the weights
+26
+
+0.8
+0.7
+0.6
+E
+MSI
+0.5
+0.4
+0.3
+0
+Q0QT
+2000
+QOCE
+EpochCHAPTER 3. Deep learning and Bayesian Inference
+at once in the single iteration. This figure is from σ = 0.5 case in Figure 1.1.
+The training cost keeps decreasing in the figure, while the validation cost shows
+a stagnation (or increase) after decreasing. This shows the network is over-fitted
+to the data points at epoch = 3000 since the network follows the training data
+points well compared to the validation data points. In other words, the network
+generality is degenerated. Therefore, the network at epoch ∼ 2000 is possibly
+optimal where the validation cost is about to increase. It is worth mentioning
+that I construct the neural network having four hidden layers and 300 nodes
+each. The activation used is swish function.
+The generalized equational forms for the neural network are as follows:
+�y = f(xW 1 + b)W 2,
+EW 1,W 2,b(X, Y ) =
+1
+2N
+N
+�
+i=1
+||yi − �yi||2,
+L(W 1, W 2, b) ≡ EW 1,W 2,b(X, Y ) + λ1||W 1||2 + λ2||W 2||2 + λ3||b||2
+(3.3)
+where we slightly change a notation such that y is the observed data, the boldface
+of the uppercase letters are the matrices, the boldfaces of the lowercase letters
+are the vectors, and the lowercase letters are the scalars.
+X and Y are the
+observed input and output data.
+Based on these notations, I will relate the
+neural network to Bayesian inference to quantify the predictive uncertainty, i.e.,
+Bayesian neural network. Furthermore, the training method is related to the
+principle of Occam’s razor (if no evidence, avoid over-fitting), which will be also
+discussed in the following sections.
+3.1.1
+Bayesian Inference
+Before discussing Bayesian neural network, I would like to explain Bayesian infer-
+ence. The power of Bayes’ theorem is the fact that the probability of hypothesis
+being true given data is linked to the probability of the data being able to be
+observed if the hypothesis was true:
+prob(hypothesis|data, I) ∝ prob(data|hypothesis, I) × prob(hypothesis|I).
+(3.4)
+27
+
+CHAPTER 3. Deep learning and Bayesian Inference
+where prob(hypothesis|I) is the prior probability (representing our state of igno-
+rance before the data have been measured regarding the truth of the hypothesis),
+prob(data|hypothesis, I) is the likelihood probability (modifying the prior by the
+measurements), and prob(hypothesis|data, I) is the posterior probability (illus-
+trating our state of knowledge in the data point of view regarding the truth of the
+hypothesis). prob(data|I) that is not shown in the equation is called evidence
+which plays an important role in some situations like modelselection.
+The
+quantities on the right hand side can be denoted as prob(data, hypothesis|I) =
+prob(data|hypothesis, I)×prob(hypothesis|I), which means that if we first spec-
+ify how much we believe that the hypothesis is true, and then state how much we
+believe that the data is true given that the hypothesis is true, then we must im-
+plicitly have specified how much we believe that both the data and the hypothesis
+are true [86].
+In light of the neural network, the quantities of interest to be found through
+Bayesian inference are the weights. Given training inputs X and their corre-
+sponding outputs Y , the posterior probability of the network weights is:
+p
+�
+ω|X, Y
+�
+= p
+�
+Y |X, ω
+�
+p(ω)
+p
+�
+Y |X
+�
+(3.5)
+where ω is the weight matrix of the network. The posterior represents the most
+probable weights given the training data.
+Like the evidence that I describe above, we can perform an integration of
+the posterior over the space of the weights which is called marginalization as
+shown below:
+p
+�
+Y |X
+�
+=
+�
+p
+�
+Y |X, ω
+�
+p
+�
+ω)dω,
+(3.6)
+which is in other words we marginalize over all unknown parameters, i.e., an
+weighted average of ω with respect to its prior distribution.
+In light of real world observations, inferring p
+�
+ω|X, Y
+�
+analytically is often
+unavailable. Therefore, an arbitrary variational distribution whose parameter
+is θ, qθ(ω), is defined to be used for the inference straightforwardly. qθ(ω) is
+suggested to be closer to the original posterior distribution, driving us to use
+28
+
+CHAPTER 3. Deep learning and Bayesian Inference
+the Kullback-Leibler (KL) divergence over θ. This tells us how similar both two
+distributions are:
+KL
+�
+qθ(ω)
+����p
+�
+ω|X, Y
+��
+=
+�
+qθ(ω) log
+qθ(ω)
+p
+�
+ω|X, Y
+�dω.
+(3.7)
+Minimizing the KL divergence is identical to maximization of the evidence
+lower bound (ELBO) with respect to qθ(ω) also known as variational lower bound,
+i.e.,
+LV I(θ) ≡
+�
+qθ(ω) log p
+�
+Y |X, ω
+�
+dω − KL
+�
+qθ(ω)
+����p(ω)
+�
+≤ log p
+�
+Y |X
+�
+=
+�
+qθ(ω) log p
+�
+Y |X, ω
+�
+dω
+−
+�
+qθ(ω) log qθ(ω)dω +
+�
+qθ(ω) log p
+�
+ω
+�
+dω
+−
+�
+qθ(ω) log p
+�
+Y |X
+�
+dω +
+�
+qθ(ω) log p
+�
+Y |X
+�
+dω
+(3.8)
+where we can find the evidence of the posterior on the far right in the first line.
+This plays a role of “Occam’s razor” which penalize qθ(ω) since the first term
+in the middle of the first line increases the degree of freedom of qθ(ω), while the
+second term in the same line let qθ(ω) be as close as the prior p(ω). This will
+show up in Appendix A to explain that this also governs the degree of freedom
+of the network.
+The procedure above is known as variational inference (VI) which results in
+capturing model uncertainty, and allows us to replace the marginalization with
+the optimization. The Bayes’ theorem and the marginalization have enormously
+attracted attention in nuclear fusion in light of Bayesian forward models [87–89]
+and physical parameter regressions [90–94].
+3.1.2
+Sine function Regression: Part 1
+With Appendix A explaining what Bayesian deep learning is, we have explored
+dropout in terms of Bayesian neural networks and predictive uncertainty. To im-
+plement the uncertainty mentioned in Chapter 1 from dropout, we simply need
+29
+
+CHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.3: A Bayesian neural network posterior with various SNR of the
+observed sine functions. The networks have the dropout probability p = 0.2.
+This figure is identical to Figure 1.1 except the predictive uncertainty expressed
+in the red area.
+to go through the stochastic process of dropout. In other words, we can obtain a
+Bayesian neural network posterior if dropout is applied during the training, nat-
+urally giving us the network’s uncertainty over the network’s parameter space.
+I apply this process for the sine function regressions, which I have covered pre-
+viously. As a coincidence, I already used dropout for the problem, and let me
+confirm the predictive uncertainty of the network with the scattered data points
+of the sine functions.
+Figure 3.3 shows the Bayesian neural network posteriors with their uncer-
+30
+
+ = 0.05
+α = 0.5
+α=3CHAPTER 3. Deep learning and Bayesian Inference
+tainty expressed in the red areas. Same with Figure 1.1, the black line is the
+noise-free sine functions, the blue and orange dots are the training and validation
+sets, and the red areas represent 1 σ standard deviation. Since I synthesized a
+total of 1024 data points, I used the dropout probability of 0.2 following Figure
+6.14 in Ref. [95]. Without being caught in over-fitting (following all the data
+points exactly), the network results are close to the correct answers (black line)
+with reasonable uncertainty even though the observed data are quite sporadic.
+Furthermore, the thickness of the red area is gradually noticeably increased when
+SNR of the sine data is increased. This means that the magic approach men-
+tioned in Chapter 1 is no longer magic, rather is expressed in the quantified
+uncertainty through Bayesian inference, convincing us it is reliable.
+Now, I would like to mention that we partially prove the neural networks
+are out of the black box except that we yet prove the networks can understand
+physics explained in Chapter 1. To make this a total belief, we extend our result
+to show neural networks learning physical theories.
+3.1.3
+Sine function Regression: Part 2
+With Appendix B describing neural network differentiation, I, here, wish to train
+a neural network by Equation B.3 whose solution is t(x) = sin (14πx) + const
+where we simply set const to zero. Following the procedure explained before, I
+train the neural network which has four hidden layers with 100 neurons and a bias
+each by using Equation B.3 as a cost function. The training data is generated
+from the first order derivative of the solution, i.e., 14π cos (14πx) between zero
+and one on the x-axis without adding noises. Figure 3.4 (b) shows the first order
+derivative as the black line. Similarly, Figure 3.4 (a) shows the solution as well
+as I prepare the second order derivative as well in Figure 3.4 (c). In the figure,
+the blue lines are the network results.
+As one can see, the network is capable of generating its first order derivative
+with respect to the input x corresponding to our differential equation. Further-
+more, its own output and the second order derivative (with respect to x) are
+truly matched with the solution and the second order derivative of Equation B.3
+31
+
+CHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.4: (a) The black line is sin (14πx) which is the solution of Equation.
+(b) The first order derivative of the solution with respect to x. (c) The second
+order derivative. The red areas are the network results with their uncertainty,
+while the blue lines are the means of them. (d) The distribution of the random
+offset from 300 different networks.
+as long as we shift the blue line in Figure 3.4 (a) to the origin. This shift results
+from the fact that I do not explicitly control an offset (bias) of the network out-
+put from the cost function. Instead, I provide Figure 3.4 (d), i.e., a distribution
+of the random offset from 300 different networks which seemingly follows a nor-
+mal distribution. Lastly, Bayesian neural network posterior is also applied here
+where the red (and orange) areas indicate the network uncertainties analyzed by
+dropout. Thus, this fulfills the concept of the total belief such that we believe
+not only the network is able to quantify its confidence but also it can grasp a
+differential equation or a certain physical theory.
+So far, how to teach a network physics has been introduced with the simple
+32
+
+offsetCHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.5: A fundamental GAN architectures
+first order differential equation. It is worth to mention that this training method
+is somewhat close to supervised learning since the network can be taught with the
+data generated from the cosine function although it never notices how the sine
+function looks like. Then what if we would like to teach high order differential
+equations or what if we cannot prepare not only solutions of differential equations
+but also their corresponding derivatives at all? Could it be called supervised
+learning as well? In fact, these are raised when I deal with applying a network to
+the purpose of tokamak control based on a plasma governing equation. I teach
+a second order (elliptical) partial differential equation without having a dataset
+for its derivatives through a neural network. Therefore, one can find answers to
+the questions in the following chapters.
+3.2
+Advanced topic: GAN
+This section is prepared to find other research fields where the method we have
+looked at can be helpful. Generative Adversarial Networks (GANs) [96,97] have
+emerged as a type of unsupervised learning to generate network representations
+from distributions of data without experiencing them explicitly. Figure 3.5 shows
+a basic structure of GAN.
+In this figure, there are the generator G and the discriminator D which act
+as the forger and the expert. The forger falsifies a network output to be realistic
+33
+
+real
+fake
+D
+(z)
+x
+ZCHAPTER 3. Deep learning and Bayesian Inference
+data from a random noise, while the expert identifies real data from the forgeries.
+The equation below is a realization of the forger-expert relation as a cost function
+of GAN:
+min
+G max
+D V (D, G) =Ex∼pdata(x)[log D(x)]
++ Ez∼pz(z)[log(1 − D(G(z)))]
+(3.9)
+where the first line on the right hand side is a cost for the discriminator, the
+second line is for the generator, x is the real data, and z is the random noise.
+This is powerful for data generation even not being contained in a prepared
+dataset. Thus, there was studies to use GANs to replace typical numerical simu-
+lations in the field of physics such as accelerator [98–100] and materials [101,102].
+I would like to briefly introduce the use of GAN in the field of tokamak control
+by using plasma equilibria database. Plasma equilibrium is a reconstructed mag-
+netic topology of the plasma which will be discussed in the next chapter. Below
+are the relevant python codes using TensorFlow [103].
+1 import
+h5py
+2 import
+matplotlib.pyplot as plt
+3 import
+numpy as np
+4
+5 import
+tensorflow as tf
+6 from
+tensorflow.keras.layers
+import
+Activation ,
+BatchNormalization , Dense , Dropout , Flatten , Reshape
+7 from
+tensorflow.keras.layers
+import
+LeakyReLU , ZeroPadding2D
+8 from
+tensorflow.keras.layers
+import Conv2D , Conv2DTranspose
+9 from
+tensorflow.keras
+import
+Input
+10 from
+tensorflow.keras.layers
+import
+InputLayer
+11 from
+tensorflow.keras.models
+import
+Sequential
+12 from
+tensorflow.keras.optimizers
+import
+Adam
+13
+14 from
+sklearn.model_selection
+import
+train_test_split
+15 from
+collections
+import
+defaultdict
+16 import
+argparse
+Listing 3.1: The use of GAN with plasma equilibria: Load essential libraries.
+34
+
+CHAPTER 3. Deep learning and Bayesian Inference
+1 X = f3[’psi’][:]. transpose (2, 0, 1)
+2
+3 ix = list(range(X.shape [0]))
+4 np.random.shuffle(ix)
+5 # ix = ix[: results.nb_points]
+6
+7 X = X[ix]
+8 X_train , X_test = train_test_split (X, train_size =0.9)
+9 X_train = np.expand_dims(X_train , axis =-1)
+10 X_test = np.expand_dims(X_test , axis =-1)
+11 X_train = X_train.astype(np.float32)
+12 X_test = X_test.astype(np.float32)
+13
+14 nb_train , nb_test = X_train.shape [0], X_test.shape [0]
+Listing 3.2: The use of GAN with plasma equilibria: Load equilibria.
+1 img_rows = 64
+2 img_cols = 64
+3 channels = 1
+4
+5 # input
+image
+dimension
+6 img_shape = (img_rows , img_cols , channels)
+7
+8 # latent
+space
+dimension
+9 z_dim = 100
+10
+11 def
+build_generator (z_dim):
+12
+13
+model = Sequential ()
+14
+# From
+Dense 8x8x256
+15
+model.add(Dense (256 * 8 * 8, input_dim=z_dim))
+16
+model.add(Reshape ((8, 8, 256)))
+17
+# 8x8x256 => 16 x16x128
+18
+model.add( Conv2DTranspose (128,
+kernel_size =3, strides =2,
+padding=’same ’))
+19
+model.add( BatchNormalization ())
+20
+model.add(LeakyReLU(alpha =0.01))
+35
+
+CHAPTER 3. Deep learning and Bayesian Inference
+21
+# 16 x16x128 => 32 x32x64
+22
+model.add( Conv2DTranspose (64, kernel_size =3, strides =2,
+padding=’same ’))
+23
+model.add( BatchNormalization ())
+24
+model.add(LeakyReLU(alpha =0.01))
+25
+# 32 x32x64 => 32 x32x32
+26
+model.add( Conv2DTranspose (32, kernel_size =3, strides =1,
+padding=’same ’))
+27
+model.add( BatchNormalization ())
+28
+model.add(LeakyReLU(alpha =0.01))
+29
+# 32 x32x32 => 64 x64x1
+30
+model.add( Conv2DTranspose (1, kernel_size =3, strides =2,
+padding=’same ’))
+31
+model.add(Activation(tf.nn.leaky_relu))
+32
+33
+return
+model
+34
+35 def
+build_discriminator (img_shape):
+36
+37
+model = Sequential ()
+38
+model.add(Input(shape=img_shape))
+39
+40
+model.add(
+41
+Conv2D (32,
+42
+kernel_size =3,
+43
+strides =2,
+44
+padding=’same ’))
+45
+model.add(LeakyReLU(alpha =0.01))
+46
+# 32 x32x32
+-> 16 x16x64
+47
+model.add(
+48
+Conv2D (64,
+49
+kernel_size =3,
+50
+strides =2,
+51
+padding=’same ’))
+52
+model.add(LeakyReLU(alpha =0.01))
+53
+# 16 x16x64
+-> 8x8x128
+54
+model.add(
+36
+
+CHAPTER 3. Deep learning and Bayesian Inference
+55
+Conv2D (128,
+56
+kernel_size =3,
+57
+strides =2,
+58
+padding=’same ’))
+59
+model.add(LeakyReLU(alpha =0.01))
+60
+# 8x8x128
+-> 4x4x256
+61
+model.add(
+62
+Conv2D (256,
+63
+kernel_size =3,
+64
+strides =2,
+65
+padding=’same ’))
+66
+model.add(LeakyReLU(alpha =0.01))
+67
+model.add(Flatten ())
+68
+model.add(Dense (1, activation=’sigmoid ’))
+69
+70
+return
+model
+71
+72 def
+build_gan(generator , discriminator):
+73
+74
+model = Sequential ()
+75
+model.add(generator)
+76
+model.add(discriminator)
+77
+78
+return
+model
+Listing 3.3: The use of GAN with plasma equilibria: Define the GAN
+architecture.
+1 # d model
+2 discriminator = build_discriminator (img_shape)
+3 discriminator.compile(loss=’binary_crossentropy ’,
+4
+optimizer=Adam (),
+5
+metrics =[’accuracy ’])
+6 # g model
+7 generator = build_generator (z_dim)
+8 # let d be non -trainable
+9 discriminator.trainable = False
+10 # g + d compile
+37
+
+CHAPTER 3. Deep learning and Bayesian Inference
+11 gan = build_gan(generator , discriminator)
+12 gan.compile(loss=’binary_crossentropy ’, optimizer=Adam ())
+Listing 3.4: The use of GAN with plasma equilibria: Compile the GAN defined.
+1 train_history = defaultdict(list)
+2 test_history = defaultdict(list)
+3 nb_epochs = 100
+4 batch_size = 100
+5 latent_size = 100
+6
+7 real = np.ones (( batch_size , 1))
+8 fake = np.zeros (( batch_size , 1))
+9
+10 for epoch in range(nb_epochs):
+11
+print(’Epoch {} of {}’.format(epoch + 1, nb_epochs))
+12
+13
+nb_batches = int(X_train.shape [0] / batch_size)
+14
+epoch_gen_loss = []
+15
+epoch_disc_loss = []
+16
+17
+for index in range(nb_batches):
+18
+19
+if index % 100 == 0:
+20
+print(’processed
+{}/{}
+batches ’.format(index + 1,
+nb_batches))
+21
+22
+# generate a new batch of noise
+23
+noise = np.random.normal (0, 1, (batch_size , latent_size))
+24
+# get a batch of real
+images
+25
+image_batch = X_train[index * batch_size :( index + 1) *
+batch_size]
+26
+27
+# generate a batch of fake images ,
+28
+# using the
+generated
+labels as a
+29
+# conditioner. We reshape
+the
+sampled
+labels to be
+30
+# (batch_size , 1) so that we can feed them
+31
+# into the
+embedding
+38
+
+CHAPTER 3. Deep learning and Bayesian Inference
+32
+# layer as a length one
+sequence
+33
+generated_images = generator.predict(noise)
+34
+35
+# see if the
+discriminator
+can figure
+itself out ...
+36
+real_batch_loss = discriminator. train_on_batch(
+37
+image_batch , real
+38
+)
+39
+40
+# note that a given
+batch
+should
+have
+41
+# either *only* real or *only* fake ,
+42
+# as we have both
+minibatch
+discrimination
+43
+# and batch
+normalization , both
+44
+# of which
+rely on batch
+level
+stats
+45
+fake_batch_loss = discriminator. train_on_batch(
+46
+generated_images , fake
+47
+)
+48
+d_loss , accuracy =
+0.5 * np.add(real_batch_loss ,
+fake_batch_loss )
+49
+50
+epoch_disc_loss .append(d_loss)
+51
+52
+# we want to train the
+genrator to trick
+53
+# the
+discriminator
+54
+# For the generator , we want all the {fake , real} labels
+55
+# to say real
+trick = np.ones(batch_size)
+56
+gen_losses = []
+57
+58
+# we do this
+twice
+simply to match the number of batches
+59
+# per epoch
+used to
+60
+# train the
+discriminator
+61
+for _ in range (2):
+62
+noise = np.random.normal (0, 1, (batch_size ,
+latent_size))
+63
+64
+gen_losses.append(gan. train_on_batch(
+65
+noise ,
+66
+real
+39
+
+CHAPTER 3. Deep learning and Bayesian Inference
+Figure 3.6: (a) Examples from the equilibrium database, (b) Examples of the
+GAN results.
+67
+))
+Listing 3.5: The use of GAN with plasma equilibria: Train the GAN.
+As one may have noticed, there are no physical constraints in this training
+procedure although Figure 3.6 shows a great similarity between the prepared
+database and the GAN results except wrinkled features in the GAN. Of course,
+this is a simple example but the cost function of GAN does not contain any
+physical restrictions. Therefore, applying our approach in the previous section
+to a GAN may result in a physically constrained GAN result which might be
+helpful to be used for simulations instead.
+3.3
+Outlook
+I have reviewed a part of constituents for learning physics via neural networks in
+this thesis. I explain how the neural networks can be trained with not only their
+output but also derivatives. From this perspective, we can gain insight into an
+interesting paradigm that the networks can learn a physical system if the system
+is governed by physical theories, then the networks can use the theories as their
+40
+
+CHAPTER 3. Deep learning and Bayesian Inference
+cost functions even if simulated data for the phenomenon is not prepared yet to
+train the networks. It can be asserted that the network results can be more reli-
+able than a usual training procedure since the networks literally understand the
+physics theories based on the novel paradigm. If the network results become more
+credible, humans can trust the networks and entrust them to more tasks related
+to the physical system (especially, tokamak operations). Perhaps, this paradigm
+might be regarded as a cornerstone of a pure autonomous tokamak control via
+deep learning. Anyhow, as a test bed, reconstructing plasma equilibria in the
+field of magnetic confinement fusion is chosen to prove this idea. Reconstruct-
+ing plasma equilibria requires solving a second-order partial differential equation,
+which will be introduced in the next chapter.
+41
+
+Chapter 4
+Bayesian neural network in
+fusion research
+Here, Chapter 4 constitutes the main outcome of this thesis. The findings listed
+in this chapter are applications of the principles and methods that are described
+in the previous chapters in order to reconstruct plasma equilibria as scientific
+and practical usages of deep learning in nuclear fusion research.
+With the Korea Superconducting Tokamak Advanced Research (KSTAR),
+Article IV has been developed to show that a neural network can learn a plasma
+‘theory’ with the support of a database prepared from a numerical algorithm by
+reconstructing plasma equilibria based on the Grad-Shafranov (GS) equation.
+This is a preliminary application for the network to provide the possibility of a
+complete unsupervised learning for the reconstruction such that the neural net-
+work can understand the GS equation itself, and the database from the numerical
+algorithm is no longer required. This is described in Article V, providing how
+a principle of the unsupervised learning works, and why this kind of network
+is required for tokamak control. Article I, Article II and Article III have been
+developed to preprocess KSTAR measurements used to inputs of our networks
+since baseline increases of measured signals in time (signal drift), missing signals
+due to mechanical issues and inconsistency between signals should be handled
+to use our networks in any experimental circumstances. From Bayesian neural
+networks, our applications are able to quantify the epistemic uncertainty related
+to the plasma theory by obtaining inference results of the GS equation as well
+as plasma information such as positions and locations of the plasmas (which are
+hard to be measured directly) in the KSTAR.
+Again, the principles and methods that I have used for the applications are
+42
+
+CHAPTER 4. Bayesian neural network in fusion research
+explained in the previous chapters, thus the reader who wants to take a look at
+these is recommended to read chapter 2 and chapter 3.
+4.1
+Article I: Signal drift correction
+This approach deals with Bayesian based numerical method for real-time cor-
+rection of signal drifts in magnetic measurements from tokamaks1, which is
+largely taken from Ref [78], as a part of preprocessing magnetic measurements
+via Bayesian inference and neural networks.
+This article is to model signal drift which is a phenomenon that baselines of
+measured signals increase or decrease in time by using Bayesian inference. Mag-
+netic signals such as magnetic fields and fluxes typically measured from inductive
+coils with analogue integrators can be obtained by integrating voltages induced
+in the coils by time-varying magnetic fields from current sources. KSTAR usu-
+ally has the poloidal field coils and the plasma as the current sources, and vessel
+currents (induced current in KSTAR vessel structure) are often regarded as sig-
+nificant current sources as well. Besides, KSTAR measures the poloidal magnetic
+fields and fluxes from magnetic pick-up coils and flux loops installed on the vac-
+uum vessel wall. When the voltages induced from the sources are integrated,
+spurious offsets are also often accumulated, causing the magnetic signals to tend
+to be increased (or decreased) over time. This phenomenon should be compen-
+sated properly to be used for various plasma analyses based on the magnetic
+signals such as EFIT (plasma equilibrium fitting).
+Thus, the Bayesian model for the KSTAR pick-up coils and flux loops are
+suggested with information of initial magnetization stage which is a step that all
+the poloidal field coils are being charged to be ready for tokamak discharges. In
+this stage, currents of the poloidal field coils become a steady state after being
+fully charged, meaning that the magnetic signals also have ideally no variance
+1Reproduced from S. Joung et al. the Appendix in ’Deep neural network Grad–Shafranov
+solver constrained with measured magnetic signals’. In: Nuclear Fusion, Vol.60.1 (3rd Dec.
+2019), page 016034, DOI:10.1088/1741-4326/ab555f
+43
+
+CHAPTER 4. Bayesian neural network in fusion research
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+R [m]
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+Z [m]
+←20
+←21
+←22
+←19
+←18
+←17
+←16
+←15
+←28
+←27
+←26
+←25
+←24
+←23
+← 6
+FL 1→
+FL12→
+FL23→
+FL34→
+←37
+FL45→
+← 1
+← 2
+← 3
+← 4
+← 5
+← 7
+← 8
+← 9
+←11
+←12
+←13
+←14
+←29
+←30
+←31
+←32
+←33
+←34
+←35
+←36
+←38
+←39
+←40
+←41
+←42
+Figure 4.1: Configuration of magnetic diagnostics on a poloidal cross-section
+of KSTAR at a certain toroidal position. Blue dots show the positions of both
+MPn and MPt, and red open circles for the positions of the FLs. The black
+thick line shows the first wall. Note that we only show five FL sensor numbers
+out of 45 of them for simplicity.
+in time. Thus, any variances in this phase can be considered as the signal drift
+which is alleviated by our Bayesian model. To model the signal drift, linearly
+increased drift model is assumed.
+This can reasonably handle the measured
+signals from KSTAR short-pulse discharges (≤ 20 sec), while being required to
+be improved for applications of KSTAR long-pulse discharges. Nevertheless, this
+method is quite effective in KSTAR discharges where the short-pulse discharges
+account for the majority. Thus, Article II–V employs this development in order
+to preprocess the signal drifts in the magnetic fields and fluxes. Note that this
+article I is a long version of an appendix in Article IV.
+44
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.1.1
+Introduction
+Magnetic diagnostics (MDs) are one of the most fundamental and widely used
+sensors installed in almost all (if not all) magnetic-confinement fusion devices,
+for instance LHD [104], MAST [105], DIII-D [106], TCV [107], EAST [108],
+JET [109], ITER [110] and KSTAR [2, 49]. Reference [111] also discusses mag-
+netic diagnostics on TFTR, JET, JT-60 and DIII-D. Various magnetic signals
+from MDs play significant roles in real-time plasma controls, detecting MHD
+(magnetohydrodynamics) events [112–116] as well as reconstructing magnetic
+equilibria [117–120], e.g., EFIT [73]. Albeit such important roles, baselines of
+the measured magnetic signals often suffer from drifts in time mainly due to ca-
+pacitor leakage in analogue integrators [121] and possibly radiations [122]. This
+phenomenon is typically called ‘signal drift’ whose error must be eliminated in
+order to conform with required accuracy for EFIT [73], magnetic control [123]
+and neural network applications [5,7,124]. In this paper, we propose a novel algo-
+rithm that removes the signal drifts in real-time only based on the experimentally
+measured data.
+Most of previous researches resolve the signal drifts by modifying hardware
+systems [53, 61, 125–128] which is a good solution but more cumbersome than
+having a simple numerical solution. We develop a novel numerical method capa-
+ble of inferring how much magnetic signals drift and correcting the signal drifts
+in real-time that can work with existing MDs without any modification of the
+hardware systems.
+The method is based on Bayesian probability theory [86], and finds the slope
+and the offset of the drift sequentially, thus a ‘two-step drift correction method,’
+during the initial magnetization stage, i.e., before the plasma initiation. This
+allows one to have not only more accurate magnetic signals for post-discharge
+analyses but also to improve real-time monitoring and control systems such as
+real-time EFIT [75]. We note that existing numerical algorithms to correct such
+drifts require post discharge information [63,64,125,126] which inhibits real-time
+application.
+In this work, we first present a detailed description of the Bayesian based
+45
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.2: An example of temporal evolutions of (a) currents in the PF coils,
+(b) normal and (c) tangential components of magnetic fields measured by an
+MPn and an MPt, respectively, and (d) magnetic flux measured by an FL
+during the initial magnetization stage, i.e., t < 0, for a typical KSTAR
+discharge. Information from the time interval d1 (d2) is used to estimate am
+i
+(bm
+i ).
+real-time two-step correction method in Sec. 4.1.2. We, then, provide how the
+method is applied to existing KSTAR experimental data and how effectively the
+method removes the signal drifts from the magnetic measurements in Sec. 4.1.4,
+followed by discussions of our proposed method on the short pulse discharge
+(< 40 sec in terms of poloidal field (PF) coil operation time) and long pulse
+discharge (> 40 sec) as well as abnormal magnetic signals in Sec. 4.1.5. Our
+conclusions are stated in Sec. 4.1.6.
+46
+
+(a)
+5000
+d2
+d1
+A
+0
+-5000
+-10000
+-15
+-10
+-5
+0
+(b)
+E
+0.04
+Bn 06
+B
+0
+-15
+-10
+-5
+0
+(c)
+0
+E
+Bt 27
+B
+-0.06
+-15
+-10
+-5
+0
+(d)
+ [Wb]
+0
+-FL 23
+-3
+-15
+-10
+-5
+0
+time [sec]CHAPTER 4. Bayesian neural network in fusion research
+4.1.2
+Real-time drift correction based on Bayesian infer-
+ence
+Fig. 4.1 shows the locations of the magnetic diagnostics (MDs) with the sensor
+numbers [2] at a certain toroidal position of KSTAR [129]. The blue dots are
+the magnetic probes (MPs) measuring both normal (Bn measured by MPn) and
+tangential (Bt measrued by MPt) components of the magnetic fields. Note that
+MP #10 does not exist at this toroidal position. The red circles are the flux loops
+(FLs) measuring magnetic fluxes. There are total of 45 FLs on KSTAR, but we
+only show five sensor numbers out of 45 of them in the figure for simplicity.
+In this work, we focus on correcting the signal drifts in real-time for the total
+number of 127 magnetic signals, i.e., 2 × 41 MPs for both MPn and MPt and 45
+FLs.
+4.1.3
+Two-step drift correction method
+To remove the signal drifts, we deem a priori that the signals drift linearly in
+time [121,126,130], which we substantiate our assumption based on the measured
+data obtained during actual plasma operations in Sec. 4.1.4. Therefore, we take
+the drifting components of the signals (ym
+i ) from various types of MDs to follow:
+ym
+i = am
+i t + bm
+i ,
+(4.1)
+where t is the time. am
+i
+and bm
+i
+are the slope and the offset, respectively, of a
+drift signal for the ith magnetic sensor of a type m (MPn, MPt or FL). Then,
+our goal simply becomes finding am
+i
+and bm
+i
+for all i and m of interests before
+a plasma starts or the blip time (t = 0) so that ym
+i
+can be subtracted from the
+measured magnetic signals in real-time. Here, we assume that am
+i and bm
+i do not
+change over one plasma discharge. One can consider such linearization in time
+as taking up to the first order of Taylor expanded drifting signals. Therefore, we
+have to examine carefully our proposed method for long pulsed discharges with
+large nonlinearities, which is discussed in Sec. 4.1.5.
+47
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.3: Examples of the proposed two-step drift correction method for the
+MDs of (a) MPn #6, (b) MPt #27 and (c) FL #45. Left and middle panels
+show the posteriors of the slope and the offset for each MD where the red dots
+depict the maximum a posterior. Right panel shows both the original magnetic
+signals with the signal drifts (red) and the drift corrected signals (blue).
+We use two different time intervals during the initial magnetization stage for
+every plasma discharge to find am
+i and bm
+i , sequentially, thus the name ‘two-step
+drift correction method.’ Fig. 4.2 shows an example of temporal evolutions of
+currents in the poloidal field (PF) coils, Bn and Bt measured by an MPn and an
+MPt, respectively, and magnetic flux by an FL up to the blip time (t = 0) of a
+typical KSTAR discharge.
+During the time interval d1 in Fig. 4.2, all the magnetic signals must be
+constant in time because there are no changes in currents of all the PF coils as
+well as there are no plasmas yet that can change the magnetic signals. Therefore,
+any temporal changes in a magnetic signal during d1 can be regarded as due to
+a non-zero am
+i . With the knowledge of am
+i from d1 time interval, we obtain the
+48
+
+Slope Posterior
+Offset Posterior
+Correction result
+0.06
+Drifted Bn
+(a)
+Corrected Bn
+0.8
+0.8
+0.04
+6 0.6
+0 0.6
+E
+g
+ 0.4
+ 0.4
+B 0.02
+0.2
+0.2
+0
+0
+0
+-1.3
+-1.2
+-1.1
+-1.7 -1.68-1.66-1.64-1.62
+-10
+0
+10
+×104
+×10-3
+0.15
+1
+-Drifted Bt
+(b)
+0.8
+0.8
+Corrected Bt
+0.1
+b0.6
+b0.6
+E 0.05
+g
+g
+ 0.4
+ 0.4
+B
+0
+0.2
+0.2
+-0.05
+0
+0
+2.1
+2.2
+2.3
+2.85
+3.05
+-10
+2.92.95
+3
+0
+10
+×10-4
+×10-3
+2
+Drifted flux
+(c)
+Corrected flux
+0.8
+0.8
+b 0.6
+6 0.6
+0
+P 0.4
+P 0.4
+-2
+0.2
+0.2
+-3 
+0
+0
+-1.7
+-1.6
+-1.5
+-0.022
+-0.0214
+-10
+0
+10
+slope
+offset
+×10-3
+time [sec]CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.4: Histograms of the validation errors for randomly selected 297
+KSTAR discharges before (left panel) and after (right panel) the two-step drift
+correction for (a) m =MPn measuring Bn, (b) m =MPt measuring Bt, and (c)
+m =FL measuring magnetic fluxes. MD # in horizontal axes denote the MD
+sensor numbers, i.e., subscript i in ϵm
+i,s. Colors represent the relative occurrence
+normalized to a unity for every sensor. Non-existing magnetic signals are
+displayed as white streaks.
+value of bm
+i
+using the fact that all the magnetic signals must be zeros during
+the time interval d2 because there are no sources of magnetic fields, i.e., all the
+currents in the PF coils are zeros.
+Summarizing our procedure, (1) we first obtain the slopes am
+i based on the
+fact that all the magnetic signals must be constant in time during d1 time interval,
+and then (2) find the offsets bm
+i based on the fact that all the magnetic signals,
+after the linear drifts in time are removed based on the knowledge of am
+i , must
+be zeros during d2 time interval.
+49
+
+(a)
+MPn(drift)
+MPn(TwoStepMethod)
+20
+20
+MPn36
+MPn36
+0.9
+10
+10
+val
+E
+0.8
+1
+0
+10
+20
+30
+40
+10
+20
+30
+40
+0.7
+(q)
+Normalized counts
+MPt(drift)
+MPt(TwoStepMethod)
+20
+20
+0.6
+10
+10
+0.5
+val
+E
+0.4
+0
+0
+10
+20
+30
+40
+10
+20
+30
+40
+0.3
+(c)
+FL25
+FL(drift)
+FL(TwoStepMethod)
+40
+40
+FL25
+0.2
+FL01
+FL35
+ 20
+FL23
+FL35
+20
+FL34
+0.1
+E
+FL01
+FL23
+FL34
+0
+0
+10
+20
+30
+40
+10
+20
+30
+40
+MD #
+MD #CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.5: Averaged validation errors ⟨ϵm
+i ⟩ for 297 KSTAR discharges for (a)
+the normal (MPn) and (b) the tangential (MPt) components of magnetic
+signals, and for (c) the flux loop (FL) measurements. Blue circles indicate the
+validation errors after the two-step drift correction method, and red crosses
+mean the validation errors before applying our correction method.
+Bayesian inference
+Bayesian probability theory [86] has a general form of
+p (W|D) = p (D|W) p (W)
+p (D)
+,
+(4.2)
+where W is a (set of) parameter(s) we wish to infer, i.e., am
+i and bm
+i for our case,
+and D is the measured data, i.e., measured magnetic signals during the time
+intervals of d1 and d2 in Fig. 4.2. The posterior p (W|D) provides us probability
+of having a certain value for W given the measured data D which is proportional
+to a product of likelihood p (D|W) and prior p (W). Then, we use the maximum
+a posterior (MAP) to select the value of W. The evidence p (D) (or marginalized
+likelihood) is typically used for a model selection and is irrelevant in this study
+50
+
+(a)
+× MPn(drift) O MPn(TwoStepMethod)
+10
+xX
+8
+Ox
+6+
+XX
+0
+val
+XX
+E
+08
+1
+08
+0
+0
+0.5
+10
+20
+30
+40
+(q)
+X
+MPt(drift)
+MPt(TwoStepMethod)
+10
+X
+8
+X
+val
+区
+x0.8.8
+++
+E
+X
+8
+X
+1
+00
+0.5
+10
+20
+30
+40
+(c)
+× FL(drift) O FL(TwoStepMethod)
+60
+X
+10
+X
+X 0 X
+X
+8
+0808 8 0x000888
+880.0
+E
+1
+0
+0.2
+10
+20
+30
+40
+MD #CHAPTER 4. Bayesian neural network in fusion research
+as we are only interested in estimating the parameter W, i.e., am
+i and bm
+i .
+We estimate values of the slope am
+i and the offset bm
+i based on Eq. (4.2) in
+two steps as described in Sec. 4.1.3:
+Step (1) : p(am
+i | ⃗D
+m
+i,d1) ∝ p( ⃗Dm
+i,d1|am
+i )p(am
+i ),
+(4.3)
+Step (2) : p(bm
+i | ⃗D
+m
+i,d2, am∗
+i ) ∝ p( ⃗Dm
+i,d2|bm
+i , am∗
+i )p(bm
+i ),
+(4.4)
+where ⃗D
+m
+i,d1 ( ⃗D
+m
+i,d2) are the time series data from the ith magnetic sensor of a type
+m (MPn, MPt or FL) during the time intervals of d1 (d2) as shown in Fig. 4.2.
+am∗
+i
+is the MAP, i.e., the value of am
+i maximizing the posterior p(am
+i | ⃗D
+m
+i,d1). Since
+we have no prior knowledge on am
+i and bm
+i , we take priors, p(am
+i ) and p(bm
+i ), to
+be uniform allowing all the real numbers. We mention that the posterior for
+bm
+i
+should, rigorously speaking, be obtained by marginalizing over all possible
+am
+i , i.e., p(bm
+i | ⃗D
+m
+i,d2) =
+�
+p(bm
+i | ⃗D
+m
+i,d2, am
+i )p(am
+i | ⃗D
+m
+i,d1)dam
+i . However, as we are only
+interested in MAP rather than obtaining full probability distribution of bm
+i , we
+omit the marginalization procedure and simply use am∗
+i . Furthermore, as we are
+interested in real-time application, we must consider the computation time as
+well.
+With Eq. (4.1), we model likelihoods, p( ⃗Dm
+i,d1|am
+i ) and p( ⃗Dm
+i,d2|bm
+i , am∗
+i ), as
+Gaussian:
+p( ⃗Dm
+i,d1|am
+i ) =
+1
+�
+(2π)L|σm
+i,d1|
+×exp
+�
+�
+�
+�
+�−
+L�
+tl∈d1
+�
+am
+i (tl − t0) −
+�
+Dm
+i,d1(tl) −
+�
+Dm
+i,d1(t0)
+���2
+2(σm
+i,d1)2
+)
+�
+�
+�
+�
+� ,
+(4.5)
+51
+
+CHAPTER 4. Bayesian neural network in fusion research
+p( ⃗Dm
+i,d2|bm
+i ,am∗
+i ) =
+1
+�
+(2π)K|σm
+i,d2|
+×exp
+�
+�
+�
+�
+�−
+K
+�
+tk∈d2
+�
+bm
+i −
+�
+Dm
+i,d2(tk) − am∗
+i tk
+��2
+2(σm
+i,d2)2
+�
+�
+�
+�
+� ,
+(4.6)
+which simply state that noises in the measured signals follow Gaussian distribu-
+tions. Here, σm
+i,d1 and σm
+i,d2 are the experimentally obtained noise levels for the
+ith magnetic sensor of a type m (MPn, MPt or FL) during the time intervals of
+d1 and d2 in Fig. 4.2, respectively. tl and tk define the actual time intervals of
+d1 and d2, i.e., tl ∈ [−6, −1] sec and tk ∈ [−14, −13] sec with L and K being the
+numbers of the data points in each time interval, respectively. t0 can be any value
+within the d1 time interval, and we set t0 = −2 sec in this work.
+�
+Dm
+i,d1(t0)
+�
+,
+removing the offset effect to obtain only the slope, is the time averaged value of
+Dm
+i,d1(t) for t ∈ [t0 −0.5, t0 +0.5] sec. We use the time averaged value to minimize
+the effect of the noise in Dm
+i,d1(t) at t = t0.
+With our choice of uniform distributions for priors in Eqs. (4.3) and (4.4),
+MAPs for am
+i
+and bm
+i , which we denote them as am∗
+i
+and bm∗
+i , coincide with
+the maximum likelihoods which can be analytically obtained by maximizing Eqs.
+(4.5) and (4.6) with respect to am
+i and bm
+i , respectively:
+am∗
+i
+=
+L�
+tl∈d1
+��
+Dm
+i,d1(tl) −
+�
+Dm
+i,d1(t0)
+��
+(tl − t0)
+�
+L�
+tl∈d1
+[tl − t0]2
+,
+(4.7)
+bm∗
+i
+= 1
+K
+K
+�
+tk∈d2
+�
+Dm
+i,d2(tk) − am∗
+i tk
+�
+.
+(4.8)
+Now, we have attained simple algebraic equations based on Bayesian probability
+theory which can provide us values of the slope am
+i and the offset bm
+i before the
+blip time, i.e., before t = 0.
+52
+
+CHAPTER 4. Bayesian neural network in fusion research
+20
+25
+30
+-0.05
+0
+0.05
+B [T]
+(a) MPt#14 shot#:17016
+20
+25
+30
+time [sec]
+0
+5000
+10000
+IPF [A]
+(c) shot#:17016 PFcoils
+22
+24
+26
+28
+30
+32
+-0.05
+0
+0.05
+(b) MPt#14 shot#:9387
+Raw signal
+LinearFit
+TwoStepMethod
+DischargeEnd
+22
+24
+26
+28
+30
+32
+time [sec]
+0
+5000
+10000
+(d) Shot#:9387 PFcoils
+Figure 4.6: Qualitative comparisons between a typical chi-square linear fitting
+method (blue line) and our proposed two-step method (red line) with the raw
+(before correction) signal (green line) in (a) KSTAR shot #17016 and (b)
+#9387 for the tangential component of magnetic signal MPt #14. (c) and (d)
+show temporal evolutions of currents through KSTAR PF coils, and vertical
+dotted lines indicate the time where we expect all the magnetic signals return
+to zeros if there were no signal drifts. Note that the blue line in (b) is almost
+overlapped with the red line, but it is slightly more off from the zero compared
+to the red line.
+As will be discussed in Sec. 4.1.4, we find slopes and offsets for all 127 MDs
+shown in Fig. 4.1 within ∼ 0.2 sec (before the plasma starts for each shot) using
+MATLAB on a typical laptop within of the order of 1% average validation errors,
+except few abnormal events which are also discussed in Sec. 4.1.5. This means
+that we can correct the drifts of magnetic signals in real-time.
+4.1.4
+Results with KSTAR experimental data
+As examples of the results of the proposed two-step drift correction method
+described in Sec. 4.1.2, Fig. 4.3 shows posteriors of the slopes (left panel) and
+the offsets (middle panel) of a few MDs: (a) MPn #6 for the normal component of
+53
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.7: Histograms of the degree of corrections (DoC’s), where signal drift
+corrections are performed based on a typical chi-square linear fitting method
+(left panel) and our proposed two-step drift correction method (right panel) for
+(a) MPn measuring Bn, (b) MPt measuring Bt, and (c) FL measuring magnetic
+fluxes. MD # in horizontal axes denote the MD sensor numbers. Colors
+represent the relative occurrence normalized to a unity for every sensor. Same
+sets of magnetic signals used to generate Fig. 4.4 are used. Non-existing
+magnetic signals are displayed as white streaks.
+the magnetic field Bn, (b) MPt #27 for the tangential component of the magnetic
+field Bt and (c) FL #45 for the poloidal magnetic flux from KSTAR shot #8775.
+The right panel shows results of removing the signal drifts (blue lines) from the
+original magnetic signals (red lines), where the slopes and the offsets are selected
+as the values corresponding to the maximum a posterior (MAP), i.e., the values
+with the maximum probabilities depicted as red dots in the left and middle panels
+of Fig. 4.3. It is indisputable how effectively the proposed method removes the
+signal drifts.
+For the purpose of real-time correction during a plasma operation, it is not
+54
+
+(a)
+MPn(LinearFit)
+MPn(TwoStepMethod)
+100
+100
+DoC [%]
+0.9
+0.8
+-100
+.100
+10
+20
+30
+40
+10
+20
+30
+40
+0.7
+(q)
+MPt(LinearFit)
+MPt(TwoStepMethod)
+Normalized counts
+100
+100
+0.6
+DoC [%]
+0.5
+0.4
+-100
+-100
+10
+20
+30
+40
+10
+20
+30
+40
+(c)
+FL(LinearFit)
+FL(TwoStepMethod)
+0.3
+100
+100
+DoC [%]
+0.2
+0.1
+-100
+10
+20
+30
+40
+10
+20
+30
+40
+MD #
+MD #CHAPTER 4. Bayesian neural network in fusion research
+necessary to generate full posteriors based on Eqs. (4.3)-(4.6), rather we can
+simply calculate the MAPs of the slope and the offset using Eqs. (4.7) and (4.8).
+For a post-discharge analysis, having full posteriors is beneficial as they provide
+quantitative uncertainties of the estimated slopes and offsets which are required
+information to perform a proper error propagation.
+It is worthwhile to mention that ‘drift signals’ in this work are actually
+“corrected” signals in some degrees. KSTAR executes a 60-sec-long shot with the
+predefined waveforms on the PF coils to calibrate (to obtain the slopes and the
+offsets of) magnetic signals without plasmas every morning during a campaign.
+As right panel of Fig. 4.3 shows such calibration retains observable non-zero
+values in correcting drift signals. Our two-step drift correction method is applied
+in these ‘corrected’ drift signals.
+Validation error: How good is the two-step drift correction method?
+As a measure of merit of the proposed two-step drift correction method, we define
+a validation error ϵm
+i,s of a KSTAR shot number s for the ith sensor of a type m
+(MPn, MPt or FL) as follow:
+ϵm
+i,s = 100 ×
+δm
+i,s
+max
+���f m
+i,s(t)
+���
+flat-top
+[%],
+(4.9)
+⟨ϵm
+i ⟩ = 1
+N
+�
+s
+ϵm
+i,s,
+(4.10)
+where f m
+i,s(t) is a magnetic signal of the KSTAR shot #s, and a max [|·|]flat-top
+operator selects the maximum absolute value of the argument during the flat-top
+phase. δm
+i,s is the mean value of the f m
+i,s(t) after all the currents of the KSTAR
+PF coils are returned to zeros, i.e., we expect δm
+i,s to be zero if signal drifts are
+correctly removed (or if there were no signal drifts).
+N is the total number
+of KSTAR shots we have used to estimate the average values of the validation
+errors.
+The validation error defined in Eq. (4.9) quantifies how close δm
+i,s is to zero
+relative to the maximum magnetic signal during a flat-top plasma operation. We
+55
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.8: Averaged validation errors as in Fig. 4.5 before (red crosses) and
+after the correction (blue circle) for (a) the normal component (MPn) and (b)
+the tangential component (MPt) of magnetic signals and for (c) flux loop
+measurements. Left panels show the results for the 286 short pulse discharges
+(< 40 sec), while the right panels show the results for the 11 long pulse
+discharges (> 40 sec). Note the different scales for y-axis.
+normalize δm
+i,s because its absolute value near zero is arbitrary, i.e., we cannot
+quantify how close to zero is close enough in absolute sense.
+Therefore, this
+validation error provides us quantitative measure of effectiveness of the proposed
+two-step drift correction method as well as goodness of the assumptions that
+signal drifts are linear in time, and the slopes and the offsets do not change
+significantly over one plasma discharge 2.
+Fig. 4.4 shows histograms of the validation errors for (a) the normal (MPn)
+and (b) the tangential (MPt) components of magnetic signals, and for (c) the
+2If we have a large validation error, then we do not know whether the estimated slope and
+offset are inaccurate, or the assumptions are not valid. On the other hand, if we have a small
+validation error, then it is likely that the assumptions are valid, AND the slope and the offset
+are accurately estimated.
+56
+
+(a)
+Short pulse MPn
+Long pulse MPn
+40
+40
+60
+10
+10
+X
+++
+0
+XO
+X
+X
+val
+×0×x
+E
+00
+1
+0.5
+0.5
+10
+20
+30
+40
+10
+20
+30
+40
+(b)
+Short pulse MPt
+Long pulse MPt
+25
+25
+X
+X
+X
+10
+10
+8
+ox
+0
+80
+8
+08
+val
+αx
+8
+X
+E
+Q0X
+1
+0.4
+0.4
+10
+20
+30
+40
+10
+20
+30
+40
+(c)
+Short pulse FL
+Long pulse FL
+100
+100
+X
+10
+10
+X0X
+8
+80080080
+0,α0:00
+E
+0
+0.2
+0.2
+10
+20
+30
+40
+10
+20
+30
+40
+MD #
+TwoStepMethod
+MD #
+DriftCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.9: Temporal evolutions of the magnetic signals measured by MPn
+#07 (blue) and MPn #36 (red) for (a) KSTAR shot #16051 (abnormal MPn
+#36) and (b) #16447 (normal MPn #36). These two magnetic sensors are
+located at the up-down symmetric positions as shown in Fig. 4.1, and the
+discrepancy between MPn #07 and #36 in (a) are too large compared to (b) to
+be explained by the slight up-down asymmetry of the KSTAR plasmas.
+Vertical dotted lines indicate where all the currents through the PF coils are
+returned to zeros.
+flux loop (FL) measurements; while left and right panels show before and after
+the two-step drift correction, respectively. MD # (horizontal axes) indicate the
+MD sensor numbers, i.e., subscript i in ϵm
+i,s, and vertical axes are the validation
+errors. Colors representing the number of relative occurrence within a magnetic
+sensor are normalized to a unity for every sensor. We have randomly selected
+297 KSTAR discharges from the 2013 KSTAR campaign to the 2017 campaign
+with a constraint that magnetic signals must exist after all the currents of the
+PF coils are returned to zeros 3 so that we can estimate the validation errors.
+Non-existing magnetic signals are displayed as white streaks. It is evident that
+large validation errors are suppressed by our proposed method as the widths of
+the histograms are reduced to in the range of smaller values of the validation
+errors.
+3Existence of the data after all the currents of the PF coils are returned to zeros is necessary
+to estimate the validation error, but it is not required for real-time application of our two-step
+drift correction method.
+57
+
+(a) Abnormal MPn36 case
+(b) Normal MPn36 case
+Shot#16051
+Shot#16447
+.......
+0.06
+0.1
+0.08
+0.04
+E
+0.06
+B
+0.02
+0.04
+0.02
+0
+0
+-10
+0
+10
+20
+-10
+0
+10
+20
+time [sec]
+time [sec]
+.......MPn07 
+-MPn36CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.10: Temporal evolutions of the magnetic signals measured by (a) FL
+#25 (KSTAR shot #14262), (b) FL #27 (KSTAR shot #17320) and (c) FL
+#35 (KSTAR shot #16369). These signals are basically noises (see Fig. 4.3(c)
+as an example of working FL signal). Vertical dotted lines indicate where all
+the currents through the PF coils are returned to zeros.
+There are a few notable magnetic sensors indicated by red(MPn #36, FL
+#25, FL #27 and FL #35) and green(FL #01, FL #23 and FL #34) arrows in
+Fig. 4.4. As we discuss in more detail regarding these magnetic sensors in the
+discussion section (Sec. 4.1.5), we just briefly mention that red arrowed magnetic
+sensors correspond to a case where the two-step drift correction method does not
+work, i.e., large validation errors (large drift) before the correction is not improved
+by the proposed method, due to abnormal magnetic signals. Contrarily, we assert
+that our proposed method works well even on the sensors with large drifts as long
+as magnetic signals are not abnormal as indicated by green arrows. Note that
+there are many similar cases, i.e., large validation errors before the correction and
+small validation errors after the correction, for MPn and MPt signals as attested
+by the data in Fig. 4.4.
+Fig. 4.5 shows the averaged validation errors ⟨ϵm
+i ⟩ for N = 297 (same data
+sets used to generate Fig. 4.4), showing that the validation errors are indeed
+reduced for MPn and MPt signals. Note that the drift corrected signal of MPt
+#20 is worse than the value before the correction, but we argue that this is not
+so much a problem since the validation error is still less than the others. MPn
+#16 is also worse after the correction, but the difference in the validation error is
+negligibly small. Our method is less effective for the FL measurements. However,
+58
+
+(a) Abnormal FL25
+(b) Abnormal FL27
+(c) Abnormal FL35
+Shot#14262
+Shot#17320
+Shot#16369
+0.02
+0.02
+0.02
+0.01
+0.01
+0.01
+0
+0
+0
+-0.011
+-0.01
+-0.01
+-0.02
+-0.02
+-0.02
+-10
+0
+10
+0
+20
+40
+60
+-10
+0
+10
+time [sec]
+time [sec]
+time [sec]CHAPTER 4. Bayesian neural network in fusion research
+large errors such as FL #01, #23, #25, #27, #29 and #34 are certainly reduced
+by our proposed method.
+Note that Figs. 4.4 and 4.5 summarize all the 297 KSTAR discharges whose
+pulse length (in terms of PF coil operation time) is less than 90 sec. In Sec.
+4.1.5, we break down our results into short (< 40 sec) and long (> 40 sec) pulses,
+and discuss the appropriateness and limitations of our proposed method.
+Degree of Correction: Is the two-step drift correction method better
+than a typical linear fitting method?
+We now turn our attention to show how good our proposed method is compared
+to a typical chi-square linear fitting method. The slopes (am
+i ) and the offsets
+(bm
+i ) in Eq. (4.1) are estimated simultaneously (rather than the two-step method
+as proposed) using the magnetic data from the time interval of d2 in Fig. 4.2.
+Since our method is proposed for a real-time control purpose, we must compare
+with the existing method that can be applied to a real-time control as well.
+As qualitative comparisons, we show two cases in Fig. 4.6: (a) and (c) for
+KSTAR shot #17016, and (b) and (d) for KSTAR shot #9387. (a) and (b)
+show tangential component of magnetic signal MPt #14; while (c) and (d) show
+temporal evolutions of currents through the KSTAR PF coils. Vertical dotted
+lines indicate the time where we expect all the magnetic signals return to zeros
+if there were no signal drifts.
+Fig.
+4.6(a) shows a case where a typical chi-
+square linear fitting method (blue line) makes the error worse compared to the
+raw data (green line), i.e., before any correction, while our two-step method (red
+line) makes the error much smaller, i.e., closer to zero. Fig. 4.6(b) shows a case
+where a typical chi-square linear fitting method (blue line) works well bringing
+the magnetic signal closer to zero, but our proposed method (red line) is even
+better.
+For more thorough and quantitative comparison, we define a degree of cor-
+rection (DoC) as
+DoC [%] =
+�
+δm
+i,s
+�
+raw −
+�
+δm
+i,s
+�
+corr
+�
+δm
+i,s
+�
+raw
+× 100,
+(4.11)
+59
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.11: Temporal evolutions of the magnetic signals measured by (a) FL
+#01 (KSTAR shot #17321), (b) FL #23 (KSTAR shot #13366) and (c) FL
+#34 (KSTAR shot #17039). Blue (green) line is the signal after (before) the
+correction. Vertical dotted lines indicate where all the currents through the PF
+coils are returned to zeros.
+where
+�
+δm
+i,s
+�
+has the same meaning as in Eq.(4.9). The subscript ‘raw’ means
+before the correction, and ‘corr’ stands for after the correction using either a
+typical chi-square linear fitting method (denoted as Linear Fit) or our proposed
+two-step drift correction method. If the DoC is 100 %, then the correction is
+perfect, i.e.,
+�
+δm
+i,s
+�
+corr = 0 bringing the magnetic signal back to zero after the cor-
+rection; while 0 < DoC [%] < 100 means that the applied method has corrected
+the signal in finite degrees. However, DoC [%] ≤ 0 corresponds to a case where
+applied method makes no correction or even worse than a before-correction case.
+Fig. 4.7 shows histograms of the DoC’s for (a) the normal (MPn) and (b)
+the tangential (MPt) components of magnetic signals, and for (c) the flux loop
+(FL) measurements; while the right (left) panels show the results based on our
+proposed two-step method (a linear fitting method). Here, same sets of magnetic
+signals as in Fig. 4.4 are used, i.e., 297 KSTAR discharges, and horizontal axes
+and color contours (normalized counts) represent same as in Fig. 4.4.
+The calculated DoC’s support that our proposed method, in general, brings
+the magnetic signals closer to zeros, i.e., the values of DoC’s are typically within
+0 to 100 %. In addition, it works better than a typical chi-square linear fitting
+method. Again, corrections on the FL signals are less effective (but still effective),
+which can be anticipated from the results of the validation errors shown in Fig.
+4.5(c).
+60
+
+(a) Strongly drifted FL01 case
+(b) Strongly drifted FL23 case
+(c) Strongly drifted FL34 case
+Shot#17321
+Shot#13366
+Shot#17039
+1
+Drifted flux
+4
+4
+Corrected flux
+0
+[Wb]
+2
+2
+-1
+0
+0
+-2
+2
+-2
+-3
+0
+50
+100
+-10
+0
+10
+20
+0
+20406080
+time [sec]
+time [sec]
+time [sec]CHAPTER 4. Bayesian neural network in fusion research
+As we do not claim that our proposed method is a perfect solution (rather we
+claim that it is an easy and better solution), we argue that our proposed method
+is a meaningful and valid solution based on the measures of the validation error
+and the degree of correction.
+4.1.5
+Discussions
+There exist at least two questions that need to be addressed. First, how good or
+applicable is the assumption of linear model as in Eq. (4.1)? Mathematically, this
+is a Taylor expansion of the true drift signals neglecting higher order (nonlinear)
+terms. Therefore, it is evident that our proposed method will not work for long
+pulse discharges. This is also true even if we are able to obtain the second order
+term, i.e., nonlinear term forcing the drift model to be nonlinear, since it is still
+an approximation neglecting even higher order terms. Thus, a valid question we
+need to raise is: how long a discharge can be without a failure of our proposed
+method?
+Another question is on the issue of abnormal magnetic signals which is briefly
+mentioned in Sec. 4.1.4. How do abnormal magnetic signals affect our proposed
+method? What good does our proposed method do for abnormal magnetic sig-
+nals?
+Short pulse vs. Long pulse
+We define a discharge pulse length based on the PF coil operation time in this
+work rather than a usual plasma operation time since we need to be able to
+estimate the validation error for quantitative judgement, and validation error
+can only be estimated after all the currents through the PF coils are returned to
+zeros. We have examined 286 short pulse (< 40 sec) discharges and 11 long pulse
+(> 40 sec) discharges, summing up to 297 KSTAR discharges from 2013 to 2017
+campaigns. Notice that the number of long pulse discharges are much smaller
+than the short pulse ones because smaller number of long pulse experiments have
+been carried out, and we have randomly selected KSTAR discharges.
+61
+
+CHAPTER 4. Bayesian neural network in fusion research
+Fig. 4.8 shows the averaged validation errors ⟨ϵm
+i ⟩ (defined in Eq. (4.10)) as
+in Fig. 4.5 for (a) the normal component (MPn) and (b) the tangential component
+(MPt) of magnetic signals and for (c) flux loop measurements. Left and right
+panels show the results for the short and long pulse discharges, respectively. It is
+clear that our proposed method performs reasonably good corrections on the drift
+signals if a discharge pulse length is less than 40 sec. We also have scrutinized the
+validation errors with a ten-second step, such as 0 − 10 sec, 10 − 20 sec, 20 − 30
+sec, etc., and we have confirmed that 40 sec is an impartial and justifiable pulse
+length limitation for our proposed method to work properly.
+For the investigated long pulse discharges, the two-step drift correction
+method is modestly working for MPn and MPt signals, whereas the corrections
+on the flux loop measurements make the results worse. If we take a careful look
+on the results of the flux loop measurements in Fig. 4.8(c), we notice that the
+validation errors before the correction (red crosses) are smaller for the long pulse
+discharges compared to the short pulse discharges, while levels of the validation
+errors after the correction (blue circles) are similar for short and long pulse dis-
+charges. Although not conclusive, such results can be explained if a slope of the
+drift signal, i.e., am
+i
+in Eq. (4.1), changes its sign over a long pulse discharge,
+certainly a nonlinear effect.
+Having discussed on the limitation of our proposed method due to a finite
+nonlinear effect, we enunciate that our two-step drift correction method do work
+properly (Sec. 4.1.4) and better than a typical linear fitting method (Sec. 4.1.4)
+at least for the pulse length less than 40 sec. Existing magnetic confinement
+devices such as tokamaks, stellarators, linear machines with non-superconducting
+magnetic coils, in general, would not suffer from such a limitation as pulse lengths
+tend to be shorter. Therefore, our proposed method can readily be used for those
+existing devices without modifying any hardware systems.
+For future machines such as ITER, DEMO or even fusion power plants, this
+limitation must be overcome for steady-state long pulse discharges. One possible
+numerical solution is based on the laws of physics. We can conceive correcting
+the drift signals using physics constrained Bayesian probability theory [86] and
+62
+
+CHAPTER 4. Bayesian neural network in fusion research
+Gaussian processes [131] since the measured magnetic signals must conform with
+Amp`ere’s law (∇ × ⃗B = µ0 ⃗J ignoring the displacement current term as usual)
+and Gauss’s law for magnetism (∇ · ⃗B = 0) as has been done for imputation of
+faulty magnetic sensors [3]. Needless to say, the best solution will be based on
+the development of new kinds of hardwares.
+Abnormal magnetic signals
+As mentioned before (Sec. 4.1.4) some of the magnetic signals are not corrected
+by our proposed method as indicated by the red arrows in Fig. 4.4, i.e., MPn
+#36, FL #25, FL #27 and FL #35. This is due to malfunction of the magnetic
+sensors for the investigated KSTAR discharges.
+Fig. 4.9 shows the temporal evolutions of MPn #7 and #36, where these
+sensors are located at the up-down symmetric positions as shown in Fig. 4.1.
+Slight up-down asymmetry of KSTAR plasmas cannot explain such large dis-
+crepancy in these two signals shown in Fig. 4.9(a). If the sensor were working
+properly, we would expect that these two magnetic sensors output similar tem-
+poral behaviour as shown in Fig. 4.9(b) which is a case with normal MPn #36
+signal. Therefore, we conclude that abnormal MPn #36 signal has contributed
+such a large validation error even after applying our proposed method to the
+signal.
+Fig. 4.10 shows examples of FL #25, FL #27 and FL #35 signals selected
+from three different KSTAR discharges to substantiate that these sensors are
+not working properly. They just show features of random noises compared to a
+proper flux loop measurement as shown in the right panel of Fig. 4.3(c). Notice
+the scale difference of y-axes in Figs. 4.3 and 4.10. Again, we conclude that
+abnormal FL #25, FL #27 and FL #35 signals have resulted in large validation
+errors even after applying our proposed method to the signals.
+Contrarily, we have many cases for MPn, MPt and FL signals where the
+large validation errors before the corrections become noticeably smaller after the
+corrections. Such examples are indicated by the green arrows in Fig. 4.4(c), i.e.,
+FL #01, FL #23 and FL #34. This means that large drifts are well corrected
+63
+
+CHAPTER 4. Bayesian neural network in fusion research
+by our proposed method as shown in Fig. 4.11.
+With these observations that abnormal signals have the large validation
+errors both before and after the correction while normal signals have the small
+validation errors after the correction even if the validation errors are large before
+the correction, we argue that the estimated average validation errors can be used
+to detect flawed magnetic sensors automatically without scrutinizing hundreds
+of magnetic signals.
+4.1.6
+Conclusions
+Magnetic measurements with many kinds of magnetic probes and flux loops
+are indispensable for preparing, operating and analyzing magnetically confined
+plasmas. Yet, they suffer from the drifts in many cases, and many engineers
+and scientists are required to provide non-trivial efforts to correct the obtained
+signals.
+We have proposed the two-step drift correction method which resolves the
+drift problem in real-time. The method is based on Bayesian probability the-
+ory and obtains necessary information to correct the drifts before each plasma
+discharge initiates. This means that we can correct the drifts in real-time and
+provide more accurate information for real-time control of plasmas such as for
+real-time EFIT reconstruction. Our method is capable of correcting the drifts
+within of the order of 1% average validation errors at least for the pulse length
+(in terms of PF coil operation time) less than 40 sec.
+Furthermore, the av-
+erage validation errors can be used to automatically detect defected magnetic
+sensors without going through hundreds of magnetic signals one-by-one to find
+such flawed ones.
+Many real-time applications are developed or proposed based on neural net-
+works these days. If one attempts to utilize neural networks with magnetic signals
+as inputs to the networks, then our method can also be heavily used for such
+applications.
+64
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.2
+Article II: Imputation
+This approach deals with the imputation of faulty magnetic sensors with coupled
+Bayesian and Gaussian processes to reconstruct the magnetic equilibrium in real
+time4, which is largely taken from Ref [3], as a part of preprocessing magnetic
+measurements via Bayesian inference and neural networks.
+This article describes a Bayesian modelling of a magnetic diagnostic system
+to infer one (or more) missing magnetic signals based on Maxwell’s equations.
+This Bayesian model has been applied to normal and tangential magnetic pick-
+up coils at the Korea Superconducting Tokamak Advanced Research (KSTAR).
+These pick-up coils measure the poloidal magnetic field, respectively, normal
+and tangential to the vacuum vessel wall where the coils are installed. As the
+pick-up coils are subject to impairment during plasma operations, faulty plasma
+operations and incorrect data analyses can be caused by the missing magnetic
+fields. Thus, the normal pick-up coils are forward-modelled together by Gauss’s
+law for magnetism, and Amp`ere’s law is used to build a forward model for the
+tangential pick-up coils.
+We divide the missing magnetic signals from the measured signals while
+forward-modelling the signals in order that the missing signals can be inferred
+consistently with the measured magnetic signals as long as they satisfy Maxwell’s
+equation. These models reasonably work when the number of missing signals is
+only one although we obtain an infinite number of solutions from the maximum a
+posteriori method if there are more than one unknown of the missing components.
+Thus, Gaussian processes assisted forward models are introduced to restrict the
+solution spaces by arbitrarily relating the missing and the measured signals with
+each other based on non-parametric Gaussian process regressions. Therefore, all
+of the signals can be represented as a function of one arbitrary missing signal,
+and after the selected missing signal is determined from the forward model, then
+multiple signals can be subsequently inferred with the Gaussian processes. This
+4S. Joung, J. Kim, S. Kwak, K. Park, S.H. Hahn, H.S. Han, H.S. Kim, J.G.
+Bak, S.G. Lee and Y.-c. Ghim
+Review of Scientific Instruments, Vol.89.10 (7th May 2018), DOI:10.1063/ 1.5038938
+65
+
+CHAPTER 4. Bayesian neural network in fusion research
+approach, therefore, can infer the missing fields even if they are more than one.
+Note that the results of Article I have been used here in order to preprocess the
+signal drift.
+4.2.1
+Introduction
+Magnetic pick-up coils installed on magnetic confinement devices such as toka-
+maks and stellarators in addition to Rogowski and flux loop coils provide mag-
+netic information such that high temperature fusion-grade plasmas can be con-
+trolled in real time and that magnetic equilibria can be reconstructed for data
+analyses. Neural networks also have been developed to provide the positions
+of X-point and plasma boundary in real time [5, 7] where input signals to the
+networks are magnetic signals. Therefore, integrity of the magnetic signals is of
+paramount importance. As magnetic probes are subject to impairment during
+plasma operations, faulty plasma operations and incorrect data analyses can be
+caused by missing magnetic signals. For the case of neural networks trained with
+full sets of magnetic signals, even a single missing signal may cause the networks
+not to work properly. [132]
+We present how one can numerically infer, thus impute, missing magnetic
+signals in real time based on a Bayes’ model [86] coupled with the Gaussian
+Process [131] (GP). Likelihood is constructed using Gauss’s law for magnetism
+and Amp`ere’s law and ensuring the consistency with the measured data.
+A
+couple of algorithms to detect faulty magnetic sensors in real time have been
+developed, [133,134] and an inference method for just one faulty signal has also
+been proposed. [134] Our proposed method in this work is tested with up to nine
+non-consecutive missing magnetic probe signals installed on KSTAR. [129] We
+find that the method infers the correct values in less than 1 msec on a typical
+personal computer.
+Then, a full set of raw data, i.e., inferred ones together
+with measured ones, can be passed for real-time EFIT reconstruction [73, 75]
+and neural networks.
+Detailed descriptions on how we generate the likelihood and estimate the
+maximum a posteriori of the Bayes’ model and how well the model infers the
+66
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.12: Schematics of (a) the Amperian loop (blue line connecting blue
+dots) for ∇ × ⃗B = µ0 ⃗J and (b) the pancake-shaped Gaussian surface with three
+surfaces s1, s2 and s3 for ∇ · ⃗B = 0. Blue dots with the numbers in (a) indicate
+the magnetic probes. [2]
+missing values as well as its limitation are provided in section 4.2.2. The limita-
+tion on the Bayes’ model motivates us to use the GP discussed in section 4.2.3
+which also has a certain drawback. In section 4.2.4, we present improved perfor-
+mance, i.e., resolving the defects of the Bayes’ model and the GP while retaining
+their advantages, achieved by coupling the Bayes’ model with the GP. To test
+our proposed method we assume that the intact magnetic signals are missing
+and compare the measured signals with the inferred values. Our conclusion is
+presented in section 4.2.5.
+4.2.2
+Imputation Scheme: Based on Bayes’ model
+Magnetic probes, [2] depicted in Fig. 4.12(a) as the blue dots with the probe
+numbers, installed on KSTAR at a certain toroidal location measure tangential
+(Bt) and normal (Bn) components of the magnetic fields with respect to the
+wall. Missing tangential components are inferred using Amp`ere’s law with the
+measured plasma currents by Rogowski coils, i.e., ∇× ⃗B = µ0 ⃗J neglecting ∂ ⃗E/∂t
+term based on a usual magnetohydrodynamic assumption, [135] and missing
+67
+
+(a)1.5
+(b)
+6
+9
+8
+7
+17
+6
+-18
+Z
+0.5
+924284
+ns2
+E
+Plasma
+0
+current
+Bt
+N
+ns3
+39
+-0.5
+38
+25
+37
+R
+-1
+36
+35
+8
+34
+-1.5
+29
+1
+1.5
+2
+2.5
+3
+R [m]CHAPTER 4. Bayesian neural network in fusion research
+Log-Posterior
+-0.06
+-0.05
+-0.04
+-0.03
+-0.02
+-0.01
+Bt 16 [T]
+-0.01
+0
+0.01
+0.02
+Bt 15 [T]
+-1200
+-1000
+-800
+-600
+-400
+-200
+Prob
+[a.u.]
+Figure 4.13: Log-posterior, ln[p(B∗
+⊕|B⊕, Ω⊕)], of the missing magnetic signals
+inferred by the Bayes’ model with the Maxwell’s equations, when two
+tangential components (Bt from MPs #15 and #16) of the magnetic signals are
+missing. Thick black line marks where the posterior is maximum indicating
+that infinite number of solutions are possible. Data are inferred for KSTAR
+shot #9010 at 0.1 sec.
+normal components using Gauss’s law for magnetism, i.e., ∇ · ⃗B = 0.
+With the Amperian loop, the blue line connecting the blue dots shown in
+Fig. 4.12(a), the tangential components of the magnetic signals Bt must approx-
+imately satisfy
+µ0Ip
+=
+�
+L
+⃗B · d⃗l ≈
+�
+L
+�
+BMP
+t
+− BPF
+t
+�
+dl
+≈
+� Nm
+�
+m=1
+∆l∗
+m
+�
+B∗MP
+t,m − B∗PF
+t,m
+�
++
+Ni
+�
+i=1
+∆li
+�
+BMP
+t,i − BPF
+t,i
+�
+�
+=
+λ∗T �
+B∗MP
+t
+− B∗PF
+t
+�
++
+λT �
+BMP
+t
+− BPF
+t
+�
+,
+(4.12)
+where Ip is the total plasma current assuming that the effect of transient eddy
+currents is negligible [136] which, in general, is acceptable at least during a flat-
+top phase. BMP
+t
+and BPF
+t
+are the tangential components of the magnetic fields
+measured by the magnetic probes (MP) and induced by the poloidal field (PF)
+coils, respectively. Note that KSTAR has 14 PF coils, and their contributions
+are not perfectly canceled out due to change of integral form to a summation.
+Therefore, we remove the PF coil contributions. m and i are the indices for the
+68
+
+CHAPTER 4. Bayesian neural network in fusion research
+missing and the intact magnetic signals; whereas Nm and Ni are the total num-
+bers of the missing and the intact signals, respectively. ∆l, an approximation of
+dl, denotes the segment distance between the magnetic probes, i.e., the distance
+between the consecutive probe numbers in Fig. 4.12(a). ∆l is different for dif-
+ferent probes as can be seen in Fig. 4.12(a). Superscripted asterisk means the
+missing magnetic signal. The last line in Eq. (4.12) is just a reformulation of the
+second line using the vector notations, i.e., λ(∗) = {∆l(∗)
+i(m)} and B(∗)
+t
+= {B(∗)
+t,i(m)}.
+Moret et al. [107] has used Eq. (4.12) to obtain plasma currents in TCV tokamak;
+whereas we apply the same idea to obtain the missing magnetic signals based on
+the plasma currents measured by Rogowski coils.
+For the normal components of the magnetic signals, we utilize the pancake-
+shaped Gaussian surface as depicted in Fig. 4.12(b) consisting of three surfaces
+s1, s2 and s3.
+We force the Gaussian surface to be flat enough, so that the
+magnetic fluxes through the surfaces of ˆns1 and ˆns3 cancel each other as ˆns1·ˆns3 =
+−1, where ˆn is a unit normal vector. Then, ∇ · ⃗B = 0 can be written as
+0 =
+�
+s1+s2+s3
+⃗B · d⃗S ≈
+�
+s2
+Bn dA ≈ ∆w
+�
+L
+Bn dl,
+(4.13)
+where dA (= ∆w dl) is the differential area normal to the surface s2 (parallel to
+Bn) with ∆w being the thickness of the Gaussian surface. dl is the differential
+length encompassing the minor radius (or the poloidal cross-section) and essen-
+tially same as the blue line in Fig. 4.12(a). Since ∆w ̸= 0, we have, again with
+the vector notations,
+0
+=
+�
+L
+Bn dl ≈ λ∗TB∗
+n + λTBn.
+(4.14)
+Assuming that the noise in magnetic signals is Gaussian, the likelihood is
+p(B⊕|B∗
+⊕, Ω⊕)
+=
+1
+√
+2πσ ×
+exp
+�
+−
+�
+λ∗TB∗
+⊕ −
+�
+Ω⊕ − λTB⊕
+��2
+2σ2
+�
+,
+(4.15)
+where B(∗)
+⊕ is either B(∗)MP
+t
+− B(∗)PF
+t
+or B(∗)
+n
+depending on whether we are inter-
+ested in the tangential or normal component, respectively. Likewise, the value of
+69
+
+CHAPTER 4. Bayesian neural network in fusion research
+Ω⊕ is µ0Ip for the tangential component or simply 0 for the normal component.
+σ is the noise standard deviation based on the measured magnetic signals with
+the uncertainty propagation, and measured to be O(10−4).
+Finally, we obtain posterior as
+p(B∗
+⊕|B⊕, Ω⊕) ∝ p(B⊕|B∗
+⊕, Ω⊕) p(B∗
+⊕|Ω⊕),
+(4.16)
+providing us inferred values of the missing magnetic signals (B∗
+⊕) consistent with
+the measured signals (B⊕ and σ) and the Maxwell’s equations (Ω⊕) assuming
+that p(Ω⊕) = 1. With a uniform prior p(B∗
+⊕|Ω⊕), it is obvious that we obtain
+infinite number of solutions from maximum a posteriori (MAP) method if we
+have more than one unknown of the same component. In simpler words, we have
+only one equation for the tangential (Amp`ere’s law) or the normal (Gauss’s law
+for magnetism) component; thus, more than one unknown of the same component
+results in infinite number of solutions. Fig. 4.13 shows an estimated log-posterior
+distribution, ln[p(B∗
+⊕|B⊕, Ω⊕)], where we have removed two Bt measurements,
+i.e., probe numbers #15 and #16, and confirms this effect clearly as depicted
+by the thick black line corresponding to the MAPs. This is the limitation of
+the imputation scheme solely based on the Bayes’ model consistent with the
+Maxwell’s equations.
+4.2.3
+Based on Gaussian Process
+Motivated by the limitation of the Baye’s model with the Maxwell’s equations,
+we introduce Gaussian Process [131] (GP) in our imputation scheme. We express
+the probability distribution of B∗ (Nm × 1 column vector) given the measured
+data B (Ni × 1 column vector) without any analytic expression of the data a
+priori as described elsewhere [131,137]
+p (B∗|B) = N
+�
+¯¯K∗
+¯¯K−1B,
+¯¯K∗∗ −
+¯¯K∗
+¯¯K−1
+¯¯K∗T�
+,
+(4.17)
+70
+
+CHAPTER 4. Bayesian neural network in fusion research
+10
+20
+30
+40
+-0.2
+-0.1
+0
+0.1
+B [T]
+(a)
+10
+20
+30
+40
+-0.1
+0
+0.1
+(b)
+measured
+GP-predicted
+10
+20
+30
+40
+probe #
+-0.04
+-0.02
+0
+B [T]
+(c)
+10
+20
+30
+40
+probe #
+-0.02
+0
+0.02
+(d)
+Figure 4.14: Successful GP predictions (red crosses) compared with the actual
+data (blue circles) for (a) Bt and (b) Bn at 3.70 sec of KSTAR shot #9010
+where we remove nine non-consecutive signals (indicated by red arrows)
+simultaneously to examine the proposed GP imputation scheme. On the other
+hand, if the magnetic signals are spatially varying fast such as (c) Bt of MPs
+#15 and #16 and (d) Bn of MPs #17 and #18 at 0.10 sec of the same shot,
+the GP imputation scheme fails to infer the correct values.
+with
+¯¯K ≡
+¯¯K (X, X) + σ2
+n¯¯I,
+(Ni × Ni matrix)
+¯¯K∗ ≡
+¯¯K (X∗, X) ,
+(Nm × Ni matrix)
+¯¯K∗∗ ≡
+¯¯K (X∗, X∗) ,
+(Nm × Nm matrix),
+where N( , ) is the usual notation for a normal distribution, and
+¯¯I the iden-
+tity matrix. σ2
+n ∼ O(10−4) is determined by treating it as a hyperparameter
+for the numerical stability during matrix inversion. [131, 138, 139] Recall that
+Ni(Nm) is the total number of intact (missing) magnetic signals. Here, X(∗) is
+the 2×Ni(Nm) matrix containing the physical positions of all the intact (missing)
+71
+
+CHAPTER 4. Bayesian neural network in fusion research
+magnetic probes in two dimensional space, i.e., physical R and Z positions at a
+fixed toroidal location.
+The ith and jth component of a covariance matrix
+¯¯K(∗ or ∗∗) is defined as
+K(∗ or ∗∗)
+ij
+�
+x(∗)
+i , x(∗)
+j
+�
+=
+σ2
+f exp
+�
+�−1
+2
+�
+x(∗)
+i
+− x(∗)
+j
+�T
+�
+ℓ2
+R
+0
+0
+ℓ2
+Z
+�−1 �
+x(∗)
+i
+− x(∗)
+j
+�
+�
+� ,
+(4.18)
+where x(∗)
+i
+is the ith column vector of the X(∗), i.e., 2×1 column vector containing
+the physical positions of the ith magnetic probe in R and Z coordinate. Hyperpa-
+rameters σ2
+f, ℓR and ℓZ are the signal variance and the length scales in R and Z
+directions, respectively. These hyperparameters govern the characteristic of the
+Gaussian process, i.e., Eq. (4.17), and we select the hyperparameters such that
+the evidence p(B) is maximized [140] with an assumption [141] of ℓR = ℓZ for
+simplicity. As searching for the hyperparameters may become time consuming,
+thus not applicable for real-time control, one can obtain these values beforehand
+using many existing plasma discharges as for the case of density reconstruc-
+tion. [138] Once we have values for the hyperparameters, i.e., σf ∼ O(10−2) and
+ℓR = ℓZ ∼ O(10−1) in this study, we use Eq. (4.17) to obtain the values of the
+missing magnetic signals B∗, i.e., B∗ =
+¯¯K∗
+¯¯K−1B.
+Fig. 4.14(a) and (b) show that our proposed GP imputation scheme suc-
+cessfully infers the missing magnetic signals both for (a) Bt and (b) Bn where the
+red crosses are the inferred values and the blue circles are the measured (actual)
+values. We have examined our scheme with up to nine non-consecutive missing
+signals indicated by the red arrows.
+We have also found that the GP imputation scheme fails to infer the correct
+values if the magnetic signals are varying fast in space as shown in Fig. 4.14(c)
+for Bt and (d) for Bn. This is the limitation of the GP-only imputation scheme.
+72
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.15: (a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and
+#18 from KSTAR shot #9010 at 0.1 sec as shown in Fig. 4.14(c) and (d).
+Green triangles obtained by the Bayes’ mode with the GP match the measured
+values (blue circles) well, while the GP-only method (red crosses) fails to do so
+as has been discussed in Sec. 4.2.3. Comparisons of temporal evolutions for (c)
+Bt from MP #15 and (d) Bn from MP #17 from KSTAR shot #9427 where
+blue line is the measured values, red line for the GP-only and green line for the
+Baye’s model with the GP. Green lines agree well with blue lines well
+throughout the whole discharge including ramp-up and ramp-down phases.
+4.2.4
+Based on Bayes’ model coupled with Gaussian Pro-
+cess
+As we find the limitations of the Bayes’ model (infinite number of solutions
+for more than one missing magnetic signal) and the GP (incorrect inference for
+spatially fast-varying missing magnetic signals), we resolve such weaknesses by
+combining the two schemes: for instance, if we have seven missing signals, we
+select one missing signal among the seven. Then, we use the GP to infer the non-
+selected six missing ones based on the intact signals together with the selected
+missing one which is inferred based on the Bayes’ model.
+73
+
+(h)0
+GD
+E-0.02
+0.02
+B
+0
+-0.04
+-0.02
+Q
+10
+20
+30
+40
+10
+20
+30
+4
+probe #
+probe #
+(c)
+(d)
+0.2
+Bn17 (GP)
+0.1
+(GP-Bayes)
+E
+0.05
+-(Measured)
+0
+B
+Bt15 (GP)
+0
+(GP-Bayes)
+-0.05
+(Measured)
+-0.2
+0
+2
+4
+6
+0
+2
+4
+6
+time [sec]
+time [sec]0CHAPTER 4. Bayesian neural network in fusion research
+Let us denote the selected missing magnetic signal as B∗
+k, and define ˇX∗ to
+contain the positions of R and Z for all the missing magnetic signals except the
+ones corresponding to B∗
+k resulting in 2 × (Nm − 1) matrix; while ˇX containing
+those of B∗
+k in addition to intact magnetic signals becoming 2 × (Ni + 1) matrix,
+i.e., concatenate those of B∗
+k at the last column of X. With ˇX∗ and ˇX our
+covariance matrices become
+ˇ
+¯¯K ≡ ˇ
+¯¯K
+� ˇX, ˇX
+�
++ σ2
+n¯¯I, ((Ni + 1) × (Ni + 1) matrix)
+ˇ
+¯¯K∗ ≡ ˇ
+¯¯K
+� ˇX∗, ˇX
+�
+,
+((Nm − 1) × (Ni + 1) matrix)
+ˇ
+¯¯K∗∗ ≡ ˇ
+¯¯K
+� ˇX∗, ˇX∗�
+,
+((Nm − 1) × (Nm − 1) matrix).
+We separate out the last column of the (Nm − 1) × (Ni + 1) matrix of ˇ
+¯¯K∗ ˇ
+¯¯K−1
+containing B∗
+k information and denote this column vector as L and the rest of
+the matrix, i.e., without the last column of ˇ
+¯¯K∗ ˇ
+¯¯K−1, be
+¯¯Λ. Since we have found
+that B∗ =
+¯¯K∗
+¯¯K−1B in Sec. 4.2.3, we obtain
+ˇB∗
+⊕ =
+¯¯ΛB⊕ + LB∗
+k⊕,
+(4.19)
+stating that once B∗
+k is determined, then all the other missing magnetic signals
+ˇB∗ are determined by the GP. We find the unknown B∗
+k using the Bayes’ model
+where it is perfectly applicable since we have only one missing signal as discussed
+in Sec. 4.2.2. Thus, λ∗TB∗
+⊕ in Eq. (4.15) is
+λ∗TB∗
+⊕
+=
+λ∗
+kB∗
+k⊕ + ˇλ∗T ˇB∗
+⊕
+=
+�
+λ∗
+k + ˇλ∗TL
+�
+B∗
+k⊕ + ˇλ∗T
+¯¯ΛB⊕,
+(4.20)
+where λ∗
+k and ˇλ∗ are the segment distances for the selected missing one B∗
+k⊕ and
+for the rest of the missing signals, respectively.
+Slightly modifying Eq. (4.15) to include the GP scheme, our likelihood for
+the Bayes’ model, then, becomes
+p(B⊕|B∗
+k⊕, Ω⊕)
+=
+1
+√
+2πσ exp
+� 1
+2σ2
+��
+λ∗
+k + ˇλ∗TL
+�
+B∗
+k⊕
+−
+�
+Ω⊕ − λTB⊕ − ˇλ∗T
+¯¯ΛB⊕
+��2�
+.
+(4.21)
+74
+
+CHAPTER 4. Bayesian neural network in fusion research
+The likelihood now contains only one unknown B∗
+k, and all the rest of the missing
+signals are treated as known ones using the GP, i.e,. Eq. (4.19).
+We construct the prior p(B∗
+k⊕|Ω⊕) to follow a Gaussian distribution with
+the mean of Bpair
+k⊕ and the variance of σ2
+prior. Bpair
+k⊕ is the signal of the magnetic
+probe from the up-down symmetric position of the missing signal B∗
+k⊕. MPs
+#6 and #37, MPs #12 and #31, and MPs #19 and #24 in Fig. 4.12(a) are
+examples. We use such a paired magnetic signal as a prior mean of the missing
+signal because KSTAR discharges are quite up-down symmetric, so that a typical
+correlation between the paired signals is about 0.9. Regarding the prior variance
+σ2
+prior, to minimize possible biases we set it to be 500 which means that the prior
+distribution is largely uniform since the actual values of the magnetic signals are
+not much larger than 0.1 T as shown in Fig. 4.14.
+We finally obtain the posterior following Eq. (4.16) as
+p(B∗
+k⊕|B⊕, Ω⊕)
+∝
+exp
+�
+��−
+�
+B∗
+k⊕ − B⋆
+k⊕
+�2
+2σ2
+GP
+−
+�
+B∗
+k⊕ − Bpair
+k⊕
+�2
+2σ2
+prior
+�
+�� ,
+(4.22)
+where
+B⋆
+k⊕
+=
+Ω⊕ − λTB⊕ − ˇλ∗T
+¯¯ΛB⊕
+λ∗
+k + ˇλ∗TL
+σ2
+GP
+=
+�
+σ
+λ∗
+k + ˇλ∗TL
+�2
+.
+Thus, maximum a posteriori (MAP) denoted as BMAP
+k⊕
+can be analytically esti-
+mated and is
+BMAP
+k⊕
+=
+�
+B⋆
+k⊕
+σ2
+GP
++ Bpair
+k⊕
+σ2
+prior
+� � 1
+σ2
+GP
++
+1
+σ2
+prior
+�−1
+(4.23)
+with the posterior variance σ2
+post = (1/σ2
+GP + 1/σ2
+prior)−1. Once BMAP
+k⊕
+is found,
+then all the other missing signals are determined by Eq. (4.19). This completes
+the imputation process.
+To validate our proposed imputation scheme based on the Bayes’ model
+coupled with the GP, we take the same examples shown in Fig. 4.14(c) and
+75
+
+CHAPTER 4. Bayesian neural network in fusion research
+(d). Fig. 4.15(a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and
+#18 show considerable improvements where the green triangles inferred by the
+Bayes’ model coupled with the GP are very close to the blue circles which are
+the measured values. Again, the red crosses obtained only by the GP fails to do
+so.
+Fig 4.15(c) Bt from MP #15 and (d) Bn from MP #17 from KSTAR shot
+#9427 show temporal evolutions of the inferred values where the blue line is the
+measured values, the red line for the GP only and the green line for the Bayes’
+model with the GP. Typically, the GP-only method fails largely during ramp-up
+and ramp-down phases while it is not too bad during the flat-top phase; whereas
+the Bayes’ model with the GP finds the correct values throughout the whole
+discharge.
+Eq. (4.23) contains no unknowns which means that BMAP
+k⊕
+can be estimated
+in real-time. In fact, our proposed method takes less than 1 msec on a typical
+personal computer.
+The hyperparameters are prepared beforehand based on
+many previous discharges, and missing or faulty signals can be identified [133,134]
+in real-time. What one requires to do is simply to perform the following three
+steps in real-time: (1) select a missing signal (B∗
+k⊕) among all the missing ones
+(B∗
+⊕), (2) estimate noise levels (σ) of the measured signals and (3) apply Eq.
+(4.23) and Eq. (4.19) to impute more than one missing magnetic signals. Good
+choice of a missing signal (B∗
+k⊕) is from the ones that spatially vary fast if they
+exist. In KSTAR such signals are Bt from MPs #15 and #16, and Bn from MP
+#17 and #18 in almost all cases, if not all.
+4.2.5
+Discussion and Conclusion
+We have developed and presented a real-time inference scheme, thus imputation
+scheme, for missing or faulty magnetic signals. Our method, Bayes’ model with
+the likelihood constructed based on Gauss’s law for magnetism and Amp`ere’s law,
+coupled with the Gaussian process, allows one to infer the correct values even if
+more than one missing signal that is spatially varying fast exists. The coupled
+method outperforms the Baye’s-only and the GP-only methods without losing
+76
+
+CHAPTER 4. Bayesian neural network in fusion research
+their own advantages. We have examined our method up to nine non-consecutive
+missing magnetic signals.
+The proposed method takes less than 1 msec on a typical personal computer,
+so that the method can be applied to fusion-grade plasma operations where real-
+time reconstruction of magnetic equilibria is crucial. It can also be used for a
+neural network trained with a complete set of magnetic signals without fearing
+the possible loss of magnetic signals during plasma operations.
+As a possible future work, developing a real-time searching algorithm for
+the hyperparameters in the Gaussian process that optimizes the evidence will be
+beneficial. Although results with the predetermined hyperparameters based on
+many previous discharges can be satisfying, the hyperparameters specific to a
+current discharge may provide much better plasma controls especially for those
+discharges that we have not yet explored much. In addition, including the effect
+of eddy currents can improve the performance of our method especially during
+the ramp-up and down phases and disruptions.
+77
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.3
+Article III: Preprocessing flux loop
+This approach deals with A deep learning approach to recover hidden consis-
+tency of KSTAR flux loop signals5, which is largely taken from Ref [142], as a
+part of preprocessing magnetic measurements via Bayesian inference and neural
+networks.
+This article describes a deep neural network applied to the KSTAR poloidal
+flux loops to recover consistency between the measured flux signals. The poloidal
+magnetic signals are typically utilized to reconstruct a plasma equilibrium which
+is a state when a plasma is assumed to be in an ideal magnetohydrodynamic
+equilibrium state. The plasma equilibrium can be obtained by iteratively solv-
+ing the Grad-Shafranov equation, together with the measured poloidal magnetic
+fields and fluxes: first estimate toroidal current density from the Grad-Shafranov
+equation by using assumed equilibrium; second, calculate magnetic signals from
+the current density, and then update the current by comparing the calculated
+signals with the measured signals based on the Grad-Shafranov equation; finally,
+update the equilibrium, and repeat these procedure until the calculated signals
+are close enough to the measured signals within a criterion.
+However, the reconstruction procedure is often abortive when all of the
+measured magnetic signals (the fields and the fluxes) are used simultaneously
+although impaired signals are expelled from the reconstruction. Especially, the
+intact signals measured from flux loops cannot be utilized at once since they yield
+unreasonable reconstructions, making humans pick only a few of them meticu-
+lously. The deep neural network is developed to compensate for the inconsistency
+between the flux loops and generate cleaned fluxes as well as the missing fluxes
+from its output. Thus, the network generated fluxes can be used for the recon-
+struction procedure at the same time, and the reconstruction results are quite
+reasonable compared to existing equilibrium databases reconstructed by humans
+with their careful decisions about selections of the magnetic signals. Note that
+5S. Joung, J. Kim, H.S. Han, J.G. Bak and Y.-c. Ghim
+Scientific Reports, (2022), in preparation
+78
+
+CHAPTER 4. Bayesian neural network in fusion research
+Article V employs this approach in order to reconstruct plasma equilibria solely
+based on neural networks without depending on humans.
+4.3.1
+Introduction
+Plasma is an ionized gas which is a fuel of thermonuclear fusion [37,38], a sus-
+tainable and clean energy source. Tokamak is a device that confines the plasma
+in the magnetic fields to help the fusion reactions continue. Thus, it is impor-
+tant to measure magnetic signals inside the tokamak generated from the magnet
+coils as well as the plasma. To this end, an induction coil-type diagnostics with
+the integrator [48] are widely used for measuring the poloidal magnetic field,
+the magnetic flux, and the plasma current in various magnetic confinement de-
+vices [2,49,104–109,111] including ITER, the International Thermonuclear Ex-
+perimental Reactor [110], which is built to prove the possibility for constructing
+the fusion power plant.
+Basically, magnetic diagnostics are installed on the vacuum vessel wall of the
+tokamak far away from the plasma since the plasma temperature can reach about
+100 million degrees. Thus, the magnetic data solely contains indirect information
+about the internal properties of the plasma related to the plasma geometry or
+large-scale magnetohydrodynamic (MHD) activities [73,112–120]. Here we focus
+on real-time control of the plasma shape and position which are obtained from
+the plasma reconstruction by solving the Grad-Shafranov (GS) equation [43,44]
+where the GS equation is derived based on the MHD equation in equilibrium
+state [42]. To this end, KSTAR [1] has 84 magnetic probes and 45 flux loops
+(FLs) which measure the poloidal magnetic fields and fluxes, respectively [2,49].
+However, compared with the probes, there are inconsistencies between the
+magnetic fluxes hindering the plasma from being reconstructed reasonably, al-
+though we can compensate impaired probes [3] as well as signal drifts (signals
+tending to unintentionally increase or decrease over time) in magnetic measure-
+ments [78] through Bayesian inference [86]. These inconsistencies give rise to the
+dependency on human expert knowledge which possibly causes biases to select
+the specific signals for the reconstruction process.
+79
+
+CHAPTER 4. Bayesian neural network in fusion research
+Thus, with tensorflow [103], we propose a method to recover the consistency
+based on the capability of deep neural networks which are able to learn differ-
+ential equations by themselves. Recently, this capability was used for various
+research fields such as fluid dynamics [143–145], quantum mechanics [146–149],
+and plasma physics [150]. By means of differentiating neural networks analyti-
+cally with respect to their inputs, we present that the network can produce the
+consistent magnetic fluxes based on the measured magnetic fields. Using the
+network outputs, we also prove that reconstructing plasma equilibrium at the
+level of the expert is plausible without relying on the expert knowledge.
+4.3.2
+Magnetic data collection
+We collect 701 shots among the KSTAR 2020 year campaign experiments whose
+discharge length is greater than or equal to 10 sec. In each shot, the magnetic
+signals from 200 msec to the half of the whole discharge length are collected
+at intervals of ∼10 msec. Thus, we extract a total of 369,610 time slices for
+the magnetic probes, the flux loops, the plasma current, and the poloidal field
+coil currents. To train the neural network, we have a total of 13,675,570 (=
+37×369, 610) magnetic fields normal to the wall, and 14,414,790 (= 39×369, 610)
+magnetic fields tangential to the wall, and we also have a total of 11,827,520
+magnetic fluxes obtained from 32 FLs. 90% of these collected signals are used
+for the network training, 5% for the network validation, and the remaining 5%
+for the test dataset.
+4.3.3
+Domain knowledge regarding the poloidal magnetic
+field
+The magnetic fields normal and tangential to the wall where the probes are
+installed can be converted into the R and Z components of the fields based on
+the angle (Fig. 1A, upper right) between the normal direction to the wall and the
+80
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.16: Schematic diagram of FL recovery via a deep neural network. (A)
+The positions of magnetic measurements on the KSTAR poloidal cross-section
+where both Bn and Bt exist (blue dots), only Bn exists (pink dot), only Bt
+exists (green dots), and FLs exist (red crosses). (B) Schematics of the deep
+neural network whose output stands for the flux function converted into BR
+and BZ through analytic differentiation. (C) Temporal evolution of the plasma
+current for KSTAR 24445 shot. (D–G) The network results (blue area) at the
+red dotted lines in (C) are presented compared with the measured signals (red
+dots). First row is for BR, second row is for BZ, and the last row is for FL.
+R direction on the R–Z plane. Thus, we compute BR and BZ as shown below.
+BR,i = Bt,icos(θi) − Bn,isin(θi)
+BZ,i = Bt,isin(θi) + Bn,icos(θi)
+(4.24)
+where the subscript i denotes the channel number of the probes, Bt is the tangen-
+tial magnetic field, and Bn is the normal magnetic field. From the Gauss’s law
+for the magnetism, we can relate the BR and BZ with the poloidal flux function,
+81
+
+1.5
+D
+G
+0.5
+1
+1.5
+2.5
+time [sec]
+0.5
+1.5
+2.5
+Rm
+FL Rocovory
+Deep neural network
+BrBz
+BrIBz
+DiffNN
+@ref
+NNCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.17: Statistical analysis of the trained network with test dataset. (A)
+Statistics of the coefficient of determination between the measured and the
+network BR (left) and BZ (right) from the ramp-up phase, and (B) from the
+flat-top phase. (C) Distributions of the plasma current measured from the
+Rogowski coil (purple line) and the network (purple area) of the ramp-up phase
+(top) and the flat-top phase (bottom). (D) Using 24445 shot, Statistics on the
+difference between the measured ψ and the network ψa
+rel of the ramp-up phase
+(blue) and the flat-top phase (red).
+ψ, based on the vector potential on the cylindrical coordinates, i.e.,
+BR,i = − 1
+R
+dψ
+dZi
+BZ,i = 1
+R
+dψ
+dRi
+(4.25)
+where the subscript i denotes the channel number of the probes, Ri and Zi are
+the position where the probe is on the R–Z domain, and ψ is the poloidal flux
+function which is equal to the poloidal flux measured from the flux loop divided
+by 2π.
+4.3.4
+Modelling the network architecture
+Based on the relationship between the magnetic field and the flux, we construct
+the network architecture whose output is the flux function turning out to be BR
+and BZ through the analytic differentiation of the network (Fig. 4.16B). The
+82
+
+R2=0.9997
+R2=0.9999
+R2=0.9988
+R2=0.9997CHAPTER 4. Bayesian neural network in fusion research
+network is a 4-layer fully-connected network with 100 hidden neurons and one
+bias per hidden layer. The network weights are randomly initialized [151], and
+the activation function is the swish function [152], i.e.,
+swish(x) = x × sigmoid(x) =
+x
+1 − exp (−x)
+(4.26)
+The cost function for training the network is e = e1 + e2 where e1 is built with
+BR and BZ from the probe positions having both the tangential and the normal
+fields (Fig. 4.16A, blue dots)
+e1 = 1
+N
+N
+�
+i=1
+�
+BNN
+R,i − BMD
+R,i
+�2 + 1
+N
+N
+�
+i=1
+�
+BNN
+Z,i − BMD
+Z,i
+�2
+(4.27)
+where N is 11,985,084 which is the total number of BR and BZ signals in the
+training set. On the other hand, e2 is for the normal (Fig. 4.16A, pink dot) or
+the tangential probes (Fig. 4.16A, green dots) where there is no signals being
+paired, i.e.,
+e2 = 1
+N2
+N2
+�
+i=1
+��
+αt(n),iBR,i + βt(n),iBZ,i
+�NN − BMD
+t(n),i
+�2
+(4.28)
+where the subscript i is the no-pair channel number of the probes, N2 is 1,330,596
+which is the number of the no-pair signals in the training dataset, αt(n) is sin(θ)
+(or cos(θ)), and βt(n) is cos(θ) (or −sin(θ)). The superscript NN stands for the
+network results, and the superscript MD refers to the measurements. Addition-
+ally, since the network output only learns the relative value for ψ, we process ψrel
+to be the absolute value ψa
+rel as follows,
+ψa
+rel,i = ψrel,i − 1
+45
+45
+�
+i=1
+ψref,i + 1
+32
+32
+�
+i=1
+ψFL,i
+2π
+(4.29)
+where the subscript i means the channel number of the flux loops, and ψFL is
+the poloidal flux measured from the flux loops.
+83
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.18: Comparison of equilibrium reconstructions based on the network
+(black), the expert (green) and the novice (orange). (A) Left: comparison of
+the equilibrium results at 498.5 msec of 24445 shot. Right: a novice producing
+equilibrium overlaid with the plasma boundaries from the network and the
+expert (dotted lines). (B) Spatial profiles of the plasma current density at Z=0
+location. (C) Chi-square results of the ψ. (D-F) Same results with (A-C) at
+2704.3 msec.
+4.3.5
+Recovering flux loop consistency via the deep neural
+network
+To restore the consistency between magnetic fluxes, we apply the method using
+the deep neural network in which the network output itself is learned by training
+the derivatives of it [150]. From the relationship between the magnetic fields and
+the magnetic fluxes based on Maxwell’s equations, we can model the network
+architecture (Fig. 4.16B) whose output is the poloidal magnetic flux function,
+ψ, which can be transformed into the poloidal magnetic fields in the R and Z
+84
+
+1.5
+1.5
+Current density (Z=0)
+80
+60
+1
+1
+J [A/cm"]
+40
+20
+0.5
+0.5
+-
+[m]
+20
+0
+0
+1.2
+1.3
+1.4
+1.5
+1.6
+1.7
+1.8
+1.9
+2
+2.1
+2.2
+N
+R [m]
+-0.5
+-0.5
+-1
+1
+-1.55
+-1.5
+1
+1.5
+2
+2.5
+1
+1.5
+2
+2.5
+R [m]
+R [m]
+1.5
+Current density (Z=0)
+150
+100
+[A/cm′
+0.5
+0.5
+50
+[w]
+0
+0
+0
+1.3
+1.4
+1.5
+1.6
+1.7
+1.8
+1.9
+2
+2.1
+2.2
+2.3
+N
+R [m]
+-0.5
+-0.5
+-1
+-1
+-1.5
+-1.5
+1
+1.5
+2
+2.5
+1
+1.5
+2
+2.5
+R [m]
+R [m]CHAPTER 4. Bayesian neural network in fusion research
+direction, BR and BZ, via the analytic differentiation of the network ψ, while the
+network is fed with the spatial positions R and Z, the magnetic fields, the plasma
+current, and the poloidal field coil currents. Since the network ψrel trained from
+its derivatives has no information about the absolute value, we turn ψrel into
+ψa
+rel to have the information by using the measured FL signals (see Methods
+subsection ‘Domain knowledge regarding the poloidal magnetic field’).
+Using 36 BR and 36 BZ signals at the blue dots in Fig. 4.16A which are
+computed based on the normal and tangential components of the poloidal mag-
+netic fields with respect to the vessel wall where the probes are installed, we
+generate the network results qualitatively based on KSTAR 24445 shot. Typi-
+cally, the plasma current which is the induced current in the plasma starts being
+discharged at 0 sec, reaches the flat-top phase where the current is approximately
+in equilibrium state after passing through the ramp-up phase where the current
+increases in time (Fig. 4.16C, black line). During the discharge, we choose four
+different time slices (Fig. 4.16C, red dotted lines) to generate the network results
+with its uncertainties [153] (Fig. 4.16D–G, blue areas) in comparison with the
+measured magnetic data (Fig. 4.16D–G, red dots).
+The first and second rows in Fig. 4.16D–G shows the spatial profiles of BR
+and BZ where the x-axes stand for the probe channel numbers, while the figures
+in the last row represent the spatial profiles of ψ. We can find that the measured
+ψ are sporadically scattered, being laid within the network uncertainties. We
+presume that this scatteredness is not due to the mechanical uncertainties of the
+FLs since the uncertainty scale of the FL is about 10−3. Thus, this makes us
+confirm that the scatteredness is elminated in the network results, meaning that
+the network can recover the inconsistency between the FL signals.
+4.3.6
+Quantitative assessment of the network
+So far, we have qualitatively demonstrated that the consistency between FLs
+is reasonably recovered through the deep neural network. Here we show that
+statistical approaches to evaluate the network quality by using the test dataset.
+First, we use the R2 metric, the coefficient of determination [154], for validating
+85
+
+CHAPTER 4. Bayesian neural network in fusion research
+the network generality based on the training targets, i.e., BR and BZ. We present
+that the network BR and BZ signals from the 36 probes each show a fairly linear
+relation with those of the measurements for the ramp-up phase (Fig. 4.17A; Left:
+R2 of BR = 0.9997, Right: R2 of BZ = 0.9999). Similarly, the R2 results for the
+flat-top phase also show considerable linearity (Fig. 4.17B; Left: R2 of BR =
+0.9988, Right: R2 of BZ = 0.9997), indicating that our network can fully imitate
+the test dataset.
+To validate the network quality including the excluded BR and BZ signals
+out of the 42 probes each, we estimate the plasma current from the poloidal
+magnetic fields tangential to the vessel wall by computing the network BR and
+BZ along with the Ampere’s law [3]. Compared with the distributions of the
+measured plasma current at the ramp-up (top) and the flat-top phase (bottom)
+(Fig. 4.17C, purple lines), the network quite well picks up the features of the
+plasma currents from various KSTAR discharges (Fig. 4.17C, purple areas). In
+addition, we calculate the differences between the measured ψ and the network
+ψa
+rel over KSTAR 24445 shot for the ramp-up (Fig. 4.17D, blue bars) and the
+flat-top (Fig. 4.17D, red bars) phases in order to indicate that the network can
+produce a similar level of the ψa
+rel with respect to the measurements over the
+discharge.
+4.3.7
+Equilibrium reconstruction using the network mag-
+netic flux
+We now demonstrate that the use of the network can help the plasma be recon-
+structed at the level of the expert without depending on the expert decisions.
+Thus, we reconstruct the plasma equilibria using KSTAR 24445 shot based on
+the network results, the expert selection, and a novice’s trial. Note that, in Fig.
+4.18, all the black colors refer to the network results, while the green colors are
+for the expert, and the orange colors are related to the novice. To reconstruct
+the plasma, we use an algorithm called EFIT [73] which is a reconstruction code
+widely used in various tokamaks [74,79,155–157], where we use all 45 recovered ψ
+86
+
+CHAPTER 4. Bayesian neural network in fusion research
+signals for the network case, but, the expert only uses 8 selected FL signals. For
+mimicking the novice’s trial, we randomly choose 15 FL signals for the ramp-up
+phase, and 21 FL signals for the flat-top phase which account for half of the total
+number of the FL.
+Overall, we can find that the network helps to pick up the flux surfaces (Fig.
+4.18A and D) and the current density profiles (Fig. 4.18B and E) comparable to
+the expert’s reconstructions, while the novice creates unreasonable and signifi-
+cantly different reconstruction results although the plasma boundaries are similar
+with those of the network and the expert (Fig. 4.18A and D, dotted lines). This
+indicates that the plasma reconstruction can be highly distorted by the recon-
+struction attempts of the unskilled, which possibly gives an adverse impact to
+the real-time control of the plasma.
+Furthermore, as a result of χ2 = ((ψEFIT − ψused)/σ)2 (Fig.
+4.18C and
+F), we can clearly distinguish the reconstruction qualities such that the χ2 for
+the novice’s trial is significantly higher than those of the expert as well as the
+network. It also would be noted that the total summation of the network χ2 for
+the ramp-up case (Fig. 4.18C) is 2.78 which is lower than the expert’s case, i.e.,
+the total sum of χ2 = 3.77 where only 8 signals participate in the reconstruction.
+This informs that the expert-level of the reconstruction can be achieved by even
+non-experts if the network results are utilized. Thus, we can expect that we
+can exclude the expert decision during the reconstruction so that a complete
+automation of the process potentially comes true.
+4.3.8
+Discussion
+We have developed a method that recovers the flux loop consistency by means
+of the network ability to be able to understand differential equations. Based on
+how the network output is learned by itself from its derivatives, we have applied
+this approach to produce the poloidal flux function in order to remove its innate
+scatteredness based on the poloidal magnetic fields. Through the neural network,
+the consistent flux signals are available to be used for the plasma reconstruction
+where the expert-quality of the reconstruction can be attainable with no needs
+87
+
+CHAPTER 4. Bayesian neural network in fusion research
+to become proficient about magnetic diagnostics. In conclusion, we can expect
+the fully automated reconstruction process can possibly be realized.
+As future works, we deal with the other magnetic measurements installed
+in KSTAR such as saddle loops measuring radial magnetic fluxes, Mirnov coils
+detecting MHD activities, and a diamagnetic loop measuring a diamagnetic flux
+by means of the deep neural network. Additionally, we expand our technique to
+the long-pulse discharge sustaining the plasma over 300 sec where deterioration
+in the magnetic signals are likely to occur, e.g., due to the signal drift with
+assistance of Bayesian statistical analysis.
+88
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.4
+Article IV: Preliminary result under super-
+vised learning
+This approach deals with deep neural network Grad–Shafranov solver constrained
+with measured magnetic signals6, which is largely taken from Ref [158], as a part
+of reconstruction of plasma equilibria via deep neural networks.
+This article describes a deep neural network approach to reconstruct plasma
+equilibria in real time by using the existing equilibrium database.
+This also
+proves that the solution of the Grad-Shafranov equation can be achieved by the
+neural network although the network is trained based on a supervised learning
+manner. As discussed in the synopsis of Article III, the equilibrium reconstruc-
+tion requires the iterative estimation which takes time not to be suitable for a
+real-time application. The reconstruction informs tokamak controllers of posi-
+tions of the plasma, and thus the controllers regulate powers of the poloidal field
+coils to manage the magnetic fields inside the tokamak. Therefore, to control
+tokamak plasmas precisely, the reconstruction should be done in real time.
+However, due to the iterative scheme, simplifying the original reconstruc-
+tion algorithm is applied such as limiting the number of iterations or reusing
+equilibria reconstructed previously. In this sense, the network trained based on
+the database estimated by the original algorithm is suggested in order to take
+advantage of the original-like (or off-line-EFIT-like) equilibrium in real time.
+This network is fed with the poloidal magnetic fields and fluxes as its input,
+and produces a solution of the Grad-Shafranov equation as its output. To make
+the network generate rigorous equilibria satisfying the Grad-Shafranov equation,
+the equation itself is used as a cost function for the network training. Further-
+more, This adopts the results of Article II in case of inferring missing inputs,
+which guarantees the use of the network in any circumstances. Since this Article
+proves that a neural network is able to encode rigorous plasma equilibria to its
+6S. Joung, J. Kim, S. Kwak, J.G. Bak, S.G. Lee, H.S. Han, H.S. Kim, G. Lee,
+D. Kwon and Y.-c. Ghim
+Nuclear Fusion, Vol.60.1 (3rd Dec. 2019), DOI:10.1088/1741-4326/ab555f
+89
+
+CHAPTER 4. Bayesian neural network in fusion research
+architecture, Article V is developed based on this approach.
+4.4.1
+Introduction
+Magnetic equilibrium is one of the most important information to understand
+the basic behavior of plasmas in magnetically confined plasmas, and the off-line
+EFIT [73] code has been extensively used to reconstruct such equilibria in toka-
+maks. Its fundamentals are basically finding a solution to an ideal magnetohydro-
+dynamic equilibrium with toroidal axisymmetry, known as the Grad-Shafranov
+(GS) equation [42]:
+∆∗ψ ≡
+�
+R ∂
+∂R
+1
+R
+∂
+∂R + ∂2
+∂Z2
+�
+ψ
+= −µ0Rjφ
+= −µ0R2dp(ψ)
+dψ
+− F(ψ)dF(ψ)
+dψ
+,
+(4.30)
+where ψ = ψ (R, Z) is the poloidal flux function, jφ = jφ (R, Z) the toroidal
+current density function, p(ψ) the plasma pressure. F(ψ) is related to the net
+poloidal current. Here, R, φ and Z denote the usual cylindrical coordinate sys-
+tem. As the ∆∗ is a two-dimensional nonlinear partial differential operator, the
+off-line EFIT [73] finds a solution with many numerical iterations and has been
+implemented in many tokamaks such as DIII-D [74], JET [157], NSTX [155],
+EAST [156] and KSTAR [79] to name some as examples.
+With an aim of real-time control of tokamak plasmas, real-time EFIT (rt-
+EFIT) [75] code is developed to provide a magnetic equilibrium fast enough whose
+results are different from the off-line EFIT results. As pulse lengths of tokamak
+discharges become longer [159–165], demand on more elaborate plasma control
+is ever increased. Furthermore, some of the ITER relevant issues such as ELM
+(edge localized mode) suppression with RMP (resonant magnetic perturbation)
+coils [166] and the detached plasma scenarios [167, 168] require sophisticated
+plasma controls, meaning that the more accurate magnetic equilibria we have in
+real time, the better performance we can achieve.
+90
+
+CHAPTER 4. Bayesian neural network in fusion research
+1
+2
+3
+R [m]
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+Z [m]
+Figure 4.19: A poloidal cross-section of KSTAR with the first wall (blue
+dotted line). Green dotted line indicates a Rogowski coil measuring the plasma
+current (Ip). Green open circles and crosses depict locations of the magnetic
+pick-up coils measuring 32 normal (Bn) and 36 tangential (Bt) magnetic fields,
+respectively, whereas green triangles represent 22 flux loops measuring poloidal
+magnetic fluxes (ΨFL). Black asterisks (22 × 13 spatial positions) show
+locations where we obtain the values of ψ from the off-line EFIT results.
+There has been an attempt to satisfy such a requirement of acquiring a more
+accurate, i.e., closer to the off-line EFIT results compared to the rt-EFIT results,
+magnetic equilibrium in real-time using graphics processing units (GPUs) [76] by
+parallelizing equilibrium reconstruction algorithms. The GPU based EFIT (P-
+EFIT) [76] enabled one to calculate a well-converged equilibrium in much less
+time; however, the benchmark test showed similar results to the rt-EFIT rather
+than the off-line results [169].
+Thus, we propose a reconstruction algorithm based on a neural network that
+satisfies the GS equation as well as the measured magnetic signals to obtain accu-
+rate magnetic equilibrium in real time. We note that usage of neural networks in
+fusion community is increasing rapidly, and examples are radiated power estima-
+91
+
+CHAPTER 4. Bayesian neural network in fusion research
+tion [170], identifying instabilities [171], estimating neutral beam effects [172],
+classifying confinement regimes [173], determination of scaling laws [174, 175],
+disruption prediction [19, 176, 177], turbulent transport modelling [25–27, 178],
+plasma tomography with the bolometer system [179,180], coil current prediction
+with the heat load pattern in W7-X [181], filament detection on MAST-U [182],
+electron temperature profile estimation via SXR with Thomson scattering [183]
+and equilibrium reconstruction [5,7,13,124,184,185] together with an equilibrium
+solver [8]. Most of previous works on the equilibrium reconstruction with neural
+networks have paid attention to finding the poloidal beta, the plasma elongation,
+positions of the X-points and plasma boundaries, i.e., last closed flux surface, and
+gaps between plasmas and plasma facing components, rather than reconstructing
+the whole internal magnetic structures we present in this work.
+The inputs to our developed neural networks consist of plasma current mea-
+sured by a Rogowski coil, normal and tangential components of magnetic fields
+by magnetic pick-up coils, poloidal magnetic fluxes by flux loops and a position
+in (R, Z) coordinate system, where R is the major radius, and Z is the height as
+shown in Figure 4.19. The output of the neural networks is a value of poloidal
+flux ψ at the specified (R, Z) position. To train and validate the neural networks,
+we have collected a total of 1, 118 KSTAR discharges from two consecutive cam-
+paigns, i.e., 2017 and 2018 campaigns. We, in fact, generate three separate neural
+networks which are NN2017, NN2018 and NN2017, 2018 where subscripts indicate the
+year(s) of KSTAR campaign(s) that the training data sets are obtained from. Ad-
+ditional 163 KSTAR discharges (from the same two campaigns) are collected to
+test the performance of the developed neural networks.
+We train the neural networks with the KSTAR off-line EFIT results, and let
+them be accurate magnetic equilibria. Note that disputing on whether the off-
+line EFIT results we use to train the networks are accurate or not is beyond the
+scope of this work. If we find more accurate EFIT results, e.g., MSE(Motional
+Stark Effect)-constrained EFIT or more sophisticated equilibrium reconstruction
+algorithms that can cope with current-hole configurations (current reversal in
+the core) [186–188], then we can always re-train the networks with new sets of
+92
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.20: Before (blue) and after (red) the magnetic signal adjustments for
+(a) normal and (b) tangential components of magnetic fields measured by the
+magnetic pick-up coils, and (c) poloidal magnetic flux measured by one of the
+flux loops. The signals return closer to zeros after the adjustment when all the
+external magnetic coils (except the toroidal field coils) are turned off at around
+30 sec in this KSTAR discharge.
+data as long as the networks follow the trained EFIT data with larger similarity
+than the rt-EFIT results do. This is because supervised neural networks are
+limited to follow the training data.
+Hence, as a part of the training sets we
+use the KSTAR off-line EFIT results as possible examples of accurate magnetic
+equilibria to corroborate our developed neural networks.
+To calculate the output data a typical neural network requires the same
+set of input data as it has been trained. Therefore, even a single missing input
+(out of input data set) can result in a flawed output [132].
+Such a case can
+be circumvented by training the network with possible combinations of missing
+inputs. As a part of input data, we have 32 normal and 36 tangential magnetic
+fields measured by the magnetic pick-up coils. If we wish to cover a case with
+one missing input data, then we will need to repeat the whole training procedure
+with 68 (32 + 36) different cases. If we wish to cover a case with two or three
+missing input data, then we will need additional 2, 278 and 50, 116 different
+cases to be trained on, respectively. This number becomes large rapidly, and
+it becomes formidable, if not impossible, to train the networks with reasonable
+93
+
+(a) Bn
+(b) Bt
+TI ()
+0.01
+0.05
+5
+0
+0
+E
+0.01
+0
+B
+2
+-0.05
+-0.02
+Before adjust.
+After adjust.
+-0.03
+-0.1
+-5
+0
+20
+0
+20
+0
+20
+time [sec]
+time[sec
+time [sec]CHAPTER 4. Bayesian neural network in fusion research
+computational resources.
+Since the magnetic pick-up coils are susceptible to
+damages, we have developed our networks to be capable of inferring a few missing
+signals of the magnetic pick-up coils in real-time by invoking an imputation
+scheme [3] based on Bayesian probability [86] and Gaussian processes [131].
+In addition to reconstructing accurate magnetic equilibria in real-time, the
+expected improvements with our neural networks compared to the previous stud-
+ies are at least fourfold: (1) the network is capable of providing whole internal
+magnetic topology, not limited to boundaries and locations of X-points and/or
+magnetic axis; (2) spatial resolution of reconstructed equilibria is arbitrarily ad-
+justable within the first wall of KSTAR since (R, Z) position is a part of the
+input data; (3) the required training time and computational resources for the
+networks are reduced by generating a coarse grid points also owing to (R, Z)
+position being an input, and (4) the networks can handle a few missing signals
+of the magnetic pick-up coils using the imputation method.
+We, first, present how the data are collected to train the neural networks
+and briefly discuss real-time preprocessing of the measured magnetic signals in
+Sec. 4.4.2. For the readers who are interested in thorough description of the
+real-time preprocessing, Article I provides the details.
+Then, we explain the
+structure of our neural networks and how we train them in Sec. 4.4.3. In Sec.
+4.4.4, we present the results of the developed neural network EFIT (nn-EFIT) in
+four aspects. First, we discuss how well the NN2017, 2018 network reproduces the
+off-line EFIT results. Then, we make comparisons among the three networks,
+NN2017, NN2018 and NN2017, 2018, by examining in-campaign and cross-campaign
+performance. Once the absolute performance qualities of the networks are estab-
+lished, we compare relative performance qualities between nn-EFIT and rt-EFIT.
+Finally, we show how the imputation method support the networks when there
+exist missing inputs. Our conclusions are presented in Sec. 4.4.5.
+4.4.2
+Collection and real-time preprocessing of data
+Figure 4.19 shows locations where we obtain the input and the output data with
+the first wall (blue dotted line) on a poloidal cross-section of KSTAR. The green
+94
+
+CHAPTER 4. Bayesian neural network in fusion research
+Table 4.1: Summary of the data samples to train and validate the networks
+Parameter
+Definition
+Data size
+No. of samples
+Ip
+Plasma current
+1
+(Rogowski coil)
+Bn
+Normal magnetic field
+32
+(Magnetic pick-up coils)
+217,820
+Bt
+Tangential magnetic field
+36
+(time slices)
+(Magnetic pick-up coils)
+ΨFL
+Poloidal magnetic flux
+22
+(Flux loops)
+R
+Position in major radius
+1
+286
+(22 × 13 grids)
+Z
+Position in height
+1
+Network Input size
+93 (+1 for bias)
+Total no. of samples
+62,296,520
+dotted line indicates a Rogowski coil measuring the plasma current (Ip). The
+green open circles and crosses show locations of the magnetic pick-up coils mea-
+suring 32 normal (Bn) and 36 tangential (Bt) components of magnetic fields, re-
+spectively, whereas the green triangles show 22 flux loops measuring the poloidal
+magnetic fluxes (ΨFL). These magnetic signals are selectively chosen out of all
+the magnetic sensors in KSTAR [2] whose performance has been demonstrated
+for many years, i.e., less susceptible to damages.
+Although KSTAR calibrates the magnetic sensors (magnetic pick-up coils
+and flux loops) regularly during a campaign to remove drifts in the magnetic
+signals, it does not guarantee to fully eliminate such drifts. Thus, we preprocess
+the signals to adjust the drifts. Figure 4.20 shows examples of before (blue) and
+after (red) the drift adjustment for (a) normal and (b) tangential components of
+magnetic fields measured by the magnetic pick-up coils and (c) poloidal magnetic
+flux measured by one of the flux loops. Here, a KSTAR discharge is sustained
+95
+
+CHAPTER 4. Bayesian neural network in fusion research
+until about 20 sec, and all the external magnetic coils (except the toroidal field
+coils) are turned off at about 30 sec. Therefore, we expect all the magnetic signals
+to return to zeros at around 30 sec. If not, we envisage that there has been
+residual drifts. This means that we need to be able to preprocess the magnetic
+signals in real-time so that the input signal characteristics for predictions are
+similar to the trained ones. Article I describes in detail how we preprocess the
+magnetic signals in real-time.
+The black asterisks in Figure 4.19 show the 22 × 13 grid points where we
+obtain the values of ψ from the off-line EFIT results as outputs of the networks.
+We note that the original off-line EFIT provides the values of ψ with 65 × 65
+grid points. The 22×13 grid points are selected such that the distances between
+the neighboring channels in R and Z directions are as similar as possible while
+covering whole region within the first wall. By generating such coarse grid points
+we can decrease the number of samples to train the network, thus consuming less
+amount of computational resources.
+Nevertheless, we do not lose the spatial
+resolution since (R, Z) position is an input, i.e., the network can obtain the
+value of ψ at any position within the first wall (see Sec. 4.4.4).
+With an additional input for the spatial position R and Z, each data sam-
+ple contains 93 inputs (and yet another input for bias) and one output which
+is a value of ψ at the specified (R, Z) location. We randomly collect a total
+of 1, 118 KSTAR discharges from 2017 and 2018 campaigns.
+Since each dis-
+charge can be further broken into many time slices, i.e., every 50 msec follow-
+ing the temporal resolution of the off-line EFIT, we obtain 217, 820 time slices.
+With a total of 286 value of ψ from 22 × 13 spatial points, we have a total of
+62, 296, 520 (= 217, 820 × 286) samples to train and validate the networks. 90%
+of the samples are used to train the networks, while the other 10% are used to
+validate the networks to avoid overfitting problems. Note that an overfitting
+problem can occur if a network is overly well trained to the training data follow-
+ing the very details of them. This inhibits generalization of the trained network
+to predict unseen data, and such a problem can be minimized with the validation
+data set. All the inputs except R and Z are normalized such that the maximum
+96
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.21: An example of the two networks’ results trained with the cost
+function (a) ϵ and (b) ϵnew for KSTAR shot# 17939 at 0.950 sec. Both
+networks (red dashed line) reproduce the ψTarget (black line) well (left panels),
+but only the network trained with ϵnew reproduces ∆∗ψTarget (right panels).
+and minimum values within the whole samples become 1 and −1, respectively.
+We use the actual values of R and Z in the unit of meters.
+Table 4.1 summarizes the training and validation samples discussed in this
+section. Additionally, we also have randomly collected another 163 KSTAR dis-
+charges in the same way discussed here which are different from the 1, 118 KSTAR
+discharges to test the performance of the networks.
+4.4.3
+Neural network model and training
+Neural network model
+We develop the neural networks that not only output a value of ψ but also satisfies
+Eq. (4.30), the GS equation. With the total of 94 input nodes (91 for a plasma
+97
+
+(a) KSTAR Shot#17939, 0.950 sec (with E)
+山
+△*b
+1.5
+1.5
+7
+0.5
+6.
+0.5
+0
+0
+N
+-0.5
+-0.5
+.1
+-1
+1.4 1.61.8 2 2.2
+1.4 1.6 1.8 2 2.2
+△*b
+1.5
+1.5
+1
+0.5
+0.5
+E
+0
+0
+N
+-0.5
+-0.5
+-1
+-1
+1.41.61.8 2 2.2
+1.41.61.8 2 2.2
+R [m]
+R [m]CHAPTER 4. Bayesian neural network in fusion research
+current and magnetic signals, two for R and Z position, one for the bias) and
+one output node for a value of ψ, each network has three fully connected hidden
+layers with an additional bias node at each hidden layer. Each layer contains
+61 nodes including the bias node. The structure of our networks is selected by
+examining several different structures by error and trials.
+Denoting the value of ψ calculated by the networks as ψNN, we have
+ψNN =s0 +
+60
+�
+l=1
+sl
+× f
+�
+ul0+
+60
+�
+k=1
+ulkf
+�
+vk0+
+60
+�
+j=1
+vkjf
+�
+wj0+
+93
+�
+i=1
+wjixi
+���
+,
+(4.31)
+where xi is the ith input value with i = 1, . . . , 93, i.e., 91 measured values with the
+various magnetic diagnostics and two for R and Z positions. wji is an element in
+a 61×94 matrix, whereas vkj and ulk are elements in 61×61 matrices. sl connects
+the lth node of the third (last) hidden layer to the output node. w, v, u and s
+are the weighting factors that need to be trained to achieve our goal of obtaining
+accurate ψ. wj0, vk0, ul0 and s0 are the weighting factors connecting the biases,
+where values of all the biases are fixed to be unity. We use a hyperbolic tangent
+function as the activation function f giving the network non-linearity [189]:
+f(t) = tanh(t) =
+2
+1 + e−2t − 1.
+(4.32)
+The weighting factors are initialized as described in [151] so that a good
+training can be achieved. They are randomly selected from a normal distribution
+whose mean is zero with the variance set to be an inverse of total number of
+connecting nodes. For instance, our weighting factor w connects the input layer
+(94 nodes with bias) and the first hidden layer (61 nodes with bias), therefore
+the variance is set to be 1/(94 + 61). Likewise, the variances for v, u and s are
+1/(61 + 61), 1/(61 + 61) and 1/(61 + 1), respectively.
+Training
+With the aforementioned network structure, training (or optimizing) the weight-
+ing factors to predict the correct value of ψ highly depends on a choice of the
+98
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.22: The descending feature of training (blue line) and validation (red
+dashed line) errors as a function of iterations. Shaded areas represent standard
+deviation of the errors.
+cost function. A typical choice of such cost function would be:
+ϵ = 1
+N
+N
+�
+i=1
+�
+ψNN
+i
+− ψTarget
+i
+�2
+,
+(4.33)
+where ψTarget is the target value, i.e., the value of ψ from the off-line EFIT results
+in our case, and N the number of data sets.
+As will be shown shortly, minimizing the cost function ϵ does not guarantee
+to satisfy the GS equation (Eq. (4.30)) even if ψNN and ψTarget matches well, i.e.,
+the network is well trained with the given optimization rule. Since ∆∗ψ provides
+information on the toroidal current density directly, it is important that ∆∗ψNN
+matches ∆∗ψTarget as well. We have an analytic form representing ψNN as in Eq.
+(4.31); therefore, we can analytically differentiate ψNN with respect to R and
+Z, meaning that we can calculate ∆∗ψNN during the training stage. Thus, we
+introduce another cost function:
+ϵnew = 1
+N
+N
+�
+i=1
+�
+ψNN
+i
+− ψTarget
+i
+�2
++ 1
+N
+N
+�
+i=1
+�
+∆∗ψNN
+i
+− ∆∗ψTarget
+i
+�2
+,
+(4.34)
+where we obtain the value of ∆∗ψTarget from the off-line EFIT results as well.
+To acknowledge difference between the two cost functions ϵ and ϵnew, we first
+discuss the results. Figure 4.21 shows the outputs of the two trained networks
+99
+
+10~2
+.........................
++.............................
+...............................
+.................................
+一Training error
+- -Validation error
+............
++..............
++...............
+................
+10
+.......
+One epoch
+....
+...
+0
+0.5
+1
+1.5
+2
+2.5
+Training iteration
+×10CHAPTER 4. Bayesian neural network in fusion research
+with the cost function (a) ϵ and (b) ϵnew. It is evident that in both cases the
+network output ψNN (red dashed line) reproduces the off-line EFIT ψTarget (black
+line). However, only the network trained with the cost function ϵnew reproduces
+the off-line EFIT ∆∗ψTarget. Both networks are trained well, but the network
+with the cost function ϵ does not achieve our goal, that is correctly predicting
+ψTarget and ∆∗ψTarget.
+Since our goal is to develop a neural network that solves the GS equation,
+we choose the cost function to be ϵnew to train the networks. We optimize the
+weighting factors by minimizing ϵnew with the Adam [190] which is one of the
+gradient-based optimization algorithms. With 90% and 10% of the total data
+samples for training and validation of the networks, respectively, we stop training
+the networks with a fixed number of iterations that is large enough but not too
+large such that the validation errors do not increase, i.e., to avoid overfitting
+problems. The whole workflow is carried out with Python and Tensorflow [103].
+With the selected cost function we create three different networks that differ
+only by the training data sets.
+NN2017, NN2018 and NN2017, 2018 refer to the
+three networks trained with the data sets from only 2017 (744 discharges), from
+only 2018 (374 discharges) and from both 2017 and 2018 (744 + 374 discharges)
+campaigns, respectively.
+The descending feature of the cost function ϵnew as a function of the training
+iteration for NN2017,2018 network is shown in Figure 4.22. Both the training errors
+(blue line) and validation errors (red dashed line) decrease together with similar
+values which means that the network is well generalized.
+Furthermore, since
+the validation errors do not increase, the network does not have an overfitting
+problem. Note that fluctuations in the errors, i.e., standard deviation of the
+errors, are represented as shaded areas.
+Small undulations repeated over the iterations in Figure 4.22 are due to the
+mini-batch learning. Contrary to the batch learning, i.e., optimizing the network
+with the entire training set in one iteration, the mini-batch learning divides the
+training set into some number of small subsets (1, 000 subsets for our case) to
+optimize the networks sequentially. One cycle that goes through all the subsets
+100
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.23: Performance tests of the NN2017,2018 network on the unseen
+KSTAR discharges from (a)(b) 2017 campaign and (c)(d) 2018 campaign. The
+values of R2 and histograms of (a)(c) ψNN vs. ψTarget and (b)(d) ∆∗ψNN vs.
+∆∗ψTarget with colors representing number of counts manifest goodness of the
+NN2017,2018 network. Red dashed line is the y = x line.
+once is called an epoch.
+The mini-batch learning helps to escape from local
+minima in the weighting factor space [191] via the stochastic gradient descent
+scheme [192].
+4.4.4
+Performance of the developed neural networks: Bench-
+mark tests
+In this section, we present how well the developed networks perform.
+Main
+figures of merit we use are peak signal-to-noise ratio (PSNR) and mean structural
+similarity (MSSIM) as have been used perviously [179] in addition to the usual
+statistical quantity R2, coefficient of determination. We note that obtaining full
+flux surface information ψ (R, Z) on 22 × 13 or 65 × 65 spatial grids with our
+networks takes less than 1 msec on a typical personal computer.
+First, we discuss the benchmark results of the NN2017,2018 network. Then,
+101
+
+×105
+×104
+10
+2
+0
+0.5
+R2=0.998
+8
+Counts
+R2=0.999
+1.5
+-2
+NN
+NN
+6
+0
+1
+4
+0.5
+-6
+2
+-0.5
+-0.5
+0
+0.5
+-6 -4 -2 0
+×104
+×104
+12
+0
+R2=0.999
+5
+0.5
+Counts
+10
+R?=0.997
+Counts
+-2
+4
+8
+NN
+3
+9
+-4
+2
+4
+2
+9-
+-0.5
+-0.5
+0
+0.5
+-6 -4 -2
+0
+EFITCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.24: The actual reconstruction results for the KSTAR shot#18057,
+comparing the network results and off-line EFIT reconstructions for ramp-up
+((b) and (c)), flat-top ((d) and (e)), ramp-down ((f) and (g)) phases following
+(a) the plasma current evolution. Black lines indicate the flux surfaces from the
+off-line EFIT, overlaid with the red dotted lines which stand for the NN
+reconstructions. As a figure of merit, magnitudes of PSNR metric are written
+on each figure.
+we compare the performance of NN2017, NN2018 and NN2017,2018 networks. Here,
+we also investigate cross-year performance, for instance, applying the NN2017
+network to predict the discharges obtained from 2018 campaign and vice versa.
+Then, we evaluate the performance of the networks against the rt-EFIT results
+to examine possibility of supplementing or even replacing the rt-EFIT with the
+networks. Finally, we show how the imputation scheme supports the networks’
+performance.
+Here, all the tests are performed with the unseen (to all three
+networks, i.e., NN2017, NN2018 and NN2017,2018) KSTAR discharges which are 88
+and 75 KSTAR discharges from 2017 and 2018 campaigns, respectively.
+102
+
+(a) Plasma current (KSTAR Shot#18057)
+0.8
+(b) :
+(c)i
+(d)
+A0.6
+M
+0.4
+0.2
+(e)i
+(f)i
+(g)
+0
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+4.5
+5
+time [sec]
+(b) Ramp-up 1
+(c) Ramp-up 2
+@EFIT
+NN)
+(d) Flat-top 1
+1.5
+1.5
+1.5
+1.5
+1.5
+PSNR55.2
+1.5
+PSNR33.6
+PSNR58.4
+PSNR 39.8
+PSNR 55.1
+PSNR34.5
+1
+1
+1
+1
+1
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+E
+0
+0
+0
+0
+0
+0
+N
+-0.5
+0.5
+-0.5
+0.5
+-0.5
+-0.5
+-1
+-1
+-1
+1.62
+1.6
+2
+1.62
+1.6
+1.6
+1.62
+2
+(e) Flat-top 2
+(f) Ramp-down 1
+(g) Ramp-down 2
+1.5
+1.5
+1.5
+PSNR51.6
+1.5
+1.5
+PSNR37.4
+VPSNR54.7
+PSNR 35.7
+PSNR46.3
+1.5
+PSNR26.6
+1
+1
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+E
+0
+0
+0
+0
+0
+0
+N
+-0.5
+-0.5
+-0.5
+-0.5
+-0.5
+-0.5
+1
+.1
+1.62
+1.62
+1.6
+2
+1.6 2
+1.62
+1.6
+R [m]
+R [m]
+R [m]
+R [m]
+R [m]
+R [m]CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.25: Same as Figure 4.23 for the the NN2017 network, i.e., trained with
+the data sets from 2017 campaign.
+Benchmark results of the NN2017,2018 network
+Figure 4.23 show the benchmark results of the NN2017,2018 network, i.e., network
+trained with the data sets from both 2017 and 2018 campaigns. (a) and (b)
+show the results with the test discharges from 2017 campaign; while (c) and (d)
+present the results with the test discharges from 2018 campaign. Histograms of
+(a)(c) ψNN vs. ψTarget and (b)(d) ∆∗ψNN vs. ∆∗ψTarget are shown with colors
+representing the number of counts. For instance, there is a yellow colored point
+in Figure 4.23(a) around (−0.1, −0.1)±ε, where ε is a bin size for the histogram.
+Since yellow represents about 2 × 105 counts, there are approximately 2 × 105
+data whose neural network values and EFIT values are −0.1 ± ε simultaneously
+within our test data set. Note that each KSTAR discharge contains numerous
+time slices whose number depends on the actual pulse length of a discharge, and
+each time slice generates the total of 22 × 13 = 286 data points. The values of
+ψTarget and ∆∗ψTarget are obtained from the off-line EFIT results. It is clear that
+the network predicts the target values well.
+103
+
+×104
+×104
+0
+R2=0.996
+0.5
+R²=0.999
+Counts
+15
+-2
+8
+NN
+10
+6
+-4
+4
+5
+2
+-6
+-0.5
+-0.5
+0
+0.5
+-6 -4 -2
+0
+×104
+X104
+6
+R²=0.999
+12
+0
+R?=0.996
+0.5
+Counts
+Counts
+10
+4
+。
+8
+NN
+6
+-4
+2
+4
+2
+-6
+-0.5
+-0.5
+0
+0.5
+-6
+-4-2
+0
+EFIT
+EFITCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.26: Same as Figure 4.23 for the the NN2018 network, i.e., trained with
+the data sets from 2018 campaign.
+As a figure of merit, we introduce the R2 metric (coefficient of determination)
+defined as
+R2 = 1 −
+�L
+i=1
+�
+yTarget
+i
+− yNN
+i
+�2
+�L
+i=1
+�
+yTarget
+i
+− 1
+L
+�L
+j=1 yTarget
+j
+�2,
+(4.35)
+where y takes either ψ or ∆∗ψ, and L is the number of test data sets. The
+calculated values are written in Figure 4.23, and they are indeed close to unity,
+implying the existence of very strong linear correlations between the predicted
+(from the network) and target (from the off-line EFIT) values. Note that R2 = 1
+means the perfect prediction. The red dashed lines on the figures are the y = x
+lines.
+Figure 4.24 is an example of reconstructed magnetic equilibria using KSTAR
+shot #18057 from 2017 campaign. (a) shows the evolution of the plasma current.
+The vertical dashed lines indicate the time points where we show and compare
+the equilibria obtained from the network (red) and the off-line EFIT (black)
+which is our target. (b) and (c) are taken during the ramp-up phase, (d) and (e)
+104
+
+×104
+×104
+0
+R2=0.998
+6
+0.5
+R?=0.999
+15
+Counts
+'ount
+NN
+4
+NN
+10
+-4
+5
+2
+-6
+-0.5
+-0.5
+0
+0.5
+-6 -4
+-2
+0
+×104
+×104
+12
+R2=0.998
+R?=0.999
+0
+6
+0.5
+10
+punts
+-2
+8
+4
+NN
+6
+-4
+4
+2
+C
+2
+-6
+-0.5
+-0.5
+0
+0.5
+-6
+-4
+-2
+0
+EFIT
+EFITCHAPTER 4. Bayesian neural network in fusion research
+during the flat-top phase, and (f) and (g) during the ramp-down phase. In each
+sub-figure from (b) to (g), left panels compare ψ, and right panels are for ∆∗ψ.
+We mention that the equilibria in Figure 4.24 are reconstructed with 65×65 grid
+points even though the network is trained with 22×13 grid points demonstrating
+how spatial resolution is flexible in our networks.
+For a quantitative assessment of the network, we use an image relevant figure
+of merit that is peak signal-to-noise ratio (PSNR) [193] originally developed
+to estimate a degree of artifacts due to an image compression compared to an
+original image. Typical PSNR range for the JPEG image, which preserves the
+original quality with a reasonable degree, is generally in 30–50 dB [179,194]. For
+our case, the networks errors relative to the off-line EFIT results can be treated
+as artifacts. As listed on Figure 4.24(b)-(g), PSNR for ψ is very good, while we
+achieve acceptable values for ∆∗ψ.
+The NN2017, NN2018 and NN2017,2018 networks
+Similar to shown in Figure 4.23, we show the benchmark results of the NN2017
+(trained with the data sets from 2017 campaign) and the NN2018 (trained with the
+data sets from 2018 campaign) in Figures 4.25 and 4.26, respectively. R2 metric
+is also provided on the figures. Again, overall performance of the networks are
+good.
+The NN2017 and NN2018 networks are trained with only in-campaign data
+sets, e.g., NN2018 with the data sets from only 2018 campaign, and we find
+slightly worse results, but still good, on predicting cross-campaign magnetic
+equilibria, e.g.
+NN2018 predicting equilibria for 2017 campaign.
+Notice that
+the NN2017 seems to predict cross-campaign equilibria better than in-campaign
+ones by comparing Figure 4.25(a) and (c) which contradicts our intuition. Al-
+though the histogram in Figure 4.25(c) seems tightly aligned with the y = x line
+(red dashed line), close inspection reveals that the NN2017 network, in general,
+underestimates the off-line EFIT results from 2018 campaign marginally. This
+will be evident when we compare image qualities.
+Mean structural similarity (MSSIM) [195] is another image relevant figure
+105
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.27: Histograms of MSSIM (left panel) and PSNR (right panel) for
+(a) NN2017, (b) NN2018 and (c) NN2017,2018. Red (green) line indicates the test
+results on the data sets from 2017 (2018) campaign. In each sub-figure, top
+(bottom) panel show the results for ψ (∆∗ψ). The off-line EFIT results are
+used as reference.
+106
+
+(a) NN201z test results
+Test set from 2018
+Counts
+Testsetfrom2017
+500
+102
+0
+0.94
+0.96
+0.98
+1
+20
+40
+60
+500
+*山
+*山
+Counts
+102
+0.94
+0.96
+0.98
+20
+40
+60
+MSSIM
+PSNR
+(b) NN2018 test results
+ITest set from2018
+山
+500
+山
+Test set from 2017
+0
+0.94
+0.96
+0.98
+1
+20
+40
+60
+400
+△*山
+*
+Counts
+102
+200
+5
+0
+0.94
+0.96
+0.98
+1
+20
+40
+60
+MSSIM
+PSNR
+(c) NN2017,2018 test results
+ITest set from 2018
+山
+山
+Counts
+Testsetfrom2017
+500
+102
+0
+0.94
+0.96
+0.98
+1
+20
+40
+60
+△*山
+400
+*
+Counts
+102
+200
+100
+0
+0.94
+0.96
+0.98
+1
+20
+40
+60
+MSSIM
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+of merit used to estimate perceptual similarity (or perceived differences) between
+the true and reproduced images based on inter-dependence of adjacent spatial
+pixels in the images. MSSIM ranges from zero to one, where the closer to unity
+the better the reproduced image is.
+Together with PSNR, Figure 4.27 shows MSSIM for (a) NN2017, (b) NN2018
+and (c) NN2017,2018 where the off-line EFIT results are used as reference. Notice
+that counts in all the histograms of MSSIM and PSNR in this work correspond
+to the number of reconstructed magnetic equilibria (or a number of time slices)
+since we obtain a single value of MSSIM and PSNR from one equilibrium; whereas
+counts in Figures 4.23, 4.25 and 4.26 are much bigger since 286(= 22 × 13) data
+points are generated from each time slice. Red (green) line indicates the test
+results on the data sets from 2017 (2018) campaign. In general, whether the test
+data sets are in-campaign or cross-campaign, image reproducibility of all three
+networks, i.e., predicting the off-line EFIT results, is good as attested by the fact
+that MSSIM is quite close to unity and PSNR for ψ (∆∗ψ) ranges approximately
+40 to 60 (20 to 40). It is easily discernible that in-campaign results are better
+for both NN2017 and NN2018 unlike what we noted in Figure 4.25(a) and (c). Not
+necessarily guaranteed, we find that the NN2017,2018 network works equally well
+for both campaigns as shown in Figure 4.27(c).
+Comparisons among nn-EFIT, rt-EFIT and off-line EFIT
+It is widely recognized that rt-EFIT results and off-line results are different from
+each other. If we allow the off-line EFIT results used to train the networks to
+be accurate ones, then the reconstruction of equilibria with the neural networks
+(nn-EFIT) must satisfy the following criterion: nn-EFIT results must be more
+similar to the off-line EFIT results than rt-EFIT results are to the off-line EFIT
+as mentioned in Sec. 4.4.1. Once this criterion is satisfied, then we can always
+improve the nn-EFIT as genuinely more accurate EFIT results are collected.
+For this reason, we make comparisons among the nn-EFIT, rt-EFIT and off-line
+EFIT results.
+Figure 4.28 shows an example of reconstructed magnetic equilibria for (a)
+107
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.28: An example of reconstructed ψ (R, Z) (left panel) and
+∆∗ψ (R, Z) (right panel) for KSTAR shot #17975 at 0.7 sec comparing (a)
+rt-EFIT (green) and off-line EFIT (black) and (b) nn-EFIT (NN2017,2018) (red)
+and off-line EFIT (black).
+rt-EFIT vs. off-line EFIT and (b) nn-EFIT (the NN2017,2018 network) vs. off-
+line EFIT for KSTAR shot #17975 at 0.7 sec with ψ (left panel) and ∆∗ψ
+(right panel). Green, red and black lines indicate rt-EFIT, nn-EFIT and off-line
+EFIT results, respectively. This simple example shows that the nn-EFIT is more
+similar to the off-line EFIT than the rt-EFIT is to the off-line EFIT, satisfying
+the aforementioned criterion.
+To validate the criterion statistically, we generate histograms of MSSIM
+and PSNR for the nn-EFIT and the rt-EFIT with reference to the off-line EFIT.
+This is shown in Figure 4.29 as histograms, where MSSIM (left panel) and PSNR
+(right panel) of ψ (top) and ∆∗ψ (bottom) are compared between the nn-EFIT
+(black) and the rt-EFIT (green). Here, the nn-EFIT results are obtained with
+the NN2017,2018 network on the test data sets.
+We confirm that the criterion
+108
+
+△*
+1.5
+1.5
+0
+1
+0.5
+0.5
+E
+0
+0
+N
+-0.5
+-0.5
+-1
+1.41.61.822.2
+1.41.61.8 22.2
+*
+1.5
+1.5
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+-1
+-1
+1.41.61.8.2.2.2
+1.41.61.8 2 2.2
+R [m]
+R [m]CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.29: Histograms of MSSIM (left panel) and PSNR (right panel) of ψ
+(top) and ∆∗ψ (bottom) calculated by the nn-EFIT (black) and the rt-EFIT
+(green), where the nn-EFIT is the NN2017,2018. For both the nn-EFIT and the
+rt-EFIT, the off-line EFIT is treated as reference.
+is satisfied with the NN2017,2018 network as the histograms in Figure 4.29 are
+in favour of the nn-EFIT, i.e., larger MSSIM and PSNR are obtained by the
+nn-EFIT. This is more conspicuous for ∆∗ψ than ψ.
+We perform the similar statistical analyses for the other two networks,
+NN2017 and NN2018, which are shown in Fig. 4.30 and 4.31. Since these two
+networks are trained with the data sets from only one campaign, we show the
+results where the test data sets are prepared from (a) 2017 campaign or (b) 2018
+campaign so that in-campaign and cross-campaign effects can be assessed sepa-
+rately. We find that whether in- or cross-campaign, the criterion is fulfilled for
+both ψ and ∆∗ψ.
+The NN2017,2018 network with the imputation scheme
+If one or a few magnetic pick-up coils which are a part of the inputs to the
+nn-EFIT are impaired, then we will have to re-train the network without the
+damaged ones or hope that the network will reconstruct equilibria correctly by
+padding a fixed value, e.g., zero-padding, to the broken ones. Of course, one can
+anticipate training the network by considering possible combinations of impaired
+109
+
+(Test set from 2017, 2018)
+104
+INN2017,2018
+Counts
+rt-EFIT
+200
+102
+100
+0
+0.9
+1
+20
+40
+60
+104
+心
+△*山
+△*山
+200
+Counts
+102
+100
+100
+0
+0.9
+1
+20
+40
+60
+MSSIM
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.30: Same as Figure 4.29 with the NN2017 as the nn-EFIT where the
+test data sets are obtained from (a) 2017 campaign and (b) 2018 campaign.
+magnetic pick-up coils. With the total number of 68 signals from the magnetic
+pick-up coils being inputs to the network in our case, we immediately find that
+the number of possible combinations increases too quickly to consider it as a
+solution.
+Since inferring the missing values is better than the null replacement [132],
+we resolve the issue by using the recently proposed imputation method [3] based
+on Gaussian processes (GP) [131] and Bayesian inference [86], where the likeli-
+hood is constructed based on Maxwell’s equations. The imputation method infers
+the missing values fast enough, i.e., less than 1 msec to infer at least up to nine
+missing values on a typical personal computer; thus, we can apply the method
+during a plasma discharge by replacing the missing values with the real-time
+inferred values.
+110
+
+(a) NN2017 and rt-EFIT
+(Test set from 2017)
+104
+JNN2017
+山
+200
+Counts
+Irt-EFIT
+102
+100
+100
+0
+0.9
+1
+20
+40
+60
+104
+200
+△*山
+△*
+Counts
+102
+100
+100
+0
+0.9
+1
+20
+40
+60
+MSSIM
+PSNR
+(b) NN2017 and rt-EFIT
+(Test set from 2018)
+104
+150
+JNN2017
+Counts
+Irt-EFIT
+100
+102
+50
+100
+0
+0.9
+1
+20
+40
+60
+104
+150
+△*
+*
+Counts
+100
+102
+50
+0
+0.9
+1
+20
+40
+60
+MSSIM
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.31: Same as Figure 4.29 with the NN2018 as the nn-EFIT where the
+test data sets are obtained from (a) 2017 campaign and (b) 2018 campaign.
+We have applied the imputation method to KSTAR shot #20341 at 2.1
+sec for the normal (Bn) and tangential (Bt) components of the magnetic pick-
+up coils as an example. We have randomly chosen nine signals from the 32 Bn
+measurements and another nine from the 36 Bt measurements and pretended that
+all of them (9 + 9) are missing simultaneously. Figure 4.32 shows the measured
+(blue open circles) and the inferred (red crosses with their uncertainties) values
+for (a) Bn and (b) Bt. Probe # on the horizontal axis is used as an identification
+index of the magnetic pick-up coils. Table 4.2 provides the actual values of the
+measured and inferred ones for better comparisons. We find that the imputation
+method infers the correct (measured) values very well except Probe #37 of Bn.
+Inferred (missing) probes are Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn and
+Probe #4, 6, 8, 11, 17, 29, 30, 32, 35 for Bt. Here, we provide all the Probe #’s
+111
+
+(a) NN2018 and rt-EFIT
+(Test set from 2017)
+104
+INN2018
+山
+200
+Counts
+Irt-EFIT
+102
+100
+100
+0
+0.9
+1
+20
+40
+60
+104
+200
+△*山
+*
+Counts
+102
+100
+0
+0.9
+1
+20
+40
+60
+MSSIM
+PSNR
+(b) NN2018 and rt-EFIT
+(Test set from 2018)
+104
+200
+INN2018
+山
+Counts
+rt-EFIT
+102
+100
+100
+0
+0.9
+1
+20
+40
+60
+104
+150
+*
+△*
+Counts
+100
+102
+50
+100
+0
+0.9
+1
+20
+40
+60
+MSSIM
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.32: Measured (blue open circles) and inferred with the imputation
+method [3] (red crosses with their uncertainties) values for (a) Bn and (b) Bt.
+Probe # on the horizontal axis is used as an identification index of magnetic
+pick-up coils. Inferred probes are Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn
+and Probe #4, 6, 8, 11, 17, 29, 30, 32, 35 for Bt.
+used for the neural network: Bn Probe #[2, . . . , 6, 8, 9, 11, . . . , 15, 17, . . . , 20,
+23, . . . , 26, 28, . . . , 32, 34, 35, 37, . . . , 41] (a total of 32) and Bt Probe #[2, . . . ,
+6, 8, 9, 11, . . . , 32, 34, 35, 37, . . . , 41] (a total of 36).
+Comparisons between the nn-EFIT without any missing values, which we
+treat as reference values, and the nn-EFIT with the imputation method or with
+the zero-padding method are made. Here, nn-EFIT results are obtained using the
+NN2017,2018 network. Top panel of Figure 4.33 shows ψ (R, Z) obtained from the
+nn-EFIT without any missing values (black line) and from the nn-EFIT with the
+two missing values replaced with the inferred values (green line), i.e., imputation
+method, or with zeros (pink dashed line), i.e., zero-padding method for (a) Bn
+(left panel) and (b) Bt (right panel) at 2.1 sec of KSTAR shot #20341. Probe #14
+and 30 for Bn and Probe #4 and 8 for Bt are treated as the missing ones. Bottom
+panels compare histograms of MSSIM and PSNR using the imputation method
+(green) and the zero-padding method (pink) for all the equilibria obtained from
+KSTAR shot #20341.
+112
+
+(a) Bn
+(b) Bt
+-@-measured
+X inferred
+0.08
+0.05
+0.06
+0
+0.04
+-0.05
+0.02
+E
+0
+-0.1
+B
+0
+-0.02
+-0.15
+-0.04
+-0.2
+-0.06
+-0.08
+-0.25
+20
+40
+20
+40
+probe #
+probe #CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.33: Top panel: nn-EFIT (NN2017,2018 network) reconstructed
+equilibria without any missing values (black line), and with two missing values
+replaced with the inferred values using the imputation method (green line) or
+with the zeros using the zero-padding method (pink dashed line), where the
+missing values are (a) Bn Probe #14 and 30 (left panel) and (b) Bt Probe #4
+and 8 (right panel). Bottom panels: histograms of MSSIM and PSNR using the
+imputation method (green) and the zero-padding method (pink) for all the
+equilibria obtained from KSTAR shot #20341, where the reference values are
+those obtained using nn-EFIT without any missing values. Note that there are
+many more counts less than 0.9 for MSSIM with the zero-padding method.
+113
+
+KSTAR Shot #20341
+a) Bn: 2 probes
+(b) Bt: 2 probes
+w/o 14th, 30th probes
+w/o 4th, 8th probes
+2.1 sec
+2.1 sec
+[u] 
+0
+0
+1.6.2
+1.62
+R [m]
+R [m]
+15
+Counts
+10
+IMP
+4
+ZEROS
+2
+5
+0.9
+0.95
+0.9
+0.95
+1
+1
+MSSIM
+MSSIM
+30
+30
+Counts
+20
+20
+10
+10
+0
+0
+20
+4060
+20
+40 
+60
+PSNR
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Table 4.2: The imputation results shown in Figure 4.32 with KSTAR shot
+#20341 at 2.1 sec.
+Bn [T] ×10−2
+Bt [T] ×10−2
+No.
+Measured
+Inferred
+No.
+Measured
+Inferred
+3
+-1.45
+-1.88±0.22
+4
+-14.69
+-13.97±0.47
+4
+-1.72
+-2.31±0.24
+6
+-12.38
+-11.42±0.97
+6
+4.62
+4.45±0.65
+8
+-7.82
+-7.88±0.67
+14
+6.13
+6.36±0.27
+11
+-3.15
+-3.22±0.65
+18
+-8.27
+-8.11±0.48
+17
+0.10
+0.30±0.52
+24
+1.86
+1.65±0.30
+29
+3.84
+2.65±0.64
+30
+-7.52
+-7.19±0.18
+30
+1.15
+0.49±0.61
+35
+-7.93
+-7.08±0.65
+32
+-2.65
+-2.11±0.62
+37
+-4.27
+-1.41±0.93
+35
+-8.07
+-8.87±0.55
+It is clear that nn-EFIT with the imputation method (green line) is not only
+much better than that with the zero-padding method (pink dashed line) but it
+also reconstructs the equilibrium close to the reference (black). In fact, the zero-
+padding method is too far off from the reference (black line) to be relied on for
+plasma controls.
+Motivated by such a successful result of the nn-EFIT with the imputation
+method on the two missing values, we have increased number of missing values as
+shown in Figures 4.34 and 4.35 for the same KSTAR discharge, i.e., KSTAR shot
+#20341. Let us first discuss Figure 4.34 which are with (a) the eight (except only
+Probe #6) and (b) nine (all) missing values of Bt. Color codes are same as in
+Figure 4.33, i.e., the reference is black, and nn-EFIT with the imputation method
+green or with the zero-padding method pink. It is evident that the nn-EFIT with
+the imputation method performs well at least up to nine missing values. Such a
+result is, in fact, expected since the imputation method has inferred the missing
+values well as shown in Figure 4.32(b) in addition to the fact that a well-trained
+neural network typically has a reasonable degree of resistance on noises. Again,
+the nn-EFIT with the zero-padding method is not reliable.
+Figure 4.35 (a) and (b) are results with the eight (except only Probe #37)
+and nine (all) missing values of Bn, respectively. Color codes are same as in Figure
+4.33. We find that the nn-EFIT with the eight missing values reconstructs the
+equilibrium similar to the reference one, while the reconstruction quality becomes
+114
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.34: Same color code as in Figure 4.33. Missing values are (a) eight
+Bt (except only Probe #6) and (b) all nine Bt.
+notably worse for nine missing values. This is caused mostly due to poor inference
+of Probe #37 by the imputation method (see Figure 4.32(a)).
+Nevertheless,
+the result is still better than the zero-padding method. Figure 4.36 shows the
+reconstruction results with the same color codes as in Figure 4.33 when we have
+(a) 4+4 and (b) 9+9 combinations of Bn and Bt missing values simultaneously.
+All these results suggest that the nn-EFIT with the imputation method re-
+constructs equilibria reasonably well except when the imputation infers the true
+value poorly, e.g., Bn Probe #37 in Figure 4.32(a) and Table 4.2. In fact, the
+suggested imputation method [3] infers the missing values based on the neigh-
+boring intact values (using Gaussian processes) while satisfying the Maxwell’s
+equations (using Bayesian probability theory). Consequently, such a method be-
+comes less accurate if (1) the neighboring channels are also missing AND (2)
+115
+
+KSTAR Shot #20341
+a) Bt: 8 probes
+(b) Bt: 9 probes
+except 6th probe
+w/o all
+2.1 sec
+2.1 sec
+[w]  
+0
+1.62
+1.6. 2
+R [m]
+R [m]
+15
+15
+Counts
+IMP
+10
+10
+ZEROS
+5
+5
+0.9
+0.95
+0.9
+0.95
+1
+MSSIM
+MSSIM
+40
+40
+Counts
+20
+20
+0
+0
+30 40 50
+30 40 50
+PSNR
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.35: Same color code as in Figure 4.33. Missing values are (a) eight
+Bn (except only Probe #37), (b) all nine Bn.
+the true values change fast from the neighboring values. In fact, Bn Probe #37
+happens to satisfy these two conditions, i.e., Probe #35 is also missing, and the
+true values of Probe #35, #37 and #38 are changing fast as one can discern
+from Figure 4.32(a).
+4.4.5
+Discussions and Conclusions
+We have developed and presented the neural network based Grad-Shafranov
+solver constrained with the measured magnetic signals. The networks take the
+plasma current from a Rogowski coil, 32 normal and 36 tangential components
+of the magnetic fields from the magnetic pick-up coils, 22 poloidal fluxes from
+the flux loops, and (R, Z) position of the interest as inputs. With three fully
+connected hidden layers consisting of 61 nodes each layer, the network outputs
+116
+
+KSTAR Shot #20341
+(a) Bn: 8 probes
+(b) Bn: 9 probes
+except 37th probe
+w/o all
+2.1 sec
+2.1 sec
+E
+0
+0
+N
+1.62
+1.6
+2
+R [m]
+R [m]
+20
+20
+IMP
+Counts
+10
+ZEROS
+10
+0
+0
+0.5
+1
+0.5
+1
+MSSIM
+MSSIM
+30
+30
+Counts
+20
+20
+10
+10
+0
+0
+20
+40
+60
+20
+40
+60
+PSNR
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.36: Same color code as in Figure 4.33. Combinations of missing Bn
+and Bt are examined: (a) four missing Bn and four mssing Bt case and (b) nine
+missing Bn and nine missing Bt case.
+a value of poloidal flux ψ. We set the cost function used to train the networks
+to be a function of not only the poloidal flux ψ but also the Grad-Shafranov
+equation ∆∗ψ itself. The networks are trained and validated with 1, 118 KSTAR
+discharges from 2017 and 2018 campaigns.
+Treating the off-line EFIT results as accurate magnetic equilibria to train
+the networks, our networks fully reconstruct magnetic equilibria, not limited to
+obtaining selected information such as positions of magnetic axis, X-points or
+plasma boundaries, more similar to the off-line EFIT results than the rt-EFIT
+is to the off-line EFIT. Owing to the fact that (R, Z) position is a part of the
+input, our networks have adjustable spatial resolution within the first wall. The
+imputation method supports the networks to obtain the nn-EFIT results even if
+117
+
+KSTAR Shot #20341
+a)Bn:4,Bt:4 probes
+(b)Bn:9,Bt:9 probes
+Bn: w/o 3rd,6th.18th,24th
+Bn: w/o all
+Bt: w/o 4th,8th,17th,29th
+Bt: w/o all
+2.1 sec
+2.1 sec
+E
+0
+0
+N
+1.62
+1.6
+R [m]
+R [m]
+10
+IMP
+6
+Counts
+ZEROS
+5
+4
+2
+0.9
+0.95
+0.5
+MSSIM
+MSSIM
+Counts
+20
+20
+0
+0
+20
+40
+20
+40
+PSNR
+PSNRCHAPTER 4. Bayesian neural network in fusion research
+there exist a few missing inputs.
+As all the necessary computation time is approximately 1 msec, the networks
+have potential to be used for real-time plasma control. In addition, the networks
+can be used to provide large number of automated EFIT results fast for many
+other data analyses requiring magnetic equilibria.
+118
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.5
+Article V: Plasma reconstruction via unsu-
+pervised learning
+This approach deals with GS-DeepNet: Mastering tokamak plasma equilibria
+with deep neural networks and the Grad-Shafranov equation7, which is largely
+taken from Ref [150], as a part of reconstruction of plasma equilibria via deep
+neural networks.
+This article embodies the essence of this thesis, taking advantage of all
+the principles and methods described previously, in order to reconstruct plasma
+equilibria in a magnetic confinement fusion experiment via deep neural networks.
+KSTAR serves as a test bed for an application of this approach. As the networks
+demonstrated the fact that the plasma equilibrium can be encoded in the network
+architecture, this article taking one step forward brings up a question that neural
+networks can directly solve plasma equilibria by themselves unlike Article IV.
+Here, solving plasma equilibria denotes obtaining plasma equilibria by solv-
+ing the Grad-Shafranov equation. Since this approach does not rely on training
+database containing solutions of the Grad-Shafranov equation, i.e., the EFIT
+database used in Article IV, a large number of different measurement data em-
+ployed in current reconstruction algorithms are collected for the networks such as
+the magnetic pick-up coils, the poloidal flux loops, KSTAR Thomson scattering
+system and KSTAR Charge exchange spectroscopy system as well as Motional
+Stark Effect system (albeit not being introduced). Since the Grad-Shafranov
+equation is derived from both the plasma force equation with equilibrium as-
+sumption and Maxwell’s equations, two neural network architectures take charge
+of each contribution for reasonably solving the whole equations. Furthermore,
+two additional modules are introduced to determine a plasma boundary (dividing
+a plasma region from a vacuum area) since solving the Grad-Shafranov equation
+is a free-boundary problem, and using only the networks is not enough to resolve
+it. From the modelling for the relations between tokamak current sources and
+7S. Joung, Y.-c. Ghim, J. Kim, S. Kwak, S. Lee, D. Kwon, H.S. Kim, J.G. Bak
+Science Advances, (2022), in preparation
+119
+
+CHAPTER 4. Bayesian neural network in fusion research
+the measured magnetic signals, the networks can learn various plasma equilibria
+via unsupervised learning manner and the gradient descent, meanwhile kinetic
+profiles of plasmas are optimally found by the network themselves. After the
+training is done, the networks can produce plasma equilibria in real time which
+can be used for tokamak operations. Note that Article V applies all the tech-
+niques suggested in Article I–IV.
+4.5.1
+Introduction
+The ultimate goal of scientific and engineering research in the field of nuclear fu-
+sion is to build a power plant producing sustainable and clean electricity through
+fusion reactions from a confined plasma heated up to ∼100 million degrees in Cel-
+sius [37,38]. A tokamak is a torus-shape vacuum vessel within which the plasma is
+confined by magnetic fields directed along the long (toroidal) and short (poloidal)
+way around the torus. In order to maintain such a high-temperature plasma for
+a long period of time (for instance, more than 400 seconds [196]), it is necessary
+to balance the plasma pressure and the Lorentz force within the entire plasma
+volume [42] during a tokamak operation. This means that spatial structures of
+plasma pressure and magnetic fields must be known in real time.
+It is often hard to make direct in situ measurements of the plasma structures
+due to its harsh environments, e.g., high temperature and radiation. Although
+there are some optics systems directly measuring internal information such as
+electron temperature and density [197] and magnetic pitch-angle [71], these mea-
+surements are spatially localized and require a magnetic field structure for the
+measured data to be mapped onto a whole plasma volume. Hence, a suite of mag-
+netic diagnostics [48], fundamental measurement devices installed on a tokamak
+wall far from the plasma, are used to obtain the magnetic field structures indi-
+rectly by solving the Grad-Shafranov (GS) equation [43, 44]. The GS equation
+describes a force balanced plasma state conforming to Maxwell’s equations with
+a toroidal axisymmetry assumption, thus finding a solution to the GS equation
+is regarded as reconstructing the magnetohydrodynamic (MHD) equilibrium of
+a toroidal plasma.
+120
+
+CHAPTER 4. Bayesian neural network in fusion research
+The GS equation, resembling the Hicks equation [198] which describes ax-
+isymmetric inviscid fluid, is a two-dimensional (poloidal cross-section), nonlinear,
+elliptic partial differential equation. Owing to its nonlinearity, finding a solution
+to the GS equation typically requires an iterative numerical approach. Compli-
+cating the problem even further, it is an inverse and free boundary problem as
+only external measurements of magnetic fields are often only available. These
+difficulties hinder a real-time application of the GS equation. Of course, a simple
+resolution for the real-time application is to sacrifice accuracy of the solution as
+in Ref. [75]. But, even if accuracy is eschewed, there exist human expert choices
+for numerical convergence. Current numerical algorithms of the reconstruction,
+chiefly EFIT [73], often require decisions made by human experts in manually
+choosing measured magnetic data. Those neglected data do not participate in re-
+constructing a plasma equilibrium, i.e., in finding a solution to the GS equation,
+as they tend to obstruct finding a converged numerical solution.
+There have been attempts to parallelize the numerical algorithms based on
+GPUs [76,199] or to use a supervised deep neural network [78], which fulfil real-
+time demand but human decisions as they are all based on the EFIT algorithm.
+Contrarily, reconstruction methods using Bayesian inference [200–202] were in-
+troduced to eliminate (or at least explicitly articulate) manual selections, but
+they are unlikely to be used for real-time purpose due to their required heavy
+computational time. We note that reconstructing more detailed plasma equilibria
+in real time using internal information is also an active research area [14,77].
+As recent scientific computing is highly supported by deep learning [203],
+there have been various approaches for neural networks to learn physics-based
+differential equations such as solving the many-electron Schr¨odinger equation
+[146, 204], the Navier-Stokes equation [145] and an atmospheric model for cli-
+mate modelling [205]. Other examples include interpolating partial differential
+equations [8, 144, 206] and regularizing neural networks with the Kohn-Sham
+equations [149]. These previous works require actual solutions [144, 206], prior
+knowledge on some of the unknown parameters [8, 145, 205], or approximated
+solution states [146,149, 204] of the target governing equations. There were at-
+121
+
+CHAPTER 4. Bayesian neural network in fusion research
+tempts of solving the GS equation using neural networks [8,207]; however, they
+work only if entire internal profiles over a plasma volume are given with a fixed
+boundary condition, e.g., from a numerical code, VMEC [8, 208], or prescribed
+polynomial-based functions [207], which may not be applicable for many of ex-
+isting tokamaks. Besides, there was an approach [209] for neural networks to
+solve a Stefan problem [210] which is a free-boundary problem and describes a
+phase-change between a liquid and a solid state. However, the method assumed
+that a boundary of the phase-change between the states is already known.
+We propose an algorithm, Grad-Shafranov Deep Neural Networks (GS-DeepNet),
+that learns plasma equilibria solely via unsupervised learning without existing
+numerical algorithms. GS-DeepNet does not depend on several aspects in both
+current reconstruction methods and other neural networks solving differential
+equations. First and foremost, it is trained by self-teaching unsupervised learn-
+ing, without use of any guess of solutions. Only known information is the GS
+equation and externally (and locally) measured data with no manual selections.
+Second, it uses typical fully-connected neural networks known as retaining real-
+time plausibility. Finally, it uses an auxiliary module that detects boundary in-
+formation based solely on network outputs. To reach these outcomes, we develop
+neural networks that are capable of solving a nonlinear elliptic partial differential
+equation in a free-boundary and inverse condition, i.e., the GS equation. As a
+simple survey, we introduce that a neural network can solve a first-order linear
+differential equation, which is discussed in Appendix.
+4.5.2
+Modelling Grad-Shafranov Deep Neural Networks
+Our novel algorithm GS-DeepNet has two deep neural networks NN 1
+Θ and NN 2
+θ
+with parameters Θ and θ, respectively. The goal of it is to discover the poloidal
+flux function, ψ, a solution of the GS equation on the spatial positions shown in
+Fig 4.37B under a given measurement state as its input.
+Figure 4.37B shows 41 × 41 grid points where a plasma potentially exists
+and the positions of the magnetic diagnostics which obtains radial and axial
+components of the poloidal magnetic field (BR and BZ) and the poloidal magnetic
+122
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.37: Self-teaching unsupervised learning scheme in
+GS-DeepNet. (A) The locations and sensor numbers of the KSTAR magnetic
+diagnostics. Colors represent the magnitude of the data. (B) 41 × 41 grid
+points where the plasmas are potentially generated. (C) Schematic
+representation of GS-DeepNet. We call the bundle of NN 1
+Θ and Diff A the
+Maxwell-Net, and NN 2
+θ is named as the Force-Balance (FB) Net. (D–E) The
+three-dimensional configurations of ∆∗ψ and ψ from GS-DeepNet. KSTAR
+poloidal field coils (gray), the vacuum vessel wall (orange) and the plasma
+facing components (blue) are also shown.
+123
+
+leasured magnetic signals
+sianas
+Bz signals
+r signals
+1.5
+FL12-
+1.5
+1.5
+ 0.5 
+[w]
+0.5
+0.5
+0
+FL23-
+0.5
+[w]
+-0.5
+826
+-1
+-1.5
+15
+-1.5
+15*
+FL34
+-1.5
+0.5
+2.5
+3.5
+100
+R [m]
+[m]
+R [m]
+Grad-Shafranov Deep neural networks (GS-DeepNet)
+1.5
+Network structure
+-μoR?p'-ff"
+1 
+BR
+DiffA
+R
+Bz
+MD =[BMD,BD,MP]
+0.5
+FL
+Z
+NN1
+[m] 
+0
+MD
+N
+NN?
+R
+MD = [BMD,BD,MD]
+p'
+-0.5
+-1
+Auxiliary Modules
+Boundary
+0.04 .
+Measuredthermal pressures
+Detection
+-1.5
+1.5
+2
+2.5
+R[m]
+_6 0.02 -
+100
+1.9
+2.2°
+500
+R [m]
+Feature #
+D
+3.
+Inferred 
+Inferred △*
+2 .
+1 、
+0
+N
+-1、
+-2 、
+-3 、
+4
+2
+y [m]
+0
+0
+2
+-2
+-4
+x [m]CHAPTER 4. Bayesian neural network in fusion research
+flux (ψFL). Taking a single spatial point (R, Z) among the spatial positions and
+a set of the magnetic data −−→
+MD = ( ⃗BR, ⃗BZ, ⃗ψFL) as an input, NN 1
+Θ outputs a flux
+function, ψ = NN 1
+Θ(R, Z, −−→
+MD). The vector of ⃗B(R(Z)) (or ψFL) means a feature
+of all obtained ⃗B(R(Z)) (or ψFL) from its measurement locations at a single time
+slice during a tokamak operation (Fig. 4.37A). This network output is fed into
+NN 2
+θ which outputs both a plasma pressure gradient and a quantity related to
+the toroidal magnetic field, (dp/dψ, fdf/dψ) = (p′, ff ′) = NN 2
+θ (ψ). Here, p
+represents the plasma pressure, and the toroidal field Bφ can turn into f = RBφ
+which is related to the poloidal plasma current. (p′, ff ′) is the variables of the GS
+equation (see equation 4). Both neural networks have multiple fully-connected
+layers [203] with dropout [211] and swish nonlinear activation functions [152]
+(See Materials and Methods).
+Since we do not depend on existing numerical algorithms, there are not any
+guesses of the solution ψ to train NN 1
+Θ. Instead, GS-DeepNet teaches itself by
+an unsupervised learning algorithm following the GS equation and the magnetic
+measurements. With a given measurement set −−→
+MD, NN 1
+Θ generates ψ all over
+the spatial positions (R, Z) where ψ is the vector representation of ψ consistent
+with the vector (R, Z), and (R, Z) is the vector representation for all the points
+in Fig.
+4.37B. Passing through the automatic differential operator [212, 213]
+(Diff A in Fig. 4.37C), the flux functions ψ turn into BR(= −1/R · ∂ψ/∂Z),
+BZ(= 1/R · ∂ψ/∂R) and ∆∗ψ{= (∂2/∂R2 + ∂2/∂Z2 − 1/R · ∂/∂R)ψ} based on
+Maxwell’s equations, where the symbol · represents the element-wise product.
+A plasma is usually placed inside a boundary called the plasma bound-
+ary (Fig. 4.37B). This boundary dividing the plasma region from the vacuum
+area cannot be defined until the solution ψ is prepared. The pressure p and the
+poloidal current function f of the plasma are ideally defined within the plasma re-
+gion. Thus, after locating the boundary through an auxiliary module for bound-
+ary detection (Fig. 4.37C) based on (BR, BZ, ψ), NN 2
+θ generates (p′, ff ′) by
+using the flux functions inside the plasma, ψin, where (p′, ff ′) is also the vector
+representations for (p′, ff ′). Then, (p′, ff ′) forms −µ0R2 · p′ − ff ′(= ∆∗ψin)
+based on the force balance equation. This is also related to the toroidal plasma
+124
+
+CHAPTER 4. Bayesian neural network in fusion research
+current density Jφ = −∆∗ψ/(µ0R) where µ0 is the vacuum permeability. Since
+−µ0R2 ·p′ −ff ′ is constrained with the given magnetic data −−→
+MD via a response
+matrix ¯¯R estimated based on the Biot-Savart law, it may be viewed as a potential
+guess of the GS equation. Thus, the main concept of the unsupervised learning
+algorithm is that NN 1
+Θ is repeatedly taught by NN 2
+θ which takes ψ from NN 1
+Θ
+as an input. We call the bundle of NN 1
+Θ and the differential operator Diff A the
+Maxwell-Net, and NN 2
+θ is named as the Force-Balance (FB) Net.
+The networks’ parameters are updated to keep their ∆∗ψ matched with
+each other. Since we theoretically have a vacuum on the outside of the plasma
+boundary, NN 1
+Θ is updated to have null current densities for ∆∗ψout estimated
+from ψout, the flux functions outside the plasma. Furthermore, the Maxwell-Net
+outputs corresponding to the measurement locations, (BR, BZ, ψ)md, are trained
+to match −−→
+MD as the initial value of a differential equation. The pipeline of this
+self-teaching procedure is presented in Fig. 4.37C.
+The Biot-Savart law explains a relationship between a magnetic field (or
+flux) and its corresponding current source. This relationship can depend on a
+single independent variable, i.e., a magnitude of the current source in Ampere
+if the locations of the magnetic field (or flux) and current source are fixed, and
+the source carries a constant current at a certain time.
+Thus, we treat the
+toroidal current density Jφ of the plasma as a constant current source, and each
+Jφ on a single R-Z grid position is modelled with an arbitrary three-dimensional
+volumetric current beam having rectangular cross-section (See fig. S4). Thus,
+we can pre-calculate a contribution of Jφ generating a magnetic field (or flux) at
+a measurement position as rij where the subscript i and j represent the indices
+of the magnetic sensor locations and J φ over all 41×41 grid points, respectively.
+We estimate rij for all grids at first due to undefined plasma boundary. This
+contribution rij can be contained in a matrix called the response matrix for the
+plasma, i.e., ¯¯Rp whose matrix size is Nmd × 412 where Nmd is the size of −−→
+MD.
+After the boundary is detected via the auxiliary module, the matrix ¯¯Rp is reduced
+to ¯¯Rp,in whose size is Nmd×Nin where Nin is the number of the grid points inside
+the boundary.
+125
+
+CHAPTER 4. Bayesian neural network in fusion research
+A tokamak has external field coils that we control to generate the poloidal
+magnetic field (see Fig. 4.37D–E). With the identical procedure with the plasma,
+we pre-calculate the contributions of the external coils as ¯¯Rext. We also pre-
+estimate the contributions of the vessel currents (currents induced in tokamak
+structures such as the vacuum vessel wall) which cannot be negligible [214,215]
+as ¯¯RV V . Therefore, we can relate −−→
+MD with every current source in the tokamak,
+i.e., −−→
+MD = ¯¯R¯¯Iφ where ¯¯R = ( ¯¯Rp,in, ¯¯Rext, ¯¯RV V ) with ¯¯Iφ containing Jφ, Jext and
+JV V as a column vector.
+The current densities of the external coils Jext are
+known, while the vessel currents JV V are required to be inferred [216] during
+the unsupervised training procedure. Further technical details are described in
+Materials and Methods.
+GS-DeepNet includes two auxiliary modules for plasma boundary detection
+and locally measured plasma pressure. Because solving the GS equation is a
+free-boundary problem, the plasma boundary cannot be determined until the flux
+function ψ is defined all over the grid points. The boundary can be regarded as an
+outermost line which connects R-Z positions whose flux functions are identical
+to one another as well as encloses a whole plasma area. Thus, the boundary
+module detects the R-Z positions by searching ψ at the boundary spots based
+on the Maxwell-Net outputs (see Methods for details).
+As explained before, the FB-Net outputs (p′, ff ′) by taking ψin, and its
+parameters are updated based on the magnetic data −−→
+MD by forming −µ0R2p′ −
+ff ′. We came up with this update procedure in case that measured data to train
+the network outputs directly is not available. Thus, the pressure module is used
+when measured plasma pressure pm is available although it is spatially localized
+in the fixed R-Z positions (see Fig. 4.37B). To use the measured pressure pm in
+order to train the FB-Net p′, the module performs Gaussian process regressions
+[131] (a non-parametric regression) to the measured pressure pm [90, 92] and
+subsequently estimates derivatives of the regressed pressure pm,GP with respect
+to ψ which is given by the Maxwell-Net. Similarly, the poloidal current function f
+can be deduced from measurements for the local pitch angle between the toroidal
+and the poloidal magnetic fields [71], which can be used to train the FB-Net ff ′
+126
+
+CHAPTER 4. Bayesian neural network in fusion research
+with using Gaussian process regressions. This is left as future works since we
+here consider a way how to use spatially localized data in GS-DeepNet, and it is
+presumably sufficient to show the method for the measured pressure.
+The neural networks in GS-DeepNet are trained by the self-teaching unsu-
+pervised training algorithm fundamentally based on the GS equation. First and
+foremost, we initialize both networks with random parameters, Θ0 and θ0, re-
+spectively. At every iteration i ≥ 1 and each feature t, a guess of the solution
+ψ = NN 1
+Θi−1(R, Z, −−→
+MDt) is generated, and (BR,t, BZ,t, ψt, ∆∗ψt) is estimated
+using the automatic differential operator Diff A. After a plasma boundary is
+determined (as well as preprocessing of pm
+t is done), (p′
+t, ff ′
+t) = NN 2
+θi−1(ψin,t) is
+generated, and (−µ0R2·p′
+t−ff ′
+t, ¯¯Iφ,t, p′
+t) is prepared. With a randomly sampled
+feature from the total feature space, renewed network parameters Θi are trained
+by (BR, BZ, ψ, ∆∗ψ) compared to (−−→
+MD, −µ0R2 · p′ − ff ′(ornulls)), while new
+network parameters θi are updated by (−µ0R2 · p′ − ff ′, ¯¯Iφ, p′) compared to
+(−−→
+MD, pm,GP) using the response matrix ¯¯R. We use gradient descent for training
+the parameters Θ and θ by means of loss functions l1:
+l1 =
+�
+(BR, BZ, ψ)md − −−→
+MD
+�2
++ (∆∗ψin + µ0R2p′ + ff ′)2 + (∆∗ψout)2 + c1||Θ||2
+(4.36)
+and l2, respectively:
+l2 = ( ¯¯R¯¯Iφ−−−→
+MD)2+
+�
+α
+Nin
+�
+i=1
+�
+Rip′
+i− ff ′
+i
+Riµ0
+�
+−Im
+P
+�2
++c2|θ|+(p′−pm,GP)2 (4.37)
+where l1 and l2 are averaged over the mean-squared errors, c1 and c2 are the
+coefficients for L2 and L1 weight regularizations, respectively, to avoid overfit-
+ting, and α �Nin
+i=1(Rip′
+i − ff ′
+i/Riµ0) is the sum of the toroidal current densities
+multiplied by the area of the rectangular cross-section α, which turns out to be
+the total plasma current IP. Im
+P is the measured total plasma current by the
+Rogowski coil [48]. The last term of l2 are only used when the measured pressure
+pm is usable.
+As an example, three-dimensional configurations of ∆∗ψ and ψ from the
+Maxwell-Net are shown in Fig. 4.37D and E, respectively, with some tokamak
+127
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.38: Statistical evaluation of GS-DeepNet training. (A) Blue
+box: the comparison of the initial values of the Maxwell-Net with the magnetic
+dataset. Red box: the comparison of the Maxwell-Net ∆∗ψ with the FB-Net
+∆∗ψ. (B–D) The Maxwell-Net BR, BZ and ψ. (E–F) Left: the configurations of
+the Maxwell-Net ∆∗ψ for a limited and diverted plasmas, respectively. Right:
+the uncertainty configurations of the Maxwell-Net ∆∗ψ. They show their
+structural consistencies with ∆∗ψ such that if ∆∗ψ increases, then uncertainty
+increases with it. (G) R2 for ∆∗ψ between the Maxwell-Net (x-axis) and the
+FB-Net (y-axis).
+structures of the KSTAR [45], one of the first research tokamaks with fully su-
+perconducting magnets in the world.
+128
+
+Network structure
+A*+
+-μoR"p' -ff"
+BR
+DiffA
+Bz
+MD = [BMD,BD,M]
+MAG NN: R2=0.9876
+MD =[BMD,BD,MP]
+MAG NN
+MD
+R2=0.9958
+MAG NN
+MD
+MAG NN
+R2=0.9944
+MD
+R2=0.9848CHAPTER 4. Bayesian neural network in fusion research
+4.5.3
+Statistical analysis of GS-DeepNet training
+Our unsupervised training scheme was performed to train our algorithm GS-
+DeepNet. From the completely random network parameters, the training con-
+tinued until it was terminated by the early stopping method (a regularization
+method to avoid losing generalization for unseen features) [217], which approxi-
+mately took a day.
+We collected 50 experimental plasma discharges of the KSTAR. A plasma
+discharge (fig. S2A–E) represents a series of experimental procedures: first, the
+external magnetic field from the external coils is built up; then, a plasma is
+initiated (or discharged) and controlled by the external magnetic field until it
+is eventually disappeared due to mechanical and physical reasons such as the
+maximum limit of coil currents. A typical discharge length of the KSTAR is
+of the order of 101-2 seconds. Among all time-steps of 50 discharges, we chose
+∼ 104 time slices (features) for the magnetic and pressure measurements. With
+approximate 2 × 102 spatial R-Z positions, network parameters were dealt with
+about 2 × 106(= 2 × 102 × 104) dataset for covering combination of the total
+features as well as all the R-Z points. 80%, 5% and 15% of the dataset went to
+the training, validation and test datasets, respectively.
+Figure 4.38 shows the statistical evaluations of GS-DeepNet training. We
+did not use solutions of the GS equation calculated from an existing numerical
+algorithm to train the networks, rather we used the magnetic measurements
+to constrain the initial values of the network solutions and the self-teaching
+unsupervised learning for the networks to acquire the knowledge of the GS
+equation.
+Thus, as instructed in Fig.
+4.38A, we compared the Maxwell-Net
+(BR, BZ, ψ)md and ∆∗ψ with the obtained magnetic data −−→
+MD and the FB-Net
+∆∗ψ(= −µ0R2 · p′ − ff ′), respectively, to prove whether GS-DeepNet has good
+understanding for both the initial values and the GS equation. Here, we did not
+use the measured plasma pressure, meaning that the last term of the loss func-
+tion l2 constraining the form of the pressure gradient did not participate during
+the self-teaching unsupervised learning.
+Figure 4.38B–D show the comparisons of the Maxwell-Net (BR, BZ, ψ)md
+129
+
+CHAPTER 4. Bayesian neural network in fusion research
+and −−→
+MD over the test dataset. KSTAR has 42 magnetic pick-coil coils each
+for ⃗BR and ⃗BZ, and 45 flux loops for ⃗ψFL [65] (see Fig. 4.37A). Among them,
+31 intact pick-up coils each were selected, while 45 flux loops were used after
+their intactness was inferred based on both a deep neural network and the intact
+pick-up coils [142]. It is worth to mention that, often, some of the magnetic
+measurements are impaired since they are susceptible to damage. The funda-
+mental difference between our GS-DeepNet and an existing numerical algorithm
+is that we used every magnetic measurement except the one that is fully out
+of order such that only null signals are measured, while an existing numerical
+algorithm yet requires human selections among those intact data for its numerial
+convergence. Moreover, we can also cover the flawed data by invoking an impu-
+tation scheme [3] that estimates the missing magnetic data based on Bayesian
+inference [86].
+As an example, the left column in Fig. 4.38B–D shows the initial values of
+the network compared to their corresponding −−→
+MD where they qualitatively well
+agree with each other within one standard deviation (1-σ) uncertainties of the
+network given by Monte Carlo (MC) dropout [153]. In addition, with the use of
+the coefficient of determination R2 [154] (BR, R2 = 0.9876; BZ, R2 = 0.9958;
+ψFL, R2 = 0.9944), these suggest that GS-DeepNet may achieve proper initial
+values for solutions ψ of the GS equation which were also used as its input.
+We presented the examples of configurations of the Maxwell-Net ∆∗ψ under
+certain features as inputs with their determined plasma boundaries using the
+boundary module (Fig. 4.38E–F). We have fundamentally two kinds of plasma
+boundaries in a tokamak [218]: a limited plasma boundary where the plasma is
+‘limited’ by hitting a solid wall (Fig. 4.38E); a diverted plasma boundary where
+a magnetic X-point, a null point whose poloidal magnetic field is zero, is created,
+and only a leg extended from the X-point touches the wall. Figure 4.38F shows
+the X-point (the point where the red line crosses) with two legs extended from it
+in the lower left corner. Note that the uncertainty configurations of the Maxwell-
+Net show their structural consistencies with ∆∗ψ configurations such that large
+uncertainty happens around large ∆∗ψ.
+130
+
+CHAPTER 4. Bayesian neural network in fusion research
+Figure 4.39: Equilibrium knowledge learned by GS-DeepNet. (A) The
+physical knowledge discovered by GS-DeepNet. (B) The limited and diverted
+plasma equilibria. (C) The histograms of plasma parameters. (D) The
+comparison of the plasma pressure from the FB-Net with the measured one.
+(E) Left: the measured tan γ (red), the estimated tan γ from GS-DeepNet
+without the kinetic constraints (green) and that from GS-DeepNet with the
+kinetic constraints (blue) are presented. Right: the comparison of RMSE of
+tan γ between GS-DeepNet with (y-axis) and without (x-axis) the kinetic
+constraints. Colors represent the histogram.
+To assess whether the GS equation was properly learned, we compared the
+Maxwell-Net ∆∗ψ (the left hand side of the GS equation) with the FB-Net ∆∗ψ
+(the right hand side of the GS equation) in Fig. 2G. Namely, the Maxwell-Net
+∆∗ψ is required to be comparable with the FB-Net ∆∗ψ generated from taking
+the Maxwell-Net ψ as the network inputs if the self-teaching training reasonably
+worked. With the coefficient of determination R2 = 0.9848 estimated with the
+test dataset, this proposes that GS-DeepNet may achieve the knowledge of the
+GS equation with its solutions ψ as well. It is worth mentioning that an example
+of comparing the FB-Net ¯¯R¯¯Iφ with −−→
+MD)2 can be found in Supplementary section
+S3.
+131
+
+*
+-HoR"p' -ff"
+BR
+MD =[BD,BD,iMP]
+MD
+MD =[BMD, yD,MP]
+EFIT
+EFIT
+EFIT
+MAG NN
+MAG NN
+MAG NN
+MAG NN
+RMSEpres = RMSEMag
+ tan yMag
+pot =peN + ppred
+tan ypres
+PtoN = 2pAN
+tan Ym
+pmCHAPTER 4. Bayesian neural network in fusion research
+Figure 4.40: Performance of GS-DeepNet with local pressure
+constraints. (A) The Maxwell-Net ∆∗ψ with the kinetic constraints is shown.
+Compared to Fig. 4.38F, the configuration become noticeably changed. (B) R2
+for BR, BZ, ψFL and ∆∗ψ. (C) Two plasma equilibria with (colored) and
+without (black) the kinetic constraints is shown. (D) The histograms of the
+plasma parameters from EFIT (green), GS-DeepNet with (orange) and without
+(purple) the kinetic constraints are shown.
+4.5.4
+Physical knowledge learned by GS-DeepNet
+GS-DeepNet understood the knowledge of the GS equation conforming to Maxwell’s
+equations as well as the force balance from its self-teaching training procedure
+with the measurement constraints. Here, we presented that GS-DeepNet also
+discovered the physical knowledge within the GS equation from the Maxwell-
+Net ψ and the FB-Net (p′
+t, ff ′
+t) (Fig. 4.39A) which were trained indirectly (or
+partially directly).
+Figure 4.39B shows two plasma equilibria (the solutions ψ) discovered by
+the Maxwell-Net corresponding to the configurations of the Maxwell-Net ∆∗ψ
+in Fig.
+4.38E–F. We compared these solutions with equilibria reconstructed
+from an existing numerical algorithm, EFIT. Note that we cannot argue whether
+or not the plasma equilibria from EFIT are the accurate solutions of the GS
+equation since they have human decisions for numerical convergence, and most
+132
+
+R2=0.9985
+R2=0.9979
+R2=0.9651
+R2=0.9936
+BR
+Bz
+FL
+△*山
+MAG NN
+EFIT
+EFIT
+EFIT
+EFIT
+KIN NN
+MAG NN
+MAG NN
+MAG NN
+MAG NN
+KIN NN
+KIN NN
+KIN NN
+KIN NNCHAPTER 4. Bayesian neural network in fusion research
+importantly there are no means to measure the equilibria directly to compare. At
+least, what we may be able to argue is that EFIT is commonly used to reconstruct
+equilibria in the field of nuclear fusion, and GS-DeepNet is capable of providing
+such equilibria without influence on several aforementioned aspects in numerical
+algorithms. In the right corners of Fig. 4.39B, we presented the uncertainty
+configurations for the Maxwell-Net ψ that show larger uncertainty at the center
+region.
+For further statistical comparison, we presented the histograms of plasma pa-
+rameters (Fig. 3C) such as minor radius a (half distance between innermost and
+outermost R positions), major radius R0 (R at the central axis of an equilibrium),
+elongation κ (ratio of vertical to horizontal sizes of a plasma) and triangularity
+δ (degree of shape closeness to triangle) (see fig. S2G in Supplementary section
+S2).
+Furthermore, we named and related the FB-Net outputs with the plasma
+pressure gradient p′ and the toroidal magnetic field Bφ = f/R, respectively.
+Thus, we presented the suitability of their terminologies compared with their
+corresponding measured data.
+Figure 4.39D shows the plasma pressure from the FB-Net compared with
+the measured one. The plasma pressure p is generally estimated based on the
+ideal gas law [219], i.e., p = nT where n is the plasma density, and T is the
+plasma temperature. A plasma is an ionized gas that contains charged particles:
+ions and electrons. This plasma is mainly heated up by using its own electrical
+resistivity [220], externally injected energetic ions (whose temperature is greater
+than the plasma) [221] and external injection of electromagnetic waves [222].
+Therefore, to assess the plasma pressure completely, it is required to know the
+electron pressure neTe, the ion pressure niTi as well as the pressure of externally
+injected energetic ions pext, i.e., p = neTe + niTi + pext.
+The electron pressure neTe can be measured by the Thomson Scattering
+(TS) system [65, 197] using the scattered and Doppler-shifted photons from an
+interaction between high-power laser photons and the plasma electrons. Since
+the plasma is known as having quasi-neutrality (ne ≈ ni) [38], the ion pressure
+133
+
+CHAPTER 4. Bayesian neural network in fusion research
+niTi can be estimated with the quasi-neutrality and measuring Ti based on the
+energetic ion injection called the Charge Exchange Spectroscopy (CES) system
+[66] by capturing the Doppler line width and deviation of a spectrum emitted
+from an interaction between the energetic and the plasma ions. Unfortunately,
+measurement systems for pext still need to be developed further [68–70], meaning
+that we cannot measure pext yet.
+Thus, to check whether or not GS-DeepNet is able to contain the physical
+knowledge for the FB-Net p′, we presented the plasma heated up by solely the
+plasma resistivity, meaning that there were no externally injected energetic ions
+to be considered. But, this fact also made measuring Ti unavailable, thus the
+pressure was estimated with an assumption that the electron temperature came
+into a thermal equilibrium with the ion temperature, i.e., p = neTe + niTi =
+2neTe (this assumption has commonly been made in the field of nuclear fusion
+[223–225]). Here, we devised two different ways of the verification: first, the
+measured pressure is known by p = 2neTe which is used to train the FB-Net p′
+based on equation 2; second, the electron pressure is only known, and the FB-Net
+p′ is in charge of inferring the ion pressure. Thus, the plasma pressure p turns
+out to be p = neTe + pNN
+pred where pNN
+pred is inferred by the FB-Net. To this end,
+we trained a neural network (using the same architecture of the FB-Net except
+the output ff ′) with respect to the electron pressure pe = neTe by only using
+the last term of equation 2, while the rest of equation 2 was used to train the
+FB-Net.
+Both ways of the verification yielded the total plasma pressures consistent
+with each other within their uncertainties (Fig. 4.39D) although they are not
+perfectly matched with each other. This suggests that the FB-Net p′ may capture
+some knowledge of the pressure gradient. These uncertainties are quantified via
+MC dropout.
+As mentioned before, the FB-Net ff ′ can be constrained with a magnetic
+pitch angle measurement which is called the Motional Stark Effect (MSE) system
+[71,72] measuring local pitch angles using the polarization of the motional Stark
+effect emission signals by the energetic ion injection. Although we left this to
+134
+
+CHAPTER 4. Bayesian neural network in fusion research
+future works, we presented the comparison between the FB-Net ff ′ and the MSE
+measurements in order to verify the knowledge learned by the FB-Net ff ′.
+KSTAR MSE system [72] has 25 channels, and each channel measures the lo-
+cal pitch angle γ given by tan γ ∼= A1BZ/(A2Bφ+A3BR) where the A coefficients
+are the fixed values related to the geometry information of the measurement sys-
+tem. We prepared GS-DeepNet results trained with and without using the last
+term of equation 2. Here, we collected the measured tan γ and neTe as well as
+Ti from 50 KSTAR discharges and let the FB-Net take charge of inferring pext.
+The FB-Net was used to generate f(= R · Bφ), and the Maxwell-Net was used
+to generate (BR, BZ) to estimate the tan γ formula. Note that the density and
+temperature data are often called the kinetic data.
+Both GS-DeepNet results with and without using the kinetic information
+qualitatively show the similarity to the measured pitch angle, tan γm, in Fig.
+4.39E even though their poloidal current functions f were trained indirectly.
+Figure 4.39E also shows the histogram of Root Mean Square Error (RMSE) of
+tan γ, i.e., RMSE = {�n
+i=1(tan γGS,i−tan γm,i)2/n}0.5 for each feature in the test
+dataset where n is the total channel number of the MSE system (n = 25), and
+tan γGS,i is the local pitch angle estimated from GS-DeepNet results. Although
+some of the RMSE results constrained with the kinetic data, RMSEPres, are
+greater than those using the magnetic data only, RMSEMag, most of RMSEPres
+are smaller than RMSEMag. This is presumably due to the fact that RMSEPres
+can contain the internal information of the plasmas even if it is localized. It is
+worth to mention that the tan γGS profiles in Fig. 4.39E have RMSEPres = 0.023
+and RMSEMag = 0.024, respectively.
+4.5.5
+Final performance of GS-DeepNet with the kinetic
+constraints
+As mentioned earlier, we applied the kinetic measurement constraints to GS-
+DeepNet via our unsupervised learning scheme.
+Since we used the localized
+internal measurements to train the FB-Net p′, the Maxwell-Net ψ and ∆∗ψ were
+135
+
+CHAPTER 4. Bayesian neural network in fusion research
+qualitatively altered, compared to Fig. 4.38F–G and Fig. 4.39B–C whose results
+depended only on the magnetic measurements.
+Figure 4.40A shows that the Maxwell-Net ∆∗ψ with the kinetic constraints
+became noticeably varied compared to Fig. 4.38F where they used the same input
+feature. But of course, GS-DeepNet caught the initial values for its solutions well
+enough with the coefficient of determination R2 of 0.9936, 0.9985 and 0.9979
+for BR, BZ and ψFL, respectively, in Fig. 4.40B. The result of comparing the
+Maxwell-Net ∆∗ψ with the FB-Net ∆∗ψ shows the coefficient of determination
+R2 = 0.9651 which slightly diminishes compared to Fig. 4.38G. We presume
+that this might happen because we kept using the same network architecture
+and the coefficients for L2 and L1 weight regularizations although the shapes
+of 4.38 became more complex when we adopted the kinetic constraints to the
+unsupervised training procedure. Thus, increasing complexity of the networks
+(in other words, decreasing the coefficients for the regularizations for instance)
+can possibly improve the network performance. In addition, we also expect that
+using the MSE measurements to constrain the FB-Net ff ′ directly may help the
+performance improved, which might bring the histogram of RMSE of tan γ in
+Fig. 4.39E much closer to zero.
+Figure 4.40C shows the comparison of two plasma equilibria corresponding to
+Fig. 4.40A and Fig. 4.38F, respectively. Unlike the significant structural change
+in ∆∗ψ, there were seemingly slight variation depending on the constraints used
+in GS-DeepNet. Nevertheless, this slight change made notable difference in ∆∗ψ
+followed by the GS equation, meaning that careful acquirement of solutions of the
+GS equation might be required for those who would like to have more complex
+structures of plasma equilibria. We also prepared the histograms of the plasma
+parameters (minor radius a, major radius R0, elongation κ and triangularity δ)
+in Fig. 4.40D for additional statistical comparisons.
+136
+
+CHAPTER 4. Bayesian neural network in fusion research
+4.5.6
+Materials and Methods
+Domain knowledge
+The plasma force-balance equation can be regarded as the well-known incom-
+pressible Navier-Stokes equations [226] under assumptions of the steady-state
+and no viscosity conditions, together with the Lorentz force as the external force
+instead of the gravitational force, i.e.,
+−∇p + ⃗J × ⃗B = 0
+(4.38)
+where p is the plasma pressure, ⃗J is the current density, and ⃗B is the mag-
+netic field. From this force-balance equation, we can derive the GS equation [42]
+(which can be explained in a form of the Hicks equation) with the toroidal sym-
+metry assumption in the cylindrical coordinates (R, φ, Z) by taking advantage of
+Maxwell’s equations as shown below:
+∆∗ψ ≡
+�
+R ∂
+∂R
+1
+R
+∂
+∂R + ∂2
+∂Z2
+�
+ψ
+= −µ0RJt
+= −R2µ0
+dp(ψ)
+dψ
+− f(ψ)df(ψ)
+dψ
+(4.39)
+where combining Maxwell’s equations, i.e., the Gauss’s law for magnetism, ∇ ·
+⃗B = 0, and the Ampere’s law, ∇× ⃗B = µ0 ⃗J, together derives the first two lines of
+the equation, R ∂
+∂R
+1
+R
+∂ψ
+∂R+ ∂2ψ
+∂Z2 = −µ0RJφ, and the force balance equation is used to
+derive the second to third lines of the equation above, −R2µ0
+dp
+dψ −f df
+dψ = −µ0RJφ.
+Here, ψ is the poloidal flux function, Jφ is the toroidal current density, µ0 is the
+vacuum permeability, p(ψ) is the plasma pressure as a function of ψ, and f(ψ)
+is the poloidal current function as a function of ψ. The poloidal current function
+f has the relation with the toroidal magnetic field Bφ such that f = RBφ.
+Technically, the toroidal current density Jφ is required to be known over the
+whole tokamak area in order to solve the GS equation, which is barely achiev-
+able due to the harsh environment of the plasma. Instead, the external magnetic
+measurements (and the spatially localized pressure measurements) are the only
+137
+
+CHAPTER 4. Bayesian neural network in fusion research
+information for the GS equation, which causes an inverse problem. In addition,
+since we only have ∼ 102 number of the measurement data to be used for dis-
+covering solutions of the GS equation on the 41 × 41(∼= 103) spatial grids for a
+certain during a tokamak operation (see Fig. 4.37B), this results in an ill-posed
+problem. Finally, the plasma boundary which divides the plasma region from the
+vacuum region can be determined after the solution ψ is found. This corresponds
+to the definition of a free-boundary problem since a boundary is unknown until
+we solve the GS equation. Therefore, solving the GS equation is a free-boundary
+and ill-posed inverse problem.
+Again, we tackled this problem by developing the Maxwell-Net, the FB-Net
+and the auxiliary modules. Starting from scratch, the Maxwell-Net generates a
+solution ψ of the GS equation and achieves initial values of the solution from
+the prepared magnetic data. This Maxwell-Net solution is used to determine a
+plasma boundary via the auxiliary module for boundary detection, and the FB-
+Net generates a toroidal current density Jφ given by the Maxwell-Net solution as
+well as the boundary information from the module, constrained with the mag-
+netic data using the response matrix ¯¯R. Therefore, the Maxwell-Net is taught
+by the FB-Net output under our self-teaching unsupervised learning algorithm.
+In case that we can use the local pressure measurements to train the FB-Net,
+we prepare the auxiliary module for plasma pressure which performs Gaussian
+process regressions to the measured pressure and takes the derivative of it with
+respect to the Maxwell-Net ψ. Thus, our GS-DeepNet is capable of solving the
+GS equation, starting tabula rasa.
+Data acquisition and preprocessing
+From 50 KSTAR experimental discharges that we collect, the measured data
+from the magnetic pick-up coils, the flux loops and the Rogowski coils for the
+plasma and external coil currents (the poloidal field coils and in-vessel coils [45])
+as well as the TS, CES and MSE systems is used for training, validation and
+testing our GS-DeepNet.
+The magnetic pick-up coils, in fact, measure the poloidal magnetic field
+138
+
+CHAPTER 4. Bayesian neural network in fusion research
+normal and tangential to the vessel wall, Bn and Bt, where the measurements
+are installed.
+Thus, we transform Bn and Bt into BR and BZ based on the
+following coordinate transformations:
+BR = −Bn sin ξ + Bt cos ξ
+BZ = Bn cos ξ + Bt sin ξ
+(4.40)
+where ξ is the angle between the direction normal to the wall and the radial
+direction (see fig. S5 in Supplementary section S5).
+A noise reduction technique is applied to the magnetic pick-up coils, the flux
+loops and the Rogowski coils based on the boxcar average with a time scale of
+1 msec which is smaller scale than a typical time scale of KSTAR equilibrium
+reconstruction.
+Furthermore, we preprocess the signal drifts in the magnetic
+measurements [78] based on Bayesian inference since the magnetic data tends to
+suffer from the signal drift in time such that the baseline of the data increases or
+decreases over time.
+Response matrix
+Following a previous approach [117] that models the plasma and external coils
+as toroidal current beams with rectangular cross sections [47], we estimate the
+response matrix ¯¯R with the following expressions for a matrix component rij
+where the subscript i is the index for the magnetic measurements:
+r(BR)
+ij
+= µ0
+2π
+� Zj,2
+Zj,1
+� Rj,2
+Rj,1
+dRdZ Zi − Z
+Ri
+�
+k
+4RRi
+�
+K(k)+ R2 + R2
+i + (Zi − Z)2
+(R − Ri)2 + (Zi − Z)2E(k)
+�
+(4.41)
+where r(BR)
+ij
+is the component for BR, and the subscript i is set to 1 ≤ i ≤ 31,
+r(BZ)
+ij
+= µ0
+2π
+� Zj,2
+Zj,1
+� Rj,2
+Rj,1
+dRdZ
+�
+k
+4RRi
+�
+K(k) + R2 − R2
+i − (Zi − Z)2
+(R − Ri)2 + (Zi − Z)2E(k)
+�
+(4.42)
+where r(BZ)
+ij
+is the component for BZ, and the subscript i is set to 32 ≤ i ≤ 62,
+r(ψF L)
+ij
+= 2µ0
+� Zj,2
+Zj,1
+� Rj,2
+Rj,1
+dRdZ
+�
+R
+Ri
+1
+√
+k
+��
+1 − 1
+2k
+�
+K(k) − E(k)
+�
+(4.43)
+139
+
+CHAPTER 4. Bayesian neural network in fusion research
+where r(ψF L)
+ij
+is the component for ψFL, and the subscript i is set to 63 ≤ i ≤
+107. Here, k is the elliptic modulus k =
+4RRi
+(R+Ri)2+(Zi−Z)2, (Ri, Zi) is the location
+of the magnetic measurement, and (Rj,1, Rj,2, Zj,3, Zj,4) represents the location
+of the rectangular cross section of the toroidal current beam (see fig.
+S4 in
+Supplementary section S4). The subscript j is set to 1 ≤ j ≤ 412(= 1,681)
+for ¯¯Rp, 1 ≤ j ≤ 30(= 14 + 16) for ¯¯Rext and 1 ≤ j ≤ 18 for ¯¯RV V .
+The
+KSTAR has 14 poloidal field coils and 16 segments of the in-vessel coils as the
+external magnetic coils.
+We divide the tokamak vessel wall into 18 current-
+carrying segments, following a previous approach used in the KSTAR [227].
+In the equations above, K(k) and E(k) are the complete elliptic integral of
+the first and the second kinds, respectively, as defined below:
+K(k) =
+�
+π
+2
+0
+dθ
+1
+�
+1 − k2 sin2 θ
+,
+E(k) =
+�
+π
+2
+0
+dθ
+�
+1 − k2 sin2 θ.
+(4.44)
+The vessel currents JV V are treated as free-parameters [117] which are optimized
+during the network optimization process based on an approach [216] suggesting
+that the vessel currents can be reasonably inferred even though actual conducting
+structures are not precisely identified.
+Auxiliary module: boundary and pressure modules
+A fundamental concept to determine a plasma boundary is finding a X-point
+by using the fact that the poloidal magnetic field at the X-point is ideally zero.
+Since a plasma boundary is a connected line of R-Z positions enclosing the
+plasma area where flux functions on the R-Z positions are all the same, we
+estimate a flux function ψ at the X-point and use it to determine a location of
+the boundary. Thus, the auxiliary module for boundary detection performs the
+following procedure: first, the module receives the Maxwell-Net (ψ, BR, BZ) over
+the spatial grids and estimate magnitudes of the poloidal magnetic field, BP, via
+BP =
+�
+B2
+R + B2
+R; second, the module searches a R-Z point where magnitude
+of its BP is the smallest; third, by feeding the R-Z point into the Maxwell-Net
+140
+
+CHAPTER 4. Bayesian neural network in fusion research
+again, the module can obtain the flux function ψ at the X-point, ψb, and use it
+to find R-Z positions whose flux functions are identical to ψb; finally, in case that
+the plasma is limited, the module compares ψb with flux functions on locations of
+the solid wall by using the Maxwell-Net. If some of the R-Z positions possessing
+ψb are out of the wall, then the module defines that the plasma is limited or vice
+versa. It is worth to mention that the plasma boundary is always changed during
+a tokamak operation (fig. S2F).
+The major role of the auxiliary module for plasma pressure module is to
+perform Gaussian process regression (GPR) to the measured plasma pressure.
+As mentioned before, this module takes the derivative of the GPR-regressed
+pressure with respect to the Maxwell-Net ψ. Here, we use a finite difference
+method to calculate the regressed pressure gradient.
+Optimization
+Our neural networks NN 1
+Θi and NN 2
+θi are trained via TensorFlow [103] with one
+GPU worker and 20 CPU cores. We pass one randomly selected measurement
+feature to the optimization process at a time, meaning that the batch-size is
+412 + 107 = 1,788 corresponding to the grid points and the locations of the mag-
+netic measurements. A total mini-batch size is approximately 8,000. Stochastic
+gradient descent is used to optimized out network parameters with the loss func-
+tions in equations 1 and 2. The coefficients for the L2 and L1 regularizations
+used in the loss functions are set to c1 = 10−3 and c2 = 10−2, respectively. At
+every iteration, a new checkpoint is saved and used to estimate the validation
+loss for the early stopping method.
+Neural network architectures
+The network NN 1
+Θ uses 31 BR, 31 BZ, 45 ψFL from a certain time slice, and a
+single R-Z point as its input whose size is 1 × 109(= 31 + 31 + 45 + 2). This
+input passes through three fully connected layers with the swish nonlinearities
+and a fully connected linear layer, then turns into a scalar. Each layers have 100
+hidden neurons and a bias. The output scalar is treated as a solution ψ on the
+141
+
+CHAPTER 4. Bayesian neural network in fusion research
+R-Z position, and processed by the automatic differential operator Diff A that
+produces BR, BZ and ∆∗ψ. Dropout with a rate of 0.05 is applied to all the fully
+connected layers.
+Similarly, the network NN 2
+θ has a fully connected layer with the swish non-
+linearity and a fully connected linear layer. Each layer has 60 and five neurons,
+respectively, and applies dropout with a rate of 0.10 as well. Taking a scalar (a
+solution ψ from the network NN 1
+Θ) as an input, this network outputs a vector of
+size 2, corresponding to the pressure gradient p′ and the poloidal current related
+variable ff ′.
+These networks are initialized to random weights based on Glorot (or Xavier)
+initialization [151].
+4.5.7
+Discussion
+Our results reasonably demonstrate that a self-teaching unsupervised learning
+scheme is applicable for deep neural networks to learn a second-order nonlinear
+differential equation such as the GS equation. Without using any guess or pre-
+calculated solutions of the GS equation, we prove that it is possible to train deep
+neural networks to acquire knowledge of the solution of the GS equation which
+is a free-boundary and inverse problem required numerical algorithms in general.
+Since our approach do not depend on existing numerical algorithms (or existing
+reconstruction methods), GS-DeepNet is unfettered with the challenges raised in
+the existing methods as mentioned earlier. Furthermore, our approach is possible
+to include not only external measurement constraints but also both external and
+internal (but localized) measurement constraints in the unsupervised training
+procedure without any significant changes.
+We introduce the method to solve a differential equation via neural networks,
+and leave using various measurements to constrain the network training as future
+works. Thus, we plan training neural networks with our unsupervised learning
+scheme by including other plasma measurements such as the MSE pitch angle
+measurement. Furthermore, we have plans to search the most suitable architec-
+ture of a neural network to improve its performance when internal constraints
+142
+
+CHAPTER 4. Bayesian neural network in fusion research
+are involved.
+Most physical phenomena can be, in general, expressed in differential equa-
+tions. Thus, our work might be helpful for other engineering and science fields to
+support solving their differential equations, starting from scratch. Furthermore,
+previous researches using GAN [96] to simulate complex physical systems such as
+accelerators [98–100] are likely to be improved based on our approach by giving
+physical knowledge to them.
+143
+
+Chapter 5
+Conclusions
+“Farewell... My brave Hobbits. My work is now
+finished. Here at last, on the shores of the
+sea...comes the end of our Fellowship. I will not
+say “Do not weep”...for not all tears are an evil.”
+— Gandalf the White,
+The Lord of the Rings
+So far, we – me and the readers of this thesis – have had a journey with the neu-
+ral networks which proved the fact that they are really able to solve a governing
+equation, i.e., the Grad-Shafranov equation in our case which is a second-order
+non-linear and elliptic partial differential equation for a two-dimensional plasma,
+by themselves.
+Here again, I would like to emphasize that the way that the
+networks solve the Grad-Shafranov equation is indeed general and applicable to
+many other governing equations in various scientific problems. Only tedious part
+that one needs to do is switching the Grad-Shafranov equation with other differ-
+ential equations, then modifying the network architectures slightly to be suitable
+for their own problems. As we have shown together previously, I have defined
+the differential equations as the cost functions of the networks. Namely, given
+measurement data and their corresponding governing equations, the networks
+are trained automatically based on gradient descents of the cost functions and
+capture physical behaviors of interest without taking a glance at any man-made
+solutions of the problems. Furthermore, one can reflect the principle of Occam’s
+razor to the networks by appropriately modifying forms of the cost functions.
+This thesis has showed that the neural networks are able to produce plasma
+equilibria whose quality is equivalent to EFIT results, which are regarded as well-
+144
+
+CHAPTER 5. Conclusions
+converged solutions of the GS equation, in real time. In addition, the consistent
+flux signals can be fitted by the neural networks, which can be available for the
+plasma reconstruction whose quality is as reasonable as the plasma equilibria
+attained by selecting some of the measurements arbitrarily based on human (ex-
+pert) decisions. Bayesian neural networks applied in fusion research have showed
+that we can quantify the uncertainty of the network models which solve a free-
+boundary and inverse problem to generate plasma equilibria. Of course, this
+thesis still needs to show applicability to long pulse discharges of tokamaks, and
+thorough consistency with the MSE diagnostic system, which is future works.
+Applying the methods used in this thesis to a method such as GAN that may
+complement existing physics simulations is also planned to be conducted for
+tokamak plasmas.
+However, we should think about this, i.e., what is better about solving dif-
+ferential equations with neural networks than with conventional methods such as
+finite difference method? There are numerous conventional methods that exist
+already to solve differential equations, and these methods also proved that they
+can be quantitatively evaluated and provide reasonable outcomes of interest. In
+other words, good (sometimes fantastic) solutions of differential equations can be
+already obtained by the existing algorithms. At this moment, what I can men-
+tion about neural networks is that a lot of trends have appeared and disappeared
+in the field of neural networks over the past decades, and the method of solving
+differential equations via networks may also be one of them. Of course, I want
+to note that networks are powerful to calculate derivatives really conveniently
+through the back-propagation.
+Nevertheless, let me suppose that neural networks are trained only with pre-
+pared solutions of governing equations of interests through supervised learning.
+The results of the trained networks, of course, will be really similar to the so-
+lutions used. However, can we affirm that the network results truly satisfy the
+governing equations used to prepare the solutions? I would say, no. I have con-
+firmed through my findings that this may not be true. As dealt with previously,
+I trained the network with the solutions of the Grad-Shafranov equation calcu-
+145
+
+CHAPTER 5. Conclusions
+lated from EFIT, but the network results did not follow the equation. Thus, I
+would argue that if networks are needed to be used for rigorous physics, they
+should obviously produce physically rigorous results. I would like to emphasize
+that attempts to learn differential equations through networks can be a stepping
+stone for neural networks to be able to be used strictly in the field of physics.
+Finally, I would also like to add that we need to find a way for networks to
+collaborate with the existing methods rather than persisting in the use of neural
+networks only as a perspective of taking advantage of each other.
+As one may have noticed, I did not answer the question, “Why is it better
+to use neural networks than the conventional methods?” A persuasive answer
+to this question will be very subjective (at this moment I guess), and I would
+like to leave it as a future work. So, let us simply enjoy our journey now
+- and beyond. It is unknown what will happen next, but at least it is really
+fascinating.
+146
+
+Chapter A
+Bayesian Deep Learning: Model
+uncertainty
+Bayesian neural networks (BNNs) was first suggested in the 1990s [228,229] where
+a brief history can be found elsewhere [95]. These networks set prior distributions
+for their weights, offering a probabilistic interpretation of their models. While
+their formulations are relatively easy, the probabilistic inference is quite tricky.
+Thus, we would like to approximate p
+�
+ω|X, Y
+�
+by means of VI. This approxi-
+mate BNN inference comes out with stochastic regularization techniques (SRTs)
+like dropout used in VI. This approach is largely taken from Ref. [95].
+To approximate the BNN inference, we would like to approximate p
+�
+ω|X, Y
+�
+in light of VI, i.e.,
+LV I(θ) ≡ −
+N
+�
+i=1
+�
+qθ(ω) log p
+�
+yi|f ω(Xi)
+�
+dω + KL
+�
+qθ(ω)
+����p(ω)
+�
+(A.1)
+where f ω is the function parameterized by ω, and the subscript i is the row or
+column of a matrix denoted in boldface. This stands for an average (or integra-
+tion) over the entire dataset, which costs heavy computations for large N, thus
+we apply the mini-batch approach to approximate it as:
+ˆLV I(θ) ≡ − N
+M
+�
+i∈S
+�
+qθ(ω) log p
+�
+yi|f ω(Xi)
+�
+dω + KL
+�
+qθ(ω)
+����p(ω)
+�
+(A.2)
+where S is the random index set of size M, and Monte Carlo (MC) integration has
+been applied to this. The data sub-sampling also gives us an optimum [230,231].
+After reparameterizing qθ(ω) and ω as p(ϵ) and g(θ, ϵ), i.e., using the path-
+wise derivative estimator (the reparametrization trick, infinitesimal perturbation
+analysis, and stochastic backpropagation [232–234]) which assumes that qθ(ω)
+147
+
+CHAPTER A. Bayesian Deep Learning: Model uncertainty
+can be re-parameterized as a parameter-free distribution p(ϵ) with a determinis-
+tic differentiable bivariate transformation g, we rewrite the sub-sampling VI as:
+ˆLV I(θ) = − N
+M
+�
+i∈S
+�
+p(ϵ) log p
+�
+yi|f g(θ,ϵ)(Xi)
+�
+dϵ + KL
+�
+qθ(ω)
+����p(ω)
+�
+.
+(A.3)
+This expression turns out to be the form below:
+ˆLMC(θ) = − N
+M
+�
+i∈S
+log p
+�
+yi|f g(θ,ϵ)(Xi)
+�
++ KL
+�
+qθ(ω)
+����p(ω)
+�
+.
+(A.4)
+where the log likelihood is replaced with its stochastic estimator. This is a new
+MC estimator.
+Now, we can optimize ˆLMC(θ) with respect to θ following a sequence for
+inference:
+�
+∆θ ← − N
+M
+�
+i∈S
+∂
+∂θ log p
+�
+yi|f g(θ,ˆϵi)(Xi)
+�
++ ∂
+∂θKL
+�
+qθ(ω)
+����p(ω)
+�
+θ ← θ + η �
+∆θ
+(A.5)
+where η is the learning rate, ˆϵi p(ϵ) is M random variables, and θ is initialized
+randomly.
+From now on, we relate the approximate inference above to SRTs used in
+deep learning. Dropout [211,235] is the most popular SRT which is easily appli-
+cable to any neural networks and used to avoid over-fitting issues. Thus, let us
+focus mainly on dropout.
+Suppose that there is a neural network having a single hidden layer, dropout
+applied. When we start to estimate the network’s outputs through dropout, two
+binary vectors �ϵ1 and �ϵ2 whose dimension corresponds to the input and the hidden
+layer, respectively, are sampled to be assigned with value 0 with probability
+0 ≤ p1(or 2) ≤ 1. Then, we multiply given input x with �ϵ1 like �x = x ⊙ �ϵ1
+making some inputs to zero (turn off activation of some input nodes). ⊙ is the
+element-wise product. Similarly, some hidden nodes h are turned off through
+�h = h⊙�ϵ2 where h = f(�xM 1 +b) and f is an activation function, and therefore
+the network’s output with given dropout �y = �hM 2. Here, M 1 and M 2 are the
+148
+
+CHAPTER A. Bayesian Deep Learning: Model uncertainty
+deterministic matrix for the network weights for the input and the hidden layer,
+respectively.
+A stark difference between BNNs and dropout is that BNNs quantify their
+uncertainty over their model parameters while dropout injects its noise into the
+feature space, i.e., x and h. Thus, let us treat the dropout noise as the parameter
+space noise from the feature space noise as shown below:
+�y = �hM 2
+= (h ⊙ �ϵ2)M 2
+= (h · diag(�ϵ2))M 2
+= h(diag(�ϵ2)M 2)
+= f
+�
+�xM 1 + b
+�
+(diag(�ϵ2)M 2)
+= f
+�
+(x ⊙ �ϵ1)M 1 + b
+�
+(diag(�ϵ2)M 2)
+= f
+�
+x
+�
+diag(�ϵ1)M 1
+�
++ b
+�
+(diag(�ϵ2)M 2)
+(A.6)
+where we define �
+W 1 ≡ diag(�ϵ1)M 1 and �
+W 2 ≡ diag(�ϵ2)M 2. �
+W is a realization
+of W , i.e., a random variable defined over the set of real matrices. This turns
+out to be:
+�y = f
+�
+x�
+W 1 + b
+�
+�
+W 2 ≡ F
+�
+W 1,�
+W 2,b(x)
+(A.7)
+where we define �ω = {�
+W 1, �
+W 2, b}.
+Therefore, we can optimize this dropout network based on:
+Ldropout(M 1, M 2, b) ≡ 1
+M
+�
+i∈S
+E
+�
+W
+i
+1,�
+W
+i
+2,b�
+xi, yi
+�
++λ1||M 1||2+λ2||M 2||2+λ3||b||2
+(A.8)
+where �
+W
+i
+1 and �
+W
+i
+2 are the contributions of �ϵi
+1 and �ϵi
+2 sampled from each data
+point i to the matrix M 1or 2, respectively. The mini-batch approach is applied
+here to sub-sample a random index set S whose size is M.
+We can rewrite EM1,M2,b(x, y) as follows [236]:
+EM1,M2,b(x, y) = 1
+2||y − F M1,M2,b(x)||2
+= −1
+τ log p(y|F M1,M2,b(x)) + const
+(A.9)
+149
+
+CHAPTER A. Bayesian Deep Learning: Model uncertainty
+where this is a form of the negative log-likelihood with an offset (constant), and
+p(y|F M1,M2,b(x)) = N(y; F M1,M2,b(x), τ −1I) with observation noise τ −1.
+For the data point i in the range of 1 ≤ i ≤ N, we can also rewrite �ω as
+follows:
+�ωi = {�
+W
+i
+1, �
+W
+i
+2, b} = {diag(ˆϵi
+1)M 1, diag(ˆϵi
+2)M 2, b}
+≡ g(θ, ˆϵi)
+(A.10)
+if we define θ = {M 1, M 2, b}, and �ϵi
+1 and �ϵi
+2 are approximately p(ϵ1) and
+p(ϵ2) where p(ϵ1(or 2)) is products of Bernoulli distributions with probabilities
+1 − p1(or 2).
+Finally, we can re-define Ldropout(M 1, M 2, b) as follows:
+ˆLdropout(M 1, M 2, b) = −
+1
+Mτ
+�
+i∈S
+log p(y|F g(θ,ˆϵi)(x))
++ λ1||M 1||2 + λ2||M 2||2 + λ3||b||2
+(A.11)
+where ˆϵ is the realization of ϵ. Thus, taking a differentiation of this with respect
+to θ is shown as:
+∂
+∂θ
+ˆLdropout(θ) = −
+1
+Mτ
+�
+i∈S
+∂
+∂θ log p(y|F g(θ,ˆϵi)(x))
++ ∂
+∂θ
+�
+λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�
+(A.12)
+Now, we can optimize ˆLdropout(θ) through the sequence below for inference:
+�
+∆θ ← − 1
+Mτ
+�
+i∈S
+∂
+∂θ log p(y|F g(θ,ˆϵi)(x)) + ∂
+∂θ
+�
+λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�
+θ ← θ + η �
+∆θ
+(A.13)
+where η is the learning rate, ˆϵi p(ϵ) is M random variables, and θ is initialized
+randomly. As can be easily noticed, except a constant scale of 1/Nτ, this is
+greatly identical to the approximate inference of a BNN if we let KL(qθ(ω)||p(ω))
+become:
+∂
+∂θKL
+�
+qθ(ω)
+����p(ω)
+�
+= ∂
+∂θNτ
+�
+λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�
+(A.14)
+150
+
+CHAPTER A. Bayesian Deep Learning: Model uncertainty
+toward the optimization as follows:
+∂
+∂θ
+ˆLdropout(θ) =
+1
+Nτ
+∂
+∂θ
+ˆLMC(θ).
+(A.15)
+This result shows that if we optimize a network’s weights by means of
+dropout, this optimization process is exactly identical to the variational opti-
+mization of a Bayesian neural network. Thus, this dropout neural network is the
+Bayesian neural network, allowing us to express the network uncertainty quanti-
+tatively with given observed data. I would like to stress that we now possess the
+tool to construct a reliable neural network being able to provide its confidence
+to given inputs, which is tested with the typical sine regressions again in chapter
+3.1.2.
+151
+
+Chapter B
+Neural Network Differentiation
+In this chapter, I would like to introduce a method to learn physical theories by a
+neural network itself. Theories are generally represented in the form of differential
+equations, i.e., differentiable physics, thus, if I can show that the network is able
+to learn differential equations, then it would become true that the network can
+be trained with the theories directly. Learning differential equations is eventually
+related to setting cost functions in terms of those equations. Therefore, we will
+confirm how to model a cost function with a differential equation through taking
+derivatives of the neural networks. To this end, suppose that we have a simple
+neural network where this has only a single hidden layer with a single input and
+output node.
+Figure B.1 shows the structure of the basic neural network. With two nodes
+in the hidden layer, there are biases in the input and the hidden layers. This is
+expressed as a basic algebra as follows:
+y = v0 +
+�
+v1f
+�
+w10 + w1x
+�
++ v2f
+�
+w20 + w2x
+��
+(B.1)
+where it is worth to note that there should be b1 and b2 multiplied to w10 and
+w20, respectively, in the equation above. Instead, I simply prescribe unity to the
+biases in order to ignore the explicit expressions. I set an activation function in
+the hidden layer to the linear function for simplicity.
+From the fact that the network can be represented analytically, this then
+gives us the ability to express a derivative of the network outputs with respect
+to the input x, together with an arbitrary activation function, f. Therefore, if
+one take first order derivative of the network, this can be represented as follows:
+∂y
+∂x = v1w1f ′�
+w10 + w1x
+�
++ v2w2f ′�
+w20 + w2x
+�
+(B.2)
+152
+
+CHAPTER B. Neural Network Differentiation
+Figure B.1: A simple neural network having only one input node (except the
+input bias), hidden layer and output node. There are two nodes in the hidden
+layer.
+where f ′(X, ...) refers to the first order partial derivative of the function f with
+respect to X, i.e., ∂f(X, ...)/∂X.
+This shows how the network output changes according to the input. Note
+that there are no restrictions for this input and output to be any quantities. This
+means that those can be any physical parameters of interest being able to be ex-
+pressed in the analytic expression through the network derivative. Namely, if
+optimal weights of the network can be found to explain related physical phenom-
+ena appropriately, then we are now capable of calculating all possible changes of
+the phenomena in, e.g., time and space. This is quite powerful since we treat the
+network as solutions of physics. However, an important issue left is how we can
+obtain the proper weights for the physics. Here, this can be simply resolved if a
+cost function of the network contains the differential equations themselves with
+a given training dataset.
+For instance, suppose that we are interested in a simple differential equation
+below:
+dˆt
+dx − 14π cos (14πx) = 0
+(B.3)
+where 14π cos (14πx) is the observed quantity. If we replace ˆt with y, the network
+output, in the equation and use the equation itself as a cost function with given
+14π cos (14πx), then we can eventually acquire the network whose output satisfies
+the equation above such that the output y = sin (14πx), i.e., the solution ˆt.
+153
+
+W1
+V1
+W10
+x
+W2
+V2
+b1
+W20
+o
+b2CHAPTER B. Neural Network Differentiation
+Likewise, we can generalize the cost function as follows:
+ϵ =
+�∂yi
+∂xi
+− ti
+�2
+(B.4)
+where subscript i refers to an arbitrary feature to be used for training the network,
+and t is a single training data point.
+Therefore, the training of the network is possible through the gradient de-
+scent method with the cost function above.
+From this, the gradients of the
+weights in the hidden layer are expressed as follows:
+∂ϵ
+∂v1
+=
+∂
+∂v1
+�∂yi
+∂xi
+− ti
+�2
+= 2√ϵ
+∂
+∂v1
+�
+v1w1f ′�
+w10 + w1xi
+�
++ v2w2f ′�
+w20 + w2xi
+�
+− ti
+�
+= 2√ϵ w1f ′�
+w10 + w1xi
+�
+(B.5)
+∂ϵ
+∂v2
+= 2√ϵ w2f ′�
+w20 + w2xi
+�
+(B.6)
+where v1 and v2 are the weights between the hidden and the output layer. Note
+that the cost function (Equation B.2) does not have v0 dependency, meaning
+that prescribed v0 cannot be trained. Thus, one can see an error message while
+training a neural network with a bias in the last hidden layer, together with the
+cost function defined before.
+Similarly, we can analytically represent the gradients of the weights between
+the input and the hidden layer as follows:
+∂ϵ
+∂w1
+= 2√ϵ v1
+�
+f ′�
+w10 + w1xi
+�
++ w1xif ′′�
+w10 + w1xi
+��
+∂ϵ
+∂w2
+= 2√ϵ v2
+�
+f ′�
+w20 + w2xi
+�
++ w2xif ′′�
+w20 + w2xi
+��
+∂ϵ
+∂w10
+= 2√ϵ v1w1f ′′�
+w10 + w1xi
+�
+∂ϵ
+∂w20
+= 2√ϵ v2w2f ′′�
+w20 + w2xi
+�
+(B.7)
+where it is worth to mention that f ′′(X) stands for the second order partial
+derivative of the function f with respect to X. In contrast to v0, the cost function
+ϵ is a function of wi0 which is updated during the process.
+154
+
+CHAPTER B. Neural Network Differentiation
+So far, we have identified how the first order derivative of the network with
+respect to the input can be trained. To check a tendency of high order derivatives
+with respect to the input, I introduce the second order derivatives regarding the
+input and show corresponding training procedure as an example. The following
+equation is the second order derivative:
+∂2y
+∂x2 = ∂
+∂x
+�
+v1w1f ′�
+w10 + w1x
+�
++ v2w2f ′�
+w20 + w2x
+��
+= v1w2
+1f ′′�
+w10 + w1x
+�
++ v2w2
+2f ′′�
+w20 + w2x
+�
+(B.8)
+where the only difference with the first order derivative is that we now have the
+square terms of w. From the cost function for the second order derivative, i.e.,
+ϵ2 =
+�∂2yi
+∂x2
+i
+− ti
+�2
+,
+(B.9)
+the gradients of the neural network weights can be expressed as follows:
+∂ϵ2
+∂v1
+= 2√ϵ2 w2
+1f ′′�
+w10 + w1xi
+�
+∂ϵ2
+∂v2
+= 2√ϵ2 w2
+2f ′�
+w20 + w2xi
+�
+∂ϵ2
+∂w1
+= 2√ϵ2 v1
+�
+2W1f ′′�
+w10 + w1xi
+�
++ w3
+1xif ′′′�
+w10 + w1xi
+��
+∂ϵ2
+∂w2
+= 2√ϵ2 v2
+�
+2W2f ′′�
+w20 + w2xi
+�
++ w3
+2xif ′′′�
+w20 + w2xi
+��
+∂ϵ2
+∂w10
+= 2√ϵ2 v1w2
+1f ′′�
+w10 + w1xi
+�
+∂ϵ2
+∂w20
+= 2√ϵ2 v2w2
+2f ′′�
+w20 + w2xi
+�
+(B.10)
+where v0 is also not updated at all during the training, and we can train the
+network output according to the second (or high) order changes in space (or
+time) of certain physical phenomena that we are concerned with. I collect the
+simple formulas for the neural network output, the first order, and the second
+order derivatives as shown below:
+y = v0 +
+�
+v1f
+�
+w10 + w1x
+�
++ v2f
+�
+w20 + w2x
+��
+∂y
+∂x = v1w1f ′�
+w10 + w1x
+�
++ v2w2f ′�
+w20 + w2x
+�
+∂2y
+∂x2 = v1w2
+1f ′′�
+w10 + w1x
+�
++ v2w2
+2f ′′�
+w20 + w2x
+�
+.
+(B.11)
+155
+
+CHAPTER B. Neural Network Differentiation
+Figure B.2: A simple neural network having two input nodes, two hidden
+layers and one output node. There are two nodes in each hidden layer.
+Could one argue that what if the activation function f is an exponential
+function?
+If the function f(X) is exp (X) where X is a certain variable, all
+the derivatives of the function f will be identical, leading us to estimate high
+order derivatives of the network easily. Then, one can raise a question like “is
+exp (X) able to play a role of non-linearity of the neural network as the sigmoid
+function, tanh and ReLU?” The answer is yes, however, I would like to leave
+this fact that exp (exp (exp (exp (1)))) ≈ e3814279. This means that the output
+given by exp (X) will be literally exponentially skyrocketing, making the training
+procedure unstable.
+Then what if we simplify w to be unity. The major difference in Equation
+B.11 is the power of w. Furthermore, it is reasonable that although w is fixed,
+non-linearity of the network can be achievable from the hidden layer as well as
+a non-linear activation function. I would like to leave this argument as a future
+work, however it is clear that if we can find proper weights, then derivatives may
+easily be estimated.
+Here, I would like to introduce an excursion into the topic that a network has
+more than one hidden layer with more input nodes. Let me take a look at what
+kind of complexity occurs when I add another hidden layer to the network used
+before. For simplicity, the hidden layers contain two hidden nodes each with
+one bias, and there are two input nodes. The functional form of the network
+156
+
+W11
+V11
+R
+h2)
+W12
+V12
+u
+W21
+V21
+W22
+V22
+U2
+Z
+h12
+h22
+b.
+b5CHAPTER B. Neural Network Differentiation
+displayed in Figure B.2 is presented as follows:
+h11 = f
+�
+w11R + w21Z + b1
+�
+h12 = f
+�
+w12R + w22Z + b2
+�
+h21 = f
+�
+v11h11 + v21h12 + b3
+�
+h22 = f
+�
+v12h11 + v22h12 + b4
+�
+(B.12)
+where b is the bias. Based on the expressions above, the output of the network
+can be expressed as follows:
+y = u1h21 + u2h22 + b5.
+(B.13)
+I would like to present here ∂y/∂R only for instance, which is
+∂y
+∂R = u1
+∂h21
+∂R + u2
+∂h22
+∂R
+= u1
+�
+v11w11 f ′�
+w11R + w21Z + b1
+�
++ v21w12 f ′�
+w12R + w22Z + b2
+��
+f ′�
+v11h11 + v21h12 + b3
+�
++ u2
+�
+v12w11 f ′�
+(w11R + w21Z + b1
+�
++ v22w12 f ′�
+w12R + w22Z + b2
+��
+f ′�
+v12h11 + v22h12 + b4
+�
+≡ u1
+�
+v11w11 ˜h11 + v21w12 ˜h12
+�
+˜h21 + u2
+�
+v12w11 ˜h11 + v22w12 ˜h12
+�
+˜h22
+(B.14)
+The derivatives of the network look like becoming more complex than those of
+the previous network which has one hidden layer. However, if we define ∆21 ≡
+v11 ˜h11 + v21 ˜h12 and ∆22 ≡ v12 ˜h11 + v22 ˜h12 with w ≡ w11 = w12 assumption and
+assume h = ˜h by using exp (X) as the activation function, then the first order
+derivative turns out to be:
+∂y
+∂R ≈ u1 w∆21h21 + u2 w∆22h22
+(B.15)
+where this is somewhat identical to Equation B.11 if we make such strict con-
+straints, e.g., ∆ should be unity, meaning that stacking more layers is futile.
+157
+
+CHAPTER B. Neural Network Differentiation
+We have seen so far the fact that how we train a neural network holds a
+differential equation itself. Recall that a differential equation is a fundamen-
+tal representative of a physical phenomenon, which is often called differentiable
+physics as well, and inculcating that kind of equation in the network through the
+procedures above means that we possibly think that the network have knowledge
+of corresponding physics that we are interested in. This might lead us to step
+forward to believe the network can be used for the scientific fields. In section
+3.1.3, I show practical results of this scheme with the usual sine function problem.
+158
+
+Bibliography
+[1] GS Lee, M Kwon, CJ Doh, BG Hong, K Kim, MH Cho, W Namkung,
+Choong-Seock Chang, YC Kim, JY Kim, et al. Design and construction of
+the KSTAR tokamak. Nuclear Fusion, 41(10):1515, 2001.
+[2] S G Lee, J G Bak, E M Ka, J H Kim, and S H Hahn. Magnetic diag-
+nostics for the first plasma operation in Korea Superconducting Tokamak
+Advanced Research. Review of Scientific Instruments, 79(10):10F117–4,
+2008.
+[3] Semin Joung, Jaewook Kim, Sehyun Kwak, Kyeo-reh Park, S H Hahn,
+H S Han, H S Kim, J G Bak, S G Lee, and Y c Ghim. Imputation of
+faulty magnetic sensors with coupled Bayesian and Gaussian processes to
+reconstruct the magnetic equilibrium in real time.
+Review of Scientific
+Instruments, 89(10):10K106, 2018.
+[4] Jonathan B Lister, HARRY Schnurrenberger, and Ph Marmillod. Imple-
+mentation of a multi-layer perceptron for a non-linear control problem.
+Technical report, LRP 398/90, CRPP-Lausanne, 1990.
+[5] J B Lister and H Schnurrenberger. Fast non-linear extraction of plasma
+equilibrium parameters using a neural network mapping. Nuclear Fusion,
+31(7):1291–1300, 1991.
+[6] L. LAGIN, R. BELL, S DAVIS, T. ECK, S. JARDIN, C. KESSEL,
+J. MCENERNEY, M. OKABAYASHI, J. POPYACK, and N. SAUTHOFF.
+APPLICATION OF NEURAL NETWORKS FOR REAL-TIME CALCU-
+LATIONS OF PLASMA EQUILIBRIUM PARAMETERS FOR PBX-M.
+In C. FERRO, M. GASPAROTTO, and H. KNOEPFEL, editors, Fusion
+Technology 1992, pages 1057–1061. North-Holland, Oxford, 1993.
+159
+
+BIBLIOGRAPHY
+[7] E Coccorese, C Morabito, and R Martone.
+Identification of noncircu-
+lar plasma equilibria using a neural network approach. Nuclear Fusion,
+34(10):1349–1363, 1994.
+[8] B Ph van Milligen, V Tribaldos, and J A Jim´enez. Neural Network Differ-
+ential Equation and Plasma Equilibrium Solver. Physical Review Letters,
+75(20):3594–3597, 1995.
+[9] Chris M. Bishop, Paul S. Haynes, Mike E. U. Smith, Tom N. Todd, and
+David L. Trotman. Real-Time Control of a Tokamak Plasma Using Neural
+Networks. Neural Computation, 7(1):206–217, 01 1995.
+[10] Colin George Windsor, Thomas Noel Todd, David Leonard Trotman, and
+Michael Edward Underhill Smith. Real-time electronic neural networks for
+iter-like multiparameter equilibrium reconstruction and control in compass-
+d. Fusion technology, 32(3):416–430, 1997.
+[11] Patrick J Mc Carthy and Francesco C Morabito. Realtime Identification
+of Plasma Shape and Position on ITER Using an Equilibrium Database.
+In Diagnostics for Experimental Thermonuclear Fusion Reactors 2, pages
+541–544. Springer, 1998.
+[12] Chris M. Bishop. Neural networks and their applications. Review of Sci-
+entific Instruments, 65(6):1803–1832, 1994.
+[13] Bo Wang, Bingjia Xiao, Jiangang Li, Yong Guo, and Zhengping Luo. Ar-
+tificial Neural Networks for Data Analysis of Magnetic Measurements on
+East. Journal of Fusion Energy, 35(2):390–400, Apr 2016.
+[14] F Carpanese, F Felici, C Galperti, A Merle, JM Moret, O Sauter, et al.
+First demonstration of real-time kinetic equilibrium reconstruction on TCV
+by coupling LIUQE and RAPTOR. Nuclear Fusion, 60(6):066020, 2020.
+[15] Jonas Degrave, Federico Felici, Jonas Buchli, Michael Neunert, Brendan
+Tracey, Francesco Carpanese, Timo Ewalds, Roland Hafner, Abbas Abdol-
+160
+
+BIBLIOGRAPHY
+maleki, Diego de Las Casas, et al. Magnetic control of tokamak plasmas
+through deep reinforcement learning. Nature, 602(7897):414–419, 2022.
+[16] JT Wai, MD Boyer, and E Kolemen. Neural net modeling of equilibria in
+NSTX-U. arXiv preprint arXiv:2202.13915, 2022.
+[17] Markus Svens´en. Neural network prediction of disruptions in a tokamak
+plasma. Master’s thesis, Aston University, 1994.
+[18] CG Windsor, G Pautasso, C Tichmann, RJ Buttery, TC Hender,
+JET EFDA Contributors, et al. A cross-tokamak neural network disrup-
+tion predictor for the JET and ASDEX Upgrade tokamaks. Nuclear fusion,
+45(5):337, 2005.
+[19] Kates-Harbeck, Julian, Svyatovskiy, Alexey, and Tang, William. Predict-
+ing disruptive instabilities in controlled fusion plasmas through deep learn-
+ing. Nature, 568(7753):526–531, 2019.
+[20] JV Hernandez, A Vannucci, T Tajima, Z Lin, W Horton, and SC McCool.
+Neural network prediction of some classes of tokamak disruptions. Nuclear
+fusion, 36(8):1009, 1996.
+[21] D Wroblewski, GL Jahns, and JA Leuer.
+Tokamak disruption alarm
+based on a neural network model of the high-beta limit. Nuclear Fusion,
+37(6):725, 1997.
+[22] G Tresset, CD Challis, X Garbet, X Litaudon, M Mantsinen, D Mazon, and
+D Moreau. Transport identification by neural network in jet itb regimes.
+In Proc. 29th EPS Conference on Controlled Fusion and Plasma Physics
+P, volume 2, page 039, 2002.
+[23] Arimitsu Wakasa, Sadayoshi MURAKAMI, Hiroshi YAMADA, Masayuki
+YOKOYAMA,
+Hening
+MAASSBERG,
+Craig
+BEIDLER,
+Kiyomasa
+WATANABE, and Shun-ichi OIKAWA.
+Development of a neoclassical
+transport database by neural network fitting in lhd.
+J. Plasma Fusion
+Res. SERIES, 6:203, 2004.
+161
+
+BIBLIOGRAPHY
+[24] Arimitsu Wakasa, Sadayoshi Murakami, and Shun-ichi Oikawa. Study of
+neoclassical transport in lhd plasmas by applying the dcom/nnw neoclas-
+sical transport database.
+Plasma and Fusion Research, 3:S1030–S1030,
+2008.
+[25] Meneghini, O, Luna, C J, Smith, S P, and Lao, L L. Modeling of transport
+phenomena in tokamak plasmas with neural networks. Physics of Plasmas,
+21(6):060702–5, June 2014.
+[26] Citrin, J, Breton, S, Felici, F, Imbeaux, F, Aniel, T, Artaud, J F, Baioc-
+chi, B, Bourdelle, C, Camenen, Y, and Garcia, J. Real-time capable first
+principle based modelling of tokamak turbulent transport. Nuclear Fusion,
+55(9):092001–7, July 2015.
+[27] O Meneghini, S P Smith, P B Snyder, G M Staebler, J Candy, E Belli,
+L Lao, M Kostuk, T Luce, T Luda, J M Park, and F Poli. Self-consistent
+core-pedestal transport simulations with neural network accelerated mod-
+els. Nuclear Fusion, 57(8):086034, 2017.
+[28] Karel Lucas van de Plassche, Jonathan Citrin, Clarisse Bourdelle, Yann
+Camenen, Francis J Casson, Victor I Dagnelie, Federico Felici, Aaron Ho,
+Simon Van Mulders, and JET Contributors. Fast modeling of turbulent
+transport in fusion plasmas using neural networks. Physics of Plasmas,
+27(2):022310, 2020.
+[29] Carl Friedrich Gauss. Theoria motus corporum coelestium in sectionibus
+conicis solem ambientium, volume 7. FA Perthes, 1877.
+[30] Christopher M Bishop and Nasser M Nasrabadi. Pattern recognition and
+machine learning, volume 4. Springer, 2006.
+[31] David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. Learning
+internal representations by error propagation. Technical report, California
+Univ San Diego La Jolla Inst for Cognitive Science, 1985.
+162
+
+BIBLIOGRAPHY
+[32] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet clas-
+sification with deep convolutional neural networks.
+Advances in neural
+information processing systems, 25, 2012.
+[33] Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed,
+Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Ra-
+binovich.
+Going deeper with convolutions.
+In Proceedings of the IEEE
+conference on computer vision and pattern recognition, pages 1–9, 2015.
+[34] Nal Kalchbrenner and Phil Blunsom.
+Recurrent continuous translation
+models.
+In Proceedings of the 2013 conference on empirical methods in
+natural language processing, pages 1700–1709, 2013.
+[35] Martin Sundermeyer, Ralf Schl¨uter, and Hermann Ney. Lstm neural net-
+works for language modeling. In Thirteenth annual conference of the inter-
+national speech communication association, 2012.
+[36] Tomas Mikolov, Martin Karafi´at, Lukas Burget, Jan Cernock`y, and San-
+jeev Khudanpur.
+Recurrent neural network based language model.
+In
+Interspeech, volume 2, pages 1045–1048. Makuhari, 2010.
+[37] Bart Verberck and Andrea Taroni.
+Nuclear fusion.
+Nature Physics,
+12(5):383–383, 2016.
+[38] Francis F Chen. An Indispensable Truth. How Fusion Power Can Save the
+Planet. Springer, apr 2011.
+[39] G Federici, L Boccaccini, F Cismondi, M Gasparotto, Y Poitevin, and
+I Ricapito. An overview of the EU breeding blanket design strategy as an
+integral part of the DEMO design effort. Fusion Engineering and Design,
+141:30–42, 2019.
+[40] Yeong-Kook Oh, WC Kim, KR Park, MK Park, HL Yang, YS Kim, Y Chu,
+YO Kim, JG Bak, EN Baang, et al. Commissioning and initial operation of
+KSTAR superconducting tokamak. Fusion Engineering and Design, 84(2-
+6):344–350, 2009.
+163
+
+BIBLIOGRAPHY
+[41] H Han, SJ Park, C Sung, J Kang, YH Lee, J Chung, TS Hahm, B Kim, J-K
+Park, JG Bak, et al. A sustained high-temperature fusion plasma regime
+facilitated by fast ions. Nature, 609(7926):269–275, 2022.
+[42] Jeffrey P. Freidberg. Ideal Magnetohydrodynamics. Plenum Press, New
+York, 1987.
+[43] Harold Grad and Hanan Rubin. Hydromagnetic equilibria and force-free
+fields. Journal of Nuclear Energy (1954), 7(3-4):284–285, 1958.
+[44] VD Shafranov. Plasma equilibrium in a magnetic field. Reviews of plasma
+physics, 2:103, 1966.
+[45] HK Kim, HL Yang, GH Kim, Jin-Yong Kim, Hogun Jhang, JS Bak, and
+GS Lee.
+Design features of the KSTAR in-vessel control coils.
+Fusion
+Engineering and Design, 84(2-6):1029–1032, 2009.
+[46] K Kim, HK Park, KR Park, BS Lim, SI Lee, Y Chu, WH Chung, YK Oh,
+SH Baek, SJ Lee, et al. Status of the KSTAR superconducting magnet
+system development. Nuclear Fusion, 45(8):783, 2005.
+[47] Laxmikant Urankar. Vector potential and magnetic field of current-carrying
+finite arc segment in analytical form, Part III: Exact computation for rect-
+angular cross section. IEEE Transactions on Magnetics, 18(6):1860–1867,
+1982.
+[48] E J Strait, E D Fredrickson, and Takechi M Moret, J M.
+Chapter 2:
+Magnetic diagnostics. Fusion Science and Technology, 53:304, 2008.
+[49] S G Lee and J G Bak. Magnetic diagnostics for Korea superconducting
+tokamak advanced research. Review of Scientific Instruments, 72(1):439–4,
+2001.
+[50] JG Bak and SG Lee. Performance test of sample coils in the Korea super-
+conducting tokamak advanced research magnetic diagnostics test chamber.
+Review of Scientific Instruments, 72(1):435–438, 2001.
+164
+
+BIBLIOGRAPHY
+[51] JG Bak, SG Lee, KSTAR Project Team, and DeRac Son. Performance of
+the magnetic sensor and the integrator for the KSTAR magnetic diagnos-
+tics. Review of scientific instruments, 75(10):4305–4307, 2004.
+[52] SG Lee and JG Bak. Fabrication details, calibrations, and installation ac-
+tivities of magnetic diagnostics for Korea Superconducting Tokamak Ad-
+vanced Research. Review of scientific instruments, 77(10):10E306, 2006.
+[53] Bak, J G, Lee, S G, Son, D, and Ga, E M. Analog integrator for the Korea
+superconducting tokamak advanced research magnetic diagnostics. Review
+of Scientific Instruments, 78(4):043504–6, 2007.
+[54] JG Bak, SG Lee, and EM Ka. Diamagnetic loop for the first plasma in the
+KSTAR machine. Review of Scientific Instruments, 79(10):10F118, 2008.
+[55] JG Bak, SG Lee, and HS Kim. Diamagnetic loop measurement in korea
+superconducting tokamak advanced research machine. Review of Scientific
+Instruments, 82(6):063504, 2011.
+[56] JH Lee, HK Na, SG Lee, JG Bak, DC Seo, SH Seo, ST Oh, WH Ko,
+J Chung, YU Nam, et al. Diagnostics for first plasma and development
+plan on KSTAR. Review of Scientific Instruments, 81(6):063502, 2010.
+[57] Heung-Su Kim, Jun-Gyo Bak, and Sang-hee Hahn. Improvements of mag-
+netic measurements for plasma control in KSTAR tokamak. Fusion Engi-
+neering and Design, 123:641–645, 2017.
+[58] S Ali-Arshad and L De Kock. Long-pulse analog integration. Review of
+scientific instruments, 64(9):2679–2682, 1993.
+[59] EJ Strait, JD Broesch, RT Snider, and ML Walker. A hybrid digital–analog
+long pulse integrator. Review of scientific instruments, 68(1):381–384, 1997.
+[60] Andreas Werner. W7-X magnetic diagnostics: Performance of the digital
+integrator. Review of scientific instruments, 77(10):10E307, 2006.
+165
+
+BIBLIOGRAPHY
+[61] Seong-Heon Seo, Andreas Werner, and M Marquardt. Development of a
+digital integrator for the KSTAR device. Review of Scientific Instruments,
+81(12):123507, 2010.
+[62] Y Wang, ZS Ji, GJ Xu, F Wang, S Li, XY Sun, and ZC Zhang. A digital
+long pulse integrator for EAST Tokamak. Fusion Engineering and Design,
+89(5):618–622, 2014.
+[63] Seong-Heon Seo. Plasma current position measurements in the Korea Su-
+perconducting Tokamak Advanced Research device. Physics of Plasmas,
+16(3):032501, 2009.
+[64] Moreau, Ph, Saint-Laurent, F, and Lister, J B. Drift-free magnetic equi-
+librium reconstruction using the response to plasma position modulation.
+Fusion Engineering and Design, 84(7-11):1339–1343, June 2009.
+[65] J. H. Lee, S. T. Oh, and H. M. Wi. Development of KSTAR Thomson
+scattering system. Review of Scientific Instruments, 81(10):10D528, 2010.
+[66] Won-Ha Ko, Hyungho Lee, Dongcheol Seo, and Myeun Kwon.
+Charge
+exchange spectroscopy system calibration for ion temperature measurement
+in KSTAR. Review of Scientific Instruments, 81(10):10D740, 2010.
+[67] YS Bae, YM Park, JS Kim, WS Han, SW Kwak, YB Chang, HT Park,
+NH Song, HL Yang, SW Yoon, et al. Commissioning of the first KSTAR
+neutral beam injection system and beam experiments. Fusion Engineering
+and Design, 87(9):1597–1610, 2012.
+[68] S Sarwar, HK Na, and JM Park.
+Effective ion charge (Zeff) measure-
+ments and impurity behavior in KSTAR. Review of Scientific Instruments,
+89(4):043504, 2018.
+[69] Junghee Kim, Jun Young Kim, SW Yoon, M Garc´ıa-Mu˜noz, M Isobe, and
+WC Kim.
+Initial measurements of fast ion loss in KSTAR.
+Review of
+Scientific Instruments, 83(10):10D305, 2012.
+166
+
+BIBLIOGRAPHY
+[70] JW Yoo, Junghee Kim, MW Lee, J Kang, W-H Ko, SG Oh, J Ko, JH Lee,
+YU Nam, L Jung, et al. Fast-ion Dα spectroscopy diagnostic at KSTAR.
+Review of Scientific Instruments, 92(4):043504, 2021.
+[71] FM Levinton, RJ Fonck, GM Gammel, R Kaita, HW Kugel, ET Pow-
+ell, and DW Roberts.
+Magnetic field pitch-angle measurments in the
+PBX-M tokamak using the motional Stark effect. Physical review letters,
+63(19):2060, 1989.
+[72] J Ko, J Chung, AGG Lange, and MFM De Bock. Polarimetric spectra anal-
+ysis for tokamak pitch angle measurements. Journal of Instrumentation,
+8(10):C10022, 2013.
+[73] L L Lao, H St John, R D Stambaugh, A G Kellman, and W Pfeiffer. Re-
+construction of current profile parameters and plasma shapes in tokamaks.
+Nuclear Fusion, 25(11):1611–1622, 1985.
+[74] L L Lao, H E St John, Q Peng, and J R Ferron.
+MHD Equilibrium
+Reconstruction in the DIII-D Tokamak. Fusion Science and Technology,
+48(2):968–977, 2005.
+[75] J R Ferron, M L Walker, L L Lao, H E St John, D A Humphreys, and J A
+Leuer. Real time equilibrium reconstruction for tokamak discharge control.
+Nuclear Fusion, 38(7):1055–1066, May 1998.
+[76] Yue, X N, Xiao, B J, Luo, Z P, and Guo, Y. Fast equilibrium reconstruc-
+tion for tokamak discharge control based on GPU. Plasma Physics and
+Controlled Fusion, 55(8):085016–10, June 2013.
+[77] JW Berkery, SA Sabbagh, L Kogan, D Ryan, JM Bialek, Y Jiang,
+DJ Battaglia, S Gibson, and C Ham. Kinetic equilibrium reconstructions
+of plasmas in the MAST database and preparation for reconstruction of the
+first plasmas in MAST upgrade. Plasma Physics and Controlled Fusion,
+63(5):055014, 2021.
+167
+
+BIBLIOGRAPHY
+[78] Semin Joung, Jaewook Kim, Sehyun Kwak, JG Bak, SG Lee, HS Han,
+HS Kim, Geunho Lee, Daeho Kwon, and Y-C Ghim. Deep neural net-
+work Grad–Shafranov solver constrained with measured magnetic signals.
+Nuclear Fusion, 60(1):016034, 2019.
+[79] Y S Park, S A Sabbagh, J W Berkery, J M Bialek, Y M Jeon, S H Hahn,
+N Eidietis, T E Evans, S W Yoon, J W Ahn, J Kim, H L Yang, K I You,
+Y S Bae, J Chung, M Kwon, Y K Oh, W C Kim, J Y Kim, S G Lee, H K
+Park, H Reimerdes, J Leuer, and M Walker. KSTAR equilibrium operating
+space and projected stabilization at high normalized beta. Nuclear Fusion,
+51(5):053001, 2011.
+[80] Warren S McCulloch and Walter Pitts.
+A logical calculus of the ideas
+immanent in nervous activity.
+The bulletin of mathematical biophysics,
+5(4):115–133, 1943.
+[81] Donald Olding Hebb. The organization of behavior: a neuropsychological
+theory. Science editions, 1949.
+[82] Frank Rosenblatt. The perceptron: a probabilistic model for information
+storage and organization in the brain. Psychological review, 65(6):386, 1958.
+[83] Marvin Minsky and Oliver G Selfridge.
+Learning in random nets, vol-
+ume 46. MIT Lincoln Laboratory, 1960.
+[84] Marvin Minsky and Seymour Papert. Perceptrons an introduction to com-
+putational geometry. MIT Press, 1969.
+[85] Marvin Minsky and Seymour Papert. Perceptrons: expanded edition. MIT
+press, 1988.
+[86] D S Sivia and J Skilling. Data Analysis: A Bayesian Tutorial. Oxford:
+Oxford University Press, 2006.
+168
+
+BIBLIOGRAPHY
+[87] Sehyun Kwak, J Svensson, M Brix, Y-c Ghim, and JET Contributors.
+Bayesian electron density inference from JET lithium beam emission spec-
+tra using Gaussian processes. Nuclear Fusion, 57(3):036017, 2017.
+[88] Sehyun Kwak, Jakob Svensson, S Bozhenkov, Joanne Flanagan, Mark
+Kempenaars, Alexandru Boboc, Y-C Ghim, and JET Contributors.
+Bayesian modelling of Thomson scattering and multichannel interferom-
+eter diagnostics using Gaussian processes. Nuclear Fusion, 60(4):046009,
+2020.
+[89] Sehyun Kwak, U Hergenhahn, U H¨ofel, M Krychowiak, A Pavone, J Svens-
+son, O Ford, R K¨onig, S Bozhenkov, G Fuchert, et al. Bayesian inference of
+spatially resolved Z eff profiles from line integrated Bremsstrahlung spectra.
+Review of Scientific Instruments, 92(4):043505, 2021.
+[90] MA Chilenski, M Greenwald, Y Marzouk, NT Howard, AE White, JE Rice,
+and JR Walk. Improved profile fitting and quantification of uncertainty in
+experimental measurements of impurity transport coefficients using Gaus-
+sian process regression. Nuclear Fusion, 55(2):023012, 2015.
+[91] MA Chilenski, MJ Greenwald, AE Hubbard, JW Hughes, JP Lee, YM Mar-
+zouk, JE Rice, and AE White. Experimentally testing the dependence of
+momentum transport on second derivatives using Gaussian process regres-
+sion. Nuclear Fusion, 57(12):126013, 2017.
+[92] Aaron Ho, Jonathan Citrin, Fulvio Auriemma, Clarisse Bourdelle, Francis J
+Casson, Hyun-Tae Kim, Pierre Manas, Gabor Szepesi, Henri Weisen, and
+JET Contributors. Application of Gaussian process regression to plasma
+turbulent transport model validation via integrated modelling.
+Nuclear
+fusion, 59(5):056007, 2019.
+[93] O Linder, J Citrin, GMD Hogeweij, C Angioni, Clarisse Bourdelle, Fran-
+cis J Casson, E Fable, A Ho, Florian Koechl, M Sertoli, et al. Flux-driven
+integrated modelling of main ion pressure and trace tungsten transport in
+ASDEX Upgrade. Nuclear Fusion, 59(1):016003, 2018.
+169
+
+BIBLIOGRAPHY
+[94] Jarrod Leddy, Sandeep Madireddy, Eric Howell, and Scott Kruger. Single
+Gaussian Process Method for Arbitrary Tokamak Regimes with a Statisti-
+cal Analysis. arXiv preprint arXiv:2202.11557, 2022.
+[95] Yarin Gal et al. Uncertainty in deep learning. PhD thesis, 2016.
+[96] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David
+Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Gener-
+ative adversarial nets. Advances in neural information processing systems,
+27, 2014.
+[97] Antonia Creswell, Tom White, Vincent Dumoulin, Kai Arulkumaran,
+Biswa Sengupta, and Anil A Bharath. Generative adversarial networks:
+An overview. IEEE Signal Processing Magazine, 35(1):53–65, 2018.
+[98] Luke de Oliveira, Michela Paganini, and Benjamin Nachman. Learning par-
+ticle physics by example: location-aware generative adversarial networks
+for physics synthesis. Computing and Software for Big Science, 1(1):1–24,
+2017.
+[99] Michela Paganini, Luke de Oliveira, and Benjamin Nachman. Calogan:
+Simulating 3d high energy particle showers in multilayer electromagnetic
+calorimeters with generative adversarial networks.
+Physical Review D,
+97(1):014021, 2018.
+[100] Michela Paganini, Luke de Oliveira, and Benjamin Nachman. Accelerating
+science with generative adversarial networks: an application to 3d particle
+showers in multilayer calorimeters. Physical review letters, 120(4):042003,
+2018.
+[101] Sungwon Kim, Juhwan Noh, Geun Ho Gu, Alan Aspuru-Guzik, and
+Yousung Jung. Generative adversarial networks for crystal structure pre-
+diction. ACS central science, 6(8):1412–1420, 2020.
+170
+
+BIBLIOGRAPHY
+[102] Baekjun Kim, Sangwon Lee, and Jihan Kim.
+Inverse design of porous
+materials using artificial neural networks. Science advances, 6(1):eaax9324,
+2020.
+[103] Mart´ın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng
+Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu
+Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving,
+Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath
+Kudlur, Josh Levenberg, Dandelion Man´e, Rajat Monga, Sherry Moore,
+Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner,
+Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Va-
+sudevan, Fernanda Vi´egas, Oriol Vinyals, Pete Warden, Martin Watten-
+berg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-
+scale machine learning on heterogeneous systems, 2015. Software available
+from tensorflow.org.
+[104] S. Sakakibara, H. Yamada, and LHD Experiment Group. Magnetic mea-
+surements in lhd. Fusion Science and Technology, 58(1):471–481, 2010.
+[105] Edlington, T, Martin, R, and Pinfold, T. MAST magnetic diagnostics.
+Review of Scientific Instruments, 72(1):421–6, 2001.
+[106] Strait, E J. Magnetic diagnostic system of the DIII-D tokamak. Review of
+Scientific Instruments, 77(2):023502–15, 2006.
+[107] J M Moret, F Buhlmann, D Fasel, F Hofmann, and G Tonetti. Magnetic
+measurements on the TCV Tokamak. Review of Scientific Instruments,
+69(6):2333–17, 1998.
+[108] Liu, G J, Wan, B N, Sun, Y W, Xiao, B J, Wang, Y, Luo, Zh P, Qian,
+J P, and Liu, D M. Analysis of uncertainty in equilibrium reconstruction
+in the EAST superconducting tokamak. Review of Scientific Instruments,
+84(7):073502–7, 2013.
+171
+
+BIBLIOGRAPHY
+[109] Simone Peruzzo, Raffaele Albanese, Giovanni Artaserse, Vincenzo Coc-
+corese, Sergei Gerasimov, Norman Lam, Francesco Maviglia, Ian Pearson,
+Phil Prior, Antonio Quercia, and Luca Zabeo. Installation and commis-
+sioning of the JET-EP magnetic diagnostic system. Fusion Engineering
+and Design, 84(7-11):1495–1498, 2009.
+[110] R Chavan, G Chitarin, R S Delogu, A Encheva, A Gallo, E R Hodgson,
+L C Ingesson, A Le-Luyer, J B Lister, Ph Moreau, J M Moret, S Peruzzo,
+J Romero, D S Testa, M Toussaint, G Vayakis, and R Vila. The magnetics
+diagnostic set for ITER. Fusion Engineering and Design, 84(2-6):295–299,
+June 2009.
+[111] D V Orlinskij and G Magyar.
+Plasma diagnostics on large Tokamaks.
+Nuclear Fusion, 28(JET-P-88-33):611–697, 1988.
+[112] D Shiraki, N Commaux, L R Baylor, N W Eidietis, E M Hollmann, V A
+Izzo, R A Moyer, and C Paz-Soldan. Characterization of MHD activity
+and its influence on radiation asymmetries during massive gas injection in
+DIII-D. Nuclear Fusion, 55(7):073029, 2015.
+[113] J A Snipes, D J Campbell, P S Haynes, et al. Large amplitude quasi-
+stationary MHD modes in JET. Nuclear Fusion, 28(6):1085–1097, 1988.
+[114] S N Gerasimov, T C Hender, J Morris, V Riccardo, L E Zakharov, and
+JET EFDA Contributors. Plasma current asymmetries during disruptions
+in JET. Nuclear Fusion, 54(7):073009, 2014.
+[115] R J Buttery, O Sauter, R Akers, M Gryaznevich, R Martin, C D Warrick,
+H R Wilson, and the MAST Team. Neoclassical Tearing Physics in the
+Spherical Tokamak MAST. Physical Review Letters, 88(12), 2002.
+[116] Y S Park, S A Sabbagh, J M Bialek, et al. Investigation of MHD insta-
+bilities and control in KSTAR preparing for high beta operation. Nuclear
+Fusion, 53(8):083029, 2013.
+172
+
+BIBLIOGRAPHY
+[117] Svensson, J, Werner, A, and JET EFDA Contributors. Current tomog-
+raphy for axisymmetric plasmas. Plasma Physics and Controlled Fusion,
+50(8):085002–26, May 2008.
+[118] S A Lazerson and the DIII-D Team. Three-dimensional equilibrium recon-
+struction on the DIII-D device. Nuclear Fusion, 55(2):023009, 2015.
+[119] Romero, J A and Svensson, J. Optimization of out-vessel magnetic diag-
+nostics for plasma boundary reconstruction in tokamaks. Nuclear Fusion,
+53(3):033009–26, February 2013.
+[120] J P Qian, L L Lao, C T Holcomb, B N Wan, Y W Sun, D Moreau, E Li,
+L Zeng, K Hanada, A M Garofalo, X Z Gong, B Shen, and B J Xiao. An
+efficient technique for magnetic equilibrium reconstruction with q profile
+constraints and its application on the EAST tokamak. Nuclear Fusion,
+57(8):084001, 2017.
+[121] Xia, Yu-Jun, Zhang, Zhong-Dian, Xia, Zhen-Xin, Zhu, Shi-Liang, and
+Zhang, Rui.
+A precision analogue integrator system for heavy current
+measurement in MFDC resistance spot welding. Measurement Science and
+Technology, 27(2):025104–12, December 2015.
+[122] T Shikama, T Nishitani, T Kakuta, S Yamamoto, S Kasai, M Narui,
+E Hodgson, R Reichle, B Brichard, A Krassilinikov, R Snider, G Vayakis,
+A Costley, S Nagata, B Tsuchiya, and K Toh. Irradiation test of diagnostic
+components for ITER application in the Japan Materials Testing Reactor.
+Nuclear Fusion, 43(7):517–521, 2003.
+[123] Marco Ariola and Alfredo Pironti. Magnetic Control of Tokamak Plasmas.
+Springer, 2008.
+[124] Chris M Bishop, Paul S Haynes, Mike E U Smith, Tom N Todd, and
+David L Trotman.
+Fast feedback control of a high temperature fusion
+plasma. Neural Computing & Applications, 2(3):148–159, 1994.
+173
+
+BIBLIOGRAPHY
+[125] S Ali Arshad and L de Kock. Long-pulse analog integration. Review of
+Scientific Instruments, 64(9):2679–2682, 1993.
+[126] E J Strait, J D Broesch, R T Snider, and M L Walker.
+A hybrid
+digital–analog long pulse integrator.
+Review of Scientific Instruments,
+68(1):381–5, 1997.
+[127] Werner, Andreas. W7-X magnetic diagnostics: Performance of the digital
+integrator. Review of Scientific Instruments, 77(10):10E307–6, 2006.
+[128] Y Wang, Z S Ji, G J Xu, F Wang, S Li, X Y Sun, and Z C Zhang. A
+digital long pulse integrator for EAST Tokamak. Fusion Engineering and
+Design, 89(5):618–622, 2014.
+[129] M Kwon et al. Overview of KSTAR initial operation. Nuclear Fusion,
+51(9), September 2011.
+[130] Ka, E M, Lee, S G, Bak, J G, and Son, D. Performance test of the in-
+tegrator system for magnetic diagnostics in KSTAR. Review of Scientific
+Instruments, 79(10):10F119–4, 2008.
+[131] C E Rasmussen and C K I Williams.
+Gaussian Processes for Machine
+Learning. The MIT Press, 2006.
+[132] J W C van Lint, S P Hoogendoorn, and H J van Zuylen. Accurate freeway
+travel time prediction with state-space neural networks under missing data.
+Transportation Research Part C: Emerging Technologies, 13(5-6):347–369,
+October 2005.
+[133] Andre C Neto, Diogo Alves, Bernardo B Carvalho, Gianmaria De Tommasi,
+Robert Felton, Horacio Fernandes, Peter J Lomas, Francesco Maviglia,
+Fernanda G Rimini, Filippo Sartori, Adam V Stephen, Daniel F Valcarcel,
+and Luca Zabeo. A Real-Time Architecture for the Identification of Faulty
+Magnetic Sensors in the JET Tokamak. IEEE Transactions on Nuclear
+Science, 61(3):1228–1235, 2014.
+174
+
+BIBLIOGRAPHY
+[134] R´emy Nouailletas, Philippe Moreau, and Sylvain Bremond.
+A generic
+method for real time detection of magnetic sensor failure on tokamaks.
+Fusion Engineering and Design, 87(3):289–297, March 2012.
+[135] Jeffrey Freidberg. Ideal MHD. Cambridge University Press, 2014.
+[136] S Tsaun and Hogun Jhang. Real-time plasma boundary reconstruction in
+the KSTAR tokamak using finite element method. Fusion Engineering and
+Design, 82(2):163–174, February 2007.
+[137] R von Mises. Mathematical Theory of Probability and Statistics. Academic
+Press, 1964.
+[138] Sehyun Kwak, J Svensson, M Brix, and Y.-c Ghim.
+Bayesian electron
+density inference from JET lithium beam emission spectra using Gaussian
+processes. Nuclear Fusion, 57(3), March 2017.
+[139] Leslie Foster et al.
+Stable and Efficient Gaussian Process Calculations.
+Journal of Machine Learning Research, 10:857, April 2009.
+[140] Sehyun Kwak, J Svensson, M Brix, Y c Ghim, and JET Contributors.
+Bayesian modelling of the emission spectrum of the Joint European Torus
+Lithium Beam Emission Spectroscopy system. Review of Scientific Instru-
+ments, 87(2):023501, 2016.
+[141] Dong Li, J Svensson, H Thomsen, F Medina, A Werner, and R Wolf.
+Bayesian soft X-ray tomography using non-stationary Gaussian Processes.
+Rev. Sci. Instrum., 84:083506, 2013.
+[142] Semin Joung, Jaewook Kim, HS Kim, JG Bak, and Y-C Ghim. A deep
+learning approach to recover hidden consistency of kstar flux loop signals.
+arXiv, 2022.
+[143] Steven G Worswick,
+James A Spencer,
+Gunnar Jeschke,
+and Ilya
+Kuprov. Deep neural network processing of deer data. Science advances,
+4(8):eaat5218, 2018.
+175
+
+BIBLIOGRAPHY
+[144] Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, and Michael P Brenner.
+Learning data-driven discretizations for partial differential equations. Pro-
+ceedings of the National Academy of Sciences, 116(31):15344–15349, 2019.
+[145] Maziar Raissi, Alireza Yazdani, and George Em Karniadakis. Hidden fluid
+mechanics: Learning velocity and pressure fields from flow visualizations.
+Science, 367(6481):1026–1030, 2020.
+[146] David
+Pfau,
+James
+S
+Spencer,
+Alexander
+GDG
+Matthews,
+and
+W Matthew C Foulkes.
+Ab initio solution of the many-electron
+schr¨odinger equation with deep neural networks. Physical Review Research,
+2(3):033429, 2020.
+[147] Kyle Mills, Michael Spanner, and Isaac Tamblyn. Deep learning and the
+schr¨odinger equation. Physical Review A, 96(4):042113, 2017.
+[148] Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer,
+Roger Melko, and Giuseppe Carleo. Neural-network quantum state tomog-
+raphy. Nature Physics, 14(5):447–450, 2018.
+[149] Li Li, Stephan Hoyer, Ryan Pederson, Ruoxi Sun, Ekin D Cubuk, Patrick
+Riley, Kieron Burke, et al. Kohn-sham equations as regularizer: Build-
+ing prior knowledge into machine-learned physics. Physical review letters,
+126(3):036401, 2021.
+[150] Semin Joung and Y-C Ghim. Mastering plasma equilibria with deep neural
+networks and grad-shafranov equation. Science Advances, 2022, submitted.
+[151] Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training
+deep feedforward neural networks.
+In Yee Whye Teh and Mike Titter-
+ington, editors, Proceedings of the Thirteenth International Conference on
+Artificial Intelligence and Statistics, volume 9 of Proceedings of Machine
+Learning Research, pages 249–256, Chia Laguna Resort, Sardinia, Italy,
+13–15 May 2010. PMLR.
+176
+
+BIBLIOGRAPHY
+[152] Prajit Ramachandran, Barret Zoph, and Quoc V Le. Searching for activa-
+tion functions. arXiv preprint arXiv:1710.05941, 2017.
+[153] Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approxima-
+tion: Representing model uncertainty in deep learning. In international
+conference on machine learning, pages 1050–1059. PMLR, 2016.
+[154] Calyampudi Radhakrishna Rao, Calyampudi Radhakrishna Rao, Math-
+ematischer Statistiker, Calyampudi Radhakrishna Rao, and Calyam-
+pudi Radhakrishna Rao. Linear statistical inference and its applications,
+volume 2. Wiley New York, 1973.
+[155] S A Sabbagh, S M Kaye, J Menard, F Paoletti, M Bell, R E Bell, J M
+Bialek, M Bitter, E D Fredrickson, D A Gates, A H Glasser, H Kugel,
+L L Lao, B P LeBlanc, R Maingi, R J Maqueda, E Mazzucato, D Mueller,
+M Ono, S F Paul, M Peng, C H Skinner, D Stutman, G A Wurden, W Zhu,
+and NSTX Research Team. Equilibrium properties of spherical torus plas-
+mas in NSTX. Nuclear Fusion, 41(11):1601–1611, 2001.
+[156] Qian Jinping, Wan Baonian, L L Lao, Shen Biao, S A Sabbagh, Sun
+Youwen, Liu Dongmei, Xiao Bingjia, Ren Qilong, Gong Xianzu, and
+Li Jiangang. Equilibrium Reconstruction in EAST Tokamak. Plasma Sci-
+ence and Technology, 11(2):142–145, 2009.
+[157] D P O’Brien, L L Lao, E R Solano, M Garribba, T S Taylor, J G Cordey,
+and J J Ellis. Equilibrium analysis of iron core tokamaks using a full domain
+method. Nuclear Fusion, 32(8):1351–1360, 1992.
+[158] Semin Joung and Y.-c. Ghim. Bayesian based real-time numerical method
+to correct signal drifts in magnetic measurements from tokamaks. 2019.
+unpublished.
+[159] D Van Houtte and Equipe TORE SUPRA. One minute pulse operation in
+the Tore Supra Tokamak. Nuclear Fusion, 33(1):137–141, 1993.
+177
+
+BIBLIOGRAPHY
+[160] A. Ekedahl, L. Delpech, M. Goniche, D. Guilhem, J. Hillairet, M. Prey-
+nas, P.K. Sharma, J. Achard, Y.S. Bae, X. Bai, C. Balorin, Y. Baranov,
+V. Basiuk, A. B´ecoulet, J. Belo, G. Berger-By, S. Br´emond, C. Castaldo,
+S. Ceccuzzi, R. Cesario, E. Corbel, X. Courtois, J. Decker, E. Delmas,
+X. Ding, D. Douai, C. Goletto, J.P. Gunn, P. Hertout, G.T. Hoang, F. Im-
+beaux, K.K. Kirov, X. Litaudon, R. Magne, J. Mailloux, D. Mazon, F. Mi-
+rizzi, P. Mollard, P. Moreau, T. Oosako, V. Petrzilka, Y. Peysson, S. Poli,
+M. Prou, F. Saint-Laurent, F. Samaille, and B. Saoutic. Validation of the
+ITER-relevant passive-active-multijunction LHCD launcher on long pulses
+in tore supra. Nuclear Fusion, 50(11):112002, sep 2010.
+[161] S Itoh, K N Sato, K Nakamura, H Zushi, M Sakamoto, K Hanada, E Jotaki,
+K Makino, S Kawasaki, H Nakashima, and A Iyomasa. Recent progress in
+the superconducting tokamak TRIAM-1m. Plasma Physics and Controlled
+Fusion, 41(3A):A587–A594, jan 1999.
+[162] H Zushi,
+S Itoh,
+K Hanada,
+K Nakamura,
+M Sakamoto,
+E Jo-
+taki, M Hasegawa, Y.D Pan, S.V Kulkarni, A Iyomasa, S Kawasaki,
+H Nakashima, N Yoshida, K Tokunaga, T Fujiwara, M Miyamoto,
+H Nakano, M Yuno, A Murakami, S Nakamura, N Sakamoto, K Shinoda,
+S Yamazoe, H Akanishi, K Kuramoto, Y Matsuo, A Iwamae, T Fuijimoto,
+A Komori, T Morisaki, H Suzuki, S Masuzaki, Y Hirooka, Y Nakashima,
+and O Mitarai. Overview of steady state tokamak plasma experiments in
+TRIAM-1m. Nuclear Fusion, 43(12):1600–1609, dec 2003.
+[163] B Saoutic. Status of long pulse experiments in magnetic fusion devices.
+Plasma Physics and Controlled Fusion, 44(12B):B11–B22, nov 2002.
+[164] H.K. Park, M.J. Choi, S.H. Hong, Y. In, Y.M. Jeon, J.S. Ko, W.H. Ko,
+J.G. Kwak, J.M. Kwon, J. Lee, J.H. Lee, W. Lee, Y.B. Nam, Y.K. Oh, B.H.
+Park, J.K. Park, Y.S. Park, S.J. Wang, M. Yoo, S.W. Yoon, J.G. Bak, C.S.
+Chang, W.H. Choe, Y. Chu, J. Chung, N. Eidietis, H.S. Han, S.H. Hahn,
+H.G. Jhang, J.W. Juhn, J.H. Kim, K. Kim, A. Loarte, H.H. Lee, K.C. Lee,
+178
+
+BIBLIOGRAPHY
+D. Mueller, Y.S. Na, Y.U. Nam, G.Y. Park, K.R. Park, R.A. Pitts, S.A.
+Sabbagh, and G.S. Yun and. Overview of KSTAR research progress and
+future plans toward ITER and k-DEMO. Nuclear Fusion, 59(11):112020,
+jul 2019.
+[165] B.N. Wan, Y. Liang, X.Z. Gong, N. Xiang, G.S. Xu, Y. Sun, L. Wang,
+J.P. Qian, H.Q. Liu, L. Zeng, L. Zhang, X.J. Zhang, B.J. Ding, Q. Zang,
+B. Lyu, A.M. Garofalo, A. Ekedahl, M.H. Li, F. Ding, S.Y. Ding, H.F. Du,
+D.F. Kong, Y. Yu, Y. Yang, Z.P. Luo, J. Huang, T. Zhang, Y. Zhang, G.Q.
+Li, T.Y. Xia, and and. Recent advances in EAST physics experiments in
+support of steady-state operation for ITER and CFETR. Nuclear Fusion,
+59(11):112003, jun 2019.
+[166] Jong-Kyu Park, YoungMu Jeon, Yongkyoon In, Joon-Wook Ahn, Raffi
+Nazikian, Gunyoung Park, Jaehyun Kim, HyungHo Lee, WonHa Ko, Hyun-
+Seok Kim, Nikolas C. Logan, Zhirui Wang, Eliot A. Feibush, Jonathan E.
+Menard, and Michael C. Zarnstroff. 3d field phase-space control in tokamak
+plasmas. Nature Physics, 14:1223, 2018.
+[167] F. Reimold, M. Wischmeier, M. Bernert, S. Potzel, A. Kallenbach, H.W.
+M˜AŒller, B. Sieglin, and U. Stroth and.
+Divertor studies in nitrogen
+induced completely detached h-modes in full tungsten ASDEX upgrade.
+Nuclear Fusion, 55(3):033004, feb 2015.
+[168] A.E. Jaervinen, C. Giroud, M. Groth, P. Belo, S. Brezinsek, M. Beurskens,
+G. Corrigan, S. Devaux, P. Drewelow, D. Harting, A. Huber, S. Jach-
+mich, K. Lawson, B. Lipschultz, G. Maddison, C. Maggi, C. Marchetto,
+S. Marsen, G.F. Matthews, A.G. Meigs, D. Moulton, B. Sieglin, M.F.
+Stamp, and S. Wiesen and.
+Comparison of h-mode plasmas in JET-
+ILW and JET-c with and without nitrogen seeding.
+Nuclear Fusion,
+56(4):046012, mar 2016.
+179
+
+BIBLIOGRAPHY
+[169] Yao Huang, BJ Xiao, ZP Luo, QP Yuan, XF Pei, and XN Yue. Implemen-
+tation of gpu parallel equilibrium reconstruction for plasma control in east.
+Fusion Engineering and Design, 112:1019–1024, 2016.
+[170] O. Barana, A. Murari, P. Franz, L. C. Ingesson, and G. Manduchi. Neural
+networks for real time determination of radiated power in jet. Review of
+Scientific Instruments, 73(5):2038–2043, 2002.
+[171] Murari, A, Arena, P, Buscarino, A, Fortuna, L, Iachello, M, and contribu-
+tors, JET-EFDA. On the identification of instabilities with neural networks
+on JET. Nuclear Inst. and Methods in Physics Research, A, 720(C):2–6,
+August 2013.
+[172] M.D. Boyer, S. Kaye, and K. Erickson.
+Real-time capable modeling of
+neutral beam injection on NSTX-u using neural networks. Nuclear Fusion,
+59(5):056008, mar 2019.
+[173] Andrea Murari, Didier Mazon, N Martin, Guido Vagliasindi, and Michela
+Gelfusa. Exploratory Data Analysis Techniques to Determine the Dimen-
+sionality of Complex Nonlinear Phenomena: The L-to-H Transition at JET
+as a Case Study. IEEE Transactions on Plasma Science, 40(5):1386–1394,
+April 2012.
+[174] A. Murari, J. Vega, D. Mazon, D. Patan, G. Vagliasindi, P. Arena, N. Mar-
+tin, N.F. Martin, G. Ratt, and V. Caloone.
+Machine learning for the
+identification of scaling laws and dynamical systems directly from data in
+fusion. Nuclear Instruments and Methods in Physics Research Section A,
+623(2):850 – 854, 2010.
+[175] P Gaudio, A Murari, M Gelfusa, I Lupelli, and J Vega. An alternative
+approach to the determination of scaling law expressions for the l–h transi-
+tion in tokamaks utilizing classification tools instead of regression. Plasma
+Physics and Controlled Fusion, 56(11):114002, oct 2014.
+180
+
+BIBLIOGRAPHY
+[176] B. Cannas, A. Fanni, G. Pautasso, G. Sias, and P. Sonato.
+An adap-
+tive real-time disruption predictor for ASDEX upgrade. Nuclear Fusion,
+50(7):075004, jun 2010.
+[177] A. Pau, A. Fanni, S. Carcangiu, B. Cannas, G. Sias, A. Murari, and F. Ri-
+mini and. A machine learning approach based on generative topographic
+mapping for disruption prevention and avoidance at JET. Nuclear Fusion,
+59(10):106017, aug 2019.
+[178] F Felici, J Citrin, A A Teplukhina, J Redondo, C Bourdelle, F Imbeaux,
+O Sauter, JET Contributors, and the EUROfusion MST1 Team. Real-time-
+capable prediction of temperature and density profiles in a tokamak using
+RAPTOR and a first-principle-based transport model.
+Nuclear Fusion,
+58(9):096006, 2018.
+[179] Matos, Francisco A, Ferreira, Diogo R, and Carvalho, Pedro J. Deep learn-
+ing for plasma tomography using the bolometer system at JET. Fusion
+Engineering and Design, 114:18–25, January 2017.
+[180] Diogo R. Ferreira, Pedro J. Carvalho, Horcio Fernandes, and JET Contrib-
+utors. Full-pulse tomographic reconstruction with deep neural networks.
+Fusion Science and Technology, 74(1-2):47–56, 2018.
+[181] Daniel B¨ockenhoff, Marko Blatzheim, Hauke H¨olbe, Holger Niemann, Fabio
+Pisano, Roger Labahn, Thomas Sunn Pedersen, and The W7-X Team.
+Reconstruction of magnetic configurations in W7-X using artificial neural
+networks. Nuclear Fusion, 58(5):056009, 2018.
+[182] B. Cannas, S. Carcangiu, A. Fanni, T. Farley, F. Militello, A. Montisci,
+F. Pisano, G. Sias, and N. Walkden. Towards an automatic filament detec-
+tor with a faster r-cnn on mast-u. Fusion Engineering and Design, 146:374
+– 377, 2019.
+[183] Clayton, D J, Tritz, K, Stutman, D, Bell, R E, Diallo, A, LeBlanc, B P,
+and Podest`a, M. Electron temperature profile reconstructions from multi-
+181
+
+BIBLIOGRAPHY
+energy SXR measurements using neural networks.
+Plasma Physics and
+Controlled Fusion, 55(9):095015–9, August 2013.
+[184] Cacciola, Matteo, Greco, Antonino, Morabito, Francesco Carlo, and Ver-
+saci, Mario. An Exhaustive Employment of Neural Networks to Search
+the Better Configuration of Magnetic Signals in ITER Machine. In Neural
+Information Processing, pages 353–360. Springer Berlin Heidelberg, Berlin,
+Heidelberg, 2006.
+[185] Young-Mu Jeon, Yong-Su Na, Myung-Rak Kim, and Y S Hwang. Newly
+developed double neural network concept for reliable fast plasma position
+control. Review of Scientific Instruments, 72(1):513–5, 2001.
+[186] Paulo Rodrigues and Jo˜ao P. S. Bizarro. Grad-shafranov equilibria with
+negative core toroidal current in tokamak plasmas.
+Phys. Rev. Lett.,
+95:015001, Jun 2005.
+[187] Paulo Rodrigues and Jo˜ao P. S. Bizarro. Tokamak equilibria with toroidal-
+current reversal in the plasma core consistent with experimental data. Phys.
+Rev. Lett., 99:125001, Sep 2007.
+[188] G.O. Ludwig, Paulo Rodrigues, and Jo˜ao P.S. Bizarro. Tokamak equilibria
+with strong toroidal current density reversal. Nuclear Fusion, 53(5):053001,
+apr 2013.
+[189] Simon Haykin. Neural Networks and Learning Machines. Pearson, 2008.
+[190] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic opti-
+mization. CoRR, abs/1412.6980, 2014.
+[191] Rong Ge, Furong Huang, Chi Jin, and Yang Yuan. Escaping from sad-
+dle points - online stochastic gradient for tensor decomposition. CoRR,
+abs/1503.02101, 2015.
+[192] L´eon Bottou. Large-scale machine learning with stochastic gradient de-
+scent. In Proceedings of COMPSTAT’2010, pages 177–186. Springer, 2010.
+182
+
+BIBLIOGRAPHY
+[193] Q Huynh-Thu and M Ghanbari. Scope of validity of PSNR in image/video
+quality assessment. Electronics Letters, 44(13):800, 2008.
+[194] JPEG vs. JPEG 2000: an objective comparison of image encoding quality,
+2004.
+[195] Z Wang, A C Bovik, H R Sheikh, and E P Simoncelli.
+Image Quality
+Assessment: From Error Visibility to Structural Similarity. IEEE Trans-
+actions on Image Processing, 13(4):600–612, 2004.
+[196] R Aymar, P Barabaschi, and Y Shimomura.
+The iter design.
+Plasma
+physics and controlled fusion, 44(5):519, 2002.
+[197] N. J. PEACOCK, D. C. ROBINSON, M. J. FORREST, P. D. WILCOCK,
+and V. V. SANNIKOV. Measurement of the electron temperature by thom-
+son scattering in tokamak t3. Nature, 224(5218):488–490, 1969.
+[198] William Mitchinson Hicks. Ii. researches in vortex motion.—part iii. on
+spiral or gyrostatic vortex aggregates. Philosophical Transactions of the
+Royal Society of London. Series A, Containing Papers of a Mathematical
+or Physical Character, (192):33–99, 1899.
+[199] Y Huang, ZP Luo, BJ Xiao, LL Lao, A Mele, A Pironti, M Mattei, G Am-
+brosino, QP Yuan, YH Wang, et al. Gpu-optimized fast plasma equilibrium
+reconstruction in fine grids for real-time control and data analysis. Nuclear
+Fusion, 60(7):076023, 2020.
+[200] GT Von Nessi, MJ Hole, MAST team, et al. A unified method for infer-
+ence of tokamak equilibria and validation of force-balance models based
+on bayesian analysis. Journal of Physics A: Mathematical and Theoretical,
+46(18):185501, 2013.
+[201] JA Romero, SA Dettrick, E Granstedt, T Roche, and Y Mok. Inference
+of field reversed configuration topology and dynamics during alfvenic tran-
+sients. Nature communications, 9(1):1–10, 2018.
+183
+
+BIBLIOGRAPHY
+[202] Sehyun Kwak. Bayesian modelling of nuclear fusion experiments. PhD
+thesis, Technische Universit¨at Berlin, Berlin, Germany, 2020.
+[203] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature,
+521(7553):436–444, 2015.
+[204] Jan Hermann, Zeno Sch¨atzle, and Frank No´e. Deep-neural-network solution
+of the electronic schr¨odinger equation. Nature Chemistry, 12(10):891–897,
+2020.
+[205] Tom Beucler, Michael Pritchard, Stephan Rasp, Jordan Ott, Pierre Baldi,
+and Pierre Gentine. Enforcing analytic constraints in neural networks em-
+ulating physical systems. Physical Review Letters, 126(9):098302, 2021.
+[206] Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P
+Brenner, and Stephan Hoyer. Machine learning–accelerated computational
+fluid dynamics. Proceedings of the National Academy of Sciences, 118(21),
+2021.
+[207] DA Kaltsas and GN Throumoulopoulos. Neural network tokamak equilibria
+with incompressible flows. Physics of Plasmas, 29(2):022506, 2022.
+[208] Steven P Hirshman and JC Whitson. Steepest-descent moment method for
+three-dimensional magnetohydrodynamic equilibria. The Physics of fluids,
+26(12):3553–3568, 1983.
+[209] Sifan Wang and Paris Perdikaris. Deep learning of free boundary and stefan
+problems. Journal of Computational Physics, 428:109914, 2021.
+[210] Johan Stefan. ¨Uber die theorie der eisbildung, insbesondere ¨uber die eis-
+bildung im polarmeere. Annalen der Physik, 278(2):269–286, 1891.
+[211] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and
+Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks
+from overfitting. The journal of machine learning research, 15(1):1929–
+1958, 2014.
+184
+
+BIBLIOGRAPHY
+[212] Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward
+Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and
+Adam Lerer. Automatic differentiation in pytorch. NIPS Workshop, 2017.
+[213] Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul,
+and Jeffrey Mark Siskind. Automatic differentiation in machine learning:
+a survey. Journal of Marchine Learning Research, 18:1–43, 2018.
+[214] SG Lee, JG Bak, EM Ka, JH Kim, and SH Hahn. Magnetic diagnostics
+for the first plasma operation in korea superconducting tokamak advanced
+research. Review of Scientific Instruments, 79(10):10F117, 2008.
+[215] YS Park, SA Sabbagh, JW Berkery, JM Bialek, YM Jeon, SH Hahn, N Ei-
+dietis, TE Evans, SW Yoon, J-W Ahn, et al. Kstar equilibrium operating
+space and projected stabilization at high normalized beta. Nuclear Fusion,
+51(5):053001, 2011.
+[216] H Urano, Y Miyata, T Suzuki, and K Kurihara. Breakdown optimiza-
+tion method based on inverse reconstruction of magnetic fluxes in jt-60sa.
+Nuclear Fusion, 60(6):066002, 2020.
+[217] Nelson Morgan and Herv´e Bourlard. Generalization and parameter esti-
+mation in feedforward nets: Some experiments. Advances in neural infor-
+mation processing systems, 2, 1989.
+[218] Alessandro Beghi and Angelo Cenedese.
+Advances in real-time plasma
+boundary reconstruction: From gaps to snakes.
+IEEE Control Systems
+Magazine, 25(5):44–64, 2005.
+[219] ´Emile Clapeyron. M´emoire sur la puissance motrice de la chaleur. Journal
+de l’´Ecole polytechnique, 14:153–190, 1834.
+[220] B Coppi. Compact experiments for o-particle heating. Tokamak Reactors
+for Breakeven: A Critical Study of the Near-Term Fusion Reactor Program,
+page 303, 2013.
+185
+
+BIBLIOGRAPHY
+[221] DR Sweetman, JG Cordey, and TS Green. Heating and plasma interactions
+with beams of energetic neutral atoms. Philosophical Transactions of the
+Royal Society of London. Series A, Mathematical and Physical Sciences,
+300(1456):589–598, 1981.
+[222] RA Cairns. Radiofrequency heating of plasmas. CRC Press, 1991.
+[223] Robert James Goldston. Heuristic drift-based model of the power scrape-
+off width in low-gas-puff h-mode tokamaks. Nuclear Fusion, 52(1):013009,
+2011.
+[224] Hyun-Tae Kim, ACC Sips, M Romanelli, CD Challis, F Rimini, L Garzotti,
+E Lerche, J Buchanan, X Yuan, S Kaye, et al. High fusion performance at
+high ti/te in jet-ilw baseline plasmas with high nbi heating power and low
+gas puffing. Nuclear Fusion, 58(3):036020, 2018.
+[225] Baptiste Jimmy Frei, Rog´erio Jorge, and Paolo Ricci. A gyrokinetic model
+for the plasma periphery of tokamak devices. Journal of Plasma Physics,
+86(2), 2020.
+[226] G K Batchelor. An introduction to fluid dynamics. Cambridge university
+press, 2000.
+[227] YS Park, SA Sabbagh, JM Bialek, JW Berkery, SG Lee, WH Ko, JG Bak,
+YM Jeon, JK Park, J Kim, et al.
+Investigation of mhd instabilities
+and control in kstar preparing for high beta operation. Nuclear Fusion,
+53(8):083029, 2013.
+[228] David JC MacKay. A practical bayesian framework for backpropagation
+networks. Neural computation, 4(3):448–472, 1992.
+[229] RM Neal. Bayesian learning for neural networks [phd thesis]. Toronto,
+Ontario, Canada: Department of Computer Science, University of Toronto,
+1995.
+186
+
+BIBLIOGRAPHY
+[230] Herbert Robbins and Sutton Monro. A stochastic approximation method.
+The annals of mathematical statistics, pages 400–407, 1951.
+[231] Matthew D Hoffman, David M Blei, Chong Wang, and John Paisley.
+Stochastic variational inference. Journal of Machine Learning Research,
+2013.
+[232] Paul Glasserman.
+Monte Carlo methods in financial engineering, vol-
+ume 53. Springer, 2004.
+[233] Diederik P Kingma and Max Welling. Auto-encoding variational bayes.
+arXiv preprint arXiv:1312.6114, 2013.
+[234] Michalis Titsias and Miguel L´azaro-Gredilla. Doubly stochastic variational
+bayes for non-conjugate inference. In International conference on machine
+learning, pages 1971–1979. PMLR, 2014.
+[235] Geoffrey E Hinton, Nitish Srivastava, Alex Krizhevsky, Ilya Sutskever, and
+Ruslan R Salakhutdinov.
+Improving neural networks by preventing co-
+adaptation of feature detectors. arXiv preprint arXiv:1207.0580, 2012.
+[236] Naftali Tishby, Esther Levin, and Sara A Solla. Consistent inference of
+probabilities in layered networks: Predictions and generalization. In Inter-
+national Joint Conference on Neural Networks, volume 2, pages 403–409.
+IEEE New York, 1989.
+187
+
+Acknowledgments in Korean
+감사했던 분들의 성함은 다 적지 못할까 염려되어 선뜻 남기기 어려웠습니다. 그
+럼에도 이야기하고자 합니다. 지난 2015년 1월을 시작으로 제가 감히 이해할 수
+없는 마음으로 여러 가르침을 주신 김영철 교수님께 감사드립니다. 아직 더 배
+움이 필요함에도 불구하고 미숙한 저의 학위 심사에 참여해주시고 많은 가르침을
+주셨던 최원호 교수님, 윤시우 박사님, 성충기 교수님, 미숙한 석사과정 학생에
+불과했던 저에게 여러 가르침과 격려를 해주셨던 김현석 박사님께 감사드립니다.
+연구의 시작점이며 방향이 되었던 곽세현 박사님께 감사드립니다. 언제나 말도
+안 되는 이야기와 주장을 해도 깊은 이해로 진지하게 받아주셨던 김재욱 박사님께
+도 감사드립니다. 좌충우돌 어디로 튈지 저 조차도 모르던 미숙함을 언제나 높은
+마음으로 이해해주셨던 김건희, 때로는 본이 되는 연구자로서 때로는 깊은 토론
+을 할 수 있는 동료로서 때로는 함께 즐길 수 있는 친구며 동생이 되어준 오태석,
+마찬가지로 깊은 연구 토론과 때로는 삶을 공유할 수 있었던 임예건, 언제나 여
+러 힘이 되어준 권대호, 미숙한 모습에도 내색없이 바라봐주었던 이정진, 정충순,
+해준 것 없는 데도 많은 도움을 주었던 유용성, 이원준, 박사 마지막 시기에 많은
+도움이 되었던 김동욱, 연구에 영어에 많은 도움을 준 Alvin 모두 다 감사드립니
+다. 언제나 저를 어여삐 여겨주신 Scott, Mandy, SeongOk, Kidoo 그리고 힘든
+시기 도움이 되어주신 여러 선생님들, 학교에서 까지 의지할 곳이 되어준 이신의
+모두 감사드립니다. 언제나 툴툴대고 선택 못 하고 하고 싶은 말이 아니라 감정에
+치우친 말이 나와도 이해해주었던 신찰범 고맙습니다. 혹여 급히 작성하느라 미처
+다 언급하지 못한 분들 및 연구실 일원들에게도 깊은 감사드립니다.
+지난 날을 되돌아 보면 기억은 빛을 바래도 추억은 보다 더 또렷해지는 순
+간들이 있습니다.
+이미 한참 지났지만 성남 구 시가지에서 친구들과 뛰어놀던
+기억에 더욱 추억이 깊습니다. 그리고 아쉽습니다. 흐려져 가는 기억들이 아깝습
+니다. 일기라도 적어놓을 것 그랬습니다. 어찌 하다보니 지금 이 순간을 맞이하게
+되었습니다. 어렸을 때의 저는 이런 공부를 하는 제가 되리라고는 전혀 생각도
+못 했었겠지요. 돌아보니 석사 졸업 시기와는 사뭇 다른 감정을 지금은 느끼는 것
+188
+
+BIBLIOGRAPHY
+같습니다. 보다 명확해진 점은 이전에는 제가 제 길을 만들려고 부단히 애를 썼지
+만 지금은 이끄시는 대로 그저 따라 가려 합니다. 이미 많이 미숙했기에 앞으로
+성숙해질 것만이 남아 있다는 점은 참 감사하게 여겨집니다. 그래서 어느 방향의
+길이든 그 끝은 다 감사하지 않을까 생각합니다. 지금 이 순간도 후에 돌아보면
+기억은 바랬지만 추억은 보다 살아남아 있을 것이라 생각합니다. 언제나 제 삶을
+지지해주시는 아버지 어머니 감사드립니다 동생들도 미안하고 사랑합니다. 마지
+막으로 혜린아 고생 정말 많았어요, 덕분에 나무 아래 누워 쉬던 날에서 일어나
+걸을 수 있었습니다. 잡은 손 놓지 않겠습니다. 감사합니다.
+1. 내 그대를 생각함은 항상 그대가 앉아 있는 배경에서 해가 지고 바람이
+부는 일처럼 사소한 일일 것이나 언젠가 그대가 한없이 괴로움 속을 헤매일 때에
+오랫동안 전해오던 그 사소함으로 그대를 불러보리라. // 2. 진실로 진실로 내
+가 그대를 사랑하는 까닭은 내 나의 사랑을 한없이 잇닿은 그 기다림으로 바꾸어
+버린 데 있었다. 밤이 들면서 골짜기엔 눈이 퍼붓기 시작했다. 내 사랑도 어디쯤
+에선 반드시 그칠 것을 믿는다. 다만 그때 내 기다림의 자세를 생각하는 것뿐이다.
+그 동안에 눈이 그치고 꽃이 피어나고 낙엽이 떨어지고 또 눈이 퍼붓고 할 것을
+믿는다. (황동규, ‘즐거운 편지’, 현대문학, 1958)
+189
+
+Curriculum Vitae
+Name
+:
+정 세 민 (SEMIN JOUNG)
+E-mail
+:
+smjoung@kaist.ac.kr, smjoungsemail@gmail.com
+Educations
+2017. 8. – 2022. 8.
+KAIST (Korea Advanced Institute of Science and Technology)
+Department of Nuclear and Quantum Engineering (PhD)
+2015. 2. – 2017. 2.
+KAIST
+Department of Nuclear and Quantum Engineering (MS)
+2011. 3. – 2015. 2.
+KYUNG HEE University
+Department of Nuclear Engineering (Bachelor’s degree)
+Publications
+1.
+S. Joung, Y.-c.
+Ghim, J. Kim, S. Kwak, S. Lee, D. Kwon, H.S.
+Kim and J.G. Bak. ‘GS-DeepNet: Mastering tokamak plasma equilibria
+with deep neural networks and the Grad-Shafranov equation’. In: Science
+Advances, (2022), In preparation.
+2.
+S. Joung, J. Kim, H.S. Han, J.G. Bak and Y.-c. Ghim. ‘A deep learning
+approach to recover hidden consistency of KSTAR flux loop signals’. In:
+Scientific Reports, (2022), In preparation.
+3.
+S. Joung, J. Kim, S. Kwak, J.G. Bak, S.G. Lee, H.S. Han, H.S. Kim,
+G. Lee, D. Kwon and Y.-c. Ghim. ‘Deep neural network Grad–Shafranov
+solver constrained with measured magnetic signals’. In: Nuclear Fusion,
+Vol.60.1 (3rd Dec. 2019), DOI:10.1088/1741-4326/ab555f
+190
+
+BIBLIOGRAPHY
+4.
+S. Joung, J. Kim, S. Kwak, K. Park, S.H. Hahn, H.S. Han, H.S. Kim,
+J.G. Bak, S.G. Lee and Y.-c.
+Ghim. ‘Imputation of faulty magnetic
+sensors with coupled Bayesian and Gaussian processes to reconstruct the
+magnetic equilibrium in real time’. In: Review of Scientific Instruments,
+Vol.89.10 (7th May 2018), DOI:10.1063/ 1.5038938
+Talks
+1.
+S. Joung, J. Kim, S. Kwak, M. Kim, H.S. Kim, J.G. Bak and Y.-c.
+Ghim. ‘Learning plasma equilibria from scratch with deep neural network
+Grad-Shafranov solver’. 63rd Annual Meeting of the APS Division of Plasma
+Physics. Pittsburgh, PA, USA, 8th Nov. 2021.
+2.
+Jiheon Song, S. Joung, Y.-c. Ghim, Jungpyo and S.H. Hahn. ‘Implement
+of machine learning U-net model for automatic ELM-burst detection in the
+KSTAR tokamak’.
+Korean Physical Society Fall Conference.
+Remote e-
+conference, 20th Oct. 2021.
+3.
+S. Joung, J. Kim, S. Kwak, H.S. Han, H.S. Kim, J.G. Bak, S.G.
+Lee and Y.-c. Ghim. ‘Learning tokamak equilibria from scratch with deep
+neural network Grad-Shafranov solver’.
+3rd International Conference on
+Data Driven Plasma Science. Remote e-conference, 29th May 2021.
+4.
+S. Joung, J. Kim, S. Kwak, Y.M. Jeon, S.H. Hahn, H.S. Kim, H.S.
+Han, J.G. Bak, S.G. Lee, G. Lee, D. Kwon and Y.-c. Ghim. ‘Data-
+driven Grad-Shafranov solver with KSTAR EFIT data based on neural net-
+work and Bayesian inference’. 3rd IAEA Technical Meeting on Fusion Data
+Processing, Validation and Analysis. Vienna, Austria, 27th May 2019.
+5.
+Y.-c. Ghim, J. Kim, S. Kwak and S. Joung. ‘Bayesian based data analy-
+sis to infer plasma parameters and to generate synthetic data in tokamaks’.
+Korean Physical Society Fall Conference.
+Changwon, South Korea, 24th
+Oct. 2018.
+6.
+S. Joung, S. Kwak, Y.M. Jeon, S.H. Hahn, H.S. Kim, H.S. Han, J.G.
+Bak, S.G. Lee and Y.-c. Ghim. ‘Neural network magnetic equilibrium
+191
+
+BIBLIOGRAPHY
+reconstruction with Bayesian based preprocessor in KSTAR’. 11th IAEA
+Technical Meeting on Control, Data Acquisition, and Remote Participation
+for Fusion Research. Greifswald, Germany, 8th May 2017.
+Posters
+1.
+S. Joung, J. Kim and Y.-c. Ghim. ‘Bayesian modelling of magnetic pick-
+up coils and flux loops using Gaussian processes for real-time control of
+plasmas’. 23rd Topical Conference on High Temperature Plasma Diagnos-
+tics. Remote e-conference, 13th Dec. 2020.
+2.
+S. Joung, H.S. Kim and Y.-c. Ghim. ‘Real-time compensation of KSTAR
+magnetic signal drifts based on Bayesian inference’.
+KSTAR Conference
+2019. COEX, Seoul, South Korea, 20th Feb. 2019.
+3.
+S. Joung, J. Kim, S. Kwak, K. Park, Y.M. Jeon, S.H. Hahn, H.S.
+Han, H.S. Kim, J.G. Bak, S.G. Lee and Y.-c. Ghim. ‘Bayesian based
+missing input imputation scheme for neural network reconstructing mag-
+netic equilibria in real time’. 22nd Topical Conference on High Temperature
+Plasma Diagnostics. San Diego, CA, USA, 16th Apr. 2018.
+4.
+S. Joung, S. Kwak, Y.M. Jeon, S.H. Hahn, H.S. Kim, H.S. Han, J.G.
+Bak, S.G. Lee and Y.-c. Ghim. ‘Neural network based real-time recon-
+struction of KSTAR magnetic equilibria with Bayesian-based preprocessing’.
+59th Annual Meeting of the APS Division of Plasma Physics. Milwaukee,
+WI, USA, 22nd Oct. 2017.
+5.
+S. Joung, S. Kwak and Y.-c. Ghim. ‘Plasma equilibrium reconstruction
+for real-time control using artificial neural network in KSTAR’. KSTAR
+Conference 2016. Daejeon, South Korea, 24th Feb. 2016.
+192
+
diff --git a/vtE_T4oBgHgl3EQf-xzf/content/tmp_files/2301.08389v1.pdf.txt b/vtE_T4oBgHgl3EQf-xzf/content/tmp_files/2301.08389v1.pdf.txt
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+arXiv:2301.08389v1  [math.AG]  20 Jan 2023
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I:
+HOLOMORPHIC ANOMALY EQUATIONS
+DENIZ GENLIK AND HSIAN-HUA TSENG
+ABSTRACT. We study the structure of higher genus Gromov-Witten theory of the quotient stack
+[Cn/Zn]. We prove holomorphic anomaly equations for [Cn/Zn], generalizing previous results of
+Lho-Pandharipande [17] for the case of [C3/Z3] and ours [7] for the case [C5/Z5] to arbitrary n ≥ 3.
+CONTENTS
+0.
+Introduction
+1
+0.1.
+Acknowledgment
+4
+1.
+Genus zero theory
+4
+1.1.
+Mirror theorem
+4
+1.2.
+Picard-Fuchs equations
+6
+1.3.
+Birkhoff factorization
+8
+1.4.
+Quantum product
+9
+1.5.
+Frobenius structure
+12
+2.
+Rings of functions
+18
+2.1.
+Preparations
+18
+2.2.
+Descriptions of the rings
+20
+3.
+Holomorphic anomaly equations
+25
+3.1.
+More on flatness equation
+25
+3.2.
+Formula for potentials
+27
+3.3.
+Proof of holomorphic anomaly equations
+34
+Appendix A.
+Stirling numbers
+36
+Appendix B.
+A note on I-functions
+37
+B.1.
+Series associated to I-functions
+37
+B.2.
+Asymptotic solutions of Picard-Fuchs equations
+39
+References
+46
+0. INTRODUCTION
+For an integer n ≥ 2, the cyclic group Zn acts naturally on Cn by letting its generator 1 ∈ Zn act
+via the n × n matrix
+diag(e
+2π
+√
+−1
+n
+,...,e
+2π
+√
+−1
+n
+).
+The quotient [Cn/Zn] is a smooth Deligne-Mumford stack. The diagonal action of the torus T =
+(C∗)n on Cn induces a T-action on [Cn/Zn], making it a toric Deligne-Mumford stack.
+Date: January 23, 2023.
+1
+
+2
+GENLIK AND TSENG
+This paper is concerned with T-equivariant Gromov-Witten invariants of [Cn/Zn]. By definition,
+these are the following integrals
+(0.1)
+⟨
+m
+∏
+i=1
+γiψki
+i ⟩
+[Cn/Zn]
+g,m
+∶= ∫[M
+orb
+g,m([Cn/Zn],0)]
+vir
+m
+∏
+i=1
+ev∗
+i (γi)ψki
+i .
+Here, [M
+orb
+g,m ([Cn/Zn],0)]vir is the (T-equivariant) virtual fundamental class of the moduli space
+M
+orb
+g,m ([Cn/Zn],0) of stable maps to [Cn/Zn]. ψi ∈ H2(M
+orb
+g,m ([Cn/Zn],0),Q) are descendant
+classes.
+evi ∶ M
+orb
+g,m ([Cn/Zn],0) → I[Cn/Zn]
+are evaluation maps, which take values in the inertia stack I[Cn/Zn] of [Cn/Zn]. γi are classes in
+the T-equivariant Chen-Ruan cohomology of [Cn/Zn],
+γi ∈ H∗
+T,Orb([Cn/Zn]) ∶= H∗
+T(I[Cn/Zn]).
+Let
+λ0,...,λn−1 ∈ H∗
+T(pt) = H∗(BT)
+be the first Chern classes of the tautological line bundles of BT = (BC∗)n. Then (0.1) takes value
+in Q(λ0,...,λn−1).
+Foundational treatments of orbifold Gromov-Witten theory can be found in many references, the
+original being [1]. The (T-equivariant) Gromov-Witten theory of the non-compact target [Cn/Zn]
+is by definition a twisted Gromov-Witten theory of the classifying stack BZn. Foundational dis-
+cussions on twisted Gromov-Witten theory of orbifolds can be found in [5] and [24].
+The main results of this paper concern structures of Gromov-Witten invariants (0.1), formulated
+in terms of generating functions. The definition of inertia stacks implies that
+I[Cn/Zn] = [Cn/Zn] ∪
+n−1
+⋃
+k=1
+BZn.
+Let
+φ0 = 1 ∈ H0
+T([Cn/Zn]),φk = 1 ∈ H0
+T(BZn),1 ≤ k ≤ n − 1.
+Then φ0,...,φn−1 is an additive basis of H∗
+T,Orb([Cn/Zn]). The orbifold Poincar´e dual {φ0,... ,φn−1}
+of this basis is given by
+φ0 = nλ0⋯λn−1φ0,
+φ1 = nφn−1,
+⋮
+φn−1 = nφ1.
+To simplify notation, in what follows we set
+φi ∶= φj
+if j ≡ i
+mod n
+and
+φi ∶= φj
+if j ≡ i
+mod n,
+for all i ≥ 0 and 0 ≤ j ≤ n − 1.
+Associated to φc1,... ,φcm ∈ H⋆
+T,Orb ([Cn/Zn]) we define the Gromov-Witten potential by
+F [Cn/Zn]
+g,m
+(φc1,... ,φcm) =
+∞
+∑
+d=0
+Θd
+d! ∫[M
+orb
+g,m+d([Cn/Zn],0)]
+vir
+m
+∏
+k=1
+ev∗
+i (φck)
+m+d
+∏
+i=m+1
+ev∗
+i (φ1).
+We also use the following standard double bracket notation,
+⟨⟨φc1,... ,φcm⟩⟩[Cn/Zn]
+g,m
+= F [Cn/Zn]
+g,m
+(φc1,... ,φcm).
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+3
+We use the following involutions throughout the paper to present equations more efficiently:
+Inv ∶ {0,...,n − 1} → {0,...,n − 1}
+with Inv(0) = 0 and Inv(i) = n − i for 1 ≤ i ≤ n − 1, and
+Ion ∶ {0,...,n} → {0,...,n}
+with Ion(0) = n, and Ion(i) = i for 1 ≤ i ≤ n − 1.
+Holomorphic anomaly equations are partial differential equations predicted by physicists as
+a part of the higher genus mirror symmetry conjecture for Calabi-Yau threefolds [3, 4]. Lho-
+Pandharipande provided mathematical proofs of holomorphic anomaly equations for local P2 [16]
+and formal quintic [18] using stable quotient theory. Their equations exactly match with physics
+calculations for these Calabi-Yau threefolds given in [2]. Motivated by local P2, Lho-Pandharipande
+also proved holomorphic anomaly equations for [C3/Z3] in [17]. We generalize their work on holo-
+morphic anomaly equations for [C3/Z3] to [Cn/Zn] for n ≥ 3.
+The main results of this paper, summarized below, are differential equations for these generat-
+ing functions F [Cn/Zn]
+g
+when n ≥ 3 and g ≥ 2 after the following specializations of equivariant
+parameters: for 0 ≤ i ≤ n − 1,
+(0.2)
+λi =
+⎧⎪⎪⎨⎪⎪⎩
+e
+2π
+√
+−1i
+n
+e
+π
+√
+−1
+n
+if n is even,
+e
+2π
+√
+−1i
+n
+if n is odd.
+Although physics prediction of holomorphic anomaly equations was meant for Calabi-Yau mani-
+folds of dimension 3, borrowing terminology from String Theory, we call the differential equations
+in our main results holomorphic anomaly equations for [Cn/Zn].
+Main Theorem (Finite generation property and holomorphic anomaly equations).
+(1) (=Corollary 3.4) The Gromov-Witten potential lies in a certain polynomial ring:
+F [Cn/Zn]
+g,m
+(φc1,... ,φcm) ∈ C[L±1][Sn][Cn].
+(2) (=Theorem 3.7) Let n ≥ 3 be an odd number with n = 2s + 1, and g ≥ 2. We have
+Cs+1
+(2s + 1)L
+∂
+∂As
+F [Cn/Zn]
+g
+= 1
+2F [Cn/Zn]
+g−1,2
+(φs,φs) + 1
+2
+g−1
+∑
+i=1
+F [Cn/Zn]
+g−i,1
+(φs)F [Cn/Zn]
+i,1
+(φs).
+(3) (=Theorem 3.8) Let n ≥ 4 be an even number with n = 2s, and g ≥ 2. We have
+Cs+1
+2sL
+∂
+∂As−1
+F [Cn/Zn]
+g
+= F [Cn/Zn]
+g−1,2
+(φs−1,φs) +
+g−1
+∑
+i=1
+F [Cn/Zn]
+g−i,1
+(φs−1)F [Cn/Zn]
+i,1
+(φs).
+We refer to Corollary 3.4, Theorem 3.7, and Theorem 3.8 for more details. Theorem 3.7 is a
+generalization of the differential equation obtained in [17] for [C3/Z3].
+The proofs of Theorems 3.7 and 3.8 follow the approach taken in [17] for the case n = 3. The
+approach is based on the cohomological field theory (in the sense of [12]) nature of Gromov-
+Witten theory of [Cn/Zn] and relies heavily on the Givental-Teleman classification [10], [23], of
+semisimple cohomological field theories. A survey of Givental-Teleman classification can be found
+in [20].
+More precisely, the proofs of Theorems 3.7 and 3.8 use a formula obtained from Givental-
+Teleman classification which expresses the potential F [Cn/Zn]
+g,m
+as a sum over graphs whose sum-
+mands only require genus 0 Gromov-Witten theory of [Cn/Zn], see equation (3.13) and Theorem
+3.3 for details. This approach thus requires a detailed study of genus 0 Gromov-Witten theory of
+
+4
+GENLIK AND TSENG
+[Cn/Zn], which is worked out in Section 1. Many specific power series arise in the analysis of the
+genus 0 theory. Properties of these power series and the rings containing them are studied in details
+in Section 2. Holomorphic anomaly equations, Theorems 3.7 and 3.8, are described and proved in
+Section 3. Appendix A contains discussions on properties of Stirling numbers used in this paper.
+Appendix B contains a detailed analysis of the I-functions of [Cn/Zn].
+Some previous studies related to holomorphic anomaly equations in dimension > 3 can be found
+in [14], [15], [19]. In [7], we use results in [14] to derive two holomorphic anomaly equations for
+[C5/Z5]. One of them is the n = 5 case of Theorem 3.7, the other is new.
+Studying higher genus Gromov-Witten theory of KPn−1 in detail and comparing its cohomolog-
+ical field theory structure to that of [Cn/Zn] described in this paper, we obtain a crepant resolution
+correspondece for KPn−1 and [Cn/Zn] in all genera [8].
+0.1. Acknowledgment. D. G. would like to thank to Aniket Shah for a discussion which turned
+out to be useful for proof of Lemma 2.3. D. G. is supported in part by a Special Graduate Assign-
+ment fellowship by OSU Department of Mathematics and H.-H. T. is supported in part by Simons
+foundation collaboration grant.
+1. GENUS ZERO THEORY
+1.1. Mirror theorem. Applying the methods of [5], we obtain1 the twisted I-function for [Cn/Zn],
+Itw(x,z) = z
+∑
+k0,...,kn−1≥0
+∏b∶0≤b<α(⃗k)
+⟨b⟩=⟨α(⃗k)⟩
+∏n−1
+i=0 (λi − bz)
+zk0+...+kn−1
+xk0
+0 ...xkn−1
+n−1
+k0!...kn−1! φnα(⃗k)
+where
+x =
+n−1
+∑
+i=0
+xiφi
+and
+α(⃗k) =
+n−1
+∑
+i=0
+iki
+n
+with
+⃗k = (k0,...,kn−1) ∈ Zn.
+The J-function of [Cn/Zn] is characterized by
+Jtw(τ,−z) = −z + τ + O(z−1).
+To get a mirror theorem, we need to find the appropriate locus to restrict twisted I-function Itw(x,z).
+For that we need the following lemma.
+Lemma 1.1. For every integer n ≥ 3 and for every integer l ∈ {2,...,n − 1} there exists an integer
+k such that n − k ≥ 1 and 1 < kl
+n < 2.
+Proof. For l = 2, let k = n − 1. For 3 ≤ l ≤ n
+2, let k = ⌊n
+l ⌋. For n
+2 < l ≤ n − 1, let k = 2.
+□
+By the existence of such k, we see that if we let all ki to be 0 except when i = l and if we let
+kl = k then the coefficient of the monomial xkl
+l has a term of z-degree greater than equal to 2. So,
+we should restrict the twisted I-function Itw(x,z) to the locus x2 = ... = xn−1 = 0 to be able to look
+for a mirror theorem by the characterization of the J-function.
+Applying [5, Theorem 4.8], we obtain the following generalization of the mirror theorem for
+[C3/Z3] in [5, Section 6.3].
+Theorem 1.2. For n ≥ 3, the twisted I-function and the J-function of [Cn/Zn] satisfies the follow-
+ing equality
+Itw (x0φ0 + x1φ1,z) = Jtw (τ 0φ0 + τ 1φ1,z)
+1Here, ⟨α⟩ is the fractional part of α.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+5
+with
+τ 0 = x0
+and
+τ 1 = ∑
+k≥0
+(−1)nkxnk+1
+1
+(nk + 1)!
+⎛
+⎝
+Γ(k + 1
+n)
+Γ( 1
+n)
+⎞
+⎠
+n
+.
+Proof. We decompose Itw (x0φ0 + x1φ1,z) as
+(1.1)
+Itw (x0φ0 + x1φ1,z) = zφ0 + ∑
+k0≥1
+1
+zk0−1
+xk0
+0
+k0! φ0 +
+∑
+k0≥0,k1≥1
+γk1(z)
+zk0+k1−1
+xk0
+0 xk1
+1
+k0!k1! φk1
+where
+γk1(z) =
+∏
+b∶0≤b< k1
+n
+⟨b⟩=⟨ k1
+n ⟩
+n−1
+∏
+i=0
+(λi − bz)
+for
+k1 ≥ 1.
+By induction on k1, we can show that γk1(z) is a polynomial of degree2 mk1 = (⌈k1
+n ⌉ − 1)n with
+the leading coefficient
+lk1 =
+⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩
+⌈ k1
+n ⌉−1
+∏
+i=1
+(i − k1
+n )
+n
+if
+n ∤ k1,
+(−1)n
+⌈ k1
+n ⌉−1
+∏
+i=1
+(−1)nin
+if
+n ∣ k1.
+When k0 ≥ 0, observe that
+deg ( γk1(z)
+zk0+k1−1) = (⌈k1
+n ⌉ − 1)n + 1 − k1 − k0 ≤ 0.
+Hence, by equation (1.1) we see that the twisted I-function Itw (x0φ0 + x1φ1,z) is of the form
+Itw(x0φ0 + x1φ1,z) = z + τ(x0φ0 + x1φ1) + O(z−1).
+To write τ(x0φ0 + x1φ1) explicitly, we need to find the summands of equation (1.1) which are
+constant in z. Clearly, the only contribution is x0φ0 from the first sum. Let γk1(z) = ∑
+mk1
+j=0 γj
+k1(z)
+where γj
+k1(z) is the monomial of degree j. Then, we have
+deg ⎛
+⎝
+γj
+k1(z)
+zk0+k1−1
+⎞
+⎠ = j + 1 − (k0 + k1) = 0 if and only if k0 = 0 and k1 = nk + 1 for some k ≥ 0.
+In this case, we have j = nk = mk1 = deg γk1(z) and the leading coefficient of γk1(z) is
+lk1 =
+k
+∏
+i=1
+(i − nk + 1
+n
+)
+n
+= (−1)nk (
+k
+∏
+i=1
+(k − i + 1
+n))
+n
+= (−1)nk ⎛
+⎝
+Γ(k + 1
+n)
+Γ( 1
+n)
+⎞
+⎠
+n
+.
+So, we see that
+τ(x0φ0 + x1φ1) = τ 0φ0 + τ 1φ1
+with
+τ 0 = x0
+and
+τ 1 = ∑
+k≥0
+(−1)nkxnk+1
+1
+(nk + 1)!
+⎛
+⎝
+Γ(k + 1
+n)
+Γ( 1
+n)
+⎞
+⎠
+n
+.
+□
+2Here, ⌈−⌉ is the ceiling function.
+
+6
+GENLIK AND TSENG
+In what follows we impose the specializations (0.2). Then we have
+n−1
+∏
+i=0
+(λi − bz) = {1 + (bz)n
+if n is even,
+1 − (bz)n
+if n is odd
+= 1 + (−1)n(bz)n.
+Using the twisted I-function Itw, the above specializations, and the convention of [16], we define
+the I-function for [Cn/Zn] :
+(1.2)
+I (x,z) =
+∞
+∑
+k=0
+xk
+zkk!
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk.
+It is easy to see that I-function (1.2) of [Cn/Zn] is of the form
+(1.3)
+I (x,z) =
+∞
+∑
+k=0
+Ik(x)
+zk
+φk =
+n−1
+∑
+i=0
+̃Ii(x,z)φi.
+By keeping track of the degrees, we see that
+Ik(x) = ∑
+l≥0
+(−1)nlxnl+k
+(nl + k)!
+⎛
+⎝
+Γ(l + k
+n)
+Γ( k
+n)
+⎞
+⎠
+n
+for 0 ≤ k ≤ n − 1.
+The small J-function for [Cn/Zn] is defined by
+J (Θ,z) = φ0 + Θφ1
+z
++
+n−1
+∑
+i=0
+φi ⟨⟨
+φi
+z(z − ψ)⟩⟩
+[Cn/Zn]
+0,1
+.
+Theorem 1.2 implies
+(1.4)
+J (Θ(x),z) = I(x,z)
+with the mirror transformation
+(1.5)
+Θ(x) = I1(x).
+1.2. Picard-Fuchs equations. Define the operator
+D ∶ C[[x]] → C[[x]]
+and its inverse
+D−1 ∶ xC[[x]] → xC[[x]]
+by
+Df(x) = xdf(x)
+dx ,
+D−1f(x) = ∫
+x
+0
+f(t)
+t
+dt.
+We have the following identity
+(1.6)
+xm dm
+dxm = D(D − 1)...(D − m + 1) =
+m
+∑
+k=1
+sm,kDk
+where sm,k are Stirling numbers of first kind. For a brief account on properties of Stirling numbers,
+see Appendix A.
+Proposition 1.3. The I-function of [Cn/Zn] satisfies the following Picard-Fuchs (type) equation
+(1.7)
+1
+xnD(D − 1)...(D − n + 1)I(x,z) − (−1)n (1
+n)
+n
+DnI(x,z) = (1
+z)
+n
+I(x,z).
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+7
+Proof. Applying the operator
+dn
+dxn to the function I(x,z) we obtain
+dn
+dxnI(x,z) =
+∞
+∑
+k=n
+xk−n
+zk(k − n)!
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk
+=
+∞
+∑
+k=0
+xk
+zk+nk!
+∏
+b∶0≤b<1+ k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk
+by shifting index and φk+n = φk
+=
+∞
+∑
+k=0
+xk
+zk+nk!
+∏
+b∶ k
+n≤b<1+ k
+n
+⟨b⟩=⟨ k
+n ⟩
+(1 + (−1)n(bz)n)
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk
+=(1
+z)
+n ∞
+∑
+k=0
+xk
+zkk!
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk
++ (−1)n (1
+n)
+n ∞
+∑
+k=0
+knxk
+zkk!
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n⟩
+(1 + (−1)n(bz)n)φk
+=(1
+z)
+n
+I(x,z) + (−1)n (1
+n)
+n
+DnI(x,z).
+Using equation (1.6), we complete the proof.
+□
+By equation (1.6), we can rewrite the Picard-Fuchs equation (1.7) as
+(1.8)
+1
+xn
+n
+∑
+k=1
+sn,kDkI(x,z) − (−1)n (1
+n)
+n
+DnI(x,z) = (1
+z)
+n
+I(x,z).
+Since sn,n = 1, we can rewrite equation (1.8) further as
+(1.9)
+x−n ((1 − (−1)n (x
+n)
+n
+)DnI(x,z) +
+n−1
+∑
+k=1
+sn,kDkI(x,z)) = z−nI(x,z).
+We define3 the following series in C[[x]]:
+(1.10)
+L(x) = x(1 − (−1)n (x
+n)
+n
+)
+− 1
+n
+.
+By Lemma 2.1 below, we obtain the following alternative form of the Picard-Fuchs equation (1.9)
+which we frequently use:
+(1.11)
+L−n (DnI(x,z) + DL
+L
+n−1
+∑
+k=1
+sn,kDkI(x,z)) = z−nI(x,z).
+Due to the particular form (1.3) of I-function, in order to define some series avoiding φk’s, we
+also introduce the function E(x,z)
+(1.12)
+E (x,z) =
+∞
+∑
+k=0
+xk
+zkk!
+∏
+b∶0≤b< k
+n
+⟨b⟩=⟨ k
+n ⟩
+(1 + (−1)n(bz)n) =
+∞
+∑
+k=0
+Ik(x)
+zk
+3When n = 3, our L differs from L defined in [17] by a sign.
+
+8
+GENLIK AND TSENG
+just by removing the φk from the expression of the I-function (1.2). Also, substituting equation
+(1.3) into Picard-Fuchs equation (1.11) and analyzing the coefficients of both sides, we obtain
+(1.13)
+DnIk + DL
+L
+n−1
+∑
+k=1
+sn,kDkIk = 0
+for 0 ≤ k ≤ n − 1.
+1.3. Birkhoff factorization. Next, we define4 the series Ei(x,z) and Ci(x) for i ≥ 0:
+(1.14)
+Ei(x,z) = MiE(x,z)
+and
+Ci(x) = Ei(x,∞)
+where M is the Birkhoff operator defined by
+(1.15)
+MF(x,z) = zD F(x,z)
+F(x,∞)
+for any F(x,z) with non-zero F(x,∞). We also define5 the series Ci(x) inductively as follows:
+(1.16)
+C0 = I0 = 1
+and
+Ci = DLi−1...L0Ii
+for
+i ≥ 1
+where
+Li = C−1
+i D
+for i ≥ 1 and L0 is the identity. For any l ≥ 0, we define the following series in x
+Kl =
+l
+∏
+i=0
+Ci.
+We have the following identities for the series Ci and Kl, proved in Appendix B.1, see Lemma B.3
+and Corollary B.4.
+(1) Ck+n = Ck for all k ≥ 1,
+(2) ∏n
+k=1 Ck = Ln ,
+(3) Ck = Cn+1−k for all 1 ≤ k ≤ n .
+(4) Kn+l = LnKl for all l ≥ 0, in particular Kn = Ln,
+(5) KlKn−l = Ln and KlKInv(l) = Ll+Inv(l) for all 0 ≤ l ≤ n − 1.
+Define the S-operator for [Cn/Zn] by
+S[Cn/Zn] (Θ,z) (γ) =
+n−1
+∑
+i=0
+φi ⟨⟨ φi
+z − ψ,γ⟩⟩
+[Cn/Zn]
+0,2
+for γ ∈ H⋆
+T,Orb ([Cn/Zn]). The S-operator satisfies the following identities :
+S[Cn/Zn] (Θ,z) (φ0) =I(x,z),
+(1.17)
+S[Cn/Zn] (Θ,z) (φi) =zLiS[Cn/Zn] (Θ,z) (φi−1)
+for
+i ≥ 1.
+(1.18)
+Equation (1.17) is a direct consequence of the definitions of J-function, S-operator, and equation
+(1.4). For equation (1.18), we see that both sides lie on the same tangent space of the Lagrangian
+cone L[Cn/Zn] and are of the form φi + O(z−1), hence by [10] they must match.
+4For a series F(x,z) ∈ C[[x, 1
+z ]], the constant term of F(x,z) with respect to 1
+z is denoted by F(x,∞).
+5It is easy to show that two definitions of Ci’s are equivalent.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+9
+Lemma 1.4. We have the following factorization of the operator acting on the left hand side of the
+Picard-Fuchs equation (1.11)
+(1.19)
+L1⋯Ln = Ln⋯L1 = L−n (Dn + DL
+L
+n−1
+∑
+k=1
+sn,kDk).
+Proof. The first equality is a direct result of the definition of Li and Lemma B.3, i.e. we have
+Li = Ln+1−i
+for all 1 ≤ i ≤ n.
+Using identities (1.17) and (1.18), we obtain the following identity
+(1.20)
+Ln⋯L1I(x,z) = z−nI(x,z).
+Due to particular form (1.3) of I-function, we see that for each 0 ≤ i ≤ n − 1 the function ̃Ii(x,z)
+is a common solution of equations (1.11) and (1.20). In other words, the set {̃Ii(x,z)}0≤i≤n−1 is a
+basis of solutions to both equations. Moreover, for all 1 ≤ i ≤ n − 1, we have
+(1.21)
+Li+1Li =
+1
+Ci+1
+D 1
+Ci
+D =
+1
+Ci+1Ci
+(D − Xi)D
+with Xi = DCi
+Ci
+.
+Applying this procedure repeatedly, we see that
+Ln⋯L1 =
+1
+∏n
+i=1 Ci
+(D + αn−1)⋯(D + α1)D
+= L−n(D − αn−1)⋯(D − α1)D
+by Lemma B.3,
+with
+αi =
+i
+∑
+j=1
+Xj
+for 1 ≤ i ≤ n − 1. This shows that equations (1.11) and (1.20) have the same leading coefficients.
+Since both equations have the same solution space and the same leading coefficient, some elemen-
+tary arguments from the theory of linear ordinary differential equations imply that (1.11) and (1.20)
+must be exactly the same equation. This completes the proof.
+□
+1.4. Quantum product. Let γ = ∑n−1
+i=0 tiφi ∈ H⋆
+T,Orb ([Cn/Zn]). The full genus 0 Gromov-Witten
+potential is defined to be
+F [Cn/Zn]
+0
+(t,Θ) =
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d! ∫[M
+orb
+0,m+d([Cn/Zn],0)]
+vir
+m
+∏
+i=1
+ev∗
+i (γ)
+m+d
+∏
+i=m+1
+ev∗
+i (Θφ1)
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d! ⟨γ,...,γ
+���������������
+m
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+.
+(1.22)
+The orbifold Poincar´e pairing
+g(−,−) ∶ H⋆
+T,Orb ([Cn/Zn]) × H⋆
+T,Orb ([Cn/Zn]) → Q(λ0,...,λn−1)
+in the basis {φ0,...,φn−1} and under the specialization (0.2), has the matrix representation G = [Gij]
+given by
+Gij = g(φi,φj) = {
+1
+n if i + j = 0
+mod n,
+0 if i + j ≠ 0
+mod n
+= 1
+nδInv(i)j = 1
+nδiInv(j).
+
+10
+GENLIK AND TSENG
+Its inverse G−1 = [Gij] is given by
+Gij = nδInv(i)j = nδiInv(j)
+where 0 ≤ i,j ≤ n − 1.
+The quantum product ●γ at γ ∈ H⋆
+T,Orb ([Cn/Zn]) is a product structure on H⋆
+T,Orb ([Cn/Zn]). It
+can be defined as follows:
+g(φi ●γ φj,φk) ∶=
+∂3
+∂ti∂tj∂tk
+F [Cn/Zn]
+0
+(t,Θ).
+In what follows, we focus on the quantum product ●γ=0 at γ = 0 ∈ H⋆
+T,Orb ([Cn/Zn]), which we
+denote by ●. Note that ● still depends on Θ.
+Lemma 1.5.
+(1.23)
+⟨⟨φi,φj⟩⟩[Cn/Zn]
+0,2
+= {0
+if
+i + j ≠ n − 1,
+1
+nLi...L0Ii+1
+if
+i + j = n − 1.
+Proof. By expanding equations (1.17), (1.18) and matching the coefficients of z−1, we obtain the
+following identity for any 0 ≤ j ≤ n − 1:
+φ0 ⟨⟨φ0,φi⟩⟩[Cn/Zn]
+0,2
++ φ1 ⟨⟨φ1,φi⟩⟩[Cn/Zn]
+0,2
++ ... + φn−1 ⟨⟨φn−1,φi⟩⟩[Cn/Zn]
+0,2
+= Li...L0Ii+1φi+1.
+Equating the coefficients, we complete the proof.
+□
+Lemma 1.6. For any 0 ≤ i,j ≤ n − 1, we have
+1
+C1
+D ⟨⟨φi,φj⟩⟩[Cn/Zn]
+0,2
+= ⟨⟨φi,φj,φ1⟩⟩[Cn/Zn]
+0,3
+.
+Proof. The proof is the following direct computation:
+1
+C1
+D ⟨⟨φi,φj⟩⟩[Cn/Zn]
+0,2
+= 1
+DΘD ⟨⟨φi,φj⟩⟩[Cn/Zn]
+0,2
+=
+1
+DΘ
+∞
+∑
+d=1
+Θd−1DΘ
+(d − 1)! ∫[M
+orb
+g,d+2([Cn/Zn],0)]
+vir ev∗
+1 (φi)ev∗
+2 (φj)
+d+2
+∏
+l=3
+ev∗
+l (φ1)
+=
+∞
+∑
+d=1
+Θd−1
+(d − 1)! ∫[M
+orb
+g,d+2([Cn/Zn],0)]
+vir ev∗
+1 (φi)ev∗
+2 (φj)
+d+2
+∏
+l=3
+ev∗
+l (φ1)
+=
+∞
+∑
+d=0
+Θd
+d! ∫[M
+orb
+g,d+3([Cn/Zn],0)]
+vir ev∗
+1 (φi)ev∗
+2 (φj)ev∗
+3 (φ1)
+d+3
+∏
+l=4
+ev∗
+l (φ1)
+= ⟨⟨φi,φj,φ1⟩⟩[Cn/Zn]
+0,3
+.
+The fist line follows from equation (1.4) and the definition of C1.
+□
+Proposition 1.7. For all i ≥ 0, the quantum product at 0 ∈ H⋆
+T,Orb ([Cn/Zn]) satisfies
+φ1 ● φi = Ci+1
+C1
+φi+1.
+Proof. Initially, we assume 0 ≤ i ≤ n − 1. Using equation (1.23) and Lemma 1.6, we obtain
+⟨⟨φ1,φi,φj⟩⟩[Cn/Zn]
+0,3
+=
+D ⟨⟨φi,φj⟩⟩[Cn/Zn]
+0,2
+C1
+= {0
+if
+i + j ≠ n − 1,
+1
+n
+Ci+1
+C1
+if
+i + j = n − 1.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+11
+Write
+φ1 ● φi =
+n−1
+∑
+l=0
+aliφl.
+Then, for 0 ≤ j ≤ n − 1, we have
+g (φ1 ● φi,φj) = 1
+naInv(j)i.
+On the other hand, the relation g(X ● Y,Z) = ⟨⟨X,Y,Z⟩⟩[Cn/Zn]
+0,3
+gives
+g (φ1 ● φi,φj) = {0
+if
+i + j ≠ n − 1,
+1
+n
+Ci+1
+C1
+if
+i + j = n − 1.
+So, we obtain
+ali = {0
+if
+i + Inv(l) ≠ n − 1,
+Ci+1
+C1
+if
+i + Inv(l) = n − 1 = Ci+1
+C1
+δi,Ion(l)−1.
+Parts (1) and (3) of Lemma B.3 finish the proof.
+□
+Corollary 1.8. For any i,j ≥ 0, the quantum product at 0 ∈ H⋆
+T,Orb ([Cn/Zn]) is given by
+φi ● φj = Ki+j
+KiKj
+φi+j
+and hence the genus 0, 3-point Gromov-Witten invariants are
+⟨⟨φi,φj,φk⟩⟩[Cn/Zn]
+0,3
+= Ki+j
+KiKj
+1
+nδInv(i+j mod n),k.
+Proof. Using Proposition 1.7 and noting that C0 = 1, inductively we show that for any l ≥ 0 we
+have
+φl = Cl
+1
+Kl
+φ1 ● ... ● φ1
+����������������������������������������������
+l−copy
+.
+This implies
+φi ● φj = Ci+j
+1
+KiKj
+φ1 ● ... ● φ1
+����������������������������������������������
+i+j−copy
+= Ci+j
+1
+KiKj
+Ki+j
+Ci+j
+1
+φi+j,
+and the genus 0, 3-point Gromov-Witten invariants part the lemma follows from
+⟨⟨φi,φj,φk⟩⟩[Cn/Zn]
+0,3
+= g(φi ● φj,φk) = Ki+j
+KiKj
+1
+nδInv(i+j mod n),k.
+□
+For all i ≥ 0, define
+(1.24)
+̃φi = Ki
+Li φi.
+Lemma 1.9. For all i,j ≥ 0, we have ̃φi+n = ̃φi and ̃φi ● ̃φj = ̃φi+j.
+
+12
+GENLIK AND TSENG
+Proof. The first part follows from
+̃φi+n = Ki+n
+Li+n φi+n = KiLn
+Li+n φi = Ki
+Li φi.
+Here, we used the properties of Ki listed in Section 1.3 and proved in Appendix B.1. The second
+part follows from
+̃φi ● ̃φj = Ki
+Li φi ● Kj
+Lj φj = KiKj
+Li+j φi ● φj = KiKj
+Li+j
+Ki+j
+KiKj
+φi+j = Ki+j
+Li+j φi+j = ̃φi+j.
+□
+Proposition 1.10. The quantum product at 0 ∈ H⋆
+T,Orb ([Cn/Zn]) is semisimple with the idempotent
+basis {eα} given by
+(1.25)
+eα = 1
+n
+n−1
+∑
+i=0
+ζ−αĩφi
+for
+α ≥ 0,
+where ζ = e
+2π
+√
+−1
+n
+is an nth root of unity.
+Proof. To show that eα ● eβ = δα,βeβ, we calculate
+eα ● eβ = 1
+n2
+n−1
+∑
+i=0
+n−1
+∑
+j=0
+ζ−αiζ−βj̃φi+j
+= 1
+n2
+n−2
+∑
+i=0
+n−2−i
+∑
+j=0
+ζ−αiζ−βj̃φi+j + 1
+n2
+n−1
+∑
+i=0
+n−1
+∑
+j=n−1−i
+ζ−αiζ−βj̃φi+j
+= 1
+n2
+n−2
+∑
+i=0
+2n−2−i
+∑
+j=n
+ζ−αiζ−β(j−n)̃φi+j−n + 1
+n2 (
+n−2
+∑
+i=0
+n−1
+∑
+j=n−1−i
+ζ−αiζ−βj̃φi+j +
+n−1
+∑
+j=0
+ζ−α(n−1)ζ−βj̃φn−1+j)
+= 1
+n2
+n−2
+∑
+i=0
+2n−2−i
+∑
+j=n
+ζ−αiζ−βj̃φi+j + 1
+n2 (
+n−2
+∑
+i=0
+n−1
+∑
+j=n−1−i
+ζ−αiζ−βj̃φi+j +
+n−1
+∑
+j=0
+ζ−α(n−1)ζ−βj̃φn−1+j)
+= 1
+n2
+n−1
+∑
+i=0
+n−1
+∑
+k=0
+ζ−αiζ−β(k−i)̃φk
+= 1
+n2
+n−1
+∑
+i=0
+ζ−(α−β)i
+�����������������������������������������������
+=nδα,β
+n−1
+∑
+k=0
+ζ−βk̃φk
+����������������������������������������
+=eβ
+.
+□
+1.5. Frobenius structure. We describe in details some ingredients of the Frobenius structure ob-
+tained from genus 0 Gromov-Witten theory of [Cn/Zn]. We refer the readers to [13] for generalities
+on Frobenius structure arising in Gromov-Witten theory.
+By the results in Section 1.4, the Frobenius structure on H⋆
+T,Orb ([Cn/Zn]) defined by the Gromov-
+Witten theory of [Cn/Zn] is semisimple in a neighborhood of 0 ∈ H⋆
+T,Orb ([Cn/Zn]).
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+13
+We first calculate the metric g in the idempotent basis {eα}:
+g (eα,eα) =g (1
+n
+n−1
+∑
+i=0
+ζ−αĩφi, 1
+n
+n−1
+∑
+j=0
+ζ−αj̃φj)
+=g (1
+n
+n−1
+∑
+i=0
+ζ−αiKi
+Li φi, 1
+n
+n−1
+∑
+j=0
+ζ−αj Kj
+Lj φj)
+= 1
+n2
+n−1
+∑
+i=0
+n−1
+∑
+j=0
+ζ−α(i+j)KiKj
+Li+j Gij
+= 1
+n2
+n−1
+∑
+i=0
+n−1
+∑
+j=0
+ζ−α(i+j)KiKj
+Li+j
+1
+nδInv(i)j
+= 1
+n3
+n−1
+∑
+i=0
+ζ−α(i+Inv(i))KiKInv(i)
+Li+Inv(i)
+= 1
+n2
+by Lemma B.4 and i + Inv(i) = 0
+mod n.
+The normalized idempotents are
+̃eα =
+eα
+√
+g (eα,eα)
+= neα.
+The transition matrix Ψ is given by Ψαi = g (̃eα,φi) where 0 ≤ α,i ≤ n − 1. We calculate
+Ψαi = g (̃eα,φi) = g (
+n−1
+∑
+j=0
+ζ−αj Kj
+Lj φj,φi)
+=
+n−1
+∑
+j=0
+ζ−αj Kj
+Lj Gji =
+n−1
+∑
+j=0
+ζ−αj Kj
+Lj
+1
+nδInv(i),j.
+So, Ψαi is given by
+Ψαi = 1
+nζ−αInv(i)KInv(i)
+LInv(i) = 1
+nζ−α(n−i)Kn−i
+Ln−i
+= 1
+nζαi Li
+Ki
+for
+0 ≤ α,i ≤ n − 1.
+Lemma 1.11. The inverse of the transition matrix Ψ−1 = [Ψ−1
+βj] is given by
+Ψ−1
+jβ = ζ−βj Kj
+Lj
+where
+0 ≤ β,j ≤ n − 1.
+Proof. We calculate
+[ΨΨ−1]αβ =
+n−1
+∑
+i=0
+ΨαiΨ−1
+iβ =
+n−1
+∑
+i=0
+1
+nζαi Li
+Ki
+ζ−βiKi
+Li
+=
+n−1
+∑
+i=0
+1
+nζi(α−β) = δα,β.
+□
+Let {uα}n−1
+α=0 be canonical coordinates associated to the idempotent basis {eα}n−1
+α=0 which satisfy
+uα (ti = 0,Θ = 0) = 0.
+
+14
+GENLIK AND TSENG
+Since eα =
+∂
+∂uα, we have
+(1.26)
+n−1
+∑
+α=0
+∂uα
+∂t1
+eα = φ1.
+Lemma 1.12. We have
+duα
+dt1
+= ζα L
+C1
+at t = 0.
+Proof. The result is obtained by the following calculation: at t = 0, we have
+duα
+dt1
+eα =
+n−1
+∑
+β=0
+duβ
+dt1
+δα,βeα
+=φ1 ● eα
+by equation (1.26)
+=1
+n
+n−1
+∑
+i=0
+ζ−αiKi
+Li φ1 ● φi
+=ζα L
+C1
+1
+n
+n−1
+∑
+i=0
+ζ−α(i+1)Ki+1
+Li+1 φi+1
+by Proposition 1.7 and Ki+1 = Ci+1Ki
+=ζα L
+C1
+1
+n
+⎛
+⎜⎜⎜⎜
+⎝
+n−2
+∑
+i=0
+ζ−α(i+1)Ki+1
+Li+1 φi+1 + ζ−αnKn
+Ln φn
+���������������������������������������������
+=1⋅1⋅φ0
+⎞
+⎟⎟⎟⎟
+⎠
+=ζα L
+C1
+1
+n (
+n−1
+∑
+i=1
+ζ−αiKi
+Li φi+1 + φ0)
+=ζα L
+C1
+1
+n
+n−1
+∑
+i=0
+ζ−αiKi
+Li φi
+�����������������������������������������������������������������������������
+=eα
+.
+□
+The R-matrix has a central role in the Givental-Teleman classification of semisimple cohomo-
+logical field theories. Let the R-matrix of the Frobenius structure associated to the (T-equivariant)
+Gromov-Witten theory of [Cn/Zn] near the semisimple point 0 be denoted by
+R(z) = Id + ∑
+k≥1
+Rkzk ∈ End(H∗
+T,Orb([Cn/Zn]))[[z]].
+By the definition of R-matrix, R(z) satisfies the symplectic condition
+R(z) ⋅ R(−z)∗ = Id.
+Let U be the diagonal matrix
+U = diag(u0,... ,un−1)
+associated to canonical coordinates {uα}n−1
+α=0. The R-matrix R(z) also satisfies the following flat-
+ness equation
+(1.27)
+z(dΨ−1)R + zΨ−1(dR) + Ψ−1R(dU) − Ψ−1(dU)R = 0,
+see [13, Chapter 1, Section 4.6] and [9, Proposition 1.1]. Here d = d
+dt.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+15
+We examine the dependence on parameters of the full genus 0 Gromov-Witten potential (1.22):
+F [Cn/Zn]
+0
+(t,Θ)
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d! ⟨γ,...,γ
+���������������
+m
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d! ⟨γ∣t1=0 + t1φ1,...,γ∣t1=0 + t1φ1
+������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
+m
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d!
+m
+∑
+b=0
+(m
+b )⟨γ∣t1=0,...,γ∣t1=0
+�������������������������������������������������������������������������
+m−b
+,t1φ1,...,t1φ1
+���������������������������������������������������������
+b
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+m
+∑
+b=0
+1
+b!d!(m − b)! ⟨γ∣t1=0,...,γ∣t1=0
+�������������������������������������������������������������������������
+m−b
+,t1φ1,...,t1φ1
+���������������������������������������������������������
+b
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+m
+∑
+b=0
+(b + d)!
+b!d!(m − b)!(b + d)! ⟨γ∣t1=0,...,γ∣t1=0
+�������������������������������������������������������������������������
+m−b
+,t1φ1,...,t1φ1
+���������������������������������������������������������
+b
+,Θφ1,...,Θφ1
+����������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+=
+∞
+∑
+m=0
+∞
+∑
+d=0
+1
+m!d! ⟨γ,...,γ
+���������������
+m
+,(Θ + t1)φ1,...,(Θ + t1)φ1
+����������������������������������������������������������������������������������������������������������������������������������������������������������
+d
+⟩
+[Cn/Zn]
+0,m+d
+,
+namely
+F [Cn/Zn]
+0
+(t,Θ) = F [Cn/Zn]
+0
+(t∣t1=0,Θ + t1).
+That is, F [Cn/Zn]
+0
+(t,Θ) depends on t1 and Θ through Θ + t1.
+It follows from the construction of semisimple Frobenius structures that its ingredients also de-
+pend on t1 and Θ through Θ + t1, for example,
+uα(t,Θ) = uα(t∣t1=0,Θ + t1).
+In particular, the operator
+(1.28)
+∂
+∂t1
+− ∂
+∂Θ
+annihilates the canonical coordinates uα. As a result, we have
+duα
+dt1
+= duα
+dΘ = duα
+dx
+dx
+dΘ.
+By Lemma 1.12, we have
+(1.29)
+duα
+dx = ζαL1
+x
+at the semisimple point 0 ∈ H∗
+T,Orb ([Cn/Zn]), i.e. at t = 0.
+Since F [Cn/Zn]
+0
+(t,Θ) depends on t1 and Θ through Θ+t1, it follows that Ψ and R(z) also depend
+on t1 and Θ through Θ+t1. Hence, the operator (1.28) also annihilates 6 Ψ and R(z), more precisely
+6An argument for this (for a different target space) from the CohFT viewpoint can be found in [22, Section 3.3].
+
+16
+GENLIK AND TSENG
+we have
+∂
+∂t1
+Ψ = ∂
+∂ΘΨ,
+∂
+∂t1
+R(z) = ∂
+∂ΘR(z).
+In equation (1.27), we set all ti’s to 0 except t1 and only consider
+d
+dt1. Since, U, Ψ and R(z) are
+annihilated by the operator (1.28), it follows that (1.27) can be written as
+z( d
+dΘΨ−1)R + zΨ−1( d
+dΘR) + Ψ−1R( d
+dΘU) − Ψ−1( d
+dΘU)R = 0.
+Using the mirror map Θ(x) = I1(x) and the chain rule
+d
+dΘ = dx
+dΘ
+d
+dx,
+we rewrite the above equation as
+z(x d
+dxΨ−1)R + zΨ−1(x d
+dxR) + Ψ−1R(x d
+dxU) − Ψ−1(x d
+dxU)R = 0.
+By matching coefficients of zk, we can futher rewrite it as
+(1.30)
+D (Ψ−1Rk−1) + (Ψ−1Rk)DU − Ψ−1 (DU)Ψ(Ψ−1Rk) = 0
+or equivalently
+(1.31)
+Ψ(DΨ−1)Rk−1 + DRk−1 + Rk (DU) − (DU)Rk = 0
+for k ≥ 0. Here D = x d
+dx as before.
+Now set t1 = 0, i.e. consider the restriction to the semisimple point 0 ∈ H∗
+T,Orb ([Cn/Zn]). By
+equation (1.29), we have
+(1.32)
+DU = diag(L,Lζ,...,Lζn−1).
+For k ≥ 0, define the matrix Pk by
+Pk = Ψ−1Rk
+after being restricted to the semisimple point 0 ∈ H∗
+T,Orb ([Cn/Zn]). Let P k
+i,j denote the (i,j) entry
+of the matrix Pk where 0 ≤ i,j ≤ n − 1.
+Lemma 1.13. For 0 ≤ i,j ≤ n − 1 and k ≥ 0, we have
+DP k−1
+i,j
+= CIon(i)P k
+Ion(i)−1,j − P k
+i,jLζj.
+Proof. Equation (1.30) can be rewritten as
+D (Ψ−1Rk−1) = Ψ−1 (DU)Ψ(Ψ−1Rk) − (Ψ−1Rk)DU
+which is the same as
+(1.33)
+DPk−1 = Ψ−1DUΨPk − PkDU.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+17
+We see that
+(Ψ−1DUΨ)ij =
+n−1
+∑
+l=0
+(Ψ−1DU)il Ψlj
+=
+n−1
+∑
+l=0
+ζ−liKi
+Li Lζl 1
+nζlj Lj
+Kj
+=1
+n
+Ki
+Kj
+Lj+1
+Li
+n−1
+∑
+l=0
+ζl(j−i+1)
+=
+⎧⎪⎪⎨⎪⎪⎩
+Ki
+Kj
+Lj+1
+Li
+if
+i = j + 1
+mod n,
+0
+otherwise
+=
+⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩
+Ci
+if
+1 ≤ i ≤ n − 1
+and
+j = i − 1,
+Cn
+if
+i = 0
+and
+j = n − 1,
+0
+otherwise.
+(1.34)
+Equation (1.34) implies
+(1.35)
+(Ψ−1DUΨPk)ij =
+n−1
+∑
+l=0
+(Ψ−1DUΨ)il P k
+l,j = CIon(i)P k
+Ion(i)−1,j
+Equations (1.33) and (1.35) finish the proof.
+□
+For 0 ≤ i,j ≤ n − 1, define
+Pi,j(z) =
+∞
+∑
+k=0
+P k
+i,jzk,
+DLj = D + Lj
+z
+and
+µj = ∫
+x
+0
+Lj(u)
+u
+du
+where Lj = Lζj. Then Lemma 1.13 is equivalent to the following.
+Lemma 1.14. For 0 ≤ i,j ≤ n − 1, we have DLjPi,j(z) = CIon(i)z−1PIon(i)−1,j(z).
+Proof. The proof is the following direct computation:
+DLjPi,j(z) =
+∞
+∑
+k=0
+DP k
+i,jzk +
+∞
+∑
+k=0
+LjP k
+i,jzk−1
+=
+∞
+∑
+k=1
+DP k−1
+i,j zk−1 +
+∞
+∑
+k=0
+LjP k
+i,jzk−1
+=
+∞
+∑
+k=0
+(DP k−1
+i,j
++ LjP k
+i,j)zk−1
+because P −1
+i,j = 0
+= {∑∞
+k=0 CnP k
+n−1,jzk−1
+if
+i = 0,
+∑∞
+k=0 CiP k
+i−1,jzk−1
+if
+1 ≤ i ≤ n − 1
+by Lemma 1.13
+= {Cnz−1Pn−1,j(z)
+if
+i = 0,
+Ciz−1Pi−1,j(z)
+if
+1 ≤ i ≤ n − 1
+= CIon(i)z−1PIon(i)−1,j(z).
+□
+
+18
+GENLIK AND TSENG
+It immediately follows that P0,j(z) satisfies the following differential equation
+(1.36)
+1
+C1
+DLj⋯ 1
+Cn
+DLjP0,j(z) = z−nP0,j(z).
+By the definition of Li and equation (B.4), this equation can be rewritten as
+(1.37)
+L1⋯Ln (e
+µj
+z P0,j(z)) = z−ne
+µj
+z P0,j(z)
+By Lemma 1.4, equation (1.37) reads as
+(1.38)
+L−n (Dn (e
+µj
+z P0,j(z)) + DL
+L
+n−1
+∑
+r=1
+sn,rDr (e
+µj
+z P0,j(z))) = z−ne
+µj
+z P0,j(z).
+We see that P0,j(z) satisfies the assumption of Lemma B.5. Hence, we obtain the following two
+results by Lemma B.5 and Corollary. B.8.
+Corollary 1.15. For 0 ≤ j ≤ n − 1 and k ≥ 0, we have P k
+0,j ∈ C[L] ⊆ C[L±1].
+Corollary 1.16. For 0 ≤ j ≤ n − 1 and k ≥ 0, we have
+(1.39)
+Lj,1(P k
+0,j) + 1
+Lj
+Lj,2(P k−1
+0,j ) + 1
+L2
+j
+Lj,3(P k−2
+0,j ) + ⋯ +
+1
+Ln−1
+j
+Lj,n(P k+1−n
+0,j
+) = 0
+where Lj,k is given by equation (B.6).
+2. RINGS OF FUNCTIONS
+The purpose of this section is to define and study rings of functions that contain various ingredi-
+ents of Gromov-Witten theory of [Cn/Zn].
+2.1. Preparations. We define the following series in C[[x]]
+Xk,l = DlCk
+Ck
+for all k,l ≥ 0. We denote Xk,1 just by Xk. Also, note that X0 = 0 since C0 = 1.
+Lemma 2.1. We have
+Xk,l = (D + Xk)l−1 Xk
+for all k ≥ 0 and l ≥ 1. In particular, Xk,l is a polynomial in {Xk,DXk,... ,Dl−1Xk} and Dl−1Xk
+is a polynomial in {Xk,1,... ,Xk,l}.
+Proof. The first part follows by induction on l. The case l = 1 is clear. The inductive step is as
+follows:
+DXk,l−1 = D (Dl−1Ck
+Ck
+) = DlCk
+Ck
+− Dl−1Ck
+Ck
+DCk
+Ck
+= Xk,l − Xk,l−1Xk
+which is equivalent to
+Xk,l = (D + Xk)Xk,l−1.
+The polynomiality of Xk,l directly follows and polynomiality of Dl−1Xk follows from a basic elim-
+ination.
+□
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+19
+Lemma 2.2. We have
+DL
+L = 1 + (−1)n Ln
+nn = Ln
+xn ,
+(2.1)
+DKi
+Ki
+=
+i
+∑
+r=0
+Xr,
+(2.2)
+nDL
+L =
+n
+∑
+r=0
+Xr,
+(2.3)
+for 0 ≤ i ≤ n.
+Proof. Observe that
+DL =x⎛
+⎝(1 − (−1)n (x
+n)
+n
+)
+− 1
+n
++ x(−1
+n)(1 − (−1)n (x
+n)
+n
+)
+− 1
+n −1 d
+dx (1 − (−1)n (x
+n)
+n
+)⎞
+⎠
+=x(1 − (−1)n (x
+n)
+n
+)
+− 1
+n
++ x2 (−1
+n)(1 − (−1)n (x
+n)
+n
+)
+− 1
+n−1
+(−(−1)nn(x
+n)
+n−1 1
+n)
+=x(1 − (−1)n (x
+n)
+n
+)
+− 1
+n
++ x(1 − (−1)n (x
+n)
+n
+)
+− 1
+n−1
+(−1)n (x
+n)
+n
+.
+This implies
+DL
+L = 1 + (1 − (−1)n (x
+n)
+n
+)
+−1
+(−1)n (x
+n)
+n
+= 1 + (−1)n xn
+nn (1 − (−1)n (x
+n)
+n
+)
+−1
+= 1 + (−1)n Ln
+nn .
+From the first equality of the above equation, we see that
+DL
+L = 1 + (1 − (−1)n (x
+n)
+n
+)
+−1
+(−1)n (x
+n)
+n
+= 1 +
+(−1)n ( x
+n)
+n
+1 − (−1)n ( x
+n)
+n = (1 − (−1)n (x
+n)
+n
+)
+−1
+= Ln
+xn .
+This completes the proof of first equation. The second equation follows directly from the definitions
+of Ki and Xr. The last equation follows from the second equation and part (1) of Lemma B.4.
+□
+For any m ≥ 1, define the following series in x
+Zm,k =
+⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩
+D−1Ck+1...D−1Cm
+if
+0 ≤ k ≤ m − 1,
+1
+if
+k = m,
+0
+if
+k > m.
+From the definition of Zm,k, we easily see that
+(2.4)
+DZm,k = Ck+1Zm,k+1
+for all k ≥ 0. We also recall that, by equation (1.16), for m ≥ 1, Im = D−1C1...D−1Cm which is just
+Zm,0. Now for k ≥ 1 define the following series in x:
+Bk,p =
+⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
+Dk−1C1
+if
+p = 1,
+k1−1
+∑
+k2=p−1...
+kp−1−1
+∑
+kp=1 (
+p−1
+∏
+i=1 (ki−1
+ki+1))(Dk1−1−k2C1)...(Dkp−1−1−kpCp−1)(Dkp−1Cp)
+if
+2 ≤ p ≤ k,
+0
+if
+p > k
+where k1 = k.
+
+20
+GENLIK AND TSENG
+Lemma 2.3. For all k,m ≥ 1, we have
+DkIm =
+k
+∑
+p=1
+Bk,pZm,p.
+Proof. Let T1 and T2 be two linear operators acting on C[[x]], and let [T1,T2] = T1T2 − T2T1 be
+their commutator, and let adj
+T1(T2) = [T1,... ,[T1,T2],... ] be its generalization. Inductively, we
+show that the commutator of the operator D and multiplication by a series A is given by
+adj
+D(A) = (DjA)
+i.e., multiplication by the series (DjA), and we show that multiplication by A followed by the
+operator Di is given by
+(2.5)
+DiA =
+i
+∑
+j=0
+(i
+j)adj
+D(A)Di−j.
+Using the fact that for m ≥ 1, Im = D−1C1...D−1Cm = Zm,0 together with equations (2.1) and (2.5),
+we inductively complete the proof.
+□
+Lemma 2.4. For all 1 ≤ m ≤ n − 1, we have
+(2.6)
+Bn,m + DL
+L
+n−1
+∑
+k=m
+sn,kBk,m = Bn,m + DL
+L
+n−1
+∑
+k=1
+sn,kBk,m = 0.
+Proof. The first equality follows from the definition of Bk,m. For the second equality, we use
+induction on m. For m = 1, it follows from Bk,1 = Dk−1C1 = DkI1 and equation (1.13). The
+following completes the inductive step:
+0 =DnIm + DL
+L
+n−1
+∑
+k=1
+sn,kDkIm
+by equation (1.13)
+=
+n
+∑
+p=1
+Bn,pZm,p + DL
+L
+n−1
+∑
+k=1
+sn,k
+k
+∑
+p=1
+Bk,pZm,p
+by Lemma 2.3
+=
+m
+∑
+p=1
+Bn,pZm,p + DL
+L
+n−1
+∑
+k=1
+sn,k
+m
+∑
+p=1
+Bk,pZm,p
+by definitions of Bk,p and Zm,p
+=
+m
+∑
+p=1
+(Bn,p + DL
+L
+n−1
+∑
+k=1
+sn,kBk,p)Zm,p
+=Bn,m + DL
+L
+n−1
+∑
+k=1
+sn,kBk,m +
+m−1
+∑
+p=1
+(Bn,p + DL
+L
+n−1
+∑
+k=1
+sn,kBk,p)
+���������������������������������������������������������������������������������������������������������������������������������������������������������
+=0 by inductive hypothesis.
+Zm,p.
+□
+2.2. Descriptions of the rings. Set
+C[L±1][DX ] ∶= C[L±1][X1,...,Xn−1,DX1,...,DXn−1,D2X1,...,D2Xn−1,...],
+and
+X ∶= {X1,...,Dn−3X1}∪,... ∪ {Xi,...,Dn−2−iXi} ∪ ... ∪ {Xn−2} = {DjXi}1≤i≤n−2,0≤j≤n−2−i.
+Lemma 2.5. C[L±1][DX] is a quotient of the ring C[L±1][X].
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+21
+Proof. Now, for any 1 ≤ p ≤ k − 1, define
+Zp,k ={X1,1,...,X1,k−p,...,Xp,1,...,Xp,k−p}
+and
+Sp,k = Zp,k ∖ {Xp,k−p},
+̃
+Zp,k ={X1,...,Dk−p−1X1,...,Xp,...,Dk−p−1Xp}
+and
+̃Sp,k = ̃
+Zp,k ∖ {Dk−p−1Xp}.
+For each of these sets, and for a fixed p we have
+(2.7)
+Sp,k ⊆ Zp,k ⊆ Sp,k+1 ⊆ Zp,k+1,
+and
+̃Sp,k ⊆ ̃
+Zp,k ⊆ ̃Sp,k+1 ⊆ ̃
+Zp,k+1.
+Note that for any k ≥ 1
+Bk,p
+Kp
+=
+⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
+X1,k−1
+if
+p = 1,
+k1−1
+∑
+k2=p−1...
+kp−1−1
+∑
+kp=1 (
+p−1
+∏
+i=1 (ki−1
+ki+1))X1,k1−k2−1...Xp−1,kp−1−kp−1Xp,kp−1
+if
+2 ≤ p ≤ k,
+0
+if
+p > k
+where k1 = k. It follows that for any 1 ≤ p ≤ k − 1, we have
+(2.8)
+Bk,p
+Kp
+= Xp,k−p + ̃Bk,p
+where ̃Bk,p is a polynomial in elements of Sp,k. Then, dividing both sides of equation (2.6) by Km
+for any 1 ≤ m ≤ n − 1, we obtain
+0 =Bn,m
+Km
++ DL
+L
+n−1
+∑
+k=m
+sn,k
+Bk,m
+Km
+=Xm,n−m + ̃Bn,m + DL
+L
+n−1
+∑
+k=m
+sn,k
+Bk,m
+Km
+�������������������������������������������������������������
+(⋆)
+.
+(2.9)
+By set inclusions (2.7) and equation (2.8), it follows that (⋆) is a polynomial in elements of Zm,n−1.
+Since we know ̃Bn,m is a polynomial in element of Sm,n and Zm,n−1 ⊆ Sm,n, it follows that Xm,n−m
+is a polynomial in elements of Sm,n ∪ {L±1} by equation (2.9) and equation (2.1). This implies
+that Dn−m−1Xm is a polynomial in elements of ̃Sm,n ∪ {L±1} by Lemma 2.1. This completes the
+proof.
+□
+For 0 ≤ i,j ≤ n − 1 and k ≥ 0, define
+̃P k
+i,j = Li
+Ki
+P k
+i,jζ(k+i)j.
+Lemma 2.6. For 0 ≤ i ≤ n − 1, we have
+̃P k
+Ion(i)−1,j = ̃P k
+i,j + 1
+LD ̃P k−1
+i,j
++ 1
+L (
+i
+∑
+r=0
+Xr − iDL
+L ) ̃P k−1
+i,j .
+Proof. This is just a reformulation of Lemma 1.13. The LHS of Lemma 1.13 becomes
+DP k−1
+i,j
+= (DKi
+Li
+− iKi
+Li
+DL
+L ) ̃P k−1
+i,j ζ−(k−1+i)j + Ki
+Li D ̃P k−1
+i,j ζ−(k−1+i)j
+
+22
+GENLIK AND TSENG
+and RHS of Lemma 1.13 becomes
+CIon(i)P k
+Ion(i)−1,j − P k
+i,jLζj =CIon(i)
+KIon(i)−1
+LIon(i)−1 ̃P k
+Ion(i)−1,jζ−(k−1+Ion(i))j − Ki
+Li−1 ̃P k
+i,jζ−(k−1+i)j
+= KIon(i)
+LIon(i)−1 ̃P k
+Ion(i)−1,jζ−(k−1+Ion(i))j − Ki
+Li−1 ̃P k
+i,jζ−(k−1+i)j
+= Ki
+Li−1 ̃P k
+Ion(i)−1,jζ−(k−1+i)j − Ki
+Li−1 ̃P k
+i,jζ−(k−1+i)j.
+Putting these together, using the definition of Ki, Corollary B.4 and cancelling out some common
+factors we obtain
+(DKi
+Ki
+− iDL
+L ) ̃P k−1
+i,j
++ D ̃P k−1
+i,j
+= ̃P k
+Ion(i)−1,jL − ̃P k
+i,jL.
+The rest follows from equation (2.2).
+□
+Now, we define the series Ai for 0 ≤ i ≤ n by
+Ai = 1
+L (iDL
+L −
+i
+∑
+r=0
+Xr).
+Set
+C[L±1][DA] ∶= C[L±1][A1,...,An−1,DA1,...,DAn−1,D2A1,...,D2An−1,...],
+and
+A ∶= {A1,...,Dn−3A1}∪,... ∪ {Ai,...,Dn−2−iAi} ∪ ... ∪ {An−2} = {DjAi}1≤i≤n−2,0≤j≤n−2−i.
+The following is immediate from Lemma 2.5.
+Corollary 2.7. C[L±1][DA] is a quotient of the ring C[L±1][A].
+In what follows we further simplify the ring C[L±1][A].
+Lemma 2.8. For the series Ai, we have the following
+(1) Ai = −An−i for all 0 ≤ i ≤ n,
+(2) A0 = An = 0, and A n
+2 = 0 if n is even,
+(3) ∑n
+i=0 Ai = 0.
+Proof. By Lemma B.3, we have Ci = Cn+1−i for all 1 ≤ i ≤ n. Hence, Xi = Xn+1−i for all 1 ≤ i ≤ n.
+This gives the following reformulation of equation (2.3) :
+i
+∑
+r=0
+Xr − iDL
+L = (n − i)DL
+L − (
+n−i
+∑
+r=0
+Xr)
+for all
+0 ≤ i ≤ n.
+This proves the first part of the lemma. The other two parts follow immediately.
+□
+Recall that by Lemma 2.6 we have
+̃P k
+Ion(i)−1,j = ̃P k
+i,j + 1
+LD ̃P k−1
+i,j
++ 1
+L (
+i
+∑
+r=0
+Xr − iDL
+L ) ̃P k−1
+i,j ,
+which is equivalent to
+(2.10)
+̃P k
+Ion(i)−1,j = ̃P k
+i,j + 1
+LD ̃P k−1
+i,j + An−i ̃P k−1
+i,j .
+We call (2.10) the modified flatness equations for [Cn/Zn].
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+23
+Now we analyze (2.10). Let k = 0. Then ̃P 0
+Ion(i)−1,j = ̃P 0
+i,j for all 0 ≤ i ≤ n − 1. This means
+̃P 0
+i,j = ̃P 0
+0,j for all 0 ≤ i ≤ n − 1. Now, let k = 1. Then, we have
+n−1
+∑
+i=0
+̃P 1
+Ion(i)−1,j
+������������������������������������������������������������
+(⋆)
+=
+n−1
+∑
+i=0
+̃P 1
+i,j
+����������������
+(⋆⋆)
++ 1
+LD
+n−1
+∑
+i=0
+̃P 0
+i,j +
+n−1
+∑
+i=0
+An−i ̃P 0
+0,j
+���������������������������������������������������
+(⋆⋆⋆)
+.
+Clearly, (⋆) and (⋆⋆) are the same and (⋆ ⋆ ⋆) is zero. Since ̃P 0
+i,j = ̃P 0
+0,j, the above equation is
+n
+LD ̃P 0
+0,j = 0.
+Hence, ̃P 0
+i,j = ̃P 0
+0,j is a constant whose value depends on the initial conditions. Now, the equations
+with k = 1 yield
+̃P 1
+n−1,j = ̃P 1
+0,j + An ̃P 0
+0,j
+̃P 1
+n−2,j = ̃P 1
+n−1,j + A1 ̃P 0
+0,j
+⋮
+̃P 1
+n−i,j = ̃P 1
+n−i+1,j + Ai−1 ̃P 0
+0,j.
+Adding these equations yields
+̃P 1
+n−i,j = ̃P 1
+0,j +
+i−1
+∑
+r=0
+Ar ̃P 0
+0,j
+for
+1 ≤ i ≤ n.
+Now, let k = 2 in equation (2.10) and plug the above equation into it, we find
+̃P 2
+Ion(i)−1,j = ̃P 2
+i,j + 1
+LD ̃P 1
+i,j + An−i ̃P 1
+i,j
+= ̃P 2
+i,j + 1
+LD ( ̃P 1
+0,j +
+n−i−1
+∑
+r=0
+Ar ̃P 0
+0,j) + An−i ( ̃P 1
+0,j +
+n−i−1
+∑
+r=0
+Ar ̃P 0
+0,j)
+= ̃P 2
+i,j + 1
+LD ̃P 1
+0,j + 1
+L
+n−i−1
+∑
+r=0
+(DAr) ̃P 0
+0,j + An−i ̃P 1
+0,j +
+n−i−1
+∑
+r=0
+An−iAr ̃P 0
+0,j.
+Summing this equality over 0 ≤ i ≤ n − 1, cancelling out ∑n−1
+i=0 ̃P 2
+Ion(i)−1,j = ∑n−1
+i=0 ̃P 2
+i,j, and noting
+that ∑n−1
+i=0 An−i ̃P 1
+0,j = 0, we obtain
+(2.11)
+n
+LD ̃P 1
+0,j + 1
+L
+n−1
+∑
+i=0
+n−i−1
+∑
+r=0
+(DAr) ̃P 0
+0,j +
+n−1
+∑
+i=0
+n−i−1
+∑
+r=0
+An−iAr ̃P 0
+0,j = 0.
+Set k = 1 in Corollary 1.16, we obtain
+Lj,1(P 1
+0,j) + 1
+Lj
+Lj,2(P 0
+0,j) = 0
+which reads as
+nDP 1
+0,j + 1
+Lj
+(n + 1
+4 )(Y 2 − Y )P 0
+0,j − 1
+Lj
+(n
+2)Y DP 0
+0,j + 1
+Lj
+(n
+2)D2P 0
+0,j = 0.
+Since P 0
+0,j = ̃P 0
+0,j is constant and P 1
+0,j = ζ−j ̃P 1
+0,j, the equation becomes
+nD ̃P 1
+0,j + 1
+L(n + 1
+4 )Y (Y − 1)P 0
+0,j = 0.
+
+24
+GENLIK AND TSENG
+By the definition of Y in (B.8), we obtain
+D ̃P 1
+0,j =1
+n
+1
+L(n + 1
+4 )Y (1 − Y ) ̃P 0
+0,j
+=(−1)n−1
+n
+(n + 1
+4 )(1 + (−1)n Ln
+nn ) Ln−1
+nn ̃P 0
+0,j ∈ C[L±1].
+Define fn(L) ∈ C[L±1] to be the right hand side of above equation without ̃P 0
+0,j:
+fn(L) = (−1)n−1
+n
+(n + 1
+4 )(1 + (−1)n Ln
+nn ) Ln−1
+nn .
+Lemma 2.9. For any n ≥ 3, we have
+n−1
+∑
+i=0
+n−i−1
+∑
+r=0
+DAr =
+⌊ n−1
+2 ⌋
+∑
+r=1
+(n − 2r)DAr
+and
+n−1
+∑
+i=0
+n−i−1
+∑
+r=0
+An−iAr = −
+⌊ n−1
+2 ⌋
+∑
+r=1
+A2
+r.
+Proof. This follows from the fact that Ai = −An−i.
+□
+By equations (2.11) and (2.2), we obtain the following
+Lemma 2.10. For any n ≥ 3, we have
+n
+Lfn(L) + 1
+L
+⌊ n−1
+2 ⌋
+∑
+r=1
+(n − 2r)(DAr) −
+⌊ n−1
+2 ⌋
+∑
+r=1
+A2
+r = 0.
+Equivalently, dividing into even and odd cases, we have
+2DAs−1 =
+s−1
+∑
+r=1
+LA2
+r −
+s−2
+∑
+r=1
+(n − 2r)DAr − 2sf2s(L)
+if
+n = 2s ≥ 4,
+DAs =
+s
+∑
+r=1
+LA2
+r −
+s−1
+∑
+r=1
+(n − 2r)DAr − (2s + 1)f2s+1(L)
+if
+n = 2s + 1 ≥ 3.
+Equations in Lemma 2.10 are generalizations7 of equation (9) in [14, Section 3] and second
+equation in [17, Lemma 9].
+Let n ≥ 3 be an odd number with n = 2s + 1, define
+Sodd = {A1,... ,Dn−3A1} ∪ ⋯ ∪ {As−1,... ,Dn−s+1As−1} ∪ {As}.
+Similarly, let n ≥ 4 be an even number with n = 2s, define
+Seven = {A1,... ,Dn−3A1} ∪ ⋯ ∪ {As−2,... ,Dn−sAs−2} ∪ {As−1}.
+In either case, we denote both Sodd, and Seven as Sn.
+Proposition 2.11. C[L±1][DA] is a quotient of the ring C[L±1][Sn].
+Proof. This follows easily from Lemmas 2.5, 2.8, and 2.10.
+□
+As in [16] and [17], we do not know if there are any further polynomial relations among the
+elements of the differential graded algebra C[L±1][DA].
+7For n = 5, this generalization is explained in more detail by matching the functions in [14] with ours.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+25
+3. HOLOMORPHIC ANOMALY EQUATIONS
+3.1. More on flatness equation. The modified flatness equations (2.10), Lemma 2.1, and Corol-
+lary 1.15 imply that ̃P k
+i,j ∈ C[L±1][DA]. Through Lemmas 2.5, 2.8, 2.10, and the modified flatness
+equations (2.10), we have a canonical lift of each ̃P k
+i,j to the free algebra C[L±1][Sn] via the fol-
+lowing order:
+̃P k
+n−1,j = ̃P k
+0,j + 1
+LD ̃P k−1
+0,j ∈ C[L±1] ⊆ C[L±1][Sn]
+̃P k
+n−2,j = ̃P k
+n−1,j + 1
+LD ̃P k−1
+n−1,j + A1 ̃P k−1
+n−1,j ∈ C[L±1][A1] ⊆ C[L±1][Sn]
+⋮
+=
+⋮
+(3.1)
+More precisely, we start with ̃P k
+0,j ∈ C[L±1] and use equation (2.10) for i = n,n − 1,...,2 in this
+descending order to inductively construction lifts of ̃P k
+i,j for i = n − 1,n − 2,...,1 in this descending
+order. In this process, unnecessary Ai’s are eliminated using Lemmas 2.8 and 2.10, and orders of
+derivatives are bounded above using Lemma 2.5.
+In the rest of this subsection, we consider this lift and denote it also as
+̃P k
+i,j ∈ C[L±1][Sn].
+Lemma 3.1 (Odd case). Let n ≥ 3 be an odd number with n = 2l+1. We have the following identity
+∂ ̃P k
+i,j
+∂Al
+= δi,l ̃P k−1
+l+1,j.
+Proof. From the modified flatness equations (2.10), and the lifting procedure (3.1) we have
+(3.2)
+∂ ̃P k
+i,j
+∂Al
+= 0
+for l + 1 ≤ i ≤ n − 1 and i = 0 since ̃P k
+i,j does not contain Al term. Now observe the following two
+equations
+̃P k
+l,j = ̃P k
+l+1,j + 1
+LD ̃P k−1
+l+1,j + Al ̃P k−1
+l+1,j ,
+(3.3)
+̃P k
+l−1,j = ̃P k
+l,j + 1
+LD ̃P k−1
+l,j
+− Al ̃P k−1
+l,j .
+(3.4)
+These are first two rows in modified flatness equations where we see Al. From the first equation
+we see that
+∂ ̃P k
+l,j
+∂Al
+= ̃P k−1
+l+1,j.
+Note that Lemma 2.10 gives
+(3.5)
+∂ (DAl)
+∂Al
+= 2LAl.
+Then, by equations (3.4) and (3.5) we have
+∂ ̃P k
+l−1,j
+∂Al
+=
+∂ ̃P k
+l,j
+∂Al
++ 1
+L
+∂ (D ̃P k−1
+l,j )
+∂Al
+− ̃P k−1
+l,j
+− Al
+∂ ̃P k−1
+l,j
+∂Al
+=
+∂ ̃P k
+l,j
+∂Al
++ 1
+L (2LAl ̃P k−2
+l+1,j + D ̃P k−2
+l+1,j) − ̃P k−1
+l,j
+− Al
+∂ ̃P k−1
+l,j
+∂Al
+,
+(3.6)
+
+26
+GENLIK AND TSENG
+and equation (3.3) implies that
+∂ ̃P k
+l−1,j
+∂Al
+= ̃P k−1
+l+1,j + 2Al ̃P k−2
+l+1,j + 1
+LD ̃P k−2
+l+1,j − ̃P k−1
+l,j
+− Al ̃P k−2
+l+1,j
+= ̃P k−1
+l+1,j + Al ̃P k−2
+l+1,j + 1
+LD ̃P k−2
+l+1,j − ̃P k−1
+l,j
+=0.
+(3.7)
+It immediately follows from the modified flatness equations and equation (3.7) that
+∂ ̃P k
+i,j
+∂Al
+= 0
+for 0 ≤ i ≤ l − 1 since ̃P k
+i,j does not contain any Al term. This completes the proof.
+□
+Lemma 3.2 (Even case). Let n ≥ 4 be an even number with n = 2l. We have the following identity
+∂ ̃P k
+i,j
+∂Al−1
+= δi,l ̃P k−1
+l+1,j + δi,(l−1) ̃P k−1
+l,j .
+Proof. From the modified flatness equations (2.10), and the lifting procedure (3.1) we have
+(3.8)
+∂ ̃P k
+i,j
+∂Al−1
+= 0
+for l+1 ≤ i ≤ n − 1 and i = 0 since ̃P k
+i,j does not contain Al−1 term. Observe the following equations
+̃P k
+l,j = ̃P k
+l+1,j + 1
+LD ̃P k−1
+l+1,j + Al−1 ̃P k−1
+l+1,j
+̃P k
+l−1,j = ̃P k
+l,j + 1
+LD ̃P k−1
+l,j
+̃P k
+l−2,j = ̃P k
+l−1,j + 1
+LD ̃P k−1
+l−1,j − Al−1 ̃P k−1
+l−1,j.
+(3.9)
+Two of these equations are first two rows in modified flatness equations where we see Al−1. From
+the first equation we see that
+∂ ̃P k
+l,j
+∂Al−1
+= ̃P k−1
+l+1,j.
+Note that by Lemma 2.10, we have
+∂ (DAl−1)
+∂Al−1
+= LAl−1.
+This implies
+∂ ̃P k
+l−1,j
+∂Al−1
+=
+∂ ̃P k
+l,j
+∂Al−1
++ 1
+L
+∂ (D ̃P k−1
+l,j )
+∂Al−1
+= ̃P k−1
+l+1,j + 1
+L (LAl−1 ̃P k−2
+l+1,j + D ̃P k−2
+l+1,j)
+= ̃P k−1
+l,j .
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+27
+The equalities obtained so far simply show that ̃P k
+l−1,j is of degree 2 with respect to Al−1. Let ̃P k
+l−1,j
+be given by
+̃P k
+l−1,j = K A2
+l−1
+2
++ HAl−1 + Q
+where K, H, are constants with respect to Al−1. Then, we see that K and H are given by
+K = ̃P k−2
+l+1,j
+and
+H = ̃P k−1
+l,j
+− ̃P k−2
+l+1,jAl−1 = ̃P k−1
+l+1,j + 1
+LD ̃P k−2
+l+1,j.
+We will need the following intermediate calculation to complete the proof:
+∂(D ̃P k
+l−1,j)
+∂Al−1
+=
+∂
+∂Al−1
+((DK)A2
+l−1
+2
++ KAl−1DAl−1 + (DH)Al−1 + H(DAl−1) + DQ)
+=(DK)Al−1 + K(DAl−1) + KLA2
+l−1 + DH + LHAl−1
+=(D ̃P k−2
+l+1,j)Al−1 + ̃P k−2
+l+1,j(DAl−1) + L ̃P k−2
+l+1,jA2
+l−1
++ D ̃P k−1
+l,j
+− (D ̃P k−2
+l+1,j)Al−1 − ̃P k−2
+l+1,j(DAl−1) + L ̃P k−1
+l,j Al−1 − L ̃P k−2
+l+1,jA2
+l−1
+=D ̃P k−1
+l,j
++ L ̃P k−1
+l,j Al−1.
+Next, we compute
+∂ ̃P k
+l−2,j
+∂Al−1
+=
+∂ ̃P k
+l−1,j
+∂Al−1
++ 1
+L
+∂ (D ̃P k−1
+l−1,j)
+∂Al−1
+− ̃P k−1
+l−1,j − Al−1
+∂ ̃P k−1
+l−1,j
+∂Al−1
+= ̃P k−1
+l,j
++ 1
+LD ̃P k−2
+l,j
++ ̃P k−2
+l,j Al−1 − ̃P k−1
+l−1,j − Al−1 ̃P k−2
+l,j
+= ̃P k−1
+l,j
++ 1
+LD ̃P k−2
+l,j
+− ̃P k−1
+l−1,j = 0.
+(3.10)
+It immediately follows from the modified flatness equations and equation (3.10) that
+∂ ̃P k
+i,j
+∂Al−1
+= 0
+for 0 ≤ i ≤ l − 2 since ̃P k
+i,j does not contain any Al−1 term. This completes the proof.
+□
+3.2. Formula for potentials.
+3.2.1. Semisimple Cohomological Field Theories. By general considerations, Gromov-Witten the-
+ory of [Cn/Zn] has the structure of a cohomological field theory (CohFT). We refer to [12] and [20]
+for discussions on CohFTs.
+By the results of Section 1, this CohFT is semisimple. The Givental-Teleman classification of
+semisimple CohFTs [10], [23] states that a semisimple CohFT Ω can be obtained from its topolog-
+ical part via the actions of its R-matrix and T-vector, where T(z) is given by z(Id −R(z)) applied
+to the unit. We refer to [20] and [21] for detailed discussions on this.
+Generating functions of a CohFT Ω can be defined by integrating CohFT classes. If Ω is semisim-
+ple, its topological part can be evaluated explicitly in the idempotent basis, see e.g. [17, Section
+2.5.1]. A consequence of the Givental-Teleman classification is that the generating functions of Ω
+can be explicitly written as sums of graphs. A reference for this can be found in [17, Section 2.5.2].
+
+28
+GENLIK AND TSENG
+The R-matrix for the Gromov-Witten theory of [Cn/Zn] is studied in Section 1. The general
+consideration on semisimple CohFTs recalled above yields a formula for the Gromov-Witten po-
+tential F [Cn/Zn]
+g,m
+(φc1,... ,φcm). In the remainder of this subsection, we work out this formula in
+details.
+3.2.2. Graphs. In order to state the formula for Gromov-Witten potentials, we need to describe
+certain graphs.
+A stable graph Γ is a tuple
+Γ = (VΓ,g ∶ VΓ → Z≥0,HΓ,ι ∶ HΓ → HΓ,LΓ,ℓ ∶ LΓ → {1,... ,m},ν ∶ HΓ ∪ LΓ → VΓ)
+satisfying:
+(1) VΓ is the set of vertices and g ∶ VΓ → Z≥0 is a genus assignment,
+(2) HΓ is the set of half-edges and ι ∶ HΓ → HΓ is an involution,
+(3) EΓ is the set of edges8 defined by the orbits of ι ∶ HΓ → HΓ, and the tuple (VΓ,EΓ) defines
+a connected graph,
+(4) LΓ is the set of legs and ℓ ∶ LΓ → {1,... ,m} is an isomorphism labeling legs,
+(5) The map ν ∶ HΓ ∪ LΓ → VΓ is a vertex assignment,
+(6) For each vertex v, let l(v) and h(v) be the number of legs and the number of edges attached
+to the vertex v respectively and hence n(v) = l(v) + h(v) be the valence of the vertex v.
+Then, for each vertex v the following (stability) condition holds:
+2g(v) − 2 + n(v) > 0.
+The genus of Γ is defined by
+g(Γ) = h1(Γ) + ∑
+v∈V
+g(v).
+In the formula for Gromov-Witten potentials, we need to work with decorated stable graphs.
+This has to do with the T-action on CohFTs. To see this, we recall the description of the T-actions
+in general, as follows. Let Ω be a CohFT based on the vector space V and let
+T(z) = T2z2 + T3z3 + ⋯
+be a V -valued power series with vanishing coefficients in degrees 0 and 1. The translation of Ω by
+T is the CohFT TΩ defined by
+TΩg,m (v1,... ,vm) = ∑
+k⩾0
+1
+k! (πk)∗ Ωg,m+k (v1,... ,vm,T (ψm+1),... ,T (ψm+k))
+where πk ∶ M g,m+k → Mg,m is the forgetful map dropping the last k marked points. Here, by above
+notation, we actually mean
+Ωg,m+k (... ,T (ψi),...) = ∑
+r⩾2
+ψr
+i Ωg,m+k (... ,Tr,...).
+Now, consider elements of V written in terms of the normalized idempotent basis,
+vj =
+n−1
+∑
+i=0
+vij̃ei
+and
+Tr =
+n−1
+∑
+i=0
+Tir̃ei.
+8self-edges are allowed
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+29
+Then, assume in addition9 that Ω is a topological field theory, we have
+TΩg,m (v1,... ,vm) = ∑
+k⩾0
+1
+k! (πk)∗ Ωg,m+k (v1,... ,vm,T (ψm+1),... ,T (ψm+k))
+= ∑
+k⩾0
+1
+k!
+∑
+r1,...,rk≥2
+(
+k
+∏
+l=1
+(πk)∗ (ψrl
+m+l))Ωg,m+k (v1,... ,vm,Tr1,... ,Trk)
+= ∑
+k⩾0
+1
+k!
+∑
+r1,...,rk≥2
+(
+k
+∏
+l=1
+(πk)∗ (ψrl
+m+l))
+×
+∑
+0≤i1,...,im+k≤n−1
+vi11⋯vimmTim+1r1⋯Tim+krkΩg,m+k (̃ei1,... ,̃eim,̃eim+1,... ,̃eim+k)
+= ∑
+k⩾0
+1
+k!
+∑
+r1,...,rk≥2
+(
+k
+∏
+l=1
+(πk)∗ (ψrl
+m+l))
+n−1
+∑
+i=0
+vi1⋯vimTir1⋯Tirkg(ei,ei)− 2g−2+m+k
+2
+=
+n−1
+∑
+i=0
+vi1⋯vim ∑
+k≥0
+g(ei,ei)− 2g−2+m+k
+2
+k!
+∑
+r1,...,rk≥2
+Tir1⋯Tirk (
+k
+∏
+l=1
+(πk)∗ (ψrl
+m+l))
+=
+n−1
+∑
+i=0
+vi1⋯vim ∑
+k≥0
+g(ei,ei)− 2g−2+m+k
+2
+k!
+(πk)∗ (ti(ψm+1)⋯ti(ψm+k)),
+(3.11)
+where
+ti(z) = ∑
+r≥2
+Tirzr.
+Note that the above derivation uses the explicit evaluation of a topological field theory in the nor-
+malized idempotent basis, c.f. [17, Section 2.5.1].
+Setting the summand of TΩg,m (v1,... ,vm) to
+̃Ωi
+g,m (v1,... ,vm) = vi1⋯vim ∑
+k≥0
+g(ei,ei)− 2g−2+m+k
+2
+k!
+(πk)∗ (ti(ψm+1)⋯ti(ψm+k))
+we can write it as
+(3.12)
+TΩg,m (v1,... ,vm) =
+n−1
+∑
+i=0
+̃Ωi
+g,m (v1,... ,vm).
+By the formula for generating functions, as described in [17, Section 2.5.2], for each vertex in a
+stable graph, a class TΩg,m is inserted. By equation (3.12), this is equivalent to inserting ̃Ωig,m if
+vertices of stable graphs carry extra labels i. This leads to the notion of decorated stable graphs.
+More precisely, a decorated stable graph
+Γ ∈ GDec
+g,m(n)
+of order n is a stable graph Γ ∈ Gg,m with an extra assignment p ∶ VΓ → {0,...,n−1} to each vertex
+v ∈ VΓ.
+9This case suffices for our purpose, because in the formula for Fg,m from Givental-Teleman classification, T acts
+on the topological part.
+
+30
+GENLIK AND TSENG
+3.2.3. Formula for Fg. By the discussions above, we have
+(3.13)
+F [Cn/Zn]
+g,m
+(φc1,... ,φcm) =
+∑
+Γ∈GDec
+g,m(n)
+ContΓ (φc1,... ,φcm).
+The following is the generalization of Proposition 15 of [16] to [Cn/Zn].
+Proposition 3.3. For each decorated stable graph Γ ∈ GDec
+g,m(n), the associated contribution is
+given by
+ContΓ (φc1,... ,φcm) =
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+∏
+v∈VΓ
+ContA
+Γ(v) ∏
+e∈EΓ
+ContA
+Γ(e) ∏
+l∈LΓ
+ContA
+Γ(l)
+where F(Γ) = ∣HΓ ∪ LΓ∣ = m + ∣HΓ∣. Here, ContA
+Γ(v), ContA
+Γ(e), and ContA
+Γ(l) are the vertex,
+edge and leg contributions with flag A−values10 (a1,... ,am,b1,... ,b∣HΓ∣) respectively, and they
+are given by
+ContA
+Γ(v) = ∑
+k≥0
+g(ep(v),ep(v))− 2g−2+n(v)+k
+2
+k!
+× ∫Mg(v),n(v)+k
+ψav1
+1 ⋯ψ
+avl(v)
+l(v) ψbv1
+l(v)+1⋯ψ
+bvh(v)
+n(v) tp(v)(ψn(v)+1)⋯tp(v)(ψn(v)+k),
+ContA
+Γ(e) =(−1)be1+be2
+n
+be2
+∑
+j=0
+(−1)j
+n−1
+∑
+r=0
+̃P be1+j+1
+Inv(r),p(v1) ̃P be2−j
+r,p(v2)
+ζ(be1+j+1+Inv(r))p(v1)ζ(be2−j+r)p(v2),
+ContA
+Γ(l) =(−1)aℓ(l)
+n
+KInv(cℓ(l))
+LInv(cℓ(l))
+̃P
+aℓ(l)
+Inv(cℓ(l)),p(ν(l))
+ζ(aℓ(l)+Inv(cℓ(l)))p(ν(l)) ,
+where
+tp(v)(z) = ∑
+i≥2
+Tp(v)izi
+with
+Tp(v)i = (−1)i
+n
+̃P i
+0,p(v)ζ−ip(v).
+Proof. To simplify notations, write {˜e} for the normalized idempotent basis {˜e0,... , ˜en−1} and {φ}
+for the basis {φ0,... ,φn−1}. Let T φ
+˜e be the transition matrix from {˜e} to {φ} and let T ˜e
+φ be its
+inverse i.e. the transition matrix from {φ} to {˜e}. Then, we have
+T φ
+˜e = Ψ−1,
+T ˜e
+φ = Ψ.
+Let G and ̃G be matrix representations of the metric g with respect to basis {φ} and {˜e}. Then,
+the relation between them is given by
+(3.14)
+̃G = (Ψ−1)
+T GΨ−1.
+And it can easily be shown that we have ̃G = Id.
+Define T(z) = z (Id − R−1(z)) ⋅ φ0. We provided R-matrix action with respect to normalized
+idempotent basis. To be consistent we need to write φ0 in terms of {˜e} basis. Since we have
+(3.15)
+φ0 =
+n−1
+∑
+i=0
+Ψi0˜ei = 1
+n (˜e0 + ... + ˜en−1),
+we see that T(z) = z (Id − R−1(z)) v where v = 1
+n[1⋯1]T .
+10Notation: The values bv1,... ,bvh(v) and be1,be2 are the entries of (a1,... ,am,b1,... ,b∣HΓ∣) corresponding to
+ContA
+Γ(v) and ContA
+Γ(e) respectively.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+31
+We now find R−1(z). By the symplectic condition, R−1(z) = Rt(−z). Here Rt(−z) means
+adjoint with respect to the metric g in the basis {˜e}. We see that
+(3.16)
+R−1(z) = Rt(−z) = ̃G−1RT(−z) ̃G = RT (−z) = (ΨP(−z))T = P T(−z)ΨT .
+Also observe that
+[ΨTv]i =1
+n
+n−1
+∑
+j=0
+ΨT
+ij = 1
+n
+n−1
+∑
+j=0
+Ψji
+=1
+n
+n−1
+∑
+j=0
+1
+nζij Li
+Ki
+= 1
+n2
+Li
+Ki
+n−1
+∑
+j=0
+ζij = 1
+n2nδi0 = 1
+nδi0.
+(3.17)
+So, we have ΨTv = 1
+n [10⋯0]T. This implies that
+(3.18)
+T(z) = z (Id − R−1(z)) v = T2z2 + T3z3 + ⋯
+with Tk is the coefficient of zk−1 in −R−1(z)v where
+Tjk = the jth entry of the coefficient of zk−1 in − R−1(z)v
+= the jth entry of the coefficient of zk−1 in − P T(−z)ΨT v
+= (−1)k
+n
+P k
+0j.
+(3.19)
+This enables us to understand the translation action by T(z) and vertex contributions after the
+translation action. Next, we will understand effects of R-matrix action and obtain the expressions
+for the contributions fully.
+Now, consider
+F(z,w) = M(z,w)
+z + w
+with both F(z,w),M(z,w) ∈ C[[z,w]],
+F(z,w) = ∑
+a,b≥0
+βa,bzawb
+and
+M(z,w) = ∑
+c,d≥0
+αc,dzcwd.
+Then, the coefficients βa,b are given by
+(3.20)
+βa,b =
+b
+∑
+m=0
+(−1)mαa+m+1,b−m.
+Now observe that
+[ΨTΨ]lj =
+n−1
+∑
+r=0
+ΨrlΨrj =
+n−1
+∑
+r=0
+1
+nζrl Ll
+Kl
+1
+nζrj Lj
+Kj
+= 1
+n2
+Ll
+Kl
+Lj
+Kj
+n−1
+∑
+r=0
+ζr(l−Inv(j)) = 1
+n2
+Ll
+Kl
+Lj
+Kj
+nδlInv(j)
+= 1
+n
+LInv(j)+j
+KInv(j)Kj
+�����������������������������������������
+=1
+δlInv(j) = 1
+nδlInv(j).
+(3.21)
+
+32
+GENLIK AND TSENG
+Next, in order to understand the edge contributions, we compute
+δij − [R−1(z)R−1(w)T]ij = δij −
+n−1
+∑
+s,r=0
+P T
+i,s(−z)[ΨTΨ]sr Pr,j(−w)
+= δij −
+n−1
+∑
+s,r=0
+P T
+i,s(−z)1
+nδsInv(r)Pr,j(−w)
+= δij − 1
+n
+n−1
+∑
+r=0
+P T
+i,Inv(r)(−z)Pr,j(−w)
+= δij − 1
+n
+n−1
+∑
+r=0
+∑
+c,d≥0
+(−1)c+dP c
+Inv(r),iP d
+r,jzcwd
+= δij − 1
+n
+n−1
+∑
+r=0
+∑
+c,d≥0
+(−1)c+dKInv(r)
+LInv(r)
+̃P c
+Inv(r),i
+ζ−(c+Inv(r))i
+Kr
+Lr
+̃P d
+r,j
+ζ−(d+r)j zcwd
+= δij − 1
+n
+n−1
+∑
+r=0
+∑
+c,d≥0
+(−1)c+d
+̃P c
+Inv(r),i ̃P d
+r,j
+ζ−(c+Inv(r))iζ−(d+r)j zcwd.
+(3.22)
+So, we have
+(3.23)
+δij − [R−1(z)R−1(w)T]ij
+z + w
+=
+∑
+b1,b2≥0
+βi,j
+b1,b2zb1wb2
+with
+(3.24)
+βi,j
+b1,b2 = (−1)b1+b2
+n
+b1
+∑
+m=0
+(−1)m
+n−1
+∑
+r=0
+̃P b1+m+1
+Inv(r),i ̃P b2−m
+r,j
+ζ−(b1+m+1+Inv(r))iζ−(b2−m+r)j
+by equation (3.20).
+In order to understand the leg contributions, we compute
+[R−1(z) ⋅ φj]i = [P T(−z)ΨT Ψ]ij = ∑
+a≥0
+(−1)a
+n−1
+∑
+r=0
+P a
+r,i
+1
+nδrInv(j)za
+= ∑
+a≥0
+(−1)a
+n
+KInv(j)
+LInv(j)
+̃P a
+Inv(j),i
+ζ−(a+Inv(j))iza
+(3.25)
+for each 0 ≤ i,j ≤ n − 1.
+Let v ∈ VΓ be a vertex of a decorated stable graph Γ with legs {lv1,... ,lvl(v)} ⊆ LΓ and edges
+{ev1,... ,evh(v)}. Then, the (cycle-valued) contribution associated to this vertex, its legs and edges
+connected to this vertex is11
+̃Ωp(v)
+g(v),l(v)+h(v)(R−1(ψ1)⋅φcℓ(lv1),... ,R−1(ψl(v)) ⋅ φcℓ(lvl(v)),̃ep(v),... ,̃ep(v)
+�����������������������������������������������������������������������
+h(v) many
+)
+×
+h(v)
+∏
+i=1
+⎛
+⎜
+⎝
+∑
+bevi,be′
+i≥0
+β
+p(v),p(v′
+i)
+bevi,be′
+i
+ψ
+bevi
+l(v)+iψ
+be′
+i
+l(v′
+i)+j
+⎞
+⎟
+⎠
+.
+11Notation: Here v′
+i is the vertex at the other end of the edge evi and ψl(v′
+i)+j is the psi class associated to the marked
+point corresponding to the other half of the edge evi.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+33
+This together with equations (3.11), (3.24), and (3.25) complete the proof after integration of cycle-
+valued contributions of graph Γ over M g,m and using functoriality of push-forward.
+□
+An immediate corollary of Proposition 3.3 is the following finite generation property of the
+Gromov-Witten potential F [Cn/Zn]
+g,m
+(φc1,... ,φcm).
+Corollary 3.4. The vertex, edge, and leg contributions of ContΓ (φc1,... ,φcm) lie in certain poly-
+nomial rings. More, precisely
+ContA
+Γ(v) ∈ C[L±1],
+ContA
+Γ(e) ∈ C[L±1][Sn],
+ContA
+Γ(e) ∈ C[L±1][Sn][Cn]
+where Cn = {C1,... ,Cn−1}. Hence, we have
+F [Cn/Zn]
+g,m
+(φc1,... ,φcm) ∈ C[L±1][Sn][Cn].
+Proof. This is immediate from Lemma 1.15, Proposition 3.3 and the modified flatness equations
+(2.10).
+□
+We should note that Ci’s are related to each other via Lemma B.3, hence Cn consists of C1,... ,C⌊ n+1
+2 ⌋.
+Also, we should emphasize that the Gromov-Witten potential F [Cn/Zn]
+g,m
+(φc1,... ,φcm) may lie in a
+smaller ring depending on insertions. For example, Fg lies in C[L±1][Sn].
+The following two lemmas are cruicial for the proof of holomoprhic anomaly equations.
+Lemma 3.5. Let n ≥ 3 be an odd number with n = 2s + 1, then we have
+∂
+∂As
+ContA
+Γ(e) = (−1)be1+be2
+2s + 1
+̃P be1
+s+1,p(v1) ̃P be2
+s+1,p(v2)
+ζ(be1+s+1)p(e1)ζ(be2+s+1)p(v2).
+Proof. The proof is the following direct computation:
+∂
+∂As
+ContA
+Γ(e) =(−1)be1+be2
+n
+be2
+∑
+m=0
+(−1)m
+n−1
+∑
+r=0
+∂
+∂As ( ̃P be1+m+1
+Inv(r),p(v1) ̃P be2−m
+r,p(v2))
+ζ(be1+m+1+Inv(r))p(v1)ζ(be2−m+r)p(v2)
+=(−1)be1+be2
+n
+be2
+∑
+m=0
+(−1)m
+̃P be1+m
+s+1,p(v1) ̃P be2−m
+s+1,p(v2)
+ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)
++ (−1)be1+be2
+n
+be2−1
+∑
+m=0
+(−1)m
+̃P be1+m+1
+s+1,p(v1) ̃P be2−m−1
+s+1,p(v2)
+ζ(be1+m+s+2)p(v1)ζ(be2−m+s)p(v2)
+=(−1)be1+be2
+n
+be2
+∑
+m=0
+(−1)m
+̃P be1+m
+s+1,p(v1) ̃P be2−m
+s+1,p(v2)
+ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)
++ (−1)be1+be2
+n
+be2
+∑
+m=1
+(−1)m−1
+̃P be1+m
+s+1,p(v1) ̃P be2−m
+s+1,p(v2)
+ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)
+=(−1)be1+be2
+2s + 1
+̃P be1
+s+1,p(v1) ̃P be2
+s+1,p(v2)
+ζ(be1+s+1)p(v1)ζ(be2+s+1)p(v2).
+The first equality is just the derivative of the edge contribution part of Proposition 3.3. The second
+equality follows from Lemma 3.1 and ̃P k
+i,j = 0 by definition if k < 0. The rest is just shifting the
+index of the first sum and cancelling out the terms of the total expression.
+□
+
+34
+GENLIK AND TSENG
+Lemma 3.6. Let n ≥ 4 be an even number with n = 2s, then we have
+∂
+∂As−1
+ContA
+Γ(e) = (−1)be1+be2
+2s
+⎛
+⎝
+̃P be1
+s+1,p(v1) ̃P be2
+s,p(v2)
+ζ(be1+s+1)p(v1)ζ(be2+s)p(v2) +
+̃P be1
+s,p(v1) ̃P be2
+s+1,p(v2)
+ζ(be1+s)p(v1)ζ(be2+s+1)p(v2)
+⎞
+⎠ .
+Proof. The proof is similar to that of Lemma 3.5. In this case, we use Lemma 3.2 instead of Lemma
+3.1.
+□
+3.3. Proof of holomorphic anomaly equations. We are now ready to present the main results of
+this paper. The results depend on the parity of n.
+Theorem 3.7. Let n ≥ 3 be an odd number with n = 2s + 1, and g ≥ 2. We have
+Cs+1
+(2s + 1)L
+∂
+∂As
+F [Cn/Zn]
+g
+= 1
+2F [Cn/Zn]
+g−1,2
+(φs,φs) + 1
+2
+g−1
+∑
+i=1
+F [Cn/Zn]
+g−i,1
+(φs)F [Cn/Zn]
+i,1
+(φs)
+in C[L±1][Sn][Cs+1].
+Proof. Let ˜e ∈ EΓ be an edge of a decorated stable graph Γ ∈ GDec
+g,0 (n) and let ˜e ∈ EΓ be connecting
+two vertices v1 and v2. Deletion of the edge ˜e results in a new graph. (By deletion, we imply that
+we break the edge ˜e into two new legs l˜e and l′
+˜e.) There are two possibilities: either the resulting
+graph is connected or it is disconnected with two connected parts.
+(i) If the resulting graph is connected, then it is an element of GDec
+g−1,2(n). In this case, we
+denote the resulting graph as Γ0
+˜e. In this case, note that ∣Aut(Γ)∣ = ∣Aut(Γ0
+˜e)∣.
+(ii) If the resulting graph is disconnected, then we denote its connected components as Γ1
+˜e ∈
+GDec
+g1,1(n) and Γ2
+˜e ∈ GDec
+g2,1(n) where g = g1 + g2. In this case, for the cardinality of the auto-
+morphism groups of the decorated stable graphs, we have12 ∣Aut(Γ)∣ = ∣Aut(Γ1
+˜e)∣∣Aut(Γ2
+˜e)∣.
+By Proposition 3.3 and Lemma 3.5, we observe that
+∂ContA
+Γ(˜e)
+∂As
+=(−1)b˜e1+b˜e2
+2s + 1
+̃P b˜e1
+s+1,p(v1) ̃P b˜e2
+s+1,p(v2)
+ζ(b˜e1+s+1)p(v1)ζ(b˜e2+s+1)p(v2)
+=(2s + 1)( Ls+1
+Ks+1
+)
+2 ⎧⎪⎪⎨⎪⎪⎩
+ContA
+Γ0
+˜e(l˜e)ContA
+Γ0
+˜e(l′
+˜e)
+for the case (i),
+ContA
+Γ1
+˜e(l˜e)ContA
+Γ2
+˜e(l′
+˜e)
+for the case (ii).
+Using Lemma B.4, we also note that
+( Ls+1
+Ks+1
+)
+2
+=
+L
+Cs+1
+.
+Then, for case (i), we easily see that we have
+ContΓ0
+˜e (φs,φs) =
+1
+∣Aut(Γ0
+˜e)∣
+∑
+A∈Z
+F(Γ0
+˜e )
+≥0
+∏
+v∈VΓ0
+˜e
+ContA
+Γ0
+˜e(v) ∏
+e∈EΓ0
+˜e
+ContA
+Γ0
+˜e(e) ∏
+l∈LΓ0
+˜e
+ContA
+Γ0
+˜e(l)
+=
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+Cs+1
+(2s + 1)L
+∂ContA
+Γ(˜e)
+∂As
+∏
+v∈VΓ
+ContA
+Γ(v) ∏
+e∈EΓ
+e≠˜e
+ContA
+Γ(e).
+(3.26)
+12There is a special case when Γ1
+˜e = Γ2
+˜e. In this case Γ has a Z2-symmetry given by interchanging Γ1
+˜e and Γ2
+˜e. Hence
+∣Aut(Γ)∣ = ∣Aut(Γ1
+˜e)∣2 × 2.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+35
+Similarly, for case (ii), we observe the following
+ContΓ1
+˜e (φs)ContΓ2
+˜e (φs)
+=
+1
+∣Aut(Γ1
+˜e)∣
+∑
+A∈Z
+F(Γ1
+˜e )
+≥0
+ContA
+Γ1
+˜e(l˜e) ∏
+v∈VΓ1
+˜e
+ContA
+Γ1
+˜e(v) ∏
+e∈EΓ1
+˜e
+ContA
+Γ1
+˜e(e)
+×
+1
+∣Aut(Γ2
+˜e)∣
+∑
+A∈Z
+F(Γ2
+˜e )
+≥0
+ContA
+Γ2
+˜e(l′
+˜e) ∏
+v∈VΓ2
+˜e
+ContA
+Γ2
+˜e(v) ∏
+e∈EΓ2
+˜e
+ContA
+Γ2
+˜e(e)
+=
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+Cs+1
+(2s + 1)L
+∂ContA
+Γ(˜e)
+∂As
+∏
+v∈VΓ
+ContA
+Γ(v) ∏
+e∈EΓ
+e≠˜e
+ContA
+Γ(e).
+(3.27)
+By Corollary 3.4, we have the following vanishing result
+∂ContA
+Γ(v)
+∂As
+= 0
+for any vertex v ∈ VΓ. This vanishing result gives us:
+∂ContΓ
+∂As
+=
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+∏
+v∈VΓ
+ContA
+Γ(v) ∂
+∂As
+( ∏
+e∈EΓ
+ContA
+Γ(e))
+=
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+∏
+v∈VΓ
+ContA
+Γ(v) ∏
+e∈EΓ
+e≠˜e
+ContA
+Γ(e)∂ContA
+Γ(˜e)
+∂As
+= ∑
+˜e∈EΓ
+1
+∣Aut(Γ)∣
+∑
+A∈ZF(Γ)
+≥0
+∂ContA
+Γ(˜e)
+∂As
+∏
+v∈VΓ
+ContA
+Γ(v) ∏
+e∈EΓ
+e≠˜e
+ContA
+Γ(e).
+(3.28)
+By equations (3.26), (3.27), and (3.28), we complete the proof after summing these equations
+over all decorated stable graphs. The reason we have a factor of 1
+2 on the right hand side of the
+holomorphic anomaly equation is compensation13 due to not having a canonical order of labelings
+of each of the legs l˜e and l′
+˜e for case (i) and connected components for case (ii) after deleting the
+edge ˜e.
+□
+Theorem 3.8. Let n ≥ 4 be an even number with n = 2s, and g ≥ 2. We have
+Cs+1
+2sL
+∂
+∂As−1
+F [Cn/Zn]
+g
+= F [Cn/Zn]
+g−1,2
+(φs−1,φs) +
+g−1
+∑
+i=1
+F [Cn/Zn]
+g−i,1
+(φs−1)F [Cn/Zn]
+i,1
+(φs)
+in C[L±1][Sn][Cs+1].
+Proof. The proof is similar to the proof of odd case. Again after deleting an edge ˜e from a decorated
+stable graph Γ, we have cases (i) and (ii) in the proof of Theorem 3.7 for the graph decomposition.
+13In the special case (ii) with Γ1
+˜e = Γ2
+˜e, there is not a double counting issue when summing over all decorated stable
+graphs unlike the other cases. In this case the factor 2 coming from Z2 symmetry is compensated again by the factor 1
+2
+in the equation.
+
+36
+GENLIK AND TSENG
+By Proposition 3.3 and Lemma 3.5, we observe that
+∂
+∂As−1
+ContA
+Γ(˜e) =(−1)be1+be2
+2s
+⎛
+⎝
+̃P be1
+s+1,p(v1) ̃P be2
+s,p(v2)
+ζ(be1+s+1)p(v1)ζ(be2+s)p(v2) +
+̃P be1
+s,p(v1) ̃P be2
+s+1,p(v2)
+ζ(be1+s)p(v1)ζ(be2+s+1)p(v2)
+⎞
+⎠
+=(2s) LsLs+1
+KsKs+1
+⎧⎪⎪⎨⎪⎪⎩
+ContA
+Γ0
+˜e(l˜e)ContA
+Γ0
+˜e(l′
+˜e) + ContA
+Γ0
+˜e(l′
+˜e)ContA
+Γ0
+˜e(l˜e)
+for (i),
+ContA
+Γ1
+˜e(l˜e)ContA
+Γ2
+˜e(l′
+˜e) + ContA
+Γ1
+˜e(l′
+˜e)ContA
+Γ2
+˜e(l˜e)
+for (ii).
+Using Lemma B.4, we note that
+LsLs+1
+KsKs+1
+=
+L
+Cs+1
+.
+The rest of the proof is identical to the proof of Theorem 3.7 ; however, this time we obtain two
+products of leg contributions for both cases (i) and (ii). This is the reason why we do not have the
+factor 1
+2 on the right hand side of holomorphic anomaly equations.
+□
+APPENDIX A. STIRLING NUMBERS
+In this section, we provide a brief account on Stirling numbers and their properties used in the
+paper. A detailed treatment of Stirling numbers can be found in [11]. Convenient online references
+for Stirling numbers include [6].
+The Stirling number of first kind sm,k is defined to be the coefficient of xk of the falling factorial:
+(A.1)
+(x)m = x(x − 1)⋯(x − m + 1) =
+m
+∑
+k=0
+sm,kxk.
+The special case s0,0 is set to be 1 and certain Stirling numbers of first kind we use to do some
+explicit computations in the paper are:
+sm,0 = 0
+for m ≥ 1,
+sm,m−1 = −(m
+2 ),
+sm,m−2 = 3m − 1
+4
+(m
+3 ),
+sm,m−3 = −(m
+2 )(m
+4 ).
+The Stirling number of second kind Sm,k is the number of ways to partition a set of m objects into
+k non-empty subsets. Stirling numbers of the second kind satisfy the following basic recurrence:
+(A.2)
+Sm,k = kSm−1,k + Sm−1,k−1
+with
+Sm,0 = δm,0.
+A well-known formula for Stirling numbers of second kind called Euler’s formula is
+(A.3)
+Sm,k = 1
+k!
+k
+∑
+i=0
+(−1)k−i(k
+i)im.
+If k is not in the range 0 ≤ k ≤ m, Stirling numbers sm,k and Sm,k are defined to be 0. The following
+relation holds
+(A.4)
+∑
+j≥0
+sm,jSj,k = ∑
+j≥0
+Sm,jsj,k = δm,k
+i.e. Striling numbers are inverses of each other when they are seen as triangular matrices.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+37
+APPENDIX B. A NOTE ON I-FUNCTIONS
+B.1. Series associated to I-functions. In this Appendix, we carry out a detailed analysis for the
+I-function of [Cn/Zn] by following the methodology of [25].
+Lemma B.1 (See [25]). Suppose y0,...,ym, f, g, a are functions of t (with f not identically 0)
+satisfying
+ymf (m) + ym−1f (m−1) + ... + y0f =0,
+ymg(m) + ym−1g(m−1) + ... + y0g =a,
+where f (k) = dkf
+dtk . Then the function h = (g/f)′ satisfies
+˜ym−1h(m−1) + ˜ym−2h(m−2) + ... + ˜y0h = a,
+where ˜ys(t) = ∑m
+r=s+1 ( r
+s+1)yr(t)f (r−1−s)(t).
+We obtain the following result that is similar to [25, Corollary 1].
+Corollary B.2. Suppose F(x,z) satisfies
+(B.1)
+m
+∑
+r=0
+Wr(x)DrF(x,z) = A(x,z)
+with A(∞,x) ≡ 0, then we have
+(
+m−1
+∑
+s=0
+˜Ws(x)Ds)MF(x,z) = zA(x,z),
+where ˜Ws(x) = ∑m
+r=s+1 ( r
+s+1)Wr(x)D(r−1−s)F(x,∞) and M is defined in (1.15).
+Proof. Apply Lemma B.1 with f(t) = F(et,∞), g(t) = F(et,z), a(t) = A(et,z), and yr(t) =
+Wr(et) for 0 ≤ r ≤ m.
+□
+Lemma B.3. The series Ck in x satisfy the following properties:
+(1) Ck+n = Ck for all k ≥ 1,
+(2) ∏n
+k=1 Ck = Ln,
+(3) Ck = Cn+1−k for all 1 ≤ k ≤ n.
+Proof. Since we basically set all φi’s in I(x,z) to 1 to obtain the series E(x,z), it also satisfies the
+Picard-Fuchs equation:
+x−n ((1 − (−1)n (x
+n)
+n
+)DnE(x,z) +
+n−1
+∑
+k=1
+sn,kDkE(x,z)) = z−nE(x,z)
+which is of the form (B.1) with F(x,z) = E(x,z), A(x,z) = z−nE(x,z), m = n, and
+Wn(x) =x−n (1 − (−1)n (x
+n)
+n
+) = L−n,
+Wr(x) =x−nsn,r
+for
+(1 ≤ r ≤ n − 1),
+W0(x) =0.
+Applying Corollary B.2 repeatedly, we obtain
+(B.2)
+n−1−p
+∑
+s=0
+Ws,p(x)DsEp+1(x,z) = z−n+p+1E(x,z)
+(0 ≤ p ≤ n − 1),
+
+38
+GENLIK AND TSENG
+where Ei(x,z) is defined in (1.14) and Ws,p(x) is given inductively by
+Ws,p(x) =
+n−p
+∑
+r=s+1
+( r
+s + 1)Wr,p−1(x)Dr−1−sCp(x).
+By induction on p, we see that the first coefficient in (B.2) is given by
+Wn−1−p,p(x) = Wn(x)
+p
+∏
+i=1
+Ci(x).
+Then, equation (B.2) for p = n − 1 gives
+(B.3)
+(Wn(x)
+n−1
+∏
+i=1
+Ci(x)) En(x,z) = E(x,z).
+Letting z = ∞ in (B.3), using E(x,∞) = 1, Wn(x) = L−n and En(x,∞) = Cn(x) we obtain
+L−n
+n
+∏
+i=1
+Ci(x) = 1.
+which proves part (2) of Lemma B.3.
+Substituting part (2) of Lemma B.3 into equation (B.3) gives
+En(x,z)
+Cn(x)
+= E(x,z).
+Applying Mk−1zD to both sides of this equality for k ≥ 1 results in
+En+k(x,z) = Ek(x,z),
+which proves part (1) of Lemma B.3.
+Now, equation (1.23) yields that for any 0 ≤ i,j ≤ n − 1 we have
+Li...L0Ii+1 = Lj...L0Ij+1
+if
+i + j = n − 1.
+Applying the operator D to both sides gives part (3) of Lemma B.3.
+□
+For any l ≥ 0, we define the following series in x
+Kl =
+l
+∏
+i=0
+Ci.
+Corollary B.4. The series Kl satisfy
+(1) Kn+l = LnKl for all l ≥ 0, in particular Kn = Ln,
+(2) KlKn−l = Ln and KlKInv(l) = Ll+Inv(l) for all 0 ≤ l ≤ n − 1.
+Proof. For the first part, the special case Kn = Ln is just part (2) of Lemma B.3. Then, general case
+Kn+l = LnKl follows from part (1) of Lemma B.3.
+For the second part, we calculate
+KlKn−l =(
+l
+∏
+i=1
+Ci)(
+n−l
+∏
+j=1
+Cj)
+=(
+l
+∏
+i=1
+Ci)(
+n−l
+∏
+j=1
+Cn+1−j)
+by part (3) of Lemma B.3
+=(
+l
+∏
+i=1
+Ci)(
+n
+∏
+i=l+1
+Ci) = Kn = Ln,
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+39
+the rest follows from the fact that K0Kn = 1 ⋅ Ln and Inv(l) = n − l for 1 ≤ l ≤ n − 1.
+□
+B.2. Asymptotic solutions of Picard-Fuchs equations. For 0 ≤ j ≤ n − 1, define
+DLj = D + Lj
+z
+and
+µj = ∫
+x
+0
+Lj(u)
+u
+du
+where Lj = Lζj.
+Lemma B.5. Assume for 0 ≤ j ≤ n − 1 a function of the form e
+µj
+z Φj(z) satisfies the Picard-Fuchs
+equation (1.11), i.e.
+L−n (Dn (e
+µj
+z Φj(z)) + DL
+L
+n−1
+∑
+r=1
+sn,rDr (e
+µj
+z Φj(z))) = z−ne
+µj
+z Φj(z)
+where
+Φj(z) =
+∞
+∑
+k=0
+Φj,kzk
+with Φj,k ∈ C[[x]] and Φj,k = 0 if k < 0.
+Then, we have Φj,k ∈ C[Lj] = C[L].
+For the rest of this section, our aim is to prove Lemma B.5, hence we adopt its assumptions. For
+any function F(x,z), observe the following
+D (e
+µj
+z F(x,z)) = e
+µj
+z DF(x,z) + Dµj
+z e
+µj
+z F(x,z)
+= e
+µj
+z DF(x,z) + Lj
+z e
+µj
+z F(x,z)
+= e
+µj
+z DLjF(x,z).
+(B.4)
+Then, the equation in Lemma B.5 reads as
+(B.5)
+LjΦj(z) = 0
+where
+Lj = −(Lj
+z )
+n
++ Dn
+Lj + DLj
+Lj
+n−1
+∑
+r=1
+sn,rDr
+Lj
+using equation (B.4), Ln = (Lj)n, and DL
+L = DLj
+Lj .
+For 1 ≤ k ≤ n, define14
+(B.6)
+Lj,k =
+k
+∑
+i=0
+((n
+i)Hn−i,k−i + DLj
+Lj
+k−i
+∑
+r=1
+(n − r
+i
+)sn,n−rHn−i−r,k−i−r)Di
+where Hm,l are defined15 by the following recursion for m ≥ 1 and 0 ≤ l ≤ m:
+(B.7)
+H0,l = δ0,l,
+and
+Hm,l = Hm−1,l + n(1 + (−1)n X
+nn)(X d
+dX + m − l
+n
+)Hm−1,l−1.
+14Note that the definition of Lj,k does not depend on j since Ln = (Lj)n, and DL
+L = DLj
+Lj .
+15Hm,l is set to be 0 outside the range m ≥ 1, 0 ≤ l ≤ m.
+
+40
+GENLIK AND TSENG
+By induction, we see that
+Hm,l =0
+if l > m,
+Hm,0 =1
+for m ≥ 0,
+Hm,1 =(m
+2 )(1 + (−1)n X
+nn)
+for m ≥ 1,
+Hm,2 =3(m
+4 )(1 + (−1)n X
+nn)
+2
++ (m
+3 )((n + 1)(1 + (−1)n X
+nn)
+2
+− n(1 + (−1)n X
+nn))
+for m ≥ 2.
+Let
+X =Ln
+j = Ln
+Y =DLj
+Lj
+= DL
+L = 1 + (−1)n Ln
+nn = 1 + (−1)n X
+nn .
+(B.8)
+Then, we see that
+DY =(−1)n Ln−1
+nn−1 DL = (−1)n Ln
+nn−1
+DL
+L = (−1)n
+1
+nn−1XY,
+DX =nLn−1DL = nLnDL
+L = nXY = nX (1 + (−1)n X
+nn).
+Also, using Stirling numbers of the first kind which are explicitly given in Appendix A, we
+compute the first two terms of Lj,k:
+Lj,1 =nD,
+Lj,2 =(n + 1
+4 )(Y 2 − Y ) − (n
+2)Y D + (n
+2)D2.
+Lemma B.6.
+Dk
+Lj =
+k
+∑
+m=0
+m
+∑
+l=0
+( k
+m)Hm,l (Lj
+z )
+m−l
+Dk−m.
+Proof. First, we prove by induction that
+Dk
+Lj =
+k
+∑
+m=0
+( k
+m)Dm
+Lj(1)Dk−m.
+We need to note that
+DLj (FDk) = (D + Lj
+z )(FDk)
+= (DF)Dk + FDk+1 + Lj
+z FDk
+= (DLjF)Dk + FDk+1.
+(B.9)
+For the base step k = 1, we have
+DLj = D + Lj
+z = D + DLj(1) =
+1
+∑
+m=0
+( 1
+m)Dm
+Lj(1)D1−m.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+41
+For the inductive step, we have
+Dk
+Lj = DLjDk−1
+Lj
+=
+k−1
+∑
+m=0
+(k − 1
+m )DLj (Dm
+Lj(1)Dk−1−m)
+=
+k−1
+∑
+m=0
+(k − 1
+m )(Dm+1
+Lj (1)Dk−1−m + Dm
+Lj(1)Dk−m)
+by equation (B.9)
+=
+k−1
+∑
+m=0
+(k − 1
+m )Dm+1
+Lj (1)Dk−1−m +
+k−1
+∑
+m=0
+(k − 1
+m )Dm
+Lj(1)Dk−m
+=
+k
+∑
+m=1
+( k − 1
+m − 1)Dm
+Lj(1)Dk−m +
+k−1
+∑
+m=0
+(k − 1
+m )Dm
+Lj(1)Dk−m
+= (k − 1
+k − 1)
+�������������������
+=(k
+k)
+Dk
+Lj(1)Dk−k +
+k−1
+∑
+m=1
+((k − 1
+m − 1) + (k − 1
+m ))
+����������������������������������������������������������������������������������������������������������������������
+=( k
+m)
+Dm
+Lj(1)Dk−m + (k − 1
+0 )
+�������������������
+=(k
+0)
+D0
+LjDk−0
+=
+k
+∑
+m=0
+( k
+m)Dm
+Lj(1)Dk−m.
+Next, using another induction we prove
+Dm
+Lj(1) =
+m
+∑
+l=0
+Hm,l (Lj
+z )
+m−l
+.
+We begin with some observations:
+DHm−1,l(X) = d
+dX Hm−1,lDX
+= n(1 + (−1)n X
+nn)X d
+dX Hm−1,l
+(B.10)
+and
+D (Lj
+z )
+m−1−l
+= (m − 1 − l)(Lj
+z )
+m−2−l
+D (Lj
+z )
+= (m − 1 − l)(Lj
+z )
+m−2−l
+(Lj
+z )(1 + (−1)n X
+nn)
+= (1 + (−1)n Xn
+nn )(m − 1 − l)(Lj
+z )
+m−1−l
+(B.11)
+and
+(B.12)
+DLj(FG) = (DF)G + F(DG) + Lj
+z (FG).
+For the base step m = 0, we have
+D0
+Lj(1) = 1 = H0,0 (Lj
+z )
+0
+.
+
+42
+GENLIK AND TSENG
+For the inductive step, assume the statement holds for m − 1, then
+Dm
+Lj
+= DLjDm−1
+Lj
+= DLj
+m−1
+∑
+l=0
+Hm−1,l (Lj
+z )
+m−1−l
+=
+m−1
+∑
+l=0
+((DHm−1,l)(Lj
+z )
+m−1−l
++ Hm−1,lD (Lj
+z )
+m−1−l
++ Hm−1,l (Lj
+z )
+m−l
+)
+by equation (B.12).
+Then, by equations (B.10) and (B.11), we see that
+Dm
+Lj
+=
+m−1
+∑
+l=0
+((n(1 + (−1)n X
+nn)(X d
+dX + m − 1 − l
+n
+)Hm−1,l)(Lj
+z )
+m−1−l
++ Hm−1,l (Lj
+z )
+m−l
+)
+=
+m
+∑
+l=1
+(n(1 + (−1)n X
+nn)(X d
+dX + m − l
+n
+)Hm−1,l−1)(Lj
+z )
+m−l
++
+m−1
+∑
+l=0
+Hm−1,l (Lj
+z )
+m−l
+=
+m
+∑
+l=0
+(n(1 + (−1)n X
+nn)(X d
+dX + m − l
+n
+)Hm−1,l−1 + Hm−1,l)(Lj
+z )
+m−l
+by Hm−1,−1 = 0, Hm−1,m = 0
+=
+m
+∑
+l=0
+Hm,l (Lj
+z )
+m−l
+.
+□
+Lemma B.7.
+Lj =
+n
+∑
+k=1
+(Lj
+z )
+n−k
+Lj,k.
+Proof. By Lemma B.6, and the definition16 of Lj we have
+Lj = −(Lj
+z )
+n
++
+n
+∑
+m=0
+m
+∑
+l=0
+Hm,l(n
+m)(Lj
+z )
+m−l
+Dn−m + DLj
+Lj
+n−1
+∑
+r=0
+r
+∑
+m=0
+�������������
+=∑m=n−1
+m=0
+∑r=n−1
+r=m
+m
+∑
+l=0
+sn,r( r
+m)Hm,l (Lj
+z )
+m−l
+Dr−m
+= −(Lj
+z )
+n
++
+n
+∑
+m=0
+m
+∑
+l=0
+Hm,l(n
+m)(Lj
+z )
+m−l
+Dn−m + DLj
+Lj
+n−1
+∑
+m=0
+m
+∑
+l=0
+n−1
+∑
+r=m
+sn,r( r
+m)Hm,l (Lj
+z )
+m−l
+Dr−m.
+By separating m = n case from the first double summation and by the change of indices via m = n−i
+and l = k − i, we obtain
+Lj = − (Lj
+z )
+n
++
+n
+∑
+l=0
+(n
+n)Hn,l (Lj
+z )
+n−l
++
+n
+∑
+i=1
+n
+∑
+k=i
+�
+=∑k=n
+k=1 ∑i=k
+i=1
+(Lj
+z )
+n−k
+(( n
+n − i)Hn−i,k−iDi + DLj
+Lj
+n−1
+∑
+r=n−i
+sn,r( r
+n − i)Hn−i,k−iDr−n+i).
+16Note that the sum in the definition of Lj in equation (B.5) can start at r = 0 since sn,0 = 0.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+43
+Change the index l to k in the first summation and shift r by n − i:
+Lj = − (Lj
+z )
+n
++
+n
+∑
+k=0
+(n
+n)Hn,l (Lj
+z )
+n−k
++
+n
+∑
+k=1
+k
+∑
+i=1
+(Lj
+z )
+n−k
+( n
+n − i)
+�����������������
+=(n
+i)
+Hn−i,k−iDi
++ DLj
+Lj
+n
+∑
+k=1
+(Lj
+z )
+n−k
+(⋆)
+�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
+k
+∑
+i=1
+i−1
+∑
+r=0
+sn,r+n−i (r + n − i
+n − i )
+��������������������������������������������
+=(r+n−i
+r
+)
+Hn−i,k−iDr .
+(B.13)
+For (⋆), we have
+k
+∑
+i=1
+i−1
+∑
+r=0
+�
+=∑r=k−1
+r=0
+∑i=k
+i=r+1
+sn,r+n−i(r + n − i
+r
+)Hn−i,k−iDr =
+k−1
+∑
+i=0
+k
+∑
+r=i+1
+sn,i+n−r(i + n − r
+i
+)Hn−r,k−rDi
+(i ↔ r)
+=
+k−1
+∑
+i=0
+k−i
+∑
+r=1
+sn,n−r(n − r
+i
+)Hn−i−r,k−i−rDi
+shift r by i
+=
+k
+∑
+i=0
+k−i
+∑
+r=1
+sn,n−r(n − r
+i
+)Hn−i−r,k−i−rDi
+since Hn−k−r,−r = 0.
+Note also that
+−(Lj
+z )
+n
++
+n
+∑
+k=0
+(n
+n)Hn,k (Lj
+z )
+n−k
+=
+n
+∑
+k=1
+(n
+n)Hn,k (Lj
+z )
+n−k
+Hence, (B.13) reads as
+Lj =
+n
+∑
+k=1
+(n
+n)Hn,k (Lj
+z )
+n−k
++
+n
+∑
+k=1
+k
+∑
+i=1
+(Lj
+z )
+n−k
+(n
+i)Hn−i,k−iDi
+������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
+These can be combined.
++ DLj
+Lj
+n
+∑
+k=1
+(Lj
+z )
+n−k k
+∑
+i=0
+k−i
+∑
+r=1
+sn,n−r(n − r
+i
+)Hn−i−r,k−i−rDi.
+So, we have
+Lj =
+n
+∑
+k=1
+(Lj
+z )
+n−k k
+∑
+i=0
+(n
+i)Hn−i,k−iDi + DLj
+Lj
+n
+∑
+k=1
+(Lj
+z )
+n−k
+k
+∑
+i=0
+k−i
+∑
+r=1
+sn,n−r(n − r
+i
+)Hn−i−r,k−i−rDi
+=
+n
+∑
+k=1
+(Lj
+z )
+n−k k
+∑
+i=0
+((n
+i)Hn−i,k−i + DLj
+Lj
+k−i
+∑
+r=1
+sn,n−r(n − r
+i
+)Hn−i−r,k−i−r)Di
+�����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
+=Lj,k
+.
+□
+Corollary B.8. For 0 ≤ j ≤ n − 1 and k ≥ 0, we have
+Lj,1(Φj,k) + 1
+Lj
+Lj,2(Φj,k−1) + 1
+L2
+j
+Lj,3(Φj,k−2) + ⋯ +
+1
+Ln−1
+j
+Lj,n(Φj,k+1−n) = 0.
+
+44
+GENLIK AND TSENG
+Proof. We calculate
+0 = LjΦj(z) =
+n
+∑
+l=1
+(Lj
+z )
+n−l
+Lj,lΦj(z)
+by Lemma B.7
+=
+n
+∑
+l=1
+∞
+∑
+k=0
+(Lj
+z )
+n−l
+Lj,lΦj,kzk
+=
+n
+∑
+l=1
+∞
+∑
+k=0
+Lj
+n−lLj,lΦj,kzk+l−n
+=
+n
+∑
+l=1
+∞
+∑
+k=l−1
+Lj
+n−lLj,lΦj,k+1−lzk+1−n
+shift k by l − 1
+=
+n
+∑
+l=1
+∞
+∑
+k=0
+Lj
+n−lLj,lΦj,k+1−lzk+1−n
+since Φj,k+1−l = 0 for k < l − 1
+=
+∞
+∑
+k=0
+n
+∑
+l=1
+Lj
+n−lLj,lΦj,k+1−lzk+1−n.
+Then equation (B.5) reads as
+n
+∑
+l=1
+Lj
+n−lLj,lΦj,k+1−l = 0
+for any k ≥ 0. By dividing out Ln−1
+j
+, we finish the proof.
+□
+Let
+I ⊂ C[L]
+be the ideal generated by XY .
+Lemma B.9. We have
+Lj,k ≡ (n
+k)(D)(D − Y )⋯(D − (k − 1)Y )
+mod I.
+Proof. Note that Y and D commute modulo I:
+D(Y F) = (DY )F + Y (DF) = (−1)n
+nn−1 XY F + Y (DF).
+Also observe that for any r ≥ 1 we have,
+Y r ≡ (Y )r−1Y
+mod I
+≡ (1 + (−1)n X
+nn)r−1Y
+mod I
+≡ Y
+mod I.
+(B.14)
+We first show by induction that
+(B.15)
+Hm,l ≡ hm,lY l
+mod I
+where hm,l = Sm,m−l is the Stirling number of the second kind. The only thing we need to prove is
+that if Hm,l ≡ hm,lY l mod I, then the numbers hm,l are given by the recursion
+h0,l = δ0,l, and hm,l = hm−1,l + (m − l)hm−1,l−1 for all m ≥ 1.
+This will imply hm,l = Sm,m−l by recursion (A.2). The base case l = 0 is given by
+Hm,0 = 1, and hm,0 = Sm,m = 1.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+45
+The recursion above is equivalent to equation (B.7):
+Hm,l ≡ Hm−1,l + nY (X d
+dX + m − l
+n
+)Hm−1,l−1
+mod I
+≡ Hm−1,l + (m − l)Y Hm−1,l−1
+mod I
+which is the same as
+hm,lY l ≡ Hm−1,lY l + (m − l)Y Hm−1,l−1Y l−1
+mod I
+≡ Hm−1,lY l + (m − l)Hm−1,l−1Y l
+mod I.
+By induction, cancelling out Y l on both sides we get what we want; that is, Hm,l ≡ hm,lY l mod I.
+By the definitions of Y and Lj,k, and using equation (B.14) in the second line, we obtain
+Lj,k ≡
+k
+∑
+i=0
+((n
+i)Hn−i,k−i + Y
+k−i
+∑
+r=1
+(n − r
+i
+)sn,n−rHn−i−r,k−i−r)Di
+mod I
+≡
+k
+∑
+i=0
+((n
+i)Hn−i,k−i +
+k−i
+∑
+r=1
+Y r(n − r
+i
+)sn,n−rHn−i−r,k−i−r)Di
+mod I
+≡
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+Y r(n − r
+i
+)sn,n−rHn−i−r,k−i−r)Di
+mod I.
+(B.16)
+Then, by equation (B.15) we have
+Lj,k ≡
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+Y r(n − r
+i
+)sn,n−rhn−i−r,k−i−rY k−i−r)Di
+mod I
+≡
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+(n − r
+i
+)sn,n−rhn−i−r,k−i−r)Y k−iDi
+mod I
+≡
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+(n − r
+i
+)sn,n−rSn−i−r,n−k)Y k−iDi
+mod I
+by hm,l = Sm,m−l.
+(B.17)
+Next, we calculate
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+(n − r
+i
+)sn,n−rSn−i−r,n−k)ti
+=
+n
+∑
+i=0
+(
+n−i
+∑
+r=0
+(n − r
+i
+)sn,n−rSn−i−r,n−k)ti
+since Sn−i−r,n−k = 0 if i + r > k
+=
+n
+∑
+i=0
+(
+n−i
+∑
+r=0
+(n − r
+i
+)sn,n−r [
+1
+(n − k)!
+n−k
+∑
+l=0
+(−1)n−k−l(n − k
+l
+)ln−r−i])ti
+by Euler’s formula (A.3)
+=
+1
+(n − k)!
+n−k
+∑
+l=0
+(−1)n−k−l(n − k
+l
+)
+n
+∑
+i=0
+n−i
+∑
+r=0
+�
+=∑n
+r=0 ∑n−r
+i=0
+sn,n−r(n − r
+i
+)ln−r−iti
+=
+1
+(n − k)!
+n−k
+∑
+l=0
+(−1)n−k−l(n − k
+l
+)
+n
+∑
+r=0
+sn,n−r(l + t)n−r
+by binomial formula
+=
+n!
+(n − k)!
+n−k
+∑
+l=0
+(−1)n−k−l(n − k
+l
+)(l + t
+n )
+by equation (A.1)
+
+46
+GENLIK AND TSENG
+=
+n!
+(n − k)!(t
+k)
+= (n
+k)t(t − 1)⋯(t − (k − 1)).
+The second-to-last equality is obtained by expanding (1 + u)tun−k = (1 + u)t((1 + u) − 1)n−k via
+binomial formula, matching coefficients of un on both sides and using Chu-Vandermonde identity:
+(s + t
+m ) =
+m
+∑
+k=0
+(s
+k)(
+t
+m − k).
+Then, we have
+k
+∑
+i=0
+(
+k−i
+∑
+r=0
+(n − r
+i
+)sn,n−rSn−i−r,n−k)yk−iti = (n
+k)t(t − y)⋯(t − (k − 1)y)
+This together with equation (B.17) completes the proof of the lemma when it is combined with the
+commutation of Y and D modulo I.
+□
+Now, we are ready to prove Lemma B.5. Since D and Y commutes modulo I, inductively we
+show that
+(D)(D − Y )⋯(D − (k − 1)Y )Lr
+j
+mod I ≡ {0
+if 0 ≤ r ≤ k − 1,
+r(r − 1)⋯(r − (k − 1))Lr
+jY k
+if r ≥ k.
+Then, Lemma B.9 implies that
+Lj,k (Lr
+j) ∈ {I
+if 0 ≤ r ≤ k − 1,
+Lr
+jY k + I
+if r ≥ k.
+From this, we conclude that Lj,k(C[Lj]) ⊆ Lk
+jY C[Lj] for any 1 ≤ k ≤ n since I is generated by
+XY and X = Ln
+j . Moreover, for the case k = 1, we have the equality Lj,1(C[Lj]) = LjY C[Lj].
+This is because we have Lj,1(Lr
+j) = nDLr
+j = nrLr
+jY for any r ≥ 1 and Lj,1(a) = nDa = 0 for any
+a ∈ C.
+It is clear that the statement is true if k = 0. Now, we prove the statement inductively. By
+Corollary 1.16, we have the following
+Lj,1(Φj,k) = −
+n
+∑
+l=2
+Lj
+1−lLj,l (Φj,k+1−l) ∈ LjY C[Lj].
+The right hand side belongs to LjY C[Lj] by inductive hypothesis since Lj,l(C[Lj]) ⊆ Ll
+jY C[Lj].
+This shows Φj,k ∈ C[Lj] and completes the proof of Lemma B.5 since Lj,1(C[Lj]) = LjY C[Lj].
+REFERENCES
+[1] D. Abramovich, T. Graber, A. Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130
+(2008), no. 5, 1337–1398.
+[2] M. Alim, E. Scheidegger, S. T. Yau, J. Zhou Special polynomial rings, quasi modular forms and duality of
+topological strings. Advances in Theoretical and Mathematical Physics (2014), 18(2), 401-467.
+[3] M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Holomorphic anomalies in topological field theories, Nuclear
+Physics B (1993), 405(2-3), 279-304.
+[4] M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Kodaira-Spencer theory of gravity and exact results for
+quantum string amplitudes, Nuclear Physics B (1994), 405(2-3), 279-304.
+[5] T. Coates, A. Corti, H. Iritani, H.-H. Tseng, Computing Genus-Zero Twisted Gromov-Witten Invariants, Duke
+Math. J. 147 (2009), no.3, 377–438.
+
+HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS
+47
+[6] Set Partitions: Stirling Numbers, Digital Library of Mathematical Functions, Section 26.8.
+[7] D. Genlik, H.-H. Tseng, Holomorphic anomaly equations for [C5/Z5], arXiv:2211.15878.
+[8] D. Genlik, H.-H. Tseng, Higher genus Gromov-Witten theory of [Cn/Zn] II: Crepant resolution correspondence,
+in preparation.
+[9] A. Givental, Elliptic Gromov-Witten invariants and the generalized mirror conjecture, in: “Integrable systems
+and algebraic geometry (Kobe/Kyoto, 1997)”, 107–155, World Sci. Publ., River Edge, NJ, 1998.
+[10] A. Givental, Symplectic geometry of Frobenius structures, in: “Frobenius manifolds”, Aspects Math., E36, 91–
+112, Friedr. Vieweg, Wiesbaden, 2004.
+[11] H.-W. Gould, J. Quaintance, Combinatorial identities for Stirling numbers: the unpublished notes of HW Gould,
+World Scientific 2015.
+[12] M. Kontsevich, Y. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm.
+Math. Phys. 164 (1994), 525–562.
+[13] Y.-P. Lee, R. Pandharipande, Frobenius manifolds, Gromov-Witten theory, and Virasoro constraints, manuscript
+available from the authors’ websites.
+[14] H. Lho, Crepant resolution conjecture for C5/Z5, arXiv:1707.02910.
+[15] H. Lho, Equivariant holomorphic anomaly equation, arXiv:1807.05503.
+[16] H. Lho, R. Pandharipande, Stable quotients and the holomorphic anomaly equation, Adv. Math. 332 (2018),
+349–402.
+[17] H. Lho, R. Pandharipande, Crepant resolution and the holomorphic anomaly equation for [C3/Z3], Proc. London
+Math. Soc. (3) 119 (2019), 781–813.
+[18] H. Lho, R. Pandharipande, Holomorphic anomaly equations for the formal quintic , Peking Mathematical Journal
+(2019), 2(1), 1-40.
+[19] G. Oberdieck, Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface,
+arXiv:2202.03361.
+[20] R. Pandharipande, Cohomological field theory calculations, Proceedings of the ICM (Rio de Janeiro 2018), Vol
+1, 869–898, World Sci. Publications: Hackensack, NJ, 2018.
+[21] R. Pandharipande, A. Pixton, D. Zvonkine, Relations on M g,n via 3-spin structures, J. Amer. Math. Soc. 28
+(2015), 279–309.
+[22] R. Pandharipande, H.-H. Tseng, Higher genus Gromov-Witten theory of Hilbn(C2) and CohFTs associated to
+local curves, Forum of Mathematics, Pi (2019), Vol. 7, e4, 63 pages, arXiv:1707.01406.
+[23] C. Teleman, The structure of 2D semi-simple field theories, Invent. Math. 188 (2012), 525–588.
+[24] H.-H. Tseng, Orbifold quantum Riemann-Roch, Lefschetz and Serre, Geom. Topol. 14 (2010), 1–81.
+[25] D. Zagier, A. Zinger, Some properties of hypergeometric series associated with mirror symmetry, In: “Modular
+forms and string duality”, 163–177, Fields Inst. Commun. 54, AMS 2008.
+DEPARTMENT OF MATHEMATICS, OHIO STATE UNIVERSITY, 100 MATH TOWER, 231 WEST 18TH AVE.,
+COLUMBUS, OH 43210, USA
+Email address: genlik.1@osu.edu
+DEPARTMENT OF MATHEMATICS, OHIO STATE UNIVERSITY, 100 MATH TOWER, 231 WEST 18TH AVE.,
+COLUMBUS, OH 43210, USA
+Email address: hhtseng@math.ohio-state.edu
+
diff --git a/vtE_T4oBgHgl3EQf-xzf/content/tmp_files/load_file.txt b/vtE_T4oBgHgl3EQf-xzf/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9634fcf4096717ef0d787594585b31f85dcbf6ba
--- /dev/null
+++ b/vtE_T4oBgHgl3EQf-xzf/content/tmp_files/load_file.txt
@@ -0,0 +1,1765 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf,len=1764
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='08389v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='AG]  20 Jan 2023  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I:  HOLOMORPHIC ANOMALY EQUATIONS  DENIZ GENLIK AND HSIAN-HUA TSENG  ABSTRACT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We study the structure of higher genus Gromov-Witten theory of the quotient stack  [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We prove holomorphic anomaly equations for [Cn/Zn], generalizing previous results of  Lho-Pandharipande [17] for the case of [C3/Z3] and ours [7] for the case [C5/Z5] to arbitrary n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  CONTENTS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Introduction  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Acknowledgment  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Genus zero theory  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Mirror theorem  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Picard-Fuchs equations  6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Birkhoff factorization  8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Quantum product  9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Frobenius structure  12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Rings of functions  18  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Preparations  18  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Descriptions of the rings  20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Holomorphic anomaly equations  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  More on flatness equation  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Formula for potentials  27  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof of holomorphic anomaly equations  34  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Stirling numbers  36  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  A note on I-functions  37  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Series associated to I-functions  37  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Asymptotic solutions of Picard-Fuchs equations  39  References  46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' INTRODUCTION  For an integer n ≥ 2, the cyclic group Zn acts naturally on Cn by letting its generator 1 ∈ Zn act  via the n × n matrix  diag(e  2π  √  −1  n  ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',e  2π  √  −1  n  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The quotient [Cn/Zn] is a smooth Deligne-Mumford stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The diagonal action of the torus T =  (C∗)n on Cn induces a T-action on [Cn/Zn], making it a toric Deligne-Mumford stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Date: January 23, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  1  2  GENLIK AND TSENG  This paper is concerned with T-equivariant Gromov-Witten invariants of [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By definition,  these are the following integrals  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  ⟨  m  ∏  i=1  γiψki  i ⟩  [Cn/Zn]  g,m  ∶= ∫[M  orb  g,m([Cn/Zn],0)]  vir  m  ∏  i=1  ev∗  i (γi)ψki  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Here, [M  orb  g,m ([Cn/Zn],0)]vir is the (T-equivariant) virtual fundamental class of the moduli space  M  orb  g,m ([Cn/Zn],0) of stable maps to [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ψi ∈ H2(M  orb  g,m ([Cn/Zn],0),Q) are descendant  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  evi ∶ M  orb  g,m ([Cn/Zn],0) → I[Cn/Zn]  are evaluation maps, which take values in the inertia stack I[Cn/Zn] of [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' γi are classes in  the T-equivariant Chen-Ruan cohomology of [Cn/Zn],  γi ∈ H∗  T,Orb([Cn/Zn]) ∶= H∗  T(I[Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let  λ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',λn−1 ∈ H∗  T(pt) = H∗(BT)  be the first Chern classes of the tautological line bundles of BT = (BC∗)n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) takes value  in Q(λ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',λn−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Foundational treatments of orbifold Gromov-Witten theory can be found in many references, the  original being [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The (T-equivariant) Gromov-Witten theory of the non-compact target [Cn/Zn]  is by definition a twisted Gromov-Witten theory of the classifying stack BZn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Foundational dis-  cussions on twisted Gromov-Witten theory of orbifolds can be found in [5] and [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The main results of this paper concern structures of Gromov-Witten invariants (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1), formulated  in terms of generating functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The definition of inertia stacks implies that  I[Cn/Zn] = [Cn/Zn] ∪  n−1  ⋃  k=1  BZn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let  φ0 = 1 ∈ H0  T([Cn/Zn]),φk = 1 ∈ H0  T(BZn),1 ≤ k ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then φ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',φn−1 is an additive basis of H∗  T,Orb([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The orbifold Poincar´e dual {φ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φn−1}  of this basis is given by  φ0 = nλ0⋯λn−1φ0,  φ1 = nφn−1,  ⋮  φn−1 = nφ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  To simplify notation, in what follows we set  φi ∶= φj  if j ≡ i  mod n  and  φi ∶= φj  if j ≡ i  mod n,  for all i ≥ 0 and 0 ≤ j ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Associated to φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm ∈ H⋆  T,Orb ([Cn/Zn]) we define the Gromov-Witten potential by  F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) =  ∞  ∑  d=0  Θd  d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∫[M  orb  g,m+d([Cn/Zn],0)]  vir  m  ∏  k=1  ev∗  i (φck)  m+d  ∏  i=m+1  ev∗  i (φ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We also use the following standard double bracket notation,  ⟨⟨φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm⟩⟩[Cn/Zn]  g,m  = F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  3  We use the following involutions throughout the paper to present equations more efficiently:  Inv ∶ {0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n − 1} → {0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n − 1}  with Inv(0) = 0 and Inv(i) = n − i for 1 ≤ i ≤ n − 1, and  Ion ∶ {0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n} → {0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n}  with Ion(0) = n, and Ion(i) = i for 1 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Holomorphic anomaly equations are partial differential equations predicted by physicists as  a part of the higher genus mirror symmetry conjecture for Calabi-Yau threefolds [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho-  Pandharipande provided mathematical proofs of holomorphic anomaly equations for local P2 [16]  and formal quintic [18] using stable quotient theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Their equations exactly match with physics  calculations for these Calabi-Yau threefolds given in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Motivated by local P2, Lho-Pandharipande  also proved holomorphic anomaly equations for [C3/Z3] in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We generalize their work on holo-  morphic anomaly equations for [C3/Z3] to [Cn/Zn] for n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The main results of this paper, summarized below, are differential equations for these generat-  ing functions F [Cn/Zn]  g  when n ≥ 3 and g ≥ 2 after the following specializations of equivariant  parameters: for 0 ≤ i ≤ n − 1,  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  λi =  ⎧⎪⎪⎨⎪⎪⎩  e  2π  √  −1i  n  e  π  √  −1  n  if n is even,  e  2π  √  −1i  n  if n is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Although physics prediction of holomorphic anomaly equations was meant for Calabi-Yau mani-  folds of dimension 3, borrowing terminology from String Theory, we call the differential equations  in our main results holomorphic anomaly equations for [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Main Theorem (Finite generation property and holomorphic anomaly equations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1) (=Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4) The Gromov-Witten potential lies in a certain polynomial ring:  F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) ∈ C[L±1][Sn][Cn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (2) (=Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7) Let n ≥ 3 be an odd number with n = 2s + 1, and g ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Cs+1  (2s + 1)L  ∂  ∂As  F [Cn/Zn]  g  = 1  2F [Cn/Zn]  g−1,2  (φs,φs) + 1  2  g−1  ∑  i=1  F [Cn/Zn]  g−i,1  (φs)F [Cn/Zn]  i,1  (φs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3) (=Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8) Let n ≥ 4 be an even number with n = 2s, and g ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Cs+1  2sL  ∂  ∂As−1  F [Cn/Zn]  g  = F [Cn/Zn]  g−1,2  (φs−1,φs) +  g−1  ∑  i=1  F [Cn/Zn]  g−i,1  (φs−1)F [Cn/Zn]  i,1  (φs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We refer to Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7, and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 is a  generalization of the differential equation obtained in [17] for [C3/Z3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The proofs of Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8 follow the approach taken in [17] for the case n = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The  approach is based on the cohomological field theory (in the sense of [12]) nature of Gromov-  Witten theory of [Cn/Zn] and relies heavily on the Givental-Teleman classification [10], [23], of  semisimple cohomological field theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' A survey of Givental-Teleman classification can be found  in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  More precisely, the proofs of Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8 use a formula obtained from Givental-  Teleman classification which expresses the potential F [Cn/Zn]  g,m  as a sum over graphs whose sum-  mands only require genus 0 Gromov-Witten theory of [Cn/Zn], see equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13) and Theorem  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This approach thus requires a detailed study of genus 0 Gromov-Witten theory of  4  GENLIK AND TSENG  [Cn/Zn], which is worked out in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Many specific power series arise in the analysis of the  genus 0 theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Properties of these power series and the rings containing them are studied in details  in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Holomorphic anomaly equations, Theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8, are described and proved in  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Appendix A contains discussions on properties of Stirling numbers used in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Appendix B contains a detailed analysis of the I-functions of [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Some previous studies related to holomorphic anomaly equations in dimension > 3 can be found  in [14], [15], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In [7], we use results in [14] to derive two holomorphic anomaly equations for  [C5/Z5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' One of them is the n = 5 case of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7, the other is new.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Studying higher genus Gromov-Witten theory of KPn−1 in detail and comparing its cohomolog-  ical field theory structure to that of [Cn/Zn] described in this paper, we obtain a crepant resolution  correspondece for KPn−1 and [Cn/Zn] in all genera [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Acknowledgment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' would like to thank to Aniket Shah for a discussion which turned  out to be useful for proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' is supported in part by a Special Graduate Assign-  ment fellowship by OSU Department of Mathematics and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' is supported in part by Simons  foundation collaboration grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' GENUS ZERO THEORY  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Mirror theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Applying the methods of [5], we obtain1 the twisted I-function for [Cn/Zn],  Itw(x,z) = z  ∑  k0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',kn−1≥0  ∏b∶0≤b<α(⃗k)  ⟨b⟩=⟨α(⃗k)⟩  ∏n−1  i=0 (λi − bz)  zk0+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='+kn−1  xk0  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='xkn−1  n−1  k0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='.kn−1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' φnα(⃗k)  where  x =  n−1  ∑  i=0  xiφi  and  α(⃗k) =  n−1  ∑  i=0  iki  n  with  ⃗k = (k0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',kn−1) ∈ Zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The J-function of [Cn/Zn] is characterized by  Jtw(τ,−z) = −z + τ + O(z−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  To get a mirror theorem, we need to find the appropriate locus to restrict twisted I-function Itw(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For that we need the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For every integer n ≥ 3 and for every integer l ∈ {2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n − 1} there exists an integer  k such that n − k ≥ 1 and 1 < kl  n < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For l = 2, let k = n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 3 ≤ l ≤ n  2, let k = ⌊n  l ⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For n  2 < l ≤ n − 1, let k = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  By the existence of such k, we see that if we let all ki to be 0 except when i = l and if we let  kl = k then the coefficient of the monomial xkl  l has a term of z-degree greater than equal to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' So,  we should restrict the twisted I-function Itw(x,z) to the locus x2 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' = xn−1 = 0 to be able to look  for a mirror theorem by the characterization of the J-function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Applying [5, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8], we obtain the following generalization of the mirror theorem for  [C3/Z3] in [5, Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For n ≥ 3, the twisted I-function and the J-function of [Cn/Zn] satisfies the follow-  ing equality  Itw (x0φ0 + x1φ1,z) = Jtw (τ 0φ0 + τ 1φ1,z)  1Here, ⟨α⟩ is the fractional part of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  5  with  τ 0 = x0  and  τ 1 = ∑  k≥0  (−1)nkxnk+1  1  (nk + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ⎛  ⎝  Γ(k + 1  n)  Γ( 1  n)  ⎞  ⎠  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We decompose Itw (x0φ0 + x1φ1,z) as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  Itw (x0φ0 + x1φ1,z) = zφ0 + ∑  k0≥1  1  zk0−1  xk0  0  k0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' φ0 +  ∑  k0≥0,k1≥1  γk1(z)  zk0+k1−1  xk0  0 xk1  1  k0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' φk1  where  γk1(z) =  ∏  b∶0≤b< k1  n  ⟨b⟩=⟨ k1  n ⟩  n−1  ∏  i=0  (λi − bz)  for  k1 ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By induction on k1, we can show that γk1(z) is a polynomial of degree2 mk1 = (⌈k1  n ⌉ − 1)n with  the leading coefficient  lk1 =  ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩  ⌈ k1  n ⌉−1  ∏  i=1  (i − k1  n )  n  if  n ∤ k1,  (−1)n  ⌈ k1  n ⌉−1  ∏  i=1  (−1)nin  if  n ∣ k1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  When k0 ≥ 0, observe that  deg ( γk1(z)  zk0+k1−1) = (⌈k1  n ⌉ − 1)n + 1 − k1 − k0 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Hence, by equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) we see that the twisted I-function Itw (x0φ0 + x1φ1,z) is of the form  Itw(x0φ0 + x1φ1,z) = z + τ(x0φ0 + x1φ1) + O(z−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  To write τ(x0φ0 + x1φ1) explicitly, we need to find the summands of equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) which are  constant in z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Clearly, the only contribution is x0φ0 from the first sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let γk1(z) = ∑  mk1  j=0 γj  k1(z)  where γj  k1(z) is the monomial of degree j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, we have  deg ⎛  ⎝  γj  k1(z)  zk0+k1−1  ⎞  ⎠ = j + 1 − (k0 + k1) = 0 if and only if k0 = 0 and k1 = nk + 1 for some k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In this case, we have j = nk = mk1 = deg γk1(z) and the leading coefficient of γk1(z) is  lk1 =  k  ∏  i=1  (i − nk + 1  n  )  n  = (−1)nk (  k  ∏  i=1  (k − i + 1  n))  n  = (−1)nk ⎛  ⎝  Γ(k + 1  n)  Γ( 1  n)  ⎞  ⎠  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  So, we see that  τ(x0φ0 + x1φ1) = τ 0φ0 + τ 1φ1  with  τ 0 = x0  and  τ 1 = ∑  k≥0  (−1)nkxnk+1  1  (nk + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ⎛  ⎝  Γ(k + 1  n)  Γ( 1  n)  ⎞  ⎠  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  2Here, ⌈−⌉ is the ceiling function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  6  GENLIK AND TSENG  In what follows we impose the specializations (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then we have  n−1  ∏  i=0  (λi − bz) = {1 + (bz)n  if n is even,  1 − (bz)n  if n is odd  = 1 + (−1)n(bz)n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using the twisted I-function Itw, the above specializations, and the convention of [16], we define  the I-function for [Cn/Zn] :  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  I (x,z) =  ∞  ∑  k=0  xk  zkk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  It is easy to see that I-function (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2) of [Cn/Zn] is of the form  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  I (x,z) =  ∞  ∑  k=0  Ik(x)  zk  φk =  n−1  ∑  i=0  ̃Ii(x,z)φi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By keeping track of the degrees, we see that  Ik(x) = ∑  l≥0  (−1)nlxnl+k  (nl + k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ⎛  ⎝  Γ(l + k  n)  Γ( k  n)  ⎞  ⎠  n  for 0 ≤ k ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The small J-function for [Cn/Zn] is defined by  J (Θ,z) = φ0 + Θφ1  z  +  n−1  ∑  i=0  φi ⟨⟨  φi  z(z − ψ)⟩⟩  [Cn/Zn]  0,1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2 implies  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4)  J (Θ(x),z) = I(x,z)  with the mirror transformation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5)  Θ(x) = I1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Picard-Fuchs equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Define the operator  D ∶ C[[x]] → C[[x]]  and its inverse  D−1 ∶ xC[[x]] → xC[[x]]  by  Df(x) = xdf(x)  dx ,  D−1f(x) = ∫  x  0  f(t)  t  dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We have the following identity  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6)  xm dm  dxm = D(D − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(D − m + 1) =  m  ∑  k=1  sm,kDk  where sm,k are Stirling numbers of first kind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For a brief account on properties of Stirling numbers,  see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The I-function of [Cn/Zn] satisfies the following Picard-Fuchs (type) equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7)  1  xnD(D − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(D − n + 1)I(x,z) − (−1)n (1  n)  n  DnI(x,z) = (1  z)  n  I(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  7  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Applying the operator  dn  dxn to the function I(x,z) we obtain  dn  dxnI(x,z) =  ∞  ∑  k=n  xk−n  zk(k − n)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk  =  ∞  ∑  k=0  xk  zk+nk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b<1+ k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk  by shifting index and φk+n = φk  =  ∞  ∑  k=0  xk  zk+nk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶ k  n≤b<1+ k  n  ⟨b⟩=⟨ k  n ⟩  (1 + (−1)n(bz)n)  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk  =(1  z)  n ∞  ∑  k=0  xk  zkk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk  + (−1)n (1  n)  n ∞  ∑  k=0  knxk  zkk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n⟩  (1 + (−1)n(bz)n)φk  =(1  z)  n  I(x,z) + (−1)n (1  n)  n  DnI(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6), we complete the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  By equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6), we can rewrite the Picard-Fuchs equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7) as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8)  1  xn  n  ∑  k=1  sn,kDkI(x,z) − (−1)n (1  n)  n  DnI(x,z) = (1  z)  n  I(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Since sn,n = 1, we can rewrite equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8) further as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  x−n ((1 − (−1)n (x  n)  n  )DnI(x,z) +  n−1  ∑  k=1  sn,kDkI(x,z)) = z−nI(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We define3 the following series in C[[x]]:  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10)  L(x) = x(1 − (−1)n (x  n)  n  )  − 1  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1 below, we obtain the following alternative form of the Picard-Fuchs equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  which we frequently use:  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11)  L−n (DnI(x,z) + DL  L  n−1  ∑  k=1  sn,kDkI(x,z)) = z−nI(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Due to the particular form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) of I-function, in order to define some series avoiding φk’s, we  also introduce the function E(x,z)  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12)  E (x,z) =  ∞  ∑  k=0  xk  zkk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∏  b∶0≤b< k  n  ⟨b⟩=⟨ k  n ⟩  (1 + (−1)n(bz)n) =  ∞  ∑  k=0  Ik(x)  zk  3When n = 3, our L differs from L defined in [17] by a sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  8  GENLIK AND TSENG  just by removing the φk from the expression of the I-function (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Also, substituting equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) into Picard-Fuchs equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11) and analyzing the coefficients of both sides, we obtain  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13)  DnIk + DL  L  n−1  ∑  k=1  sn,kDkIk = 0  for 0 ≤ k ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Birkhoff factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Next, we define4 the series Ei(x,z) and Ci(x) for i ≥ 0:  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14)  Ei(x,z) = MiE(x,z)  and  Ci(x) = Ei(x,∞)  where M is the Birkhoff operator defined by  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15)  MF(x,z) = zD F(x,z)  F(x,∞)  for any F(x,z) with non-zero F(x,∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We also define5 the series Ci(x) inductively as follows:  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16)  C0 = I0 = 1  and  Ci = DLi−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='L0Ii  for  i ≥ 1  where  Li = C−1  i D  for i ≥ 1 and L0 is the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For any l ≥ 0, we define the following series in x  Kl =  l  ∏  i=0  Ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We have the following identities for the series Ci and Kl, proved in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1, see Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3  and Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1) Ck+n = Ck for all k ≥ 1,  (2) ∏n  k=1 Ck = Ln ,  (3) Ck = Cn+1−k for all 1 ≤ k ≤ n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (4) Kn+l = LnKl for all l ≥ 0, in particular Kn = Ln,  (5) KlKn−l = Ln and KlKInv(l) = Ll+Inv(l) for all 0 ≤ l ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Define the S-operator for [Cn/Zn] by  S[Cn/Zn] (Θ,z) (γ) =  n−1  ∑  i=0  φi ⟨⟨ φi  z − ψ,γ⟩⟩  [Cn/Zn]  0,2  for γ ∈ H⋆  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The S-operator satisfies the following identities :  S[Cn/Zn] (Θ,z) (φ0) =I(x,z),  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17)  S[Cn/Zn] (Θ,z) (φi) =zLiS[Cn/Zn] (Θ,z) (φi−1)  for  i ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='18)  Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17) is a direct consequence of the definitions of J-function, S-operator, and equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='18), we see that both sides lie on the same tangent space of the Lagrangian  cone L[Cn/Zn] and are of the form φi + O(z−1), hence by [10] they must match.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  4For a series F(x,z) ∈ C[[x, 1  z ]], the constant term of F(x,z) with respect to 1  z is denoted by F(x,∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  5It is easy to show that two definitions of Ci’s are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  9  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have the following factorization of the operator acting on the left hand side of the  Picard-Fuchs equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11)  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='19)  L1⋯Ln = Ln⋯L1 = L−n (Dn + DL  L  n−1  ∑  k=1  sn,kDk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The first equality is a direct result of the definition of Li and Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' we have  Li = Ln+1−i  for all 1 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using identities (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='18), we obtain the following identity  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20)  Ln⋯L1I(x,z) = z−nI(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Due to particular form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) of I-function, we see that for each 0 ≤ i ≤ n − 1 the function ̃Ii(x,z)  is a common solution of equations (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In other words, the set {̃Ii(x,z)}0≤i≤n−1 is a  basis of solutions to both equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Moreover, for all 1 ≤ i ≤ n − 1, we have  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='21)  Li+1Li =  1  Ci+1  D 1  Ci  D =  1  Ci+1Ci  (D − Xi)D  with Xi = DCi  Ci  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Applying this procedure repeatedly, we see that  Ln⋯L1 =  1  ∏n  i=1 Ci  (D + αn−1)⋯(D + α1)D  = L−n(D − αn−1)⋯(D − α1)D  by Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3,  with  αi =  i  ∑  j=1  Xj  for 1 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This shows that equations (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20) have the same leading coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Since both equations have the same solution space and the same leading coefficient, some elemen-  tary arguments from the theory of linear ordinary differential equations imply that (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20)  must be exactly the same equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Quantum product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let γ = ∑n−1  i=0 tiφi ∈ H⋆  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The full genus 0 Gromov-Witten  potential is defined to be  F [Cn/Zn]  0  (t,Θ) =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∫[M  orb  0,m+d([Cn/Zn],0)]  vir  m  ∏  i=1  ev∗  i (γ)  m+d  ∏  i=m+1  ev∗  i (Θφ1)  =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ  ���������������  m  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='22)  The orbifold Poincar´e pairing  g(−,−) ∶ H⋆  T,Orb ([Cn/Zn]) × H⋆  T,Orb ([Cn/Zn]) → Q(λ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',λn−1)  in the basis {φ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',φn−1} and under the specialization (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2), has the matrix representation G = [Gij]  given by  Gij = g(φi,φj) = {  1  n if i + j = 0  mod n,  0 if i + j ≠ 0  mod n  = 1  nδInv(i)j = 1  nδiInv(j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  10  GENLIK AND TSENG  Its inverse G−1 = [Gij] is given by  Gij = nδInv(i)j = nδiInv(j)  where 0 ≤ i,j ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The quantum product ●γ at γ ∈ H⋆  T,Orb ([Cn/Zn]) is a product structure on H⋆  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' It  can be defined as follows:  g(φi ●γ φj,φk) ∶=  ∂3  ∂ti∂tj∂tk  F [Cn/Zn]  0  (t,Θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In what follows, we focus on the quantum product ●γ=0 at γ = 0 ∈ H⋆  T,Orb ([Cn/Zn]), which we  denote by ●.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Note that ● still depends on Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='23)  ⟨⟨φi,φj⟩⟩[Cn/Zn]  0,2  = {0  if  i + j ≠ n − 1,  1  nLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='L0Ii+1  if  i + j = n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By expanding equations (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='18) and matching the coefficients of z−1, we obtain the  following identity for any 0 ≤ j ≤ n − 1:  φ0 ⟨⟨φ0,φi⟩⟩[Cn/Zn]  0,2  + φ1 ⟨⟨φ1,φi⟩⟩[Cn/Zn]  0,2  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' + φn−1 ⟨⟨φn−1,φi⟩⟩[Cn/Zn]  0,2  = Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='L0Ii+1φi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Equating the coefficients, we complete the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For any 0 ≤ i,j ≤ n − 1, we have  1  C1  D ⟨⟨φi,φj⟩⟩[Cn/Zn]  0,2  = ⟨⟨φi,φj,φ1⟩⟩[Cn/Zn]  0,3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The proof is the following direct computation:  1  C1  D ⟨⟨φi,φj⟩⟩[Cn/Zn]  0,2  = 1  DΘD ⟨⟨φi,φj⟩⟩[Cn/Zn]  0,2  =  1  DΘ  ∞  ∑  d=1  Θd−1DΘ  (d − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∫[M  orb  g,d+2([Cn/Zn],0)]  vir ev∗  1 (φi)ev∗  2 (φj)  d+2  ∏  l=3  ev∗  l (φ1)  =  ∞  ∑  d=1  Θd−1  (d − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∫[M  orb  g,d+2([Cn/Zn],0)]  vir ev∗  1 (φi)ev∗  2 (φj)  d+2  ∏  l=3  ev∗  l (φ1)  =  ∞  ∑  d=0  Θd  d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∫[M  orb  g,d+3([Cn/Zn],0)]  vir ev∗  1 (φi)ev∗  2 (φj)ev∗  3 (φ1)  d+3  ∏  l=4  ev∗  l (φ1)  = ⟨⟨φi,φj,φ1⟩⟩[Cn/Zn]  0,3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The fist line follows from equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4) and the definition of C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For all i ≥ 0, the quantum product at 0 ∈ H⋆  T,Orb ([Cn/Zn]) satisfies  φ1 ● φi = Ci+1  C1  φi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Initially, we assume 0 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Using equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='23) and Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6, we obtain  ⟨⟨φ1,φi,φj⟩⟩[Cn/Zn]  0,3  =  D ⟨⟨φi,φj⟩⟩[Cn/Zn]  0,2  C1  = {0  if  i + j ≠ n − 1,  1  n  Ci+1  C1  if  i + j = n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  11  Write  φ1 ● φi =  n−1  ∑  l=0  aliφl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, for 0 ≤ j ≤ n − 1, we have  g (φ1 ● φi,φj) = 1  naInv(j)i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  On the other hand, the relation g(X ● Y,Z) = ⟨⟨X,Y,Z⟩⟩[Cn/Zn]  0,3  gives  g (φ1 ● φi,φj) = {0  if  i + j ≠ n − 1,  1  n  Ci+1  C1  if  i + j = n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  So, we obtain  ali = {0  if  i + Inv(l) ≠ n − 1,  Ci+1  C1  if  i + Inv(l) = n − 1 = Ci+1  C1  δi,Ion(l)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Parts (1) and (3) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 finish the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For any i,j ≥ 0, the quantum product at 0 ∈ H⋆  T,Orb ([Cn/Zn]) is given by  φi ● φj = Ki+j  KiKj  φi+j  and hence the genus 0, 3-point Gromov-Witten invariants are  ⟨⟨φi,φj,φk⟩⟩[Cn/Zn]  0,3  = Ki+j  KiKj  1  nδInv(i+j mod n),k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Using Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 and noting that C0 = 1, inductively we show that for any l ≥ 0 we  have  φl = Cl  1  Kl  φ1 ● .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ● φ1  ����������������������������������������������  l−copy  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This implies  φi ● φj = Ci+j  1  KiKj  φ1 ● .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ● φ1  ����������������������������������������������  i+j−copy  = Ci+j  1  KiKj  Ki+j  Ci+j  1  φi+j,  and the genus 0, 3-point Gromov-Witten invariants part the lemma follows from  ⟨⟨φi,φj,φk⟩⟩[Cn/Zn]  0,3  = g(φi ● φj,φk) = Ki+j  KiKj  1  nδInv(i+j mod n),k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  For all i ≥ 0, define  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='24)  ̃φi = Ki  Li φi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For all i,j ≥ 0, we have ̃φi+n = ̃φi and ̃φi ● ̃φj = ̃φi+j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  12  GENLIK AND TSENG  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The first part follows from  ̃φi+n = Ki+n  Li+n φi+n = KiLn  Li+n φi = Ki  Li φi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Here, we used the properties of Ki listed in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 and proved in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The second  part follows from  ̃φi ● ̃φj = Ki  Li φi ● Kj  Lj φj = KiKj  Li+j φi ● φj = KiKj  Li+j  Ki+j  KiKj  φi+j = Ki+j  Li+j φi+j = ̃φi+j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The quantum product at 0 ∈ H⋆  T,Orb ([Cn/Zn]) is semisimple with the idempotent  basis {eα} given by  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='25)  eα = 1  n  n−1  ∑  i=0  ζ−αĩφi  for  α ≥ 0,  where ζ = e  2π  √  −1  n  is an nth root of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' To show that eα ● eβ = δα,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='βeβ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' we calculate  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='eα ● eβ = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=n−1−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2n−2−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−β(j−n)̃φi+j−n + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2 (  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=n−1−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−α(n−1)ζ−βj̃φn−1+j)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2n−2−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2 (  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=n−1−i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−βj̃φi+j +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−α(n−1)ζ−βj̃φn−1+j)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−αiζ−β(k−i)̃φk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ζ−(α−β)i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='�����������������������������������������������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=nδα,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='β  n−1  ∑  k=0  ζ−βk̃φk  ����������������������������������������  =eβ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Frobenius structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We describe in details some ingredients of the Frobenius structure ob-  tained from genus 0 Gromov-Witten theory of [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We refer the readers to [13] for generalities  on Frobenius structure arising in Gromov-Witten theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the results in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, the Frobenius structure on H⋆  T,Orb ([Cn/Zn]) defined by the Gromov-  Witten theory of [Cn/Zn] is semisimple in a neighborhood of 0 ∈ H⋆  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  13  We first calculate the metric g in the idempotent basis {eα}:  g (eα,eα) =g (1  n  n−1  ∑  i=0  ζ−αĩφi, 1  n  n−1  ∑  j=0  ζ−αj̃φj)  =g (1  n  n−1  ∑  i=0  ζ−αiKi  Li φi, 1  n  n−1  ∑  j=0  ζ−αj Kj  Lj φj)  = 1  n2  n−1  ∑  i=0  n−1  ∑  j=0  ζ−α(i+j)KiKj  Li+j Gij  = 1  n2  n−1  ∑  i=0  n−1  ∑  j=0  ζ−α(i+j)KiKj  Li+j  1  nδInv(i)j  = 1  n3  n−1  ∑  i=0  ζ−α(i+Inv(i))KiKInv(i)  Li+Inv(i)  = 1  n2  by Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4 and i + Inv(i) = 0  mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The normalized idempotents are  ̃eα =  eα  √  g (eα,eα)  = neα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The transition matrix Ψ is given by Ψαi = g (̃eα,φi) where 0 ≤ α,i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We calculate  Ψαi = g (̃eα,φi) = g (  n−1  ∑  j=0  ζ−αj Kj  Lj φj,φi)  =  n−1  ∑  j=0  ζ−αj Kj  Lj Gji =  n−1  ∑  j=0  ζ−αj Kj  Lj  1  nδInv(i),j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  So, Ψαi is given by  Ψαi = 1  nζ−αInv(i)KInv(i)  LInv(i) = 1  nζ−α(n−i)Kn−i  Ln−i  = 1  nζαi Li  Ki  for  0 ≤ α,i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The inverse of the transition matrix Ψ−1 = [Ψ−1  βj] is given by  Ψ−1  jβ = ζ−βj Kj  Lj  where  0 ≤ β,j ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We calculate  [ΨΨ−1]αβ =  n−1  ∑  i=0  ΨαiΨ−1  iβ =  n−1  ∑  i=0  1  nζαi Li  Ki  ζ−βiKi  Li  =  n−1  ∑  i=0  1  nζi(α−β) = δα,β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Let {uα}n−1  α=0 be canonical coordinates associated to the idempotent basis {eα}n−1  α=0 which satisfy  uα (ti = 0,Θ = 0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  14  GENLIK AND TSENG  Since eα =  ∂  ∂uα, we have  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='26)  n−1  ∑  α=0  ∂uα  ∂t1  eα = φ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  duα  dt1  = ζα L  C1  at t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The result is obtained by the following calculation: at t = 0, we have  duα  dt1  eα =  n−1  ∑  β=0  duβ  dt1  δα,βeα  =φ1 ● eα  by equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='26)  =1  n  n−1  ∑  i=0  ζ−αiKi  Li φ1 ● φi  =ζα L  C1  1  n  n−1  ∑  i=0  ζ−α(i+1)Ki+1  Li+1 φi+1  by Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 and Ki+1 = Ci+1Ki  =ζα L  C1  1  n  ⎛  ⎜⎜⎜⎜  ⎝  n−2  ∑  i=0  ζ−α(i+1)Ki+1  Li+1 φi+1 + ζ−αnKn  Ln φn  ���������������������������������������������  =1⋅1⋅φ0  ⎞  ⎟⎟⎟⎟  ⎠  =ζα L  C1  1  n (  n−1  ∑  i=1  ζ−αiKi  Li φi+1 + φ0)  =ζα L  C1  1  n  n−1  ∑  i=0  ζ−αiKi  Li φi  �����������������������������������������������������������������������������  =eα  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  The R-matrix has a central role in the Givental-Teleman classification of semisimple cohomo-  logical field theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let the R-matrix of the Frobenius structure associated to the (T-equivariant)  Gromov-Witten theory of [Cn/Zn] near the semisimple point 0 be denoted by  R(z) = Id + ∑  k≥1  Rkzk ∈ End(H∗  T,Orb([Cn/Zn]))[[z]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the definition of R-matrix, R(z) satisfies the symplectic condition  R(z) ⋅ R(−z)∗ = Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let U be the diagonal matrix  U = diag(u0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,un−1)  associated to canonical coordinates {uα}n−1  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The R-matrix R(z) also satisfies the following flat-  ness equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='27)  z(dΨ−1)R + zΨ−1(dR) + Ψ−1R(dU) − Ψ−1(dU)R = 0,  see [13, Chapter 1, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6] and [9, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Here d = d  dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  15  We examine the dependence on parameters of the full genus 0 Gromov-Witten potential (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='22):  F [Cn/Zn]  0  (t,Θ)  =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ  ���������������  m  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ∣t1=0 + t1φ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ∣t1=0 + t1φ1  ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������  m  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  m  ∑  b=0  (m  b )⟨γ∣t1=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ∣t1=0  �������������������������������������������������������������������������  m−b  ,t1φ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',t1φ1  ���������������������������������������������������������  b  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  =  ∞  ∑  m=0  ∞  ∑  d=0  m  ∑  b=0  1  b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (m − b)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ∣t1=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ∣t1=0  �������������������������������������������������������������������������  m−b  ,t1φ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',t1φ1  ���������������������������������������������������������  b  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  =  ∞  ∑  m=0  ∞  ∑  d=0  m  ∑  b=0  (b + d)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (m − b)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (b + d)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ∣t1=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ∣t1=0  �������������������������������������������������������������������������  m−b  ,t1φ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',t1φ1  ���������������������������������������������������������  b  ,Θφ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Θφ1  ����������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  =  ∞  ∑  m=0  ∞  ∑  d=0  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ⟨γ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',γ  ���������������  m  ,(Θ + t1)φ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',(Θ + t1)φ1  ����������������������������������������������������������������������������������������������������������������������������������������������������������  d  ⟩  [Cn/Zn]  0,m+d  ,  namely  F [Cn/Zn]  0  (t,Θ) = F [Cn/Zn]  0  (t∣t1=0,Θ + t1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  That is, F [Cn/Zn]  0  (t,Θ) depends on t1 and Θ through Θ + t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  It follows from the construction of semisimple Frobenius structures that its ingredients also de-  pend on t1 and Θ through Θ + t1, for example,  uα(t,Θ) = uα(t∣t1=0,Θ + t1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In particular, the operator  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='28)  ∂  ∂t1  − ∂  ∂Θ  annihilates the canonical coordinates uα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' As a result, we have  duα  dt1  = duα  dΘ = duα  dx  dx  dΘ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12, we have  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='29)  duα  dx = ζαL1  x  at the semisimple point 0 ∈ H∗  T,Orb ([Cn/Zn]), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' at t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Since F [Cn/Zn]  0  (t,Θ) depends on t1 and Θ through Θ+t1, it follows that Ψ and R(z) also depend  on t1 and Θ through Θ+t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Hence, the operator (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='28) also annihilates 6 Ψ and R(z), more precisely  6An argument for this (for a different target space) from the CohFT viewpoint can be found in [22, Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  16  GENLIK AND TSENG  we have  ∂  ∂t1  Ψ = ∂  ∂ΘΨ,  ∂  ∂t1  R(z) = ∂  ∂ΘR(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='27), we set all ti’s to 0 except t1 and only consider  d  dt1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Since, U, Ψ and R(z) are  annihilated by the operator (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='28), it follows that (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='27) can be written as  z( d  dΘΨ−1)R + zΨ−1( d  dΘR) + Ψ−1R( d  dΘU) − Ψ−1( d  dΘU)R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using the mirror map Θ(x) = I1(x) and the chain rule  d  dΘ = dx  dΘ  d  dx,  we rewrite the above equation as  z(x d  dxΨ−1)R + zΨ−1(x d  dxR) + Ψ−1R(x d  dxU) − Ψ−1(x d  dxU)R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By matching coefficients of zk, we can futher rewrite it as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='30)  D (Ψ−1Rk−1) + (Ψ−1Rk)DU − Ψ−1 (DU)Ψ(Ψ−1Rk) = 0  or equivalently  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='31)  Ψ(DΨ−1)Rk−1 + DRk−1 + Rk (DU) − (DU)Rk = 0  for k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Here D = x d  dx as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now set t1 = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' consider the restriction to the semisimple point 0 ∈ H∗  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By  equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='29), we have  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='32)  DU = diag(L,Lζ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Lζn−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For k ≥ 0, define the matrix Pk by  Pk = Ψ−1Rk  after being restricted to the semisimple point 0 ∈ H∗  T,Orb ([Cn/Zn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let P k  i,j denote the (i,j) entry  of the matrix Pk where 0 ≤ i,j ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ i,j ≤ n − 1 and k ≥ 0, we have  DP k−1  i,j  = CIon(i)P k  Ion(i)−1,j − P k  i,jLζj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='30) can be rewritten as  D (Ψ−1Rk−1) = Ψ−1 (DU)Ψ(Ψ−1Rk) − (Ψ−1Rk)DU  which is the same as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='33)  DPk−1 = Ψ−1DUΨPk − PkDU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  17  We see that  (Ψ−1DUΨ)ij =  n−1  ∑  l=0  (Ψ−1DU)il Ψlj  =  n−1  ∑  l=0  ζ−liKi  Li Lζl 1  nζlj Lj  Kj  =1  n  Ki  Kj  Lj+1  Li  n−1  ∑  l=0  ζl(j−i+1)  =  ⎧⎪⎪⎨⎪⎪⎩  Ki  Kj  Lj+1  Li  if  i = j + 1  mod n,  0  otherwise  =  ⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩  Ci  if  1 ≤ i ≤ n − 1  and  j = i − 1,  Cn  if  i = 0  and  j = n − 1,  0  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='34)  Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='34) implies  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='35)  (Ψ−1DUΨPk)ij =  n−1  ∑  l=0  (Ψ−1DUΨ)il P k  l,j = CIon(i)P k  Ion(i)−1,j  Equations (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='33) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='35) finish the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  For 0 ≤ i,j ≤ n − 1, define  Pi,j(z) =  ∞  ∑  k=0  P k  i,jzk,  DLj = D + Lj  z  and  µj = ∫  x  0  Lj(u)  u  du  where Lj = Lζj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13 is equivalent to the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ i,j ≤ n − 1, we have DLjPi,j(z) = CIon(i)z−1PIon(i)−1,j(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The proof is the following direct computation:  DLjPi,j(z) =  ∞  ∑  k=0  DP k  i,jzk +  ∞  ∑  k=0  LjP k  i,jzk−1  =  ∞  ∑  k=1  DP k−1  i,j zk−1 +  ∞  ∑  k=0  LjP k  i,jzk−1  =  ∞  ∑  k=0  (DP k−1  i,j  + LjP k  i,j)zk−1  because P −1  i,j = 0  = {∑∞  k=0 CnP k  n−1,jzk−1  if  i = 0,  ∑∞  k=0 CiP k  i−1,jzk−1  if  1 ≤ i ≤ n − 1  by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13  = {Cnz−1Pn−1,j(z)  if  i = 0,  Ciz−1Pi−1,j(z)  if  1 ≤ i ≤ n − 1  = CIon(i)z−1PIon(i)−1,j(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  18  GENLIK AND TSENG  It immediately follows that P0,j(z) satisfies the following differential equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='36)  1  C1  DLj⋯ 1  Cn  DLjP0,j(z) = z−nP0,j(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the definition of Li and equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4), this equation can be rewritten as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='37)  L1⋯Ln (e  µj  z P0,j(z)) = z−ne  µj  z P0,j(z)  By Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='37) reads as  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='38)  L−n (Dn (e  µj  z P0,j(z)) + DL  L  n−1  ∑  r=1  sn,rDr (e  µj  z P0,j(z))) = z−ne  µj  z P0,j(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We see that P0,j(z) satisfies the assumption of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Hence, we obtain the following two  results by Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5 and Corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ j ≤ n − 1 and k ≥ 0, we have P k  0,j ∈ C[L] ⊆ C[L±1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ j ≤ n − 1 and k ≥ 0, we have  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='39)  Lj,1(P k  0,j) + 1  Lj  Lj,2(P k−1  0,j ) + 1  L2  j  Lj,3(P k−2  0,j ) + ⋯ +  1  Ln−1  j  Lj,n(P k+1−n  0,j  ) = 0  where Lj,k is given by equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' RINGS OF FUNCTIONS  The purpose of this section is to define and study rings of functions that contain various ingredi-  ents of Gromov-Witten theory of [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Preparations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We define the following series in C[[x]]  Xk,l = DlCk  Ck  for all k,l ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We denote Xk,1 just by Xk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Also, note that X0 = 0 since C0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Xk,l = (D + Xk)l−1 Xk  for all k ≥ 0 and l ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In particular, Xk,l is a polynomial in {Xk,DXk,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Dl−1Xk} and Dl−1Xk  is a polynomial in {Xk,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Xk,l}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The first part follows by induction on l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The case l = 1 is clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The inductive step is as  follows:  DXk,l−1 = D (Dl−1Ck  Ck  ) = DlCk  Ck  − Dl−1Ck  Ck  DCk  Ck  = Xk,l − Xk,l−1Xk  which is equivalent to  Xk,l = (D + Xk)Xk,l−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The polynomiality of Xk,l directly follows and polynomiality of Dl−1Xk follows from a basic elim-  ination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  19  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  DL  L = 1 + (−1)n Ln  nn = Ln  xn ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  DKi  Ki  =  i  ∑  r=0  Xr,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  nDL  L =  n  ∑  r=0  Xr,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  for 0 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Observe that  DL =x⎛  ⎝(1 − (−1)n (x  n)  n  )  − 1  n  + x(−1  n)(1 − (−1)n (x  n)  n  )  − 1  n −1 d  dx (1 − (−1)n (x  n)  n  )⎞  ⎠  =x(1 − (−1)n (x  n)  n  )  − 1  n  + x2 (−1  n)(1 − (−1)n (x  n)  n  )  − 1  n−1  (−(−1)nn(x  n)  n−1 1  n)  =x(1 − (−1)n (x  n)  n  )  − 1  n  + x(1 − (−1)n (x  n)  n  )  − 1  n−1  (−1)n (x  n)  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This implies  DL  L = 1 + (1 − (−1)n (x  n)  n  )  −1  (−1)n (x  n)  n  = 1 + (−1)n xn  nn (1 − (−1)n (x  n)  n  )  −1  = 1 + (−1)n Ln  nn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  From the first equality of the above equation, we see that  DL  L = 1 + (1 − (−1)n (x  n)  n  )  −1  (−1)n (x  n)  n  = 1 +  (−1)n ( x  n)  n  1 − (−1)n ( x  n)  n = (1 − (−1)n (x  n)  n  )  −1  = Ln  xn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This completes the proof of first equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The second equation follows directly from the definitions  of Ki and Xr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The last equation follows from the second equation and part (1) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  For any m ≥ 1, define the following series in x  Zm,k =  ⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩  D−1Ck+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='D−1Cm  if  0 ≤ k ≤ m − 1,  1  if  k = m,  0  if  k > m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  From the definition of Zm,k, we easily see that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4)  DZm,k = Ck+1Zm,k+1  for all k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We also recall that, by equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16), for m ≥ 1, Im = D−1C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='D−1Cm which is just  Zm,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now for k ≥ 1 define the following series in x:  Bk,p =  ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩  Dk−1C1  if  p = 1,  k1−1  ∑  k2=p−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  kp−1−1  ∑  kp=1 (  p−1  ∏  i=1 (ki−1  ki+1))(Dk1−1−k2C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(Dkp−1−1−kpCp−1)(Dkp−1Cp)  if  2 ≤ p ≤ k,  0  if  p > k  where k1 = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  20  GENLIK AND TSENG  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For all k,m ≥ 1, we have  DkIm =  k  ∑  p=1  Bk,pZm,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let T1 and T2 be two linear operators acting on C[[x]], and let [T1,T2] = T1T2 − T2T1 be  their commutator, and let adj  T1(T2) = [T1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,[T1,T2],.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ] be its generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Inductively, we  show that the commutator of the operator D and multiplication by a series A is given by  adj  D(A) = (DjA)  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=', multiplication by the series (DjA), and we show that multiplication by A followed by the  operator Di is given by  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5)  DiA =  i  ∑  j=0  (i  j)adj  D(A)Di−j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using the fact that for m ≥ 1, Im = D−1C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='D−1Cm = Zm,0 together with equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5),  we inductively complete the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For all 1 ≤ m ≤ n − 1, we have  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6)  Bn,m + DL  L  n−1  ∑  k=m  sn,kBk,m = Bn,m + DL  L  n−1  ∑  k=1  sn,kBk,m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The first equality follows from the definition of Bk,m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For the second equality, we use  induction on m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For m = 1, it follows from Bk,1 = Dk−1C1 = DkI1 and equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The  following completes the inductive step:  0 =DnIm + DL  L  n−1  ∑  k=1  sn,kDkIm  by equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13)  =  n  ∑  p=1  Bn,pZm,p + DL  L  n−1  ∑  k=1  sn,k  k  ∑  p=1  Bk,pZm,p  by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3  =  m  ∑  p=1  Bn,pZm,p + DL  L  n−1  ∑  k=1  sn,k  m  ∑  p=1  Bk,pZm,p  by definitions of Bk,p and Zm,p  =  m  ∑  p=1  (Bn,p + DL  L  n−1  ∑  k=1  sn,kBk,p)Zm,p  =Bn,m + DL  L  n−1  ∑  k=1  sn,kBk,m +  m−1  ∑  p=1  (Bn,p + DL  L  n−1  ∑  k=1  sn,kBk,p)  ���������������������������������������������������������������������������������������������������������������������������������������������������������  =0 by inductive hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Zm,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Descriptions of the rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Set  C[L±1][DX ] ∶= C[L±1][X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Xn−1,DX1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',DXn−1,D2X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',D2Xn−1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='],  and  X ∶= {X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dn−3X1}∪,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∪ {Xi,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dn−2−iXi} ∪ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∪ {Xn−2} = {DjXi}1≤i≤n−2,0≤j≤n−2−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' C[L±1][DX] is a quotient of the ring C[L±1][X].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  21  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now, for any 1 ≤ p ≤ k − 1, define  Zp,k ={X1,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',X1,k−p,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Xp,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Xp,k−p}  and  Sp,k = Zp,k ∖ {Xp,k−p},  ̃  Zp,k ={X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dk−p−1X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Xp,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dk−p−1Xp}  and  ̃Sp,k = ̃  Zp,k ∖ {Dk−p−1Xp}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For each of these sets, and for a fixed p we have  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7)  Sp,k ⊆ Zp,k ⊆ Sp,k+1 ⊆ Zp,k+1,  and  ̃Sp,k ⊆ ̃  Zp,k ⊆ ̃Sp,k+1 ⊆ ̃  Zp,k+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Note that for any k ≥ 1  Bk,p  Kp  =  ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩  X1,k−1  if  p = 1,  k1−1  ∑  k2=p−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  kp−1−1  ∑  kp=1 (  p−1  ∏  i=1 (ki−1  ki+1))X1,k1−k2−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Xp−1,kp−1−kp−1Xp,kp−1  if  2 ≤ p ≤ k,  0  if  p > k  where k1 = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' It follows that for any 1 ≤ p ≤ k − 1, we have  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8)  Bk,p  Kp  = Xp,k−p + ̃Bk,p  where ̃Bk,p is a polynomial in elements of Sp,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, dividing both sides of equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6) by Km  for any 1 ≤ m ≤ n − 1, we obtain  0 =Bn,m  Km  + DL  L  n−1  ∑  k=m  sn,k  Bk,m  Km  =Xm,n−m + ̃Bn,m + DL  L  n−1  ∑  k=m  sn,k  Bk,m  Km  �������������������������������������������������������������  (⋆)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  By set inclusions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7) and equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8), it follows that (⋆) is a polynomial in elements of Zm,n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Since we know ̃Bn,m is a polynomial in element of Sm,n and Zm,n−1 ⊆ Sm,n, it follows that Xm,n−m  is a polynomial in elements of Sm,n ∪ {L±1} by equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9) and equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This implies  that Dn−m−1Xm is a polynomial in elements of ̃Sm,n ∪ {L±1} by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This completes the  proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  For 0 ≤ i,j ≤ n − 1 and k ≥ 0, define  ̃P k  i,j = Li  Ki  P k  i,jζ(k+i)j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ i ≤ n − 1, we have  ̃P k  Ion(i)−1,j = ̃P k  i,j + 1  LD ̃P k−1  i,j  + 1  L (  i  ∑  r=0  Xr − iDL  L ) ̃P k−1  i,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This is just a reformulation of Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The LHS of Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13 becomes  DP k−1  i,j  = (DKi  Li  − iKi  Li  DL  L ) ̃P k−1  i,j ζ−(k−1+i)j + Ki  Li D ̃P k−1  i,j ζ−(k−1+i)j  22  GENLIK AND TSENG  and RHS of Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13 becomes  CIon(i)P k  Ion(i)−1,j − P k  i,jLζj =CIon(i)  KIon(i)−1  LIon(i)−1 ̃P k  Ion(i)−1,jζ−(k−1+Ion(i))j − Ki  Li−1 ̃P k  i,jζ−(k−1+i)j  = KIon(i)  LIon(i)−1 ̃P k  Ion(i)−1,jζ−(k−1+Ion(i))j − Ki  Li−1 ̃P k  i,jζ−(k−1+i)j  = Ki  Li−1 ̃P k  Ion(i)−1,jζ−(k−1+i)j − Ki  Li−1 ̃P k  i,jζ−(k−1+i)j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Putting these together, using the definition of Ki, Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4 and cancelling out some common  factors we obtain  (DKi  Ki  − iDL  L ) ̃P k−1  i,j  + D ̃P k−1  i,j  = ̃P k  Ion(i)−1,jL − ̃P k  i,jL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The rest follows from equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Now, we define the series Ai for 0 ≤ i ≤ n by  Ai = 1  L (iDL  L −  i  ∑  r=0  Xr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Set  C[L±1][DA] ∶= C[L±1][A1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',An−1,DA1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',DAn−1,D2A1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',D2An−1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='],  and  A ∶= {A1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dn−3A1}∪,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∪ {Ai,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',Dn−2−iAi} ∪ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ∪ {An−2} = {DjAi}1≤i≤n−2,0≤j≤n−2−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The following is immediate from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' C[L±1][DA] is a quotient of the ring C[L±1][A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In what follows we further simplify the ring C[L±1][A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For the series Ai, we have the following  (1) Ai = −An−i for all 0 ≤ i ≤ n,  (2) A0 = An = 0, and A n  2 = 0 if n is even,  (3) ∑n  i=0 Ai = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3, we have Ci = Cn+1−i for all 1 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Hence, Xi = Xn+1−i for all 1 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This gives the following reformulation of equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) :  i  ∑  r=0  Xr − iDL  L = (n − i)DL  L − (  n−i  ∑  r=0  Xr)  for all  0 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This proves the first part of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The other two parts follow immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Recall that by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6 we have  ̃P k  Ion(i)−1,j = ̃P k  i,j + 1  LD ̃P k−1  i,j  + 1  L (  i  ∑  r=0  Xr − iDL  L ) ̃P k−1  i,j ,  which is equivalent to  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10)  ̃P k  Ion(i)−1,j = ̃P k  i,j + 1  LD ̃P k−1  i,j + An−i ̃P k−1  i,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We call (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10) the modified flatness equations for [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  23  Now we analyze (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then ̃P 0  Ion(i)−1,j = ̃P 0  i,j for all 0 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This means  ̃P 0  i,j = ̃P 0  0,j for all 0 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now, let k = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, we have  n−1  ∑  i=0  ̃P 1  Ion(i)−1,j  ������������������������������������������������������������  (⋆)  =  n−1  ∑  i=0  ̃P 1  i,j  ����������������  (⋆⋆)  + 1  LD  n−1  ∑  i=0  ̃P 0  i,j +  n−1  ∑  i=0  An−i ̃P 0  0,j  ���������������������������������������������������  (⋆⋆⋆)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Clearly, (⋆) and (⋆⋆) are the same and (⋆ ⋆ ⋆) is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Since ̃P 0  i,j = ̃P 0  0,j, the above equation is  n  LD ̃P 0  0,j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Hence, ̃P 0  i,j = ̃P 0  0,j is a constant whose value depends on the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now, the equations  with k = 1 yield  ̃P 1  n−1,j = ̃P 1  0,j + An ̃P 0  0,j  ̃P 1  n−2,j = ̃P 1  n−1,j + A1 ̃P 0  0,j  ⋮  ̃P 1  n−i,j = ̃P 1  n−i+1,j + Ai−1 ̃P 0  0,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Adding these equations yields  ̃P 1  n−i,j = ̃P 1  0,j +  i−1  ∑  r=0  Ar ̃P 0  0,j  for  1 ≤ i ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now, let k = 2 in equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10) and plug the above equation into it, we find  ̃P 2  Ion(i)−1,j = ̃P 2  i,j + 1  LD ̃P 1  i,j + An−i ̃P 1  i,j  = ̃P 2  i,j + 1  LD ( ̃P 1  0,j +  n−i−1  ∑  r=0  Ar ̃P 0  0,j) + An−i ( ̃P 1  0,j +  n−i−1  ∑  r=0  Ar ̃P 0  0,j)  = ̃P 2  i,j + 1  LD ̃P 1  0,j + 1  L  n−i−1  ∑  r=0  (DAr) ̃P 0  0,j + An−i ̃P 1  0,j +  n−i−1  ∑  r=0  An−iAr ̃P 0  0,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Summing this equality over 0 ≤ i ≤ n − 1, cancelling out ∑n−1  i=0 ̃P 2  Ion(i)−1,j = ∑n−1  i=0 ̃P 2  i,j, and noting  that ∑n−1  i=0 An−i ̃P 1  0,j = 0, we obtain  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11)  n  LD ̃P 1  0,j + 1  L  n−1  ∑  i=0  n−i−1  ∑  r=0  (DAr) ̃P 0  0,j +  n−1  ∑  i=0  n−i−1  ∑  r=0  An−iAr ̃P 0  0,j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Set k = 1 in Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16, we obtain  Lj,1(P 1  0,j) + 1  Lj  Lj,2(P 0  0,j) = 0  which reads as  nDP 1  0,j + 1  Lj  (n + 1  4 )(Y 2 − Y )P 0  0,j − 1  Lj  (n  2)Y DP 0  0,j + 1  Lj  (n  2)D2P 0  0,j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Since P 0  0,j = ̃P 0  0,j is constant and P 1  0,j = ζ−j ̃P 1  0,j, the equation becomes  nD ̃P 1  0,j + 1  L(n + 1  4 )Y (Y − 1)P 0  0,j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  24  GENLIK AND TSENG  By the definition of Y in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8), we obtain  D ̃P 1  0,j =1  n  1  L(n + 1  4 )Y (1 − Y ) ̃P 0  0,j  =(−1)n−1  n  (n + 1  4 )(1 + (−1)n Ln  nn ) Ln−1  nn ̃P 0  0,j ∈ C[L±1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Define fn(L) ∈ C[L±1] to be the right hand side of above equation without ̃P 0  0,j:  fn(L) = (−1)n−1  n  (n + 1  4 )(1 + (−1)n Ln  nn ) Ln−1  nn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For any n ≥ 3, we have  n−1  ∑  i=0  n−i−1  ∑  r=0  DAr =  ⌊ n−1  2 ⌋  ∑  r=1  (n − 2r)DAr  and  n−1  ∑  i=0  n−i−1  ∑  r=0  An−iAr = −  ⌊ n−1  2 ⌋  ∑  r=1  A2  r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This follows from the fact that Ai = −An−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  By equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2), we obtain the following  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For any n ≥ 3, we have  n  Lfn(L) + 1  L  ⌊ n−1  2 ⌋  ∑  r=1  (n − 2r)(DAr) −  ⌊ n−1  2 ⌋  ∑  r=1  A2  r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Equivalently, dividing into even and odd cases, we have  2DAs−1 =  s−1  ∑  r=1  LA2  r −  s−2  ∑  r=1  (n − 2r)DAr − 2sf2s(L)  if  n = 2s ≥ 4,  DAs =  s  ∑  r=1  LA2  r −  s−1  ∑  r=1  (n − 2r)DAr − (2s + 1)f2s+1(L)  if  n = 2s + 1 ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Equations in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10 are generalizations7 of equation (9) in [14, Section 3] and second  equation in [17, Lemma 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let n ≥ 3 be an odd number with n = 2s + 1, define  Sodd = {A1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Dn−3A1} ∪ ⋯ ∪ {As−1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Dn−s+1As−1} ∪ {As}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Similarly, let n ≥ 4 be an even number with n = 2s, define  Seven = {A1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Dn−3A1} ∪ ⋯ ∪ {As−2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Dn−sAs−2} ∪ {As−1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In either case, we denote both Sodd, and Seven as Sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' C[L±1][DA] is a quotient of the ring C[L±1][Sn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This follows easily from Lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  As in [16] and [17], we do not know if there are any further polynomial relations among the  elements of the differential graded algebra C[L±1][DA].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  7For n = 5, this generalization is explained in more detail by matching the functions in [14] with ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' HOLOMORPHIC ANOMALY EQUATIONS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' More on flatness equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The modified flatness equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10), Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1, and Corol-  lary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15 imply that ̃P k  i,j ∈ C[L±1][DA].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Through Lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10, and the modified flatness  equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10), we have a canonical lift of each ̃P k  i,j to the free algebra C[L±1][Sn] via the fol-  lowing order:  ̃P k  n−1,j = ̃P k  0,j + 1  LD ̃P k−1  0,j ∈ C[L±1] ⊆ C[L±1][Sn]  ̃P k  n−2,j = ̃P k  n−1,j + 1  LD ̃P k−1  n−1,j + A1 ̃P k−1  n−1,j ∈ C[L±1][A1] ⊆ C[L±1][Sn]  ⋮  =  ⋮  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  More precisely, we start with ̃P k  0,j ∈ C[L±1] and use equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10) for i = n,n − 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',2 in this  descending order to inductively construction lifts of ̃P k  i,j for i = n − 1,n − 2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',1 in this descending  order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this process, unnecessary Ai’s are eliminated using Lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10, and orders of  derivatives are bounded above using Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In the rest of this subsection, we consider this lift and denote it also as  ̃P k  i,j ∈ C[L±1][Sn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1 (Odd case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 3 be an odd number with n = 2l+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have the following identity  ∂ ̃P k  i,j  ∂Al  = δi,l ̃P k−1  l+1,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' From the modified flatness equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10), and the lifting procedure (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  ∂ ̃P k  i,j  ∂Al  = 0  for l + 1 ≤ i ≤ n − 1 and i = 0 since ̃P k  i,j does not contain Al term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now observe the following two  equations  ̃P k  l,j = ̃P k  l+1,j + 1  LD ̃P k−1  l+1,j + Al ̃P k−1  l+1,j ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  ̃P k  l−1,j = ̃P k  l,j + 1  LD ̃P k−1  l,j  − Al ̃P k−1  l,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4)  These are first two rows in modified flatness equations where we see Al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' From the first equation  we see that  ∂ ̃P k  l,j  ∂Al  = ̃P k−1  l+1,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Note that Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10 gives  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5)  ∂ (DAl)  ∂Al  = 2LAl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, by equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5) we have  ∂ ̃P k  l−1,j  ∂Al  =  ∂ ̃P k  l,j  ∂Al  + 1  L  ∂ (D ̃P k−1  l,j )  ∂Al  − ̃P k−1  l,j  − Al  ∂ ̃P k−1  l,j  ∂Al  =  ∂ ̃P k  l,j  ∂Al  + 1  L (2LAl ̃P k−2  l+1,j + D ̃P k−2  l+1,j) − ̃P k−1  l,j  − Al  ∂ ̃P k−1  l,j  ∂Al  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6)  26  GENLIK AND TSENG  and equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) implies that  ∂ ̃P k  l−1,j  ∂Al  = ̃P k−1  l+1,j + 2Al ̃P k−2  l+1,j + 1  LD ̃P k−2  l+1,j − ̃P k−1  l,j  − Al ̃P k−2  l+1,j  = ̃P k−1  l+1,j + Al ̃P k−2  l+1,j + 1  LD ̃P k−2  l+1,j − ̃P k−1  l,j  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7)  It immediately follows from the modified flatness equations and equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7) that  ∂ ̃P k  i,j  ∂Al  = 0  for 0 ≤ i ≤ l − 1 since ̃P k  i,j does not contain any Al term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2 (Even case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 4 be an even number with n = 2l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have the following identity  ∂ ̃P k  i,j  ∂Al−1  = δi,l ̃P k−1  l+1,j + δi,(l−1) ̃P k−1  l,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' From the modified flatness equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10), and the lifting procedure (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8)  ∂ ̃P k  i,j  ∂Al−1  = 0  for l+1 ≤ i ≤ n − 1 and i = 0 since ̃P k  i,j does not contain Al−1 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Observe the following equations  ̃P k  l,j = ̃P k  l+1,j + 1  LD ̃P k−1  l+1,j + Al−1 ̃P k−1  l+1,j  ̃P k  l−1,j = ̃P k  l,j + 1  LD ̃P k−1  l,j  ̃P k  l−2,j = ̃P k  l−1,j + 1  LD ̃P k−1  l−1,j − Al−1 ̃P k−1  l−1,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  Two of these equations are first two rows in modified flatness equations where we see Al−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' From  the first equation we see that  ∂ ̃P k  l,j  ∂Al−1  = ̃P k−1  l+1,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Note that by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10, we have  ∂ (DAl−1)  ∂Al−1  = LAl−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This implies  ∂ ̃P k  l−1,j  ∂Al−1  =  ∂ ̃P k  l,j  ∂Al−1  + 1  L  ∂ (D ̃P k−1  l,j )  ∂Al−1  = ̃P k−1  l+1,j + 1  L (LAl−1 ̃P k−2  l+1,j + D ̃P k−2  l+1,j)  = ̃P k−1  l,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  27  The equalities obtained so far simply show that ̃P k  l−1,j is of degree 2 with respect to Al−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let ̃P k  l−1,j  be given by  ̃P k  l−1,j = K A2  l−1  2  + HAl−1 + Q  where K, H, are constants with respect to Al−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, we see that K and H are given by  K = ̃P k−2  l+1,j  and  H = ̃P k−1  l,j  − ̃P k−2  l+1,jAl−1 = ̃P k−1  l+1,j + 1  LD ̃P k−2  l+1,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We will need the following intermediate calculation to complete the proof:  ∂(D ̃P k  l−1,j)  ∂Al−1  =  ∂  ∂Al−1  ((DK)A2  l−1  2  + KAl−1DAl−1 + (DH)Al−1 + H(DAl−1) + DQ)  =(DK)Al−1 + K(DAl−1) + KLA2  l−1 + DH + LHAl−1  =(D ̃P k−2  l+1,j)Al−1 + ̃P k−2  l+1,j(DAl−1) + L ̃P k−2  l+1,jA2  l−1  + D ̃P k−1  l,j  − (D ̃P k−2  l+1,j)Al−1 − ̃P k−2  l+1,j(DAl−1) + L ̃P k−1  l,j Al−1 − L ̃P k−2  l+1,jA2  l−1  =D ̃P k−1  l,j  + L ̃P k−1  l,j Al−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Next, we compute  ∂ ̃P k  l−2,j  ∂Al−1  =  ∂ ̃P k  l−1,j  ∂Al−1  + 1  L  ∂ (D ̃P k−1  l−1,j)  ∂Al−1  − ̃P k−1  l−1,j − Al−1  ∂ ̃P k−1  l−1,j  ∂Al−1  = ̃P k−1  l,j  + 1  LD ̃P k−2  l,j  + ̃P k−2  l,j Al−1 − ̃P k−1  l−1,j − Al−1 ̃P k−2  l,j  = ̃P k−1  l,j  + 1  LD ̃P k−2  l,j  − ̃P k−1  l−1,j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10)  It immediately follows from the modified flatness equations and equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10) that  ∂ ̃P k  i,j  ∂Al−1  = 0  for 0 ≤ i ≤ l − 2 since ̃P k  i,j does not contain any Al−1 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Formula for potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Semisimple Cohomological Field Theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By general considerations, Gromov-Witten the-  ory of [Cn/Zn] has the structure of a cohomological field theory (CohFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We refer to [12] and [20]  for discussions on CohFTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the results of Section 1, this CohFT is semisimple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The Givental-Teleman classification of  semisimple CohFTs [10], [23] states that a semisimple CohFT Ω can be obtained from its topolog-  ical part via the actions of its R-matrix and T-vector, where T(z) is given by z(Id −R(z)) applied  to the unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We refer to [20] and [21] for detailed discussions on this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Generating functions of a CohFT Ω can be defined by integrating CohFT classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' If Ω is semisim-  ple, its topological part can be evaluated explicitly in the idempotent basis, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' [17, Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' A consequence of the Givental-Teleman classification is that the generating functions of Ω  can be explicitly written as sums of graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' A reference for this can be found in [17, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  28  GENLIK AND TSENG  The R-matrix for the Gromov-Witten theory of [Cn/Zn] is studied in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The general  consideration on semisimple CohFTs recalled above yields a formula for the Gromov-Witten po-  tential F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In the remainder of this subsection, we work out this formula in  details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In order to state the formula for Gromov-Witten potentials, we need to describe  certain graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  A stable graph Γ is a tuple  Γ = (VΓ,g ∶ VΓ → Z≥0,HΓ,ι ∶ HΓ → HΓ,LΓ,ℓ ∶ LΓ → {1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,m},ν ∶ HΓ ∪ LΓ → VΓ)  satisfying:  (1) VΓ is the set of vertices and g ∶ VΓ → Z≥0 is a genus assignment,  (2) HΓ is the set of half-edges and ι ∶ HΓ → HΓ is an involution,  (3) EΓ is the set of edges8 defined by the orbits of ι ∶ HΓ → HΓ, and the tuple (VΓ,EΓ) defines  a connected graph,  (4) LΓ is the set of legs and ℓ ∶ LΓ → {1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,m} is an isomorphism labeling legs,  (5) The map ν ∶ HΓ ∪ LΓ → VΓ is a vertex assignment,  (6) For each vertex v, let l(v) and h(v) be the number of legs and the number of edges attached  to the vertex v respectively and hence n(v) = l(v) + h(v) be the valence of the vertex v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, for each vertex v the following (stability) condition holds:  2g(v) − 2 + n(v) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The genus of Γ is defined by  g(Γ) = h1(Γ) + ∑  v∈V  g(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In the formula for Gromov-Witten potentials, we need to work with decorated stable graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This has to do with the T-action on CohFTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' To see this, we recall the description of the T-actions  in general, as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let Ω be a CohFT based on the vector space V and let  T(z) = T2z2 + T3z3 + ⋯  be a V -valued power series with vanishing coefficients in degrees 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The translation of Ω by  T is the CohFT TΩ defined by  TΩg,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm) = ∑  k⩾0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (πk)∗ Ωg,m+k (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm,T (ψm+1),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,T (ψm+k))  where πk ∶ M g,m+k → Mg,m is the forgetful map dropping the last k marked points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Here, by above  notation, we actually mean  Ωg,m+k (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,T (ψi),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=') = ∑  r⩾2  ψr  i Ωg,m+k (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Tr,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now, consider elements of V written in terms of the normalized idempotent basis,  vj =  n−1  ∑  i=0  vij̃ei  and  Tr =  n−1  ∑  i=0  Tir̃ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  8self-edges are allowed  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  29  Then, assume in addition9 that Ω is a topological field theory, we have  TΩg,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm) = ∑  k⩾0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (πk)∗ Ωg,m+k (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm,T (ψm+1),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,T (ψm+k))  = ∑  k⩾0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∑  r1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',rk≥2  (  k  ∏  l=1  (πk)∗ (ψrl  m+l))Ωg,m+k (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm,Tr1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Trk)  = ∑  k⩾0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∑  r1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',rk≥2  (  k  ∏  l=1  (πk)∗ (ψrl  m+l))  ×  ∑  0≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',im+k≤n−1  vi11⋯vimmTim+1r1⋯Tim+krkΩg,m+k (̃ei1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,̃eim,̃eim+1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,̃eim+k)  = ∑  k⩾0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∑  r1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',rk≥2  (  k  ∏  l=1  (πk)∗ (ψrl  m+l))  n−1  ∑  i=0  vi1⋯vimTir1⋯Tirkg(ei,ei)− 2g−2+m+k  2  =  n−1  ∑  i=0  vi1⋯vim ∑  k≥0  g(ei,ei)− 2g−2+m+k  2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  ∑  r1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',rk≥2  Tir1⋯Tirk (  k  ∏  l=1  (πk)∗ (ψrl  m+l))  =  n−1  ∑  i=0  vi1⋯vim ∑  k≥0  g(ei,ei)− 2g−2+m+k  2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (πk)∗ (ti(ψm+1)⋯ti(ψm+k)),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11)  where  ti(z) = ∑  r≥2  Tirzr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Note that the above derivation uses the explicit evaluation of a topological field theory in the nor-  malized idempotent basis, c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' [17, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Setting the summand of TΩg,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm) to  ̃Ωi  g,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm) = vi1⋯vim ∑  k≥0  g(ei,ei)− 2g−2+m+k  2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (πk)∗ (ti(ψm+1)⋯ti(ψm+k))  we can write it as  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12)  TΩg,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm) =  n−1  ∑  i=0  ̃Ωi  g,m (v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,vm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the formula for generating functions, as described in [17, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2], for each vertex in a  stable graph, a class TΩg,m is inserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12), this is equivalent to inserting ̃Ωig,m if  vertices of stable graphs carry extra labels i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This leads to the notion of decorated stable graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  More precisely, a decorated stable graph  Γ ∈ GDec  g,m(n)  of order n is a stable graph Γ ∈ Gg,m with an extra assignment p ∶ VΓ → {0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',n−1} to each vertex  v ∈ VΓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  9This case suffices for our purpose, because in the formula for Fg,m from Givental-Teleman classification, T acts  on the topological part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  30  GENLIK AND TSENG  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Formula for Fg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By the discussions above, we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13)  F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) =  ∑  Γ∈GDec  g,m(n)  ContΓ (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The following is the generalization of Proposition 15 of [16] to [Cn/Zn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For each decorated stable graph Γ ∈ GDec  g,m(n), the associated contribution is  given by  ContΓ (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) =  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  ∏  v∈VΓ  ContA  Γ(v) ∏  e∈EΓ  ContA  Γ(e) ∏  l∈LΓ  ContA  Γ(l)  where F(Γ) = ∣HΓ ∪ LΓ∣ = m + ∣HΓ∣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Here, ContA  Γ(v), ContA  Γ(e), and ContA  Γ(l) are the vertex,  edge and leg contributions with flag A−values10 (a1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,am,b1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,b∣HΓ∣) respectively, and they  are given by  ContA  Γ(v) = ∑  k≥0  g(ep(v),ep(v))− 2g−2+n(v)+k  2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  × ∫Mg(v),n(v)+k  ψav1  1 ⋯ψ  avl(v)  l(v) ψbv1  l(v)+1⋯ψ  bvh(v)  n(v) tp(v)(ψn(v)+1)⋯tp(v)(ψn(v)+k),  ContA  Γ(e) =(−1)be1+be2  n  be2  ∑  j=0  (−1)j  n−1  ∑  r=0  ̃P be1+j+1  Inv(r),p(v1) ̃P be2−j  r,p(v2)  ζ(be1+j+1+Inv(r))p(v1)ζ(be2−j+r)p(v2),  ContA  Γ(l) =(−1)aℓ(l)  n  KInv(cℓ(l))  LInv(cℓ(l))  ̃P  aℓ(l)  Inv(cℓ(l)),p(ν(l))  ζ(aℓ(l)+Inv(cℓ(l)))p(ν(l)) ,  where  tp(v)(z) = ∑  i≥2  Tp(v)izi  with  Tp(v)i = (−1)i  n  ̃P i  0,p(v)ζ−ip(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' To simplify notations, write {˜e} for the normalized idempotent basis {˜e0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' , ˜en−1} and {φ}  for the basis {φ0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φn−1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let T φ  ˜e be the transition matrix from {˜e} to {φ} and let T ˜e  φ be its  inverse i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' the transition matrix from {φ} to {˜e}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, we have  T φ  ˜e = Ψ−1,  T ˜e  φ = Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let G and ̃G be matrix representations of the metric g with respect to basis {φ} and {˜e}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then,  the relation between them is given by  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14)  ̃G = (Ψ−1)  T GΨ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  And it can easily be shown that we have ̃G = Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Define T(z) = z (Id − R−1(z)) ⋅ φ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We provided R-matrix action with respect to normalized  idempotent basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' To be consistent we need to write φ0 in terms of {˜e} basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Since we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15)  φ0 =  n−1  ∑  i=0  Ψi0˜ei = 1  n (˜e0 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' + ˜en−1),  we see that T(z) = z (Id − R−1(z)) v where v = 1  n[1⋯1]T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  10Notation: The values bv1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,bvh(v) and be1,be2 are the entries of (a1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,am,b1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,b∣HΓ∣) corresponding to  ContA  Γ(v) and ContA  Γ(e) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  31  We now find R−1(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By the symplectic condition, R−1(z) = Rt(−z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Here Rt(−z) means  adjoint with respect to the metric g in the basis {˜e}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We see that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16)  R−1(z) = Rt(−z) = ̃G−1RT(−z) ̃G = RT (−z) = (ΨP(−z))T = P T(−z)ΨT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Also observe that  [ΨTv]i =1  n  n−1  ∑  j=0  ΨT  ij = 1  n  n−1  ∑  j=0  Ψji  =1  n  n−1  ∑  j=0  1  nζij Li  Ki  = 1  n2  Li  Ki  n−1  ∑  j=0  ζij = 1  n2nδi0 = 1  nδi0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17)  So, we have ΨTv = 1  n [10⋯0]T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This implies that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='18)  T(z) = z (Id − R−1(z)) v = T2z2 + T3z3 + ⋯  with Tk is the coefficient of zk−1 in −R−1(z)v where  Tjk = the jth entry of the coefficient of zk−1 in − R−1(z)v  = the jth entry of the coefficient of zk−1 in − P T(−z)ΨT v  = (−1)k  n  P k  0j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='19)  This enables us to understand the translation action by T(z) and vertex contributions after the  translation action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Next, we will understand effects of R-matrix action and obtain the expressions  for the contributions fully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now, consider  F(z,w) = M(z,w)  z + w  with both F(z,w),M(z,w) ∈ C[[z,w]],  F(z,w) = ∑  a,b≥0  βa,bzawb  and  M(z,w) = ∑  c,d≥0  αc,dzcwd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, the coefficients βa,b are given by  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20)  βa,b =  b  ∑  m=0  (−1)mαa+m+1,b−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now observe that  [ΨTΨ]lj =  n−1  ∑  r=0  ΨrlΨrj =  n−1  ∑  r=0  1  nζrl Ll  Kl  1  nζrj Lj  Kj  = 1  n2  Ll  Kl  Lj  Kj  n−1  ∑  r=0  ζr(l−Inv(j)) = 1  n2  Ll  Kl  Lj  Kj  nδlInv(j)  = 1  n  LInv(j)+j  KInv(j)Kj  �����������������������������������������  =1  δlInv(j) = 1  nδlInv(j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='21)  32  GENLIK AND TSENG  Next,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' in order to understand the edge contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' we compute  δij − [R−1(z)R−1(w)T]ij = δij −  n−1  ∑  s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='r=0  P T  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='s(−z)[ΨTΨ]sr Pr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j(−w)  = δij −  n−1  ∑  s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='r=0  P T  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='s(−z)1  nδsInv(r)Pr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j(−w)  = δij − 1  n  n−1  ∑  r=0  P T  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Inv(r)(−z)Pr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j(−w)  = δij − 1  n  n−1  ∑  r=0  ∑  c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d≥0  (−1)c+dP c  Inv(r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='iP d  r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='jzcwd  = δij − 1  n  n−1  ∑  r=0  ∑  c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d≥0  (−1)c+dKInv(r)  LInv(r)  ̃P c  Inv(r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i  ζ−(c+Inv(r))i  Kr  Lr  ̃P d  r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j  ζ−(d+r)j zcwd  = δij − 1  n  n−1  ∑  r=0  ∑  c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='d≥0  (−1)c+d  ̃P c  Inv(r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='i ̃P d  r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='j  ζ−(c+Inv(r))iζ−(d+r)j zcwd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='22)  So, we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='23)  δij − [R−1(z)R−1(w)T]ij  z + w  =  ∑  b1,b2≥0  βi,j  b1,b2zb1wb2  with  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='24)  βi,j  b1,b2 = (−1)b1+b2  n  b1  ∑  m=0  (−1)m  n−1  ∑  r=0  ̃P b1+m+1  Inv(r),i ̃P b2−m  r,j  ζ−(b1+m+1+Inv(r))iζ−(b2−m+r)j  by equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  In order to understand the leg contributions, we compute  [R−1(z) ⋅ φj]i = [P T(−z)ΨT Ψ]ij = ∑  a≥0  (−1)a  n−1  ∑  r=0  P a  r,i  1  nδrInv(j)za  = ∑  a≥0  (−1)a  n  KInv(j)  LInv(j)  ̃P a  Inv(j),i  ζ−(a+Inv(j))iza  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='25)  for each 0 ≤ i,j ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let v ∈ VΓ be a vertex of a decorated stable graph Γ with legs {lv1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,lvl(v)} ⊆ LΓ and edges  {ev1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,evh(v)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, the (cycle-valued) contribution associated to this vertex, its legs and edges  connected to this vertex is11  ̃Ωp(v)  g(v),l(v)+h(v)(R−1(ψ1)⋅φcℓ(lv1),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,R−1(ψl(v)) ⋅ φcℓ(lvl(v)),̃ep(v),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,̃ep(v)  �����������������������������������������������������������������������  h(v) many  )  ×  h(v)  ∏  i=1  ⎛  ⎜  ⎝  ∑  bevi,be′  i≥0  β  p(v),p(v′  i)  bevi,be′  i  ψ  bevi  l(v)+iψ  be′  i  l(v′  i)+j  ⎞  ⎟  ⎠  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  11Notation: Here v′  i is the vertex at the other end of the edge evi and ψl(v′  i)+j is the psi class associated to the marked  point corresponding to the other half of the edge evi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  33  This together with equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='24), and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='25) complete the proof after integration of cycle-  valued contributions of graph Γ over M g,m and using functoriality of push-forward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  An immediate corollary of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 is the following finite generation property of the  Gromov-Witten potential F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The vertex, edge, and leg contributions of ContΓ (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) lie in certain poly-  nomial rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' More, precisely  ContA  Γ(v) ∈ C[L±1],  ContA  Γ(e) ∈ C[L±1][Sn],  ContA  Γ(e) ∈ C[L±1][Sn][Cn]  where Cn = {C1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,Cn−1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Hence, we have  F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) ∈ C[L±1][Sn][Cn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This is immediate from Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 and the modified flatness equations  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  We should note that Ci’s are related to each other via Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3, hence Cn consists of C1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,C⌊ n+1  2 ⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Also, we should emphasize that the Gromov-Witten potential F [Cn/Zn]  g,m  (φc1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' ,φcm) may lie in a  smaller ring depending on insertions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For example, Fg lies in C[L±1][Sn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The following two lemmas are cruicial for the proof of holomoprhic anomaly equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 3 be an odd number with n = 2s + 1, then we have  ∂  ∂As  ContA  Γ(e) = (−1)be1+be2  2s + 1  ̃P be1  s+1,p(v1) ̃P be2  s+1,p(v2)  ζ(be1+s+1)p(e1)ζ(be2+s+1)p(v2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The proof is the following direct computation:  ∂  ∂As  ContA  Γ(e) =(−1)be1+be2  n  be2  ∑  m=0  (−1)m  n−1  ∑  r=0  ∂  ∂As ( ̃P be1+m+1  Inv(r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2−m  r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2))  ζ(be1+m+1+Inv(r))p(v1)ζ(be2−m+r)p(v2)  =(−1)be1+be2  n  be2  ∑  m=0  (−1)m  ̃P be1+m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2−m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2)  ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)  + (−1)be1+be2  n  be2−1  ∑  m=0  (−1)m  ̃P be1+m+1  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2−m−1  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2)  ζ(be1+m+s+2)p(v1)ζ(be2−m+s)p(v2)  =(−1)be1+be2  n  be2  ∑  m=0  (−1)m  ̃P be1+m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2−m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2)  ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)  + (−1)be1+be2  n  be2  ∑  m=1  (−1)m−1  ̃P be1+m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2−m  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2)  ζ(be1+m+s+1)p(v1)ζ(be2−m+s+1)p(v2)  =(−1)be1+be2  2s + 1  ̃P be1  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v1) ̃P be2  s+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='p(v2)  ζ(be1+s+1)p(v1)ζ(be2+s+1)p(v2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The first equality is just the derivative of the edge contribution part of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The second  equality follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1 and ̃P k  i,j = 0 by definition if k < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The rest is just shifting the  index of the first sum and cancelling out the terms of the total expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  34  GENLIK AND TSENG  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 4 be an even number with n = 2s, then we have  ∂  ∂As−1  ContA  Γ(e) = (−1)be1+be2  2s  ⎛  ⎝  ̃P be1  s+1,p(v1) ̃P be2  s,p(v2)  ζ(be1+s+1)p(v1)ζ(be2+s)p(v2) +  ̃P be1  s,p(v1) ̃P be2  s+1,p(v2)  ζ(be1+s)p(v1)ζ(be2+s+1)p(v2)  ⎞  ⎠ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The proof is similar to that of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case, we use Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2 instead of Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Proof of holomorphic anomaly equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We are now ready to present the main results of  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The results depend on the parity of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 3 be an odd number with n = 2s + 1, and g ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Cs+1  (2s + 1)L  ∂  ∂As  F [Cn/Zn]  g  = 1  2F [Cn/Zn]  g−1,2  (φs,φs) + 1  2  g−1  ∑  i=1  F [Cn/Zn]  g−i,1  (φs)F [Cn/Zn]  i,1  (φs)  in C[L±1][Sn][Cs+1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let ˜e ∈ EΓ be an edge of a decorated stable graph Γ ∈ GDec  g,0 (n) and let ˜e ∈ EΓ be connecting  two vertices v1 and v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Deletion of the edge ˜e results in a new graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (By deletion, we imply that  we break the edge ˜e into two new legs l˜e and l′  ˜e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=') There are two possibilities: either the resulting  graph is connected or it is disconnected with two connected parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (i) If the resulting graph is connected, then it is an element of GDec  g−1,2(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case, we  denote the resulting graph as Γ0  ˜e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case, note that ∣Aut(Γ)∣ = ∣Aut(Γ0  ˜e)∣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (ii) If the resulting graph is disconnected, then we denote its connected components as Γ1  ˜e ∈  GDec  g1,1(n) and Γ2  ˜e ∈ GDec  g2,1(n) where g = g1 + g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case, for the cardinality of the auto-  morphism groups of the decorated stable graphs, we have12 ∣Aut(Γ)∣ = ∣Aut(Γ1  ˜e)∣∣Aut(Γ2  ˜e)∣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5, we observe that  ∂ContA  Γ(˜e)  ∂As  =(−1)b˜e1+b˜e2  2s + 1  ̃P b˜e1  s+1,p(v1) ̃P b˜e2  s+1,p(v2)  ζ(b˜e1+s+1)p(v1)ζ(b˜e2+s+1)p(v2)  =(2s + 1)( Ls+1  Ks+1  )  2 ⎧⎪⎪⎨⎪⎪⎩  ContA  Γ0  ˜e(l˜e)ContA  Γ0  ˜e(l′  ˜e)  for the case (i),  ContA  Γ1  ˜e(l˜e)ContA  Γ2  ˜e(l′  ˜e)  for the case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, we also note that  ( Ls+1  Ks+1  )  2  =  L  Cs+1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, for case (i), we easily see that we have  ContΓ0  ˜e (φs,φs) =  1  ∣Aut(Γ0  ˜e)∣  ∑  A∈Z  F(Γ0  ˜e )  ≥0  ∏  v∈VΓ0  ˜e  ContA  Γ0  ˜e(v) ∏  e∈EΓ0  ˜e  ContA  Γ0  ˜e(e) ∏  l∈LΓ0  ˜e  ContA  Γ0  ˜e(l)  =  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  Cs+1  (2s + 1)L  ∂ContA  Γ(˜e)  ∂As  ∏  v∈VΓ  ContA  Γ(v) ∏  e∈EΓ  e≠˜e  ContA  Γ(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='26)  12There is a special case when Γ1  ˜e = Γ2  ˜e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case Γ has a Z2-symmetry given by interchanging Γ1  ˜e and Γ2  ˜e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Hence  ∣Aut(Γ)∣ = ∣Aut(Γ1  ˜e)∣2 × 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  35  Similarly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' for case (ii),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' we observe the following  ContΓ1  ˜e (φs)ContΓ2  ˜e (φs)  =  1  ∣Aut(Γ1  ˜e)∣  ∑  A∈Z  F(Γ1  ˜e )  ≥0  ContA  Γ1  ˜e(l˜e) ∏  v∈VΓ1  ˜e  ContA  Γ1  ˜e(v) ∏  e∈EΓ1  ˜e  ContA  Γ1  ˜e(e)  ×  1  ∣Aut(Γ2  ˜e)∣  ∑  A∈Z  F(Γ2  ˜e )  ≥0  ContA  Γ2  ˜e(l′  ˜e) ∏  v∈VΓ2  ˜e  ContA  Γ2  ˜e(v) ∏  e∈EΓ2  ˜e  ContA  Γ2  ˜e(e)  =  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  Cs+1  (2s + 1)L  ∂ContA  Γ(˜e)  ∂As  ∏  v∈VΓ  ContA  Γ(v) ∏  e∈EΓ  e≠˜e  ContA  Γ(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='27)  By Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, we have the following vanishing result  ∂ContA  Γ(v)  ∂As  = 0  for any vertex v ∈ VΓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This vanishing result gives us:  ∂ContΓ  ∂As  =  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  ∏  v∈VΓ  ContA  Γ(v) ∂  ∂As  ( ∏  e∈EΓ  ContA  Γ(e))  =  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  ∏  v∈VΓ  ContA  Γ(v) ∏  e∈EΓ  e≠˜e  ContA  Γ(e)∂ContA  Γ(˜e)  ∂As  = ∑  ˜e∈EΓ  1  ∣Aut(Γ)∣  ∑  A∈ZF(Γ)  ≥0  ∂ContA  Γ(˜e)  ∂As  ∏  v∈VΓ  ContA  Γ(v) ∏  e∈EΓ  e≠˜e  ContA  Γ(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='28)  By equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='26), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='27), and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='28), we complete the proof after summing these equations  over all decorated stable graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The reason we have a factor of 1  2 on the right hand side of the  holomorphic anomaly equation is compensation13 due to not having a canonical order of labelings  of each of the legs l˜e and l′  ˜e for case (i) and connected components for case (ii) after deleting the  edge ˜e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Let n ≥ 4 be an even number with n = 2s, and g ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Cs+1  2sL  ∂  ∂As−1  F [Cn/Zn]  g  = F [Cn/Zn]  g−1,2  (φs−1,φs) +  g−1  ∑  i=1  F [Cn/Zn]  g−i,1  (φs−1)F [Cn/Zn]  i,1  (φs)  in C[L±1][Sn][Cs+1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The proof is similar to the proof of odd case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Again after deleting an edge ˜e from a decorated  stable graph Γ, we have cases (i) and (ii) in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 for the graph decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  13In the special case (ii) with Γ1  ˜e = Γ2  ˜e, there is not a double counting issue when summing over all decorated stable  graphs unlike the other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this case the factor 2 coming from Z2 symmetry is compensated again by the factor 1  2  in the equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  36  GENLIK AND TSENG  By Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5, we observe that  ∂  ∂As−1  ContA  Γ(˜e) =(−1)be1+be2  2s  ⎛  ⎝  ̃P be1  s+1,p(v1) ̃P be2  s,p(v2)  ζ(be1+s+1)p(v1)ζ(be2+s)p(v2) +  ̃P be1  s,p(v1) ̃P be2  s+1,p(v2)  ζ(be1+s)p(v1)ζ(be2+s+1)p(v2)  ⎞  ⎠  =(2s) LsLs+1  KsKs+1  ⎧⎪⎪⎨⎪⎪⎩  ContA  Γ0  ˜e(l˜e)ContA  Γ0  ˜e(l′  ˜e) + ContA  Γ0  ˜e(l′  ˜e)ContA  Γ0  ˜e(l˜e)  for (i),  ContA  Γ1  ˜e(l˜e)ContA  Γ2  ˜e(l′  ˜e) + ContA  Γ1  ˜e(l′  ˜e)ContA  Γ2  ˜e(l˜e)  for (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Using Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4, we note that  LsLs+1  KsKs+1  =  L  Cs+1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The rest of the proof is identical to the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' however, this time we obtain two  products of leg contributions for both cases (i) and (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' This is the reason why we do not have the  factor 1  2 on the right hand side of holomorphic anomaly equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' STIRLING NUMBERS  In this section, we provide a brief account on Stirling numbers and their properties used in the  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' A detailed treatment of Stirling numbers can be found in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Convenient online references  for Stirling numbers include [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The Stirling number of first kind sm,k is defined to be the coefficient of xk of the falling factorial:  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  (x)m = x(x − 1)⋯(x − m + 1) =  m  ∑  k=0  sm,kxk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The special case s0,0 is set to be 1 and certain Stirling numbers of first kind we use to do some  explicit computations in the paper are:  sm,0 = 0  for m ≥ 1,  sm,m−1 = −(m  2 ),  sm,m−2 = 3m − 1  4  (m  3 ),  sm,m−3 = −(m  2 )(m  4 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The Stirling number of second kind Sm,k is the number of ways to partition a set of m objects into  k non-empty subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Stirling numbers of the second kind satisfy the following basic recurrence:  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  Sm,k = kSm−1,k + Sm−1,k−1  with  Sm,0 = δm,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  A well-known formula for Stirling numbers of second kind called Euler’s formula is  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  Sm,k = 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  k  ∑  i=0  (−1)k−i(k  i)im.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  If k is not in the range 0 ≤ k ≤ m, Stirling numbers sm,k and Sm,k are defined to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The following  relation holds  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4)  ∑  j≥0  sm,jSj,k = ∑  j≥0  Sm,jsj,k = δm,k  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Striling numbers are inverses of each other when they are seen as triangular matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  37  APPENDIX B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' A NOTE ON I-FUNCTIONS  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Series associated to I-functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' In this Appendix, we carry out a detailed analysis for the  I-function of [Cn/Zn] by following the methodology of [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1 (See [25]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Suppose y0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',ym, f, g, a are functions of t (with f not identically 0)  satisfying  ymf (m) + ym−1f (m−1) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' + y0f =0,  ymg(m) + ym−1g(m−1) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' + y0g =a,  where f (k) = dkf  dtk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then the function h = (g/f)′ satisfies  ˜ym−1h(m−1) + ˜ym−2h(m−2) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' + ˜y0h = a,  where ˜ys(t) = ∑m  r=s+1 ( r  s+1)yr(t)f (r−1−s)(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We obtain the following result that is similar to [25, Corollary 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Suppose F(x,z) satisfies  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  m  ∑  r=0  Wr(x)DrF(x,z) = A(x,z)  with A(∞,x) ≡ 0, then we have  (  m−1  ∑  s=0  ˜Ws(x)Ds)MF(x,z) = zA(x,z),  where ˜Ws(x) = ∑m  r=s+1 ( r  s+1)Wr(x)D(r−1−s)F(x,∞) and M is defined in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Apply Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1 with f(t) = F(et,∞), g(t) = F(et,z), a(t) = A(et,z), and yr(t) =  Wr(et) for 0 ≤ r ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The series Ck in x satisfy the following properties:  (1) Ck+n = Ck for all k ≥ 1,  (2) ∏n  k=1 Ck = Ln,  (3) Ck = Cn+1−k for all 1 ≤ k ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Since we basically set all φi’s in I(x,z) to 1 to obtain the series E(x,z), it also satisfies the  Picard-Fuchs equation:  x−n ((1 − (−1)n (x  n)  n  )DnE(x,z) +  n−1  ∑  k=1  sn,kDkE(x,z)) = z−nE(x,z)  which is of the form (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1) with F(x,z) = E(x,z), A(x,z) = z−nE(x,z), m = n, and  Wn(x) =x−n (1 − (−1)n (x  n)  n  ) = L−n,  Wr(x) =x−nsn,r  for  (1 ≤ r ≤ n − 1),  W0(x) =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Applying Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2 repeatedly, we obtain  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2)  n−1−p  ∑  s=0  Ws,p(x)DsEp+1(x,z) = z−n+p+1E(x,z)  (0 ≤ p ≤ n − 1),  38  GENLIK AND TSENG  where Ei(x,z) is defined in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14) and Ws,p(x) is given inductively by  Ws,p(x) =  n−p  ∑  r=s+1  ( r  s + 1)Wr,p−1(x)Dr−1−sCp(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By induction on p, we see that the first coefficient in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2) is given by  Wn−1−p,p(x) = Wn(x)  p  ∏  i=1  Ci(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2) for p = n − 1 gives  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  (Wn(x)  n−1  ∏  i=1  Ci(x)) En(x,z) = E(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Letting z = ∞ in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3), using E(x,∞) = 1, Wn(x) = L−n and En(x,∞) = Cn(x) we obtain  L−n  n  ∏  i=1  Ci(x) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  which proves part (2) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Substituting part (2) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3 into equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3) gives  En(x,z)  Cn(x)  = E(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Applying Mk−1zD to both sides of this equality for k ≥ 1 results in  En+k(x,z) = Ek(x,z),  which proves part (1) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Now, equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='23) yields that for any 0 ≤ i,j ≤ n − 1 we have  Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='L0Ii+1 = Lj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='L0Ij+1  if  i + j = n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Applying the operator D to both sides gives part (3) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  For any l ≥ 0, we define the following series in x  Kl =  l  ∏  i=0  Ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The series Kl satisfy  (1) Kn+l = LnKl for all l ≥ 0, in particular Kn = Ln,  (2) KlKn−l = Ln and KlKInv(l) = Ll+Inv(l) for all 0 ≤ l ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For the first part, the special case Kn = Ln is just part (2) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Then, general case  Kn+l = LnKl follows from part (1) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For the second part, we calculate  KlKn−l =(  l  ∏  i=1  Ci)(  n−l  ∏  j=1  Cj)  =(  l  ∏  i=1  Ci)(  n−l  ∏  j=1  Cn+1−j)  by part (3) of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3  =(  l  ∏  i=1  Ci)(  n  ∏  i=l+1  Ci) = Kn = Ln,  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  39  the rest follows from the fact that K0Kn = 1 ⋅ Ln and Inv(l) = n − l for 1 ≤ l ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Asymptotic solutions of Picard-Fuchs equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ j ≤ n − 1, define  DLj = D + Lj  z  and  µj = ∫  x  0  Lj(u)  u  du  where Lj = Lζj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Assume for 0 ≤ j ≤ n − 1 a function of the form e  µj  z Φj(z) satisfies the Picard-Fuchs  equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  L−n (Dn (e  µj  z Φj(z)) + DL  L  n−1  ∑  r=1  sn,rDr (e  µj  z Φj(z))) = z−ne  µj  z Φj(z)  where  Φj(z) =  ∞  ∑  k=0  Φj,kzk  with Φj,k ∈ C[[x]] and Φj,k = 0 if k < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, we have Φj,k ∈ C[Lj] = C[L].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For the rest of this section, our aim is to prove Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5, hence we adopt its assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For  any function F(x,z), observe the following  D (e  µj  z F(x,z)) = e  µj  z DF(x,z) + Dµj  z e  µj  z F(x,z)  = e  µj  z DF(x,z) + Lj  z e  µj  z F(x,z)  = e  µj  z DLjF(x,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4)  Then, the equation in Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5 reads as  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5)  LjΦj(z) = 0  where  Lj = −(Lj  z )  n  + Dn  Lj + DLj  Lj  n−1  ∑  r=1  sn,rDr  Lj  using equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='4), Ln = (Lj)n, and DL  L = DLj  Lj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For 1 ≤ k ≤ n, define14  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6)  Lj,k =  k  ∑  i=0  ((n  i)Hn−i,k−i + DLj  Lj  k−i  ∑  r=1  (n − r  i  )sn,n−rHn−i−r,k−i−r)Di  where Hm,l are defined15 by the following recursion for m ≥ 1 and 0 ≤ l ≤ m:  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7)  H0,l = δ0,l,  and  Hm,l = Hm−1,l + n(1 + (−1)n X  nn)(X d  dX + m − l  n  )Hm−1,l−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  14Note that the definition of Lj,k does not depend on j since Ln = (Lj)n, and DL  L = DLj  Lj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  15Hm,l is set to be 0 outside the range m ≥ 1, 0 ≤ l ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  40  GENLIK AND TSENG  By induction, we see that  Hm,l =0  if l > m,  Hm,0 =1  for m ≥ 0,  Hm,1 =(m  2 )(1 + (−1)n X  nn)  for m ≥ 1,  Hm,2 =3(m  4 )(1 + (−1)n X  nn)  2  + (m  3 )((n + 1)(1 + (−1)n X  nn)  2  − n(1 + (−1)n X  nn))  for m ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Let  X =Ln  j = Ln  Y =DLj  Lj  = DL  L = 1 + (−1)n Ln  nn = 1 + (−1)n X  nn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8)  Then, we see that  DY =(−1)n Ln−1  nn−1 DL = (−1)n Ln  nn−1  DL  L = (−1)n  1  nn−1XY,  DX =nLn−1DL = nLnDL  L = nXY = nX (1 + (−1)n X  nn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Also, using Stirling numbers of the first kind which are explicitly given in Appendix A, we  compute the first two terms of Lj,k:  Lj,1 =nD,  Lj,2 =(n + 1  4 )(Y 2 − Y ) − (n  2)Y D + (n  2)D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Dk  Lj =  k  ∑  m=0  m  ∑  l=0  ( k  m)Hm,l (Lj  z )  m−l  Dk−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' First, we prove by induction that  Dk  Lj =  k  ∑  m=0  ( k  m)Dm  Lj(1)Dk−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We need to note that  DLj (FDk) = (D + Lj  z )(FDk)  = (DF)Dk + FDk+1 + Lj  z FDk  = (DLjF)Dk + FDk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  For the base step k = 1, we have  DLj = D + Lj  z = D + DLj(1) =  1  ∑  m=0  ( 1  m)Dm  Lj(1)D1−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  41  For the inductive step, we have  Dk  Lj = DLjDk−1  Lj  =  k−1  ∑  m=0  (k − 1  m )DLj (Dm  Lj(1)Dk−1−m)  =  k−1  ∑  m=0  (k − 1  m )(Dm+1  Lj (1)Dk−1−m + Dm  Lj(1)Dk−m)  by equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m )Dm+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj (1)Dk−1−m +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m )Dm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−m  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='( k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m − 1)Dm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−m +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='(k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m )Dm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−m  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='= (k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='�������������������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=(k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Dk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−k +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='((k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m − 1) + (k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m ))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='����������������������������������������������������������������������������������������������������������������������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=( k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Dm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−m + (k − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='0 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='�������������������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=(k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='0)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='D0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='LjDk−0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='∑  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='( k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='m)Dm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='Lj(1)Dk−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Next, using another induction we prove  Dm  Lj(1) =  m  ∑  l=0  Hm,l (Lj  z )  m−l  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  We begin with some observations:  DHm−1,l(X) = d  dX Hm−1,lDX  = n(1 + (−1)n X  nn)X d  dX Hm−1,l  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10)  and  D (Lj  z )  m−1−l  = (m − 1 − l)(Lj  z )  m−2−l  D (Lj  z )  = (m − 1 − l)(Lj  z )  m−2−l  (Lj  z )(1 + (−1)n X  nn)  = (1 + (−1)n Xn  nn )(m − 1 − l)(Lj  z )  m−1−l  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11)  and  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12)  DLj(FG) = (DF)G + F(DG) + Lj  z (FG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  For the base step m = 0, we have  D0  Lj(1) = 1 = H0,0 (Lj  z )  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  42  GENLIK AND TSENG  For the inductive step, assume the statement holds for m − 1, then  Dm  Lj  = DLjDm−1  Lj  = DLj  m−1  ∑  l=0  Hm−1,l (Lj  z )  m−1−l  =  m−1  ∑  l=0  ((DHm−1,l)(Lj  z )  m−1−l  + Hm−1,lD (Lj  z )  m−1−l  + Hm−1,l (Lj  z )  m−l  )  by equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, by equations (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='10) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='11), we see that  Dm  Lj  =  m−1  ∑  l=0  ((n(1 + (−1)n X  nn)(X d  dX + m − 1 − l  n  )Hm−1,l)(Lj  z )  m−1−l  + Hm−1,l (Lj  z )  m−l  )  =  m  ∑  l=1  (n(1 + (−1)n X  nn)(X d  dX + m − l  n  )Hm−1,l−1)(Lj  z )  m−l  +  m−1  ∑  l=0  Hm−1,l (Lj  z )  m−l  =  m  ∑  l=0  (n(1 + (−1)n X  nn)(X d  dX + m − l  n  )Hm−1,l−1 + Hm−1,l)(Lj  z )  m−l  by Hm−1,−1 = 0, Hm−1,m = 0  =  m  ∑  l=0  Hm,l (Lj  z )  m−l  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lj =  n  ∑  k=1  (Lj  z )  n−k  Lj,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='6, and the definition16 of Lj we have  Lj = −(Lj  z )  n  +  n  ∑  m=0  m  ∑  l=0  Hm,l(n  m)(Lj  z )  m−l  Dn−m + DLj  Lj  n−1  ∑  r=0  r  ∑  m=0  �������������  =∑m=n−1  m=0  ∑r=n−1  r=m  m  ∑  l=0  sn,r( r  m)Hm,l (Lj  z )  m−l  Dr−m  = −(Lj  z )  n  +  n  ∑  m=0  m  ∑  l=0  Hm,l(n  m)(Lj  z )  m−l  Dn−m + DLj  Lj  n−1  ∑  m=0  m  ∑  l=0  n−1  ∑  r=m  sn,r( r  m)Hm,l (Lj  z )  m−l  Dr−m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By separating m = n case from the first double summation and by the change of indices via m = n−i  and l = k − i, we obtain  Lj = − (Lj  z )  n  +  n  ∑  l=0  (n  n)Hn,l (Lj  z )  n−l  +  n  ∑  i=1  n  ∑  k=i  �  =∑k=n  k=1 ∑i=k  i=1  (Lj  z )  n−k  (( n  n − i)Hn−i,k−iDi + DLj  Lj  n−1  ∑  r=n−i  sn,r( r  n − i)Hn−i,k−iDr−n+i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  16Note that the sum in the definition of Lj in equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5) can start at r = 0 since sn,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  43  Change the index l to k in the first summation and shift r by n − i:  Lj = − (Lj  z )  n  +  n  ∑  k=0  (n  n)Hn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='l (Lj  z )  n−k  +  n  ∑  k=1  k  ∑  i=1  (Lj  z )  n−k  ( n  n − i)  �����������������  =(n  i)  Hn−i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−iDi  + DLj  Lj  n  ∑  k=1  (Lj  z )  n−k  (⋆)  �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������  k  ∑  i=1  i−1  ∑  r=0  sn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='r+n−i (r + n − i  n − i )  ��������������������������������������������  =(r+n−i  r  )  Hn−i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−iDr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13)  For (⋆), we have  k  ∑  i=1  i−1  ∑  r=0  �  =∑r=k−1  r=0  ∑i=k  i=r+1  sn,r+n−i(r + n − i  r  )Hn−i,k−iDr =  k−1  ∑  i=0  k  ∑  r=i+1  sn,i+n−r(i + n − r  i  )Hn−r,k−rDi  (i ↔ r)  =  k−1  ∑  i=0  k−i  ∑  r=1  sn,n−r(n − r  i  )Hn−i−r,k−i−rDi  shift r by i  =  k  ∑  i=0  k−i  ∑  r=1  sn,n−r(n − r  i  )Hn−i−r,k−i−rDi  since Hn−k−r,−r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Note also that  −(Lj  z )  n  +  n  ∑  k=0  (n  n)Hn,k (Lj  z )  n−k  =  n  ∑  k=1  (n  n)Hn,k (Lj  z )  n−k  Hence, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='13) reads as  Lj =  n  ∑  k=1  (n  n)Hn,k (Lj  z )  n−k  +  n  ∑  k=1  k  ∑  i=1  (Lj  z )  n−k  (n  i)Hn−i,k−iDi  ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������  These can be combined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  + DLj  Lj  n  ∑  k=1  (Lj  z )  n−k k  ∑  i=0  k−i  ∑  r=1  sn,n−r(n − r  i  )Hn−i−r,k−i−rDi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  So,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' we have  Lj =  n  ∑  k=1  (Lj  z )  n−k k  ∑  i=0  (n  i)Hn−i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−iDi + DLj  Lj  n  ∑  k=1  (Lj  z )  n−k  k  ∑  i=0  k−i  ∑  r=1  sn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−r(n − r  i  )Hn−i−r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−i−rDi  =  n  ∑  k=1  (Lj  z )  n−k k  ∑  i=0  ((n  i)Hn−i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−i + DLj  Lj  k−i  ∑  r=1  sn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='n−r(n − r  i  )Hn−i−r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k−i−r)Di  �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������  =Lj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='k  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' For 0 ≤ j ≤ n − 1 and k ≥ 0, we have  Lj,1(Φj,k) + 1  Lj  Lj,2(Φj,k−1) + 1  L2  j  Lj,3(Φj,k−2) + ⋯ +  1  Ln−1  j  Lj,n(Φj,k+1−n) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  44  GENLIK AND TSENG  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We calculate  0 = LjΦj(z) =  n  ∑  l=1  (Lj  z )  n−l  Lj,lΦj(z)  by Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7  =  n  ∑  l=1  ∞  ∑  k=0  (Lj  z )  n−l  Lj,lΦj,kzk  =  n  ∑  l=1  ∞  ∑  k=0  Lj  n−lLj,lΦj,kzk+l−n  =  n  ∑  l=1  ∞  ∑  k=l−1  Lj  n−lLj,lΦj,k+1−lzk+1−n  shift k by l − 1  =  n  ∑  l=1  ∞  ∑  k=0  Lj  n−lLj,lΦj,k+1−lzk+1−n  since Φj,k+1−l = 0 for k < l − 1  =  ∞  ∑  k=0  n  ∑  l=1  Lj  n−lLj,lΦj,k+1−lzk+1−n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5) reads as  n  ∑  l=1  Lj  n−lLj,lΦj,k+1−l = 0  for any k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By dividing out Ln−1  j  , we finish the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Let  I ⊂ C[L]  be the ideal generated by XY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' We have  Lj,k ≡ (n  k)(D)(D − Y )⋯(D − (k − 1)Y )  mod I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Note that Y and D commute modulo I:  D(Y F) = (DY )F + Y (DF) = (−1)n  nn−1 XY F + Y (DF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Also observe that for any r ≥ 1 we have,  Y r ≡ (Y )r−1Y  mod I  ≡ (1 + (−1)n X  nn)r−1Y  mod I  ≡ Y  mod I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14)  We first show by induction that  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15)  Hm,l ≡ hm,lY l  mod I  where hm,l = Sm,m−l is the Stirling number of the second kind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The only thing we need to prove is  that if Hm,l ≡ hm,lY l mod I, then the numbers hm,l are given by the recursion  h0,l = δ0,l, and hm,l = hm−1,l + (m − l)hm−1,l−1 for all m ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This will imply hm,l = Sm,m−l by recursion (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' The base case l = 0 is given by  Hm,0 = 1, and hm,0 = Sm,m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  45  The recursion above is equivalent to equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='7):  Hm,l ≡ Hm−1,l + nY (X d  dX + m − l  n  )Hm−1,l−1  mod I  ≡ Hm−1,l + (m − l)Y Hm−1,l−1  mod I  which is the same as  hm,lY l ≡ Hm−1,lY l + (m − l)Y Hm−1,l−1Y l−1  mod I  ≡ Hm−1,lY l + (m − l)Hm−1,l−1Y l  mod I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By induction, cancelling out Y l on both sides we get what we want;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' that is, Hm,l ≡ hm,lY l mod I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  By the definitions of Y and Lj,k, and using equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='14) in the second line, we obtain  Lj,k ≡  k  ∑  i=0  ((n  i)Hn−i,k−i + Y  k−i  ∑  r=1  (n − r  i  )sn,n−rHn−i−r,k−i−r)Di  mod I  ≡  k  ∑  i=0  ((n  i)Hn−i,k−i +  k−i  ∑  r=1  Y r(n − r  i  )sn,n−rHn−i−r,k−i−r)Di  mod I  ≡  k  ∑  i=0  (  k−i  ∑  r=0  Y r(n − r  i  )sn,n−rHn−i−r,k−i−r)Di  mod I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16)  Then, by equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15) we have  Lj,k ≡  k  ∑  i=0  (  k−i  ∑  r=0  Y r(n − r  i  )sn,n−rhn−i−r,k−i−rY k−i−r)Di  mod I  ≡  k  ∑  i=0  (  k−i  ∑  r=0  (n − r  i  )sn,n−rhn−i−r,k−i−r)Y k−iDi  mod I  ≡  k  ∑  i=0  (  k−i  ∑  r=0  (n − r  i  )sn,n−rSn−i−r,n−k)Y k−iDi  mod I  by hm,l = Sm,m−l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17)  Next, we calculate  k  ∑  i=0  (  k−i  ∑  r=0  (n − r  i  )sn,n−rSn−i−r,n−k)ti  =  n  ∑  i=0  (  n−i  ∑  r=0  (n − r  i  )sn,n−rSn−i−r,n−k)ti  since Sn−i−r,n−k = 0 if i + r > k  =  n  ∑  i=0  (  n−i  ∑  r=0  (n − r  i  )sn,n−r [  1  (n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  n−k  ∑  l=0  (−1)n−k−l(n − k  l  )ln−r−i])ti  by Euler’s formula (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3)  =  1  (n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  n−k  ∑  l=0  (−1)n−k−l(n − k  l  )  n  ∑  i=0  n−i  ∑  r=0  �  =∑n  r=0 ∑n−r  i=0  sn,n−r(n − r  i  )ln−r−iti  =  1  (n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  n−k  ∑  l=0  (−1)n−k−l(n − k  l  )  n  ∑  r=0  sn,n−r(l + t)n−r  by binomial formula  =  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  n−k  ∑  l=0  (−1)n−k−l(n − k  l  )(l + t  n )  by equation (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1)  46  GENLIK AND TSENG  =  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  (n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (t  k)  = (n  k)t(t − 1)⋯(t − (k − 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The second-to-last equality is obtained by expanding (1 + u)tun−k = (1 + u)t((1 + u) − 1)n−k via  binomial formula, matching coefficients of un on both sides and using Chu-Vandermonde identity:  (s + t  m ) =  m  ∑  k=0  (s  k)(  t  m − k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, we have  k  ∑  i=0  (  k−i  ∑  r=0  (n − r  i  )sn,n−rSn−i−r,n−k)yk−iti = (n  k)t(t − y)⋯(t − (k − 1)y)  This together with equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='17) completes the proof of the lemma when it is combined with the  commutation of Y and D modulo I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  □  Now, we are ready to prove Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Since D and Y commutes modulo I, inductively we  show that  (D)(D − Y )⋯(D − (k − 1)Y )Lr  j  mod I ≡ {0  if 0 ≤ r ≤ k − 1,  r(r − 1)⋯(r − (k − 1))Lr  jY k  if r ≥ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Then, Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='9 implies that  Lj,k (Lr  j) ∈ {I  if 0 ≤ r ≤ k − 1,  Lr  jY k + I  if r ≥ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  From this, we conclude that Lj,k(C[Lj]) ⊆ Lk  jY C[Lj] for any 1 ≤ k ≤ n since I is generated by  XY and X = Ln  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Moreover, for the case k = 1, we have the equality Lj,1(C[Lj]) = LjY C[Lj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This is because we have Lj,1(Lr  j) = nDLr  j = nrLr  jY for any r ≥ 1 and Lj,1(a) = nDa = 0 for any  a ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  It is clear that the statement is true if k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Now, we prove the statement inductively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' By  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='16, we have the following  Lj,1(Φj,k) = −  n  ∑  l=2  Lj  1−lLj,l (Φj,k+1−l) ∈ LjY C[Lj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  The right hand side belongs to LjY C[Lj] by inductive hypothesis since Lj,l(C[Lj]) ⊆ Ll  jY C[Lj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  This shows Φj,k ∈ C[Lj] and completes the proof of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='5 since Lj,1(C[Lj]) = LjY C[Lj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  REFERENCES  [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Abramovich, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Graber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 130  (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 5, 1337–1398.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Alim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Scheidegger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Yau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Zhou Special polynomial rings, quasi modular forms and duality of  topological strings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Advances in Theoretical and Mathematical Physics (2014), 18(2), 401-467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Bershadsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Cecotti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Ooguri, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Vafa, Holomorphic anomalies in topological field theories, Nuclear  Physics B (1993), 405(2-3), 279-304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Bershadsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Cecotti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Ooguri, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Vafa, Kodaira-Spencer theory of gravity and exact results for  quantum string amplitudes, Nuclear Physics B (1994), 405(2-3), 279-304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Coates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Corti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Iritani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Tseng, Computing Genus-Zero Twisted Gromov-Witten Invariants, Duke  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 147 (2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='3, 377–438.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  HIGHER GENUS GROMOV-WITTEN THEORY OF [Cn/Zn] I: HOLOMORPHIC ANOMALY EQUATIONS  47  [6] Set Partitions: Stirling Numbers, Digital Library of Mathematical Functions, Section 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Genlik, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Tseng, Holomorphic anomaly equations for [C5/Z5], arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='15878.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Genlik, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Tseng, Higher genus Gromov-Witten theory of [Cn/Zn] II: Crepant resolution correspondence,  in preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Givental, Elliptic Gromov-Witten invariants and the generalized mirror conjecture, in: “Integrable systems  and algebraic geometry (Kobe/Kyoto, 1997)”, 107–155, World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=', River Edge, NJ, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Givental, Symplectic geometry of Frobenius structures, in: “Frobenius manifolds”, Aspects Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=', E36, 91–  112, Friedr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Vieweg, Wiesbaden, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Gould, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Quaintance, Combinatorial identities for Stirling numbers: the unpublished notes of HW Gould,  World Scientific 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Kontsevich, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 164 (1994), 525–562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lee, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, Frobenius manifolds, Gromov-Witten theory, and Virasoro constraints, manuscript  available from the authors’ websites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho, Crepant resolution conjecture for C5/Z5, arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='02910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho, Equivariant holomorphic anomaly equation, arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='05503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, Stable quotients and the holomorphic anomaly equation, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 332 (2018),  349–402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [17] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, Crepant resolution and the holomorphic anomaly equation for [C3/Z3], Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' London  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' (3) 119 (2019), 781–813.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Lho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, Holomorphic anomaly equations for the formal quintic , Peking Mathematical Journal  (2019), 2(1), 1-40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Oberdieck, Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface,  arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='03361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, Cohomological field theory calculations, Proceedings of the ICM (Rio de Janeiro 2018), Vol  1, 869–898, World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Publications: Hackensack, NJ, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pixton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Zvonkine, Relations on M g,n via 3-spin structures, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 28  (2015), 279–309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Pandharipande, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Tseng, Higher genus Gromov-Witten theory of Hilbn(C2) and CohFTs associated to  local curves, Forum of Mathematics, Pi (2019), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 7, e4, 63 pages, arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='01406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Teleman, The structure of 2D semi-simple field theories, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 188 (2012), 525–588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Tseng, Orbifold quantum Riemann-Roch, Lefschetz and Serre, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 14 (2010), 1–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Zagier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Zinger, Some properties of hypergeometric series associated with mirror symmetry, In: “Modular  forms and string duality”, 163–177, Fields Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=' 54, AMS 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='  DEPARTMENT OF MATHEMATICS, OHIO STATE UNIVERSITY, 100 MATH TOWER, 231 WEST 18TH AVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',  COLUMBUS, OH 43210, USA  Email address: genlik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='1@osu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='edu  DEPARTMENT OF MATHEMATICS, OHIO STATE UNIVERSITY, 100 MATH TOWER, 231 WEST 18TH AVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content=',  COLUMBUS, OH 43210, USA  Email address: hhtseng@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
+page_content='ohio-state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtE_T4oBgHgl3EQf-xzf/content/2301.08389v1.pdf'}
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+arXiv:2301.13396v1  [eess.SP]  31 Jan 2023
+Study of Optical Networks, 5G, Artificial
+Intelligence and Their Applications
+Quanda Zhang
+School of Telecommunication
+Daqing Normal College
+Qi Zhang
+School of Telecommunication
+Daqing Normal College
+Abstract—This paper discusses the application of artificial
+intelligence (AI) technology in optical communication networks
+and 5G. It primarily introduces representative applications of AI
+technology and potential risks of AI technology failure caused by
+the openness of optical communication networks, and proposes
+some coping strategies, mainly including modeling AI systems
+through modularization and miniaturization, combining with
+traditional classical network modeling and planning methods,
+and improving the effectiveness and interpretability of AI tech-
+nology. At the same time, it proposes response strategies based
+on network protection for the possible failure and attack of AI
+technology.
+Index Terms—AI, 5G, Optical Networks
+I. INTRODUCTION
+Artificial intelligence (AI, artificial intelligence) technology
+is very early has been used in many fields, but for many
+years this technology has not gained high attention until
+AlphaGo defeated Chinese and Korean Go players After the
+hand, it began to become a research hotspot, and researchers
+tried to AI technology is applied in different fields, including
+optical communication network network. In the past two years,
+the United States Optical Communications Conference (OFC,
+optical fiber communication) and the European Conference
+of Optical Communications (ECOC, European conference of
+optical communication), at least 16 conference topics focused
+on AI or machine learning (ML, machine learning) technology.
+This paper combines AI technology and ML technology AI
+technologies are regarded as the same class of technologies,
+and at the same time, although AI technologies cover a wide
+range, The AI technology referred to in this article is mainly
+neural network technology.
+AI technology has received widespread attention mainly
+due to the following two reasons. First, AI technology is
+relatively easy to get started and use. it comes in black
+Model the system in a box way, through a large number of
+samples Learning, let the black box connect neurons by itself,
+and distribute neurons Connect weights without requiring the
+user to understand why neurons behave the way they do
+connections and are assigned current weights. Users only need
+to provide enough learning samples, increase the number of
+neurons and the number of hidden layers, It can improve the
+prediction accuracy of AI technology. Second, AI technology
+is After the AlphaGo incident, it has almost been deified, and
+almost everyone knows that ”people ”artificial intelligence”,
+and in the academic circle, the paper labeled AI Papers also
+seem to be easier to publish, so this also leads to a current
+phenomenon Like, that is, for almost all problems, regardless
+of whether it is suitable or not, the use of AI technology for
+modeling and solving.
+AI technology is very successful in solving some problems,
+as before Go and some image-to-speech recognition scenarios
+mentioned above, but cannot Due to the successful solution
+of a certain field or certain problems, AI is regarded as
+a ”universal method”. This paper aims at the current AI
+technology in optical communication Discuss the application
+of AI technology in the network, including the application of
+AI technology in optical communication network applicability
+in the network, and raises the potential risk of using AI
+technology Some coping strategies.
+II. AI APPLICATIONS IN OPTICAL NETWORKS
+AI technology has been widely used in the literature of
+optical communication networks [1]–[7]. A great deal of re-
+search can be found in this area. This paper introduces several
+representative applications of AI technology in optical commu-
+nication networks. 1) On receiving At the end, using the digital
+signal processing method combined with AI technology, it can
+effectively improve the detection sensitivity of optical signals
+and improve the optical fiber transmission system performance
+and improve the spectrum utilization efficiency of the network
+[7], [8]. 2) In the optical network, there are a large number
+of end-to-end optical channels, and these optical channels are
+respectively related parameters (including transmission rate,
+modulation format, number of optical fiber links, number of
+optical amplifiers and gain, etc.) and their receiving the signal
+transmission quality (QoT, quality of transmission) detected
+by the end is used as input and output, and through a lot of
+learning, it can be realized Prediction of QoT for different end-
+to-end optical channels in optical networks; where QoT often
+expressed as the signal-to-noise ratio of the optical channel
+(OSNR, optical signal to noise ratio), its accurate prediction
+can reduce the optical channel OSNR margin configuration,
+thereby improving the spectrum utilization efficiency of the
+network [9], [10]. 3) pass Continuously learn the fault events
+in the optical network, and use the fault and fault cause
+Because it is used as input and output, it can accurately
+analyze and diagnose the cause of the fault early warning of
+future failures
+[3]. 4) Combined with the need for network
+
+security, AI technology can also be used for early warning and
+identification of network attacks on the optical layer [11].
+III. AI APPLICATIONS IN 5G COMMUNICATION
+AI and ML are being utilized in 5G and mmWave com-
+munication [12]–[18] to enhance performance, reduce costs,
+and boost efficiency. Applications of AI in this field include
+network optimization, predictive maintenance, self-organizing
+networks, traffic prediction, security, resource allocation, net-
+work slicing, edge computing, interference management, and
+spectrum management. These technologies are still in the early
+stages of development but have the potential to significantly
+improve the performance, efficiency, and cost-effectiveness of
+these networks. As AI technologies continue to evolve and
+become more widely adopted, they will likely play an in-
+creasingly important role in the development and deployment
+of 5G and mmWave communication systems. However, it is
+also crucial to consider potential risks and challenges such as
+ensuring privacy, security, and ethical considerations.
+AI techniques apply the same “black box” approach to
+different application scenarios leading to method innovation
+and analysis of the underlying mechanism slack. A very typical
+example is as follows. Thanks to AI technologies such as
+deep learning can effectively recognize some image patterns,
+there are studies that the researchers applied this technology
+to the identification of lesions in different parts of the human
+body [19], [20]. Based on the same method and process,
+different human parts are continuously used bit pictures, which
+can form a large number of so-called ”research results” and
+thesis. Obviously, from the perspective of cultivating students
+and scientific research, students The development of research
+skills and professionalism acquired practically in the project
+are very few, and the actual work is only to collect relevant
+image data and Write a small amount of Python code, and
+finally hand over the training task to the graph Processor
+(GPU, graphics processing unit) to complete, no Carry out
+in-depth thinking on the method and mechanism of specific
+research questions It is obviously not conducive to innovation
+and effective innovation, and it is impossible to grasp (in fact,
+it is currently impossible to grasp) what is going on in the
+black box.
+REFERENCES
+[1] M. Zhang, C. You, H. Jiang, and Z. Zhu, “Dynamic and adaptive
+bandwidth defragmentation in spectrum-sliced elastic optical networks
+with time-varying traffic,” Journal of Lightwave Technology, vol. 32,
+no. 5, pp. 1014–1023, 2014.
+[2] W. Lu, X. Jin, and Z. Zhu, “Game theoretical flexible service provi-
+sioning in ip over elastic optical networks,” in 2017 16th International
+Conference on Optical Communications and Networks (ICOCN). IEEE,
+2017, pp. 1–3.
+[3] X. Jin, W. Lu, S. Liu, and Z. Zhu, “On multi-layer restoration in optical
+networks with encryption solution deployment,” in 2018 Optical Fiber
+Communications Conference and Exposition (OFC).
+IEEE, 2018, pp.
+1–3.
+[4] L. Gong and Z. Zhu, “Virtual optical network embedding (vone) over
+elastic optical networks,” Journal of Lightwave Technology, vol. 32,
+no. 3, pp. 450–460, 2013.
+[5] Y. Yin, H. Zhang, M. Zhang, M. Xia, Z. Zhu, S. Dahlfort, and S. B.
+Yoo, “Spectral and spatial 2d fragmentation-aware routing and spectrum
+assignment algorithms in elastic optical networks,” Journal of Optical
+Communications and Networking, vol. 5, no. 10, pp. A100–A106, 2013.
+[6] O. J. Ciceri, C. A. Astudillo, Z. Zhu, and N. L. da Fonseca, “Federated
+learning over next-generation ethernet passive optical networks,” arXiv
+preprint arXiv:2109.14593, 2021.
+[7] X. Chen, B. Li, R. Proietti, H. Lu, Z. Zhu, and S. B. Yoo, “Deeprmsa:
+a deep reinforcement learning framework for routing, modulation and
+spectrum assignment in elastic optical networks,” Journal of Lightwave
+Technology, vol. 37, no. 16, pp. 4155–4163, 2019.
+[8] X. Chen, B. Li, R. Proietti, Z. Zhu, and S. B. Yoo, “Multi-agent
+deep reinforcement learning in cognitive inter-domain networking with
+multi-broker orchestration,” in 2019 Optical Fiber Communications
+Conference and Exhibition (OFC).
+IEEE, 2019, pp. 1–3.
+[9] X. Chen, B. Li, R. Proietti, C.-Y. Liu, Z. Zhu, and S. B. Yoo,
+“Demonstration of distributed collaborative learning with end-to-end qot
+estimation in multi-domain elastic optical networks,” Optics Express,
+vol. 27, no. 24, pp. 35 700–35 709, 2019.
+[10] S. Liu, B. Li, and Z. Zhu, “Realizing ai-assisted multi-layer restoration
+in a software-defined ip-over-eon with deep learning: An experimental
+study,” in Optical Fiber Communication Conference.
+Optical Society
+of America, 2018, pp. W4F–1.
+[11] X. Tian, B. Li, R. Gu, and Z. Zhu, “Reconfiguring multicast sessions in
+elastic optical networks adaptively with graph-aware deep reinforcement
+learning,” Journal of Optical Communications and Networking, vol. 13,
+no. 11, pp. 253–265, 2021.
+[12] X. Lu, R. Zhang, Y. Zhou, J. Liu, X. Jin, Q. Guo, and C. Cao, “Con-
+volutional modeling and antenna de-embedding for wideband spatial
+mmwave channel measurement,” in 2017 IEEE Wireless Communica-
+tions and Networking Conference (WCNC).
+IEEE, 2017, pp. 1–6.
+[13] K. Shafique, B. A. Khawaja, F. Sabir, S. Qazi, and M. Mustaqim,
+“Internet of things (iot) for next-generation smart systems: A review
+of current challenges, future trends and prospects for emerging 5g-iot
+scenarios,” Ieee Access, vol. 8, pp. 23 022–23 040, 2020.
+[14] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Channel
+estimation and hybrid precoding for millimeter wave cellular systems,”
+IEEE journal of selected topics in signal processing, vol. 8, no. 5, pp.
+831–846, 2014.
+[15] P. Bhartia and I. J. Bahl, “Millimeter wave engineering and applications,”
+1984.
+[16] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G. N.
+Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wave
+mobile communications for 5g cellular: It will work!” IEEE access,
+vol. 1, pp. 335–349, 2013.
+[17] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broad-
+band systems,” IEEE communications magazine, vol. 49, no. 6, pp. 101–
+107, 2011.
+[18] M. Marcus and B. Pattan, “Millimeter wave propagation: spectrum
+management implications,” IEEE Microwave Magazine, vol. 6, no. 2,
+pp. 54–62, 2005.
+[19] A. Shrikumar, P. Greenside, A. Shcherbina, and A. Kundaje, “Not just
+a black box: Learning important features through propagating activation
+differences,” arXiv preprint arXiv:1605.01713, 2016.
+[20] M. Sendak, M. C. Elish, M. Gao, J. Futoma, W. Ratliff, M. Nichols,
+A. Bedoya, S. Balu, and C. O’Brien, “” the human body is a black box”
+supporting clinical decision-making with deep learning,” in Proceedings
+of the 2020 conference on fairness, accountability, and transparency,
+2020, pp. 99–109.
+
+This figure "fig1.png" is available in "png"� format from:
+http://arxiv.org/ps/2301.13396v1
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf,len=222
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='13396v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='SP]  31 Jan 2023  Study of Optical Networks, 5G, Artificial  Intelligence and Their Applications  Quanda Zhang  School of Telecommunication  Daqing Normal College  Qi Zhang  School of Telecommunication  Daqing Normal College  Abstract—This paper discusses the application of artificial  intelligence (AI) technology in optical communication networks  and 5G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' It primarily introduces representative applications of AI  technology and potential risks of AI technology failure caused by  the openness of optical communication networks, and proposes  some coping strategies, mainly including modeling AI systems  through modularization and miniaturization, combining with  traditional classical network modeling and planning methods,  and improving the effectiveness and interpretability of AI tech-  nology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' At the same time, it proposes response strategies based  on network protection for the possible failure and attack of AI  technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  Index Terms—AI, 5G, Optical Networks  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' INTRODUCTION  Artificial intelligence (AI, artificial intelligence) technology  is very early has been used in many fields, but for many  years this technology has not gained high attention until  AlphaGo defeated Chinese and Korean Go players After the  hand, it began to become a research hotspot, and researchers  tried to AI technology is applied in different fields, including  optical communication network network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' In the past two years,  the United States Optical Communications Conference (OFC,  optical fiber communication) and the European Conference  of Optical Communications (ECOC, European conference of  optical communication), at least 16 conference topics focused  on AI or machine learning (ML, machine learning) technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  This paper combines AI technology and ML technology AI  technologies are regarded as the same class of technologies,  and at the same time, although AI technologies cover a wide  range, The AI technology referred to in this article is mainly  neural network technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  AI technology has received widespread attention mainly  due to the following two reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' First, AI technology is  relatively easy to get started and use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' it comes in black  Model the system in a box way, through a large number of  samples Learning, let the black box connect neurons by itself,  and distribute neurons Connect weights without requiring the  user to understand why neurons behave the way they do  connections and are assigned current weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Users only need  to provide enough learning samples, increase the number of  neurons and the number of hidden layers, It can improve the  prediction accuracy of AI technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Second, AI technology  is After the AlphaGo incident, it has almost been deified, and  almost everyone knows that ”people ”artificial intelligence”,  and in the academic circle, the paper labeled AI Papers also  seem to be easier to publish, so this also leads to a current  phenomenon Like, that is, for almost all problems, regardless  of whether it is suitable or not, the use of AI technology for  modeling and solving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  AI technology is very successful in solving some problems,  as before Go and some image-to-speech recognition scenarios  mentioned above, but cannot Due to the successful solution  of a certain field or certain problems, AI is regarded as  a ”universal method”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' This paper aims at the current AI  technology in optical communication Discuss the application  of AI technology in the network, including the application of  AI technology in optical communication network applicability  in the network, and raises the potential risk of using AI  technology Some coping strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' AI APPLICATIONS IN OPTICAL NETWORKS  AI technology has been widely used in the literature of  optical communication networks [1]–[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' A great deal of re-  search can be found in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' This paper introduces several  representative applications of AI technology in optical commu-  nication networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1) On receiving At the end, using the digital  signal processing method combined with AI technology, it can  effectively improve the detection sensitivity of optical signals  and improve the optical fiber transmission system performance  and improve the spectrum utilization efficiency of the network  [7], [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 2) In the optical network, there are a large number  of end-to-end optical channels, and these optical channels are  respectively related parameters (including transmission rate,  modulation format, number of optical fiber links, number of  optical amplifiers and gain, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=') and their receiving the signal  transmission quality (QoT, quality of transmission) detected  by the end is used as input and output, and through a lot of  learning, it can be realized Prediction of QoT for different end-  to-end optical channels in optical networks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' where QoT often  expressed as the signal-to-noise ratio of the optical channel  (OSNR, optical signal to noise ratio), its accurate prediction  can reduce the optical channel OSNR margin configuration,  thereby improving the spectrum utilization efficiency of the  network [9], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 3) pass Continuously learn the fault events  in the optical network, and use the fault and fault cause  Because it is used as input and output, it can accurately  analyze and diagnose the cause of the fault early warning of  future failures  [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 4) Combined with the need for network  security, AI technology can also be used for early warning and  identification of network attacks on the optical layer [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' AI APPLICATIONS IN 5G COMMUNICATION  AI and ML are being utilized in 5G and mmWave com-  munication [12]–[18] to enhance performance, reduce costs,  and boost efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Applications of AI in this field include  network optimization, predictive maintenance, self-organizing  networks, traffic prediction, security, resource allocation, net-  work slicing, edge computing, interference management, and  spectrum management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' These technologies are still in the early  stages of development but have the potential to significantly  improve the performance, efficiency, and cost-effectiveness of  these networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' As AI technologies continue to evolve and  become more widely adopted, they will likely play an in-  creasingly important role in the development and deployment  of 5G and mmWave communication systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' However, it is  also crucial to consider potential risks and challenges such as  ensuring privacy, security, and ethical considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  AI techniques apply the same “black box” approach to  different application scenarios leading to method innovation  and analysis of the underlying mechanism slack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' A very typical  example is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Thanks to AI technologies such as  deep learning can effectively recognize some image patterns,  there are studies that the researchers applied this technology  to the identification of lesions in different parts of the human  body [19], [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Based on the same method and process,  different human parts are continuously used bit pictures, which  can form a large number of so-called ”research results” and  thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Obviously,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' from the perspective of cultivating students  and scientific research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' students The development of research  skills and professionalism acquired practically in the project  are very few,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' and the actual work is only to collect relevant  image data and Write a small amount of Python code,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' and  finally hand over the training task to the graph Processor  (GPU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' graphics processing unit) to complete,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' no Carry out  in-depth thinking on the method and mechanism of specific  research questions It is obviously not conducive to innovation  and effective innovation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' and it is impossible to grasp (in fact,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  it is currently impossible to grasp) what is going on in the  black box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  REFERENCES  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' You, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Jiang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “Dynamic and adaptive  bandwidth defragmentation in spectrum-sliced elastic optical networks  with time-varying traffic,” Journal of Lightwave Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 32,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1014–1023, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [2] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Jin, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “Game theoretical flexible service provi-  sioning in ip over elastic optical networks,” in 2017 16th International  Conference on Optical Communications and Networks (ICOCN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' IEEE,  2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [3] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Jin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Lu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Liu, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “On multi-layer restoration in optical  networks with encryption solution deployment,” in 2018 Optical Fiber  Communications Conference and Exposition (OFC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [4] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Gong and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “Virtual optical network embedding (vone) over  elastic optical networks,” Journal of Lightwave Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 32,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 450–460, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Yin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Xia, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Dahlfort, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  Yoo, “Spectral and spatial 2d fragmentation-aware routing and spectrum  assignment algorithms in elastic optical networks,” Journal of Optical  Communications and Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' A100–A106, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [6] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Ciceri, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Astudillo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' da Fonseca, “Federated  learning over next-generation ethernet passive optical networks,” arXiv  preprint arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='14593, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [7] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Proietti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Lu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Yoo, “Deeprmsa:  a deep reinforcement learning framework for routing, modulation and  spectrum assignment in elastic optical networks,” Journal of Lightwave  Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 4155–4163, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [8] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Proietti, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Yoo, “Multi-agent  deep reinforcement learning in cognitive inter-domain networking with  multi-broker orchestration,” in 2019 Optical Fiber Communications  Conference and Exhibition (OFC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [9] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Proietti, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Yoo,  “Demonstration of distributed collaborative learning with end-to-end qot  estimation in multi-domain elastic optical networks,” Optics Express,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 35 700–35 709, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Li, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “Realizing ai-assisted multi-layer restoration  in a software-defined ip-over-eon with deep learning: An experimental  study,” in Optical Fiber Communication Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  Optical Society  of America, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' W4F–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [11] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Tian, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Gu, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhu, “Reconfiguring multicast sessions in  elastic optical networks adaptively with graph-aware deep reinforcement  learning,” Journal of Optical Communications and Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 13,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 253–265, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [12] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Lu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Jin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Guo, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Cao, “Con-  volutional modeling and antenna de-embedding for wideband spatial  mmwave channel measurement,” in 2017 IEEE Wireless Communica-  tions and Networking Conference (WCNC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Shafique, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Khawaja, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Sabir, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Qazi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Mustaqim,  “Internet of things (iot) for next-generation smart systems: A review  of current challenges, future trends and prospects for emerging 5g-iot  scenarios,” Ieee Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 23 022–23 040, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Alkhateeb, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' El Ayach, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Leus, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Heath, “Channel  estimation and hybrid precoding for millimeter wave cellular systems,”  IEEE journal of selected topics in signal processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  831–846, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Bhartia and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Bahl, “Millimeter wave engineering and applications,”  1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Rappaport, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Sun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Mayzus, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Azar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  Wong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Schulz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Samimi, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Gutierrez, “Millimeter wave  mobile communications for 5g cellular: It will work!”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' IEEE access,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 335–349, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [17] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Pi and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Khan, “An introduction to millimeter-wave mobile broad-  band systems,” IEEE communications magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 49, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 101–  107, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Marcus and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Pattan, “Millimeter wave propagation: spectrum  management implications,” IEEE Microwave Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 2,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 54–62, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Shrikumar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Greenside, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Shcherbina, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Kundaje, “Not just  a black box: Learning important features through propagating activation  differences,” arXiv preprint arXiv:1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='01713, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Sendak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Elish, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Futoma, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Ratliff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Nichols,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Bedoya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' Balu, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' O’Brien, “” the human body is a black box”  supporting clinical decision-making with deep learning,” in Proceedings  of the 2020 conference on fairness, accountability, and transparency,  2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content=' 99–109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='  This figure "fig1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='png" is available in "png"� format from:  http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
+page_content='org/ps/2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vtFQT4oBgHgl3EQfvDZj/content/2301.13396v1.pdf'}
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+Hate Raids on Twitch: Echoes of the Past, New Modalities,
+and Implications for Platform Governance
+CATHERINE HAN, Computer Science Department, Stanford University, USA
+JOSEPH SEERING, Computer Science Department, Stanford University, USA
+DEEPAK KUMAR, Computer Science Department, Stanford University, USA
+JEFFREY T. HANCOCK, Communication Department, Stanford University, USA
+ZAKIR DURUMERIC, Computer Science Department, Stanford University, USA
+In the summer of 2021, users on the livestreaming platform Twitch were targeted by a wave of “hate raids,” a
+form of attack that overwhelms a streamer’s chatroom with hateful messages, often through the use of bots
+and automation. Using a mixed-methods approach, we combine a quantitative measurement of attacks across
+the platform with interviews of streamers and third-party bot developers. We present evidence that confirms
+that some hate raids were highly-targeted, hate-driven attacks, but we also observe another mode of hate
+raid similar to networked harassment and specific forms of subcultural trolling. We show that the streamers
+who self-identify as LGBTQ+ and/or Black were disproportionately targeted and that hate raid messages were
+most commonly rooted in anti-Black racism and antisemitism. We also document how these attacks elicited
+rapid community responses in both bolstering reactive moderation and developing proactive mitigations for
+future attacks. We conclude by discussing how platforms can better prepare for attacks and protect at-risk
+communities while considering the division of labor between community moderators, tool-builders, and
+platforms.
+CCS Concepts: • Human-centered computing → Human computer interaction (HCI); Collaborative
+and social computing; • Security and privacy → Social aspects of security and privacy.
+Additional Key Words and Phrases: Online harassment, online communities, moderation, platform governance
+ACM Reference Format:
+Catherine Han, Joseph Seering, Deepak Kumar, Jeffrey T. Hancock, and Zakir Durumeric. 2023. Hate Raids on
+Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance. 1, 1 (January 2023),
+28 pages. https://doi.org//
+1
+INTRODUCTION
+Content Warning: This paper studies hateful online content. When necessary for clarity, this
+paper directly quotes user-generated content that contains offensive/hateful speech, profanity,
+and other potentially triggering content.
+Livestreaming platforms have boomed in popularity in recent years and become a major part
+of many users’ Internet experience. The livestreaming industry saw a 45% uptick in viewership
+Authors’ addresses: Catherine Han, cathan@stanford.edu, Computer Science Department, Stanford University, Stanford,
+USA; Joseph Seering, jseering@stanford.edu, Computer Science Department, Stanford University, Stanford, USA; Deepak
+Kumar, kumarde@stanford.edu, Computer Science Department, Stanford University, Stanford, USA; Jeffrey T. Hancock,
+hancockj@stanford.edu, Communication Department, Stanford University, Stanford, USA; Zakir Durumeric, zakird@
+stanford.edu, Computer Science Department, Stanford University, Stanford, USA.
+Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee
+provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and
+the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored.
+Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires
+prior specific permission and/or a fee. Request permissions from permissions@acm.org.
+© 2023 Association for Computing Machinery.
+XXXX-XXXX/2023/1-ART $15.00
+https://doi.org//
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+arXiv:2301.03946v1  [cs.CY]  10 Jan 2023
+
+2
+Catherine Han et al.
+between March and April 2020 [54], likely in part due to the COVID-19 pandemic. Twitch is a
+popular livestreaming platform, and much like any other rapidly growing online platform, its
+communities have suffered from hate and harassment. July to October 2021 marked an intense
+period of harassment on Twitch with many streamers experiencing a surge of “hate raids.” In the
+most common form of hate raid, a streamer’s chatroom is overwhelmed by a rapid influx of Twitch
+accounts posting hateful messages. Because of their dissatisfaction with Twitch’s handling of hate
+raids and poor treatment of marginalized-identity streamers, these streamers and their communities
+came together, gathering resources, developing tools and strategies to protect themselves, and
+organizing a major protest [18, 39]. This series of events reflected frustration within the community—
+particularly from minority streamers—toward Twitch and its perceived inaction on issues of trust,
+security, and safety on the platform.
+In this paper, we investigate the nature of hate raids on Twitch, how they affected vulnerable
+communities, and how stakeholders reacted to hate raids. We combine an at-scale measurement
+of the hate raid phenomenon across 9,664 popular channels’ chats on Twitch with interviews of
+seven LGBTQ+ and/or Black Twitch streamers. In addition, we interview two Twitch users that
+developed third-party moderation tools in response to hate raids. In our analysis, we explore the
+following three research questions:
+RQ1: What are hate raids: how are they orchestrated and who do they target?
+We first
+seek to detail the fundamental characteristics of hate raids.1 Our measurement of hate raids across
+9,664 popular channels on Twitch reveals that 98% of hate raid messages consisted of identity-based
+attacks. However, while the content of these attacks was mostly anti-Black or antisemitic, the
+raids themselves selected targets indiscriminately with respect to streamer identity. These hate
+raids blurred the line between what prior work called “trolling” or disruptive behavior [41] and
+networked harassment [30]. To better understand how attackers selected their targets, we examined
+Twitch’s streamer tags—a feature streamers use to categorize themselves and their community.
+Among streams that use tags, we find evidence that attackers may have leveraged these tags to
+discover and attack marginalized-identity streamers: particularly with Black, African American,
+and LGBTQ+ tags.
+RQ2: How do hate raids affect members of targeted groups?
+Because a quantitative per-
+spective on hate raids cannot fully depict the lived experiences of targeted community members,
+we interviewed seven Black and/or LGBTQ+ streamers on Twitch about the impact of these at-
+tacks. Through these interviews, we find that the perspectives of targeted streamers aligned with
+mainstream media portrayals of these attacks: hate raids are seen as highly-targeted attacks often
+persecuting Black and LGBTQ+ communities on Twitch. While identity-based attacks have always
+plagued these at-risk communities online, streamers found that this wave of hate raids was distinct
+in its highly-targeted nature and the persistence of its perpetrators. Furthermore, we find that the
+community saw hate raids as one piece of a larger campaign of harassment, often involving other
+platforms and in some cases extending into more extreme offline experiences (e.g., involving law
+enforcement, swatting2).
+RQ3: How did different groups of stakeholders respond?
+To better understand the different
+ways community members and Twitch responded to hate raids, we further draw upon data from
+interviews with streamers and bot developers. We observed that streamers largely turned to their
+community and third-party bot developers for moderation, emotional, and technical support against
+1Some news reports stated that these raids began as an abuse of a built-in “raiding” feature originally intended to help grow
+a sense of community [38], but we did not find direct evidence of this in our dataset.
+2A harassment tactic that involves calling emergency services or police to a target’s residence
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+3
+hate raids. Volunteer bot developers created tools adopted by tens of thousands of streamers who felt
+that they might be targeted. These developers worked to constantly update their tools throughout
+the hate raid period, as the sophistication of hate raids evolved in response to developers’ efforts to
+combat these attacks. In addition to an influx of support via resource aggregation, tool development,
+and volunteer moderation, the community rallied together for a social movement and virtual
+walkout to raise awareness for their longstanding frustrations with Twitch. While attitudes toward
+the degree of success of these movements varied among our interviewees, these community-driven
+movements gained attention and impacted overall platform engagement.
+Our mixed-methods approach to understanding hate raids provides the following three primary
+research contributions:
+(1) We characterize a novel form of long-term harassment campaigns on Twitch; not only do we
+observe that hate raids leverage the real-time nature of livestreaming platforms, but we also
+find that they exploit automation to select targets and amplify their attacks.
+(2) We observe that the content and orchestration of hate raid messages indicate a dual motivation:
+first, hate-driven and second, attention-seeking, consistent with prior research into networked
+harassment and subcultural trolling.
+(3) We find that members of these targeted communities, unhindered by the frictions platforms
+face when developing new features and policies, rapidly assembled high-quality resources
+and produced technical tools to address their needs and the limitations of Twitch’s response.
+Grounded in our data, we conclude by discussing the implications of our findings for livestreaming
+platform design and the broader community. We argue that platforms and researchers must proac-
+tively consider the unique experiences of targeted communities online, the dependency on and
+potential for community-based moderation and tool-building, and the range of motivations behind
+the actors coordinating hate-based attacks.
+2
+RELATED WORK
+This paper builds on three key bodies of related work. First, we review literature on morally-
+motivated networked harassment [30] and subcultural trolling [41], and we identify characteristics
+of each that hate raids share. Second, we review online hate-based attacks documented in the
+literature, situating hate raids within taxonomies of their characteristics. Finally, we discuss ties to
+literature on volunteer moderation and coordinated action, identifying connections between hate
+raids and crisis informatics literature and highlighting how users’ responses to hate raids parallel
+responses to natural disasters and other crises.
+2.1
+Harassment and “trolling” in online spaces
+In this paper, we situate the Twitch hate raids within prior work that discusses online harassment
+and “trolling.” Definitions for both of these terms have varied widely; for example, trolling has been
+defined as broadly as “behavior that falls outside acceptable bounds defined by [...] communities”
+[5, p. 1] and as specifically as in Phillips’ description of “subcultural trolling” as a nuanced cultural
+phenomenon with historical and moral roots [40, 41]. Similarly, Marwick identified more than ten
+different types of behaviors listed under the umbrella term of “online harassment” in prior work
+[30, p. 2]. We operate under the definitions of the two terms provided by Marwick and Phillips,
+and we focus on the form of harassment that Marwick terms “networked harassment,” where an
+individual is harassed by many people connected by social media.
+Note that, subsequent to her original publications on subcultural trolling, Phillips wrote about
+the dangers of referring to something as “just” trolling [42, p. 2]. While in this paper, we compare
+aspects of hate raids to aspects of Phillips’ characterization of subcultural trolling, this should
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+4
+Catherine Han et al.
+not be construed to mean that hate raids are “just” trolling by any means; they cause real harm
+to targets that should not be taken lightly. Moreover, these attacks occurred in the context of a
+long history of racist, sexist, and transphobic behaviors in online spaces that have been especially
+prevalent in online gaming spaces [15, 17]. These behaviors have forced targeted users to hide their
+identities or even to withdraw from online spaces entirely [8, 15, 45, 60].
+2.2
+Characterizing hate-based attacks
+Thomas et al. [56] identify three axes on which hate-based attacks can be classified:
+(1) The Audience exposed to the attack, which can include the target and/or a different audience.
+(2) The Medium through which the attacker reaches a target, which frequently includes media
+such as text, images, or video.
+(3) The Capabilities that are required for the attack to succeed: whether the attack requires
+deception of an audience and/or a third-party authority, whether it requires amplification,
+and whether it requires privileged access to information, an account, or a device.
+In the context of online hate and harassment behaviors, the most similar to hate raids is “brigading,”
+where a single target (e.g., a YouTube video or Twitter account) is simultaneously attacked by a semi-
+coordinated set of antagonistic users. For example, 4chan users often coordinate to target YouTube
+videos that they are ideologically or otherwise opposed to [29]; Reddit users have previously, in
+large groups, entered other community spaces to harass and intimidate other subreddits [12]; Zoom
+users have leveraged legitimate insider access to join online meetings to disrupt and harass the
+other participants, otherwise known as “Zoombombing” [26].
+Of the above criteria, the medium through which hate raids took place is primarily text, though
+in some cases other media on external platforms were involved. As we discuss later in this work,
+they required an audience that included both the target and a wider array of viewers. In some
+cases, the attacks included revealing personal information of targets (“doxxing”), and they benefited
+greatly from amplification.
+However, as we discuss in Section 4.1, these attacks had a number of other attributes worth
+mentioning. For example, the capabilities required for this attack included that they were heavily
+automated and occurred over a significant period of time (several months), hearkening to more
+traditional cybersecurity attacks, such as Distributed Denial-of-Service (DDoS) [34] and for-profit
+spam and scam campaigns [23]. Though Zoombombing often operates under a notion of the
+infiltration of a private meeting, public Twitch streams share the capability of seeing the reactions
+and impact of the attack in Zoombombing attacks. Therefore, we draw upon prior work in the
+cybersecurity space to structure our understanding of abuse executed en masse via illegitimate
+accounts. Contextualizing the hate raids on Twitch through both a lens of subcultural trolling and
+morally-motivated networked harassment and a traditional cybersecurity lens better frames the
+underlying motivation and tactics of these activities.
+2.3
+Volunteer moderation, coordinated action, and crisis informatics
+Prior work examining platform governance and volunteer labor in online social spaces has high-
+lighted a variety of dynamics that inform our analysis of hate raids. While Twitch is a multi-modal
+platform incorporating text-based chat, video, and audio, the phenomenon of hate raids echoes
+the moderation challenges discussed by Jiang et al. for voice-based communities [22], as both
+Twitch and Discord share ephemeral and real-time components of user interactions. Additionally,
+we discuss the experience of hate raids and the resulting mobilization of less visible streamers
+on Twitch and members of marginalized communities on the platform more broadly. Prior work
+details the obstacles that such communities in particular face with regards to platform visibility and
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+5
+accountability [55], further contextualizing the friction we observe between Twitch and its users.
+Several examples [2, 46, 48] in the literature emphasize the importance of volunteer labor in these
+communities, reporting that volunteer moderators on livestreaming platforms — both individually
+and in collaboration — have the capacity to effectively and quickly address norm-violating behaviors.
+In Section 4.2, we discuss the impact of community moderation and community-developed auto-
+mated moderation tools, adding to conversation in prior work that has raised questions surrounding
+platform governance and the distribution of labor in content moderation [4, 24, 44, 49].
+As we detail below, one of the core characteristics of users’ responses was collective action to
+create tools and aggregate informational resources. A small number of examples of collective action
+to counter harassment at this scale have been documented in social computing literature. Blackwell
+et al. reported on “HeartMob,” a platform where users can submit reports of being harassed and
+volunteers will provide support — supportive messages, help with reporting harassment, and/or
+help documenting abuse [1]. On a much smaller scale, Mahar, Zhang, and Karger’s “Squadbox”
+allowed users to coordinate trusted friends to help shield them from harassment via email [28]. A
+small body of work from the early-mid 1990s [13, 27, 51] and early 2000s [20] also documented
+individual cases of harassment and communities’ discussions about how to respond.
+A broader related body of work, situated in part in CSCW literature, comes from the field of
+crisis informatics [36, 37]. Though this field has largely focused on responses to offline crises (e.g.,
+natural disasters [32, 52, 53, 62], terrorist attacks and mass shootings [3, 6, 37], and in some cases
+ongoing violent conflict [33, 50]), many of the core principles are also mirrored in responses to
+hateful attacks based on social media. As we discuss in Section 4.2, we observe many of the same
+behaviors in our research on Twitch hate raids that occur during natural disaster response. Per this
+literature, we have organized our results to address questions about crisis response that parallel
+questions commonly asked in crisis informatics literature.
+3
+METHODS
+We examine broad patterns in hate raids and common themes in individual messages, and we
+complement this analysis with insights from interviews with impacted individuals. In this section,
+we describe the methodologies of our (1) large-scale collection and analysis of Twitch chat messages,
+moderation actions, and channel attributes collected from 9,664 channels from September 2 to
+September 16, 2021, (2) interviews with seven Black and/or LGBTQ+ streamers, and (3) interviews
+with developers of two third-party Twitch moderation bots that were widely deployed in response
+to hate raids.
+3.1
+Twitch Chat Data Collection
+To understand how hate raids impacted high-visibility streams on Twitch, we generated a corpus of
+channels to gather messages from. We used Twitch’s API to pull information about online streamers
+ordered by their current number of viewers, from high to low. We pulled this data every hour for
+a week from May 4 to May 11, 2021 to compute an average number of viewers per stream when
+the channel was live. For our corpus, we only considered channels that had an average of at least
+100 viewers each time they streamed and that also streamed at least three times over the course of
+a week.
+We continuously gathered data from the channels on this list for two weeks in September, from
+September 2 to September 16, 2021, during which time many hate raid attacks occurred. Each
+channel on Twitch has an associated chatroom built on Internet Relay Chat (IRC) protocols. When
+connecting to each channel’s chat, we sent requests for information about the channel’s chatroom
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+6
+Catherine Han et al.
+modes—unique chat, subscribers-only mode, and slow mode.3 We also sent requests for command
+and membership capabilities, which allow us to identify the usage of certain moderation and room
+state commands and to determine when users joined or left chat; the CLEARCHAT command indicates
+that all of a specific users’ messages were purged from the chat, often as a result of a moderation
+action, like a timeout or a ban, while the membership capability reveals when specific users are
+joining and leaving the chat. In total, we collected 244,738,672 messages. For each message that was
+sent, we collected various pieces of metadata to contextualize it: what channel it was sent in, the
+account that sent the message, the text content of the message, the timestamp of when it was sent
+to the chat, the status of the chatroom (e.g., if it was in “slow mode”), and basic, publicly-visible
+information about the account that sent the message (e.g., if the account is a subscriber, follower,
+or moderator of the channel it is participating in). All data that was collected for this portion of
+this study was public to any user viewing the stream.
+3.2
+Detecting Hate Raids
+We started with a collection of 1,319,890 likely malicious bot accounts curated by and shared
+among the Twitch community so that streamers could proactively ban and block these accounts
+from participating in their chats. We searched our Twitch chat dataset for messages sent by these
+accounts, creating a seed set of messages from 516 of these likely bot accounts. We then used
+approximate string matching computed using the Levenshtein distance with a threshold of 95%
+similarity to find messages with the same content despite some evasion techniques used by hate raid
+attackers, such as prepending randomness to the same message contents across different accounts.
+We continue this process of finding approximate message content until no new messages were
+discovered. Through this method, we found matching message contents found by an additional
+1,067 discovered bot accounts for a total of 1,583 bots participating in hate raids (Figure 1). We then
+determined hate raid events to be windows of time where bot accounts in our dataset were seen
+sending messages within two minutes of prior messages sent by bots. We restricted this window to
+a short interval because raiding behavior (both benign and malicious) often involves an influx of
+similar messages sent across different accounts within a short period of time.
+3.3
+Streamer and Third-Party Bot Developer Interviews
+We conducted semi-structured interviews with seven Twitch streamers who identified as Black
+and/or LGBTQ+ and with two Twitch users who created third-party moderation bots to combat
+hate raids. These interviews were conducted from early October through mid-November 2021,
+shortly after the major spike in hate raids in late September. Interviews lasted between 20 minutes
+and one hour, with length varying based on participants’ exposure to hate raids, their roles within
+the community, and their knowledge of moderation tools. We recruited participants from lists of
+streamers who had previously participated in visible roles during LGBTQ+ focused events on Twitch,
+including featured streamers during Pride Month, streamers who were reported in news articles
+as having been heavily targeted by hate raids, and streamers who actively participated in hate
+raid-focused conversations in both public and semi-private spaces dedicated to hate raid responses.
+We recruited specifically from Black and LGBTQ+ streamers because these were the groups at the
+center of discourse surrounding hate raids and were the most visibly targeted. Interview questions
+focused on the same topics as the research questions, with a full list of primary questions presented
+in Appendix A. Due to the open-ended, semi-structured nature of these interviews, we asked
+additional follow-up questions when relevant.
+3https://help.twitch.tv/s/article/chat-commands
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+7
+Fig. 1. Compiling hate raid logs. We collected the hate raid logs in a series of four steps: (1) we began with
+a list of known malicious bot account names collected by moderators, streamers, and other community
+members on Twitch; (2) we used this to filter the chat logs for messages sent by malicious bots; (3) after
+confirming the contents of these messages are hateful, we used this seed set of messages to spider for similar
+content being sent by accounts not already in this list; (4) we iterated with this notion of message content
+similarity until no new bot accounts were detected.
+We do not report identity characteristics for each streamer individually because doing so might
+identify them, but the following are aggregated, self-reported demographic categories: four stream-
+ers identified as Black, two as Hispanic, and one as white. Five identified as women, one identified
+as nonbinary, two identified as transgender, two identified as queer, and one also identified as
+aromantic and asexual. Some interviewees identified with more than one of these categories. The
+bot developer interviewees both identified as white, male, and heterosexual.
+Following interview completion and transcription, interview text was separated into chunks.
+Each chunk contained a single idea, which ranged in length from several words to several sentences
+using a variant of the method described in Creswell [9, p. 86–89, 184–185]. These chunks were each
+given category labels, which included categories such as “Frequency of hate raids experienced,”
+“Streamers’ short-term responses to hate raids,” and “Social support received by streamers.” The full
+codebook is included in Appendix B. Initial category labels were defined by the research questions,
+but labels were iteratively added to the codebook when a chunk did not fit any existing labels. A
+Cohen’s Kappa statistic was calculated to determine inter-rater reliability, with the final round of
+coding achieving a Cohen’s Kappa of 0.91. The results of this analysis are summarized by category
+label in Section 4.2.
+3.4
+Ethical Considerations
+We gathered data from 9,664 different Twitch channels, each with at least 100 viewers on average.
+Even though chat data from all channels on Twitch is publicly viewable, we elected to restrict
+the scope of our analysis to this set of larger channels to protect any assumption of privacy that
+smaller channels and their communities might have; channels with regular audiences of 100 or
+more viewers represent an exceedingly small proportion of Twitch channels overall—in May 2021,
+nearly 99% of streams had fewer than 50 average concurrent viewers [7]. This restriction applies a
+significant limitation to our quantitative analysis, as we cannot draw conclusions regarding hate
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Bots
+Chat
+logs
+Spidertofindmessages
+withthesamecontent
+Messagessentbybots
+Moderators
+Hatefulmessagelogs
+个
+Streamers
+Known
+malicious
+8
+botlists
+8
+Othercommunitymembers
+(e.g.,bot developers)
+Verified for hateful
+Messagessentbybots
+contentbyresearcher
+(1)
+(2)
+(3)
+(4)8
+Catherine Han et al.
+raid messages sent to smaller channels, but we believe that the ethical considerations in respecting
+privacy justify this limitation. The final list contains 9,664 active channels that match these criteria.
+In the chat data we collected, we took precautions to minimize the risk of inadvertently affecting
+communities: our script did not send any messages or interact with the chat, and we did not attempt
+to de-anonymize the involved accounts.
+Furthermore, to gather our qualitative data, we interviewed members of Black and/or LGBTQ+
+communities concerning their experiences with hate raids. Because of the sensitive nature of this
+research, participants were notified of the full purpose of the interview in advance, as well as what
+types of questions would be asked. Additionally, we reminded participants both on the consent form
+and at the beginning of the interview that they could decline to answer any questions or stop at
+any time. Interviews typically lasted between 20 to 60 minutes, and participants were compensated
+with an Amazon gift code for $15 or local currency equivalent. To protect participants’ anonymity,
+we have removed any potentially personally identifiable information from their quotes. This work
+was approved by the Stanford University Institutional Review Board (IRB).
+4
+RESULTS
+We measure hate raids across the platform and present our findings of their quantitative characteris-
+tics below (Section 4.1). We pair these measurements with a synthesis of the qualitative perspectives
+of streamers from at-risk communities and community bot developers on the responses of different
+stakeholders (4.2).
+4.1
+Characterizations of Hate Raids
+Mainstream news outlets characterized the hate raids during late summer of 2021 as targeted,
+bot-mediated abuse often aimed toward marginalized streamers [11, 19, 38]. We find two forms
+hate raids: first, a broad, scattershot form of hate raids akin to classic subcultural trolling [41] that
+incorporates racist and antisemitic elements, and second, hate raids that targeted specific streamers
+based on their identities.
+4.1.1
+Quantitative Perspectives. We first sought to understand what hate raids looked like quanti-
+tatively across the platform.4 To achieve this, we characterized hate raids observed in a corpus of
+244M messages across 9,664 channels collected during a 14-day period from September 2 to Septem-
+ber 16, 2021. Of these messages, 2,947 messages were identified as being part of hate raids through
+the methods discussed above. We observed 60 hate raid attacks in 57 unique channels—three of
+these channels were hate raided twice on separate occasions.
+Technical Characteristics
+We find that 50% of channels that were hate raided had at least
+32 bot accounts involved in the attack (Figure 2). Some channels, however, experienced attacks
+with an acutely large number of bots. For example, one channel received hate raid messages
+from 222 unique bot accounts. We found that on average, there were 48 messages per raid. These
+messages were typically sent in close succession to one another. In the majority of raids, all of the
+messages were sent in less than 16 seconds (Figure 4), though a smaller proportion of raids lasted
+for minutes. Most messages were sent from unique bot accounts, with 302 bots (19.1%) sending
+more than one message in the same raid; even when these bots did send more than one message,
+the median number of messages sent by a single bot was two (Figure 5).
+Overall, bots appear to have been largely throwaway, single-use accounts often created for
+the purpose of enacting these hate raids. The usernames of the bots we observe in our dataset
+4Note that, as discussed above, we focus here on within-chat hate raids rather than on forms of follow-botting that were
+sometimes included under the umbrella term of hate raids.
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+9
+Fig. 2. CDF of the number of unique bots that participated in an instance of a hate raid. We find that the
+median bot count was 32, demonstrating the typical scale of these attacks.
+Fig. 3. CDF of the number of different channels a bot account hate raids. Almost 65% of the bot accounts we
+identified were found in only one channel, implying that the majority of these bots were created for a single
+use in our observation period, though it is possible that these bots were used additional times in channels
+that were not in our sample.
+were predominantly (99.6%) strings of letters and numbers that appear to have been automatically
+generated (e.g., y9y7n18r0g6raem). Of the bots we detected sending messages (𝑁 = 1, 583), many
+(25%) of the bots were created within a two-day window of their first use in our dataset. While
+these bots appear to have been created for use in a single hate raid, we find that 3% were made
+far in advance of their first use—these are accounts created at least several weeks before observed
+chatting in our corpus. This trend toward many single-use accounts likely controlled and created by
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+CDFof numberof uniquemaliciousbotsperhateraidattack
+1.0
+0.8
+CDF
+0.6
+0.4 
+0.2
+0
+50
+100
+150
+200
+Number of botsCDFofnumberofdifferentchannelsraidedperbot
+1.00
+0.95
+0.90
+0.85
+CDF
+0.80
+0.75
+0.70
+0.65
+1
+2
+3
+4
+5
+6
+Numberofchannels10
+Catherine Han et al.
+Fig. 4. CDF of the duration of hate raid instances in seconds. The hate raids we observed were largely a short
+burst of hateful messages sent in close succession, often within the span of seconds or minutes.
+Fig. 5. CDF of the number of messages sent per hate raid instance. The median message count is 36, showing
+the usual scale of the observed hate raids. Note that this number reflects how many messages actually
+appeared in the stream chat; reactive moderation actions taken by the streamer and/or their volunteer
+moderators may have prevented bots from sending additional messages.
+a single entity echoes the literature in “sockpuppetry,” where accounts are created and controlled by
+a “puppetmaster” for engaging in deceptive behavior influencing the surrounding community [25].
+Likewise, the small proportion of aged accounts may indicate what prior work defines as “zombie”
+accounts, which are ones that are created ahead of time but are dormant for a long period or
+indicate benign account compromise [14].
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+CDF of duration of hate raid attacks
+1.0
+0.9 
+0.8
+0.7 
+0.6
+0.5
+0.4 
+0.3
+0.2
+0
+50
+100
+150
+200
+250
+300
+Time (s)CDFofnumberof messagesperhateraidattack
+1.0
+0.8
+CDF
+0.6
+0.4
+0.2
+0
+50
+100
+150
+200
+Number of messagesHate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+11
+We found limited evidence of bot account reuse; the majority of bots were only observed
+participating in a single channel within our sample, and even then, most bots sent only one message
+(Figure 3). We also found that slightly more than 20% of the known bots sent hate raid messages in
+at least two different channels. As of the time of this analysis, there were two ways to sign up for a
+Twitch account: (1) through e-mail and (2) through phone number. The cost of creating Twitch
+accounts could thus be as low as the cost of creating e-mail accounts. During this period, Twitch did
+move quickly to disable accounts that participated in malicious activity. When querying Twitch’s
+API to understand the ages of these accounts, we successfully fetched information for only 33 (4%)
+of the bot accounts in our dataset because the malicious accounts had been disabled by the time we
+queried the API for their information.
+Only three of the 57 targeted channels experienced a hate raid attack more than once, meaning
+that our corpus contains 60 observed attacks. Two of these channels experienced two attacks in
+close succession—within 30 minutes of the first attack. Additionally, both channels experienced
+a similar pattern where, between the two attacks, the shared text of the messages spammed by
+different bot accounts in the same raid changed. For instance, in one of the channels, the message
+content spammed in the first attack was a violent, anti-Black racist statement mocking Twitch
+community efforts to organize against hate raids. Just 27 minutes later, a second attack began with
+accounts spamming a different anti-Black racist message. We note that, while both raids were
+anti-Black in nature, the target of this raid was white.
+Degree of Targeting
+Because of the tendency toward identity-based attacks we observed in the
+hate raid messages, we next more closely examined the contents of these messages for a semantic
+understanding of hate raid targeting. Although the bursty messaging pattern with identical message
+content that we observed in hate raids may appear similar to other, more benign behaviors on
+Twitch (e.g., chanting5 and pro-social raiding), the content of hate raid messages distinguishes
+them as clearly malicious. We find that the hate raids in our dataset spanned several different
+kinds of hate—most often identity-based—and weaponized these hateful ideologies via graphic and
+threatening language.
+To better characterize how hate was expressed in the raids, we categorized the content of
+the hate raid messages in our dataset. We evaluated each message along two axes: (1) what
+identities were attacked in the message, and (2) in what method this identity-based hate was
+operationalized. Following best practices for grounded theory coding, two researchers agreed upon
+a master codebook (Table 1) and independently coded 2,947 messages sent across 60 different attacks.
+The Kupper-Hafner agreement was computed to determine inter-rater agreement because some
+messages were assigned multiple labels, and the coding achieved an agreement of 0.85. Ultimately,
+the researchers met to agree on the final codes. We found that the most common category of hate
+expressed was anti-Black racism, which was present in nearly all of the hate raids in our dataset
+(59, 98.3%). We observed that anti-Black racism was most often operationalized through violent
+threats (43 of 59, 72.9%). We also noted that the content in hate raid messages was frequently an
+amalgam of hateful ideologies—for instance, while anti-Black racism is an explicit category of
+identity-based hate, messaging with anti-Black attacks often co-occured with QAnon propaganda
+(23 of 59, 39.0%). These ideologies often overlap with their hateful roots (e.g., white supremacy
+underlies anti-Black racism, antisemitism, and aspects of QAnon), but the way that these themes
+were presented together was typically disjointed, separated into different parts of a single message.
+For instance, the following message both expresses anti-Black racism and supports QAnon:
+5An experimental feature introduced by Twitch in May 2021 that allows streamers and their moderators to “suggest”
+messages to be duplicated or “chanted” by other users.
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+12
+Catherine Han et al.
+Hateful Ideology
+Meaning
+Antisemitic
+Demonstrating prejudice toward Jewish people
+Anti-Black
+Demonstrating prejudice toward Black people
+Anti-Trans
+Demonstrating prejudice toward transgender peo-
+ple
+Individual streamer
+Harassing a particular streamer or individual (not
+necessarily the streamer whose channel the mes-
+sage is sent in)
+Mode of Operation
+Meaning
+Violent threat
+Threats of violence (describing explicit actions)
+Known propaganda
+Using known hate symbols or references (e.g., most
+commonly excerpts from the Great Replacement or
+1488*)
+Direct attack
+Attacks that appear to directly address the streamer
+(e.g., attacks in the second person) or align with the
+streamer’s identity
+Fearmongering
+Inspiring fear or resignation by emphasizing the
+futility of counter-hate raid efforts
+Weaponized emote
+Coopting Twitch emotes for harassment purposes
+(e.g., TriHard**)
+Dehumanization
+Implications that a group of people is not human
+(e.g., comparisons with animals)
+Table 1. Codebook for hate raid message content—Codebooks for hate raid message content separated
+into two axes: (1) hateful ideology and (2) the mode in which they were operationalized.
+* 1488 is a pairing of two popular hate symbols, both regarding white supremacy and neo-Nazism.
+** TriHard is a global Twitch emote depicting the face of a Black streamer, TriHex, and it has been used in the
+past to alienate Black streamers.
+Violent threat Known propaganda Direct attack Fearmongering Weaponized emote
+Antisemitic
+10
+12
+2
+0
+3
+Anti-Black
+43
+11
+4
+7
+3
+Individual
+6
+0
+0
+3
+0
+Table 2. Number of raids containing categories of operationalized hate—Anti-Black racism was the
+most common form of identity-based hate we identified, and it was most often operationalized through
+violent threats. We do not list anti-Trans attacks in this table because they were not present in our dataset of
+messages, though they may have been present in hate raids we were not able to capture.
+“7i9nnde4k WayneLambright Legion | kiII -> bIacks | behead -> bIacks| <readacted> is a
+cloutchasing clown he isnt even hateraiding he is just following”
+There are four clear parts to this message, each with a separate meaning. This message’s pattern
+is a common one throughout our dataset; in this case, pipes (“|”) were used to delimit separate parts,
+as attackers presented several pieces of unrelated hateful content in one message, but other symbols
+(e.g., brackets, braces, “==>”, etc.) were also used to separate or relate concepts. In this example, the
+first component promotes Wayne Lambright, who ran for president in the United States in 2020
+on a campaign supporting QAnon, anti-Black racism, and pseudoscience. The second and third
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+13
+Stream Tags
+LGBTQIA+
+Black+AfAm
+No Tag
+Hate raided streams (N=57)
+13.5%
+9.6%
+5.2%
+Not hate raided streams (N=9,664)
+2 .4%
+0.2%
+15.6%
+p-value
+0.01
+0.01
+0.11
+Table 3. Streamer tags—The results of a two-sample proportion test of the self-assigned identity tags (e.g.,
+LGBTQIA+, Black, African American) between the channels that were and were not hate raided. We find that
+both LGBTQIA+ and Black + African American tags were disproportionately represented among hate raided
+streams.
+parts both express violent anti-Black threats. Finally, the last piece is an attack on an individual
+streamer. We note that in the messages attacking this streamer, they are neither present as a user
+in the chat nor are they the streamer of the channel itself; these attacks attempted to harass this
+streamer through fabricating negative associations between them and hate raid orchestration.
+Streamer Tags
+Because the contents of these hate raid messages were largely rooted in anti-
+Black racism and antisemitism, we next investigated the use of Twitch tags as potential vectors
+for targeting. When streaming on Twitch, streamers can choose to categorize their streams with
+“tags,” which are ways to publicly describe the stream for viewers to better search for streams
+of interest. These tags are maintained by Twitch, but the list of available tags are updated based
+upon community feedback. In May 2021, Twitch introduced over 350 opt-in tags for streamers
+to better categorize their channels into a particular community. These tags were largely identity-
+based, including “gender, sexual orientation, race, nationality, ability, mental health, and more” [59].
+However, some streamers feared that the same tags that were meant to increase visibility within a
+community could be abused to “single out minority streamers,” [38] and other members of these
+communities discouraged use of these tags as a preventative measure [21] to hide themselves from
+potential attackers. We observe 54 of 57 channels (94.7%) tag themselves with at least one such
+category; however, we focus our attention on the tags that give insight into streamer identities
+(e.g., LGBTQ+, Black, etc.) because the messages consisted of identity-based attacks.
+To better understand tags’ potential usage as a mechanism for targeting marginalized com-
+munities, we performed two-sample proportion tests to compare the presence of these identity
+tags between channels that were and were not hate raided. We find quantitative evidence that
+suggests that tags may indeed have been used to find targets for harassment at scale: both the
+LGBTQ+ and Black/African American tags were disproportionately represented (𝑝 < 0.05) in
+the hate-raided streams (Table 3). We do not find, however, any usage of the Jewish identity tag
+despite the heavy usage of anti-Semitic language in hate raid messages, and we note that the
+disproportionate representation of LGBTQ+ streamers deviates from the identities attacked in the
+contents of the messages.
+In order to more fully understand the disparity between the identities of the targeted streamers
+and the identities attacked in the content of the message, we categorized the racial identities of
+(1) the streamers who were raided and (2) a random sample (𝑁 = 370) of the broader corpus. Two
+researchers independently categorized these streamers by their perceived racial category in broad
+buckets: white, person of color (PoC), and unavailable. Two streamers in the hate-raided sample
+were unable to be categorized due to the streamer either not including a video feed of their face
+or using a racially ambiguous virtual avatar (“VTuber” model). We found that the majority of
+streamers were white in both the hate raided sample and the random sample. We found that the
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+14
+Catherine Han et al.
+mainstream sample consisted of 41% PoC streamers, which is higher than what we observed among
+hate raid victims (35%). We note that there is a very large discrepancy between the proportion of
+PoC streamers identified through manual coding versus the Black/African American tags. This
+may be because these tags are not assigned by default, and in order to apply them, streamers must
+explicitly select them. We performed a two-sample proportion test to evaluate whether the racial
+identities of the populations of (1) the victims of hate raids in our mainstream corpus and (2) our
+mainstream corpus differ. In this case, we failed to reject the null hypothesis (𝑝 > 0.05), meaning
+that we do not have evidence to say that the set of hate raids we quantified, which often missed the
+mark in the identities targeted in their content and the identities of the victim, disproportionately
+targeted PoC streamers as coded in this way. It is possible that this is in part due to an intersection
+of race and gender/sexual identity where the proportions of LGBTQ+-identifying streamers were
+unequal between racial groups, but we do not have the sample size to adequately test this within
+our sample. However, the above analysis does present evidence that hate raids occurred in different
+proportions across different identity tags, suggesting that tags may have been used as a targeting
+mechanism.
+Our sample size of 57 hate raided channels is inadequate to perform rigorous statistical testing
+to determine whether the broader set of attacks disproportionately targeted Black streamers, but
+we note that the proportion of anti-Black content in hate raid messages (98.3%) is far greater than
+the proportion of Black streamers that we detected experiencing hate raids (10.5%); further, only 2
+of these Black streamers received hate raid messages that specifically contained racist anti-Black
+language, though implicitly racist and/or antisemitic undertones and references were still present
+in some. This disparity between the identities of the streamers and the kinds of hate spewed in
+their chats indicates that many of these attacks were indiscriminate in their targets—in most but
+not all cases, they were not tailored to the specific streamer, but rather contained a consistent
+breadth of hate regardless of their target. Paired with our tag analysis, we find that the extent
+of targeting in the observed hate raids may have relied on the usage of tags due to the ease of
+automation. Through this large-scale, quantitative perspective, we find evidence of another mode
+of hate raids that included identity-based attacks but did not align the content of their messages
+with the targeted streamers’ identities. Rather, we see recurring themes and shared message text
+across hate raids in different channels regardless of the streamers’ racial identities; we describe
+such general, reused hateful content sent en masse as “canned hate.”
+4.1.2
+Perspectives of Streamers from Targeted Communities. While the content of the hate raid
+messages primarily targeted Black and Jewish identities, analysis of tags revealed that streamers
+who were attacked were disproportionately likely to be those using Black and/or LGBTQ+ tags. To
+better understand these nuances, we consider the perspectives of streamers from these targeted
+communities. We conducted a series of interviews with seven Twitch streamers (labeled as TS
+in quote attributions) that identified as Black and/or LGBTQ+. In this section, we discuss their
+accounts of how members of these communities perceived the targeted nature of hate raids and
+the different channels through which they were executed.
+Degree of Targeting
+In our interviews with streamers, we found that streamers’ experiences
+largely aligned with media descriptions of hate raids as a highly-targeted attack, often specifically
+targeted toward Black and LGBTQ+ creators on Twitch. Six of the seven streamers we interviewed
+explicitly described the primary targets of hate raids as Black, BIPOC, transgender, or LGBTQ+
+communities. In addition to these commonly targeted demographics, two streamers noted that
+visibility also played a role in attackers’ choice in targeted channels:
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+15
+“Specifically like one of my friends who has a bigger viewership, they’ve been affected a
+lot more.” – TS01
+“[My experience] was very mild in comparison to other streamers’ who were either vocally
+and proudly trans or Black or both, as those were absolutely the target demographics.” –
+TS06
+From these streamers’ perspectives, viewership and reputation factored into which streamers were
+more likely to be targeted, in addition to their race and gender.
+Additionally, while interviewees acknowledged that Black and LGBTQ+ communities have
+always been at-risk for hate and harassment on online platforms, three of seven participants stated
+that this wave of hate raids was drastically more severe than the attacks they had experienced
+before. For instance, one streamer described the hate raid they experienced in 2021 as “arguably
+the worst raid” and “most egregious iteration” they have seen to date (TS01). Per these accounts,
+we sought to examine what aspects of hate raids in 2021 distinguished them from previous attacks.
+Several streamers explained that this sharp peak in severity manifested in the persistence and scale
+of the attacks. The reported frequency of hate raids varied across the streamers; while one streamer
+stated that they were hate raided only once, two others observed a drastic increase in the duration
+and frequency of the hate raids they experienced firsthand and witnessed in other channels. One
+streamer recounted how they were hate raided for two weeks straight:
+“The highlight was the first stream that they hit me in, I had a four and a half hour stream.
+They were in my stream for about three and a half of those hours, nonstop hate raiding
+me.” – TS01
+Another streamer (TS03) contrasted their experience with hate raids before and during this particu-
+larly active period, where before, hate-driven attacks occurred as a single burst that “wasn’t an
+all day, every day or an hours long thing” and would “die out for a while.” However, in 2021, they
+witnessed hate raids that were far worse:
+“They were raided for three hours straight, just three hours of just following and trying to
+put messages in chat, trying dox them, whether it was by putting an address in a message
+or making a username with the address and just following incessantly.” – TS03
+While we did not find raids of this type within our dataset, we did not capture data from every
+targeted channel for reasons discussed above.
+TS05 notes that the degree of automation played a key role in the impact of the threat; the usage
+of bots grew over time and later reached unprecedented scale—they would use a tool to block
+suspected bot accounts all night long, blocking 300,000 to 400,000 bots at a time. They described the
+churn of newly created and weaponized bot accounts as “incessant and overwhelming.” In addition,
+TS05 commented on the sharp growth in attacks throughout the summer:
+“It went from 0-100 in no time at all. But it got scary because they were finding personal
+information about me and throwing it into however many public internet locations as
+possible. I had 70+ people sending me screenshots of an address associated with me for
+weeks.” – TS05
+Both TS03 and TS05’s experiences of these raids raised another concern—the targeted nature of
+the content of these messages. The carefully-crafted contents of these messages, in addition to
+expressing identity attacks against their targets, sought to threaten even the physical well-being of
+their targets via doxxing. The impact of such targeted attacks and the violent threats underlying
+doxxing even pushed one streamer to escalate their mitigation strategies beyond their stream:
+“Law enforcement got involved, I had to find a lawyer, [the attackers] were threatening
+violence against my children... It was a scary time for me.” – TS05
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+16
+Catherine Han et al.
+TS05’s experience was not unique. TS01 also expressed that others also experienced swatting as
+a result of being doxxed. These experiences of online harassment have manifested in potential
+psychological, physical, and even financial harm for already marginalized groups.
+Through both the incessant and bespoke nature of these attacks, we found that these streamers’
+perceptions and experiences of hate raids defined them as highly-motivated attacks on individuals
+based on their identities, targeting Black and LGBTQ+ communities in particular; while attacks on
+these marginalized communities have always existed in online spaces, the severity and persistence
+of hate raids distinguishes them from what many members of these communities had experienced
+before.
+Cross-Platform Attacks
+As explained by several streamers, the targeted nature of these attacks
+resulted in a varied set of vectors threatening their psychological and physical safety. To better
+define the range of threats hate raids posed to streamers, we asked each participant to describe
+their experiences with hate raids and what attack vectors were used. We find that four of the
+seven streamers envisioned hate raids on Twitch as one piece of a larger campaign of harassment,
+highlighting the multi-platform nature of these orchestrated attacks. For instance, TS01’s address
+and phone number were released in public locations off Twitch, and attackers even made videos
+on other platforms to help disseminate their personal information. This was then leveraged to
+flood their phone with calls. Similarly, TS02 and TS04 noted that Discord was another platform
+of concern; Discord servers of targeted streamers were attacked, and some of the hate raids were
+organized in Discord servers. TS04 described the complexity of the multi-platform nature of these
+attacks:
+“Where I find that companies really fall flat is understanding the impact of things that
+happen on their platform, the things that are planned on their platform and committed
+on another one... I think this is part of the issue with some of these hate raids is that it is
+personal info being hit. It’s people’s personal stuff outside of hate raids, outside of Twitch
+being shared. It is also being called slurs in chat, and that’s harmful absolutely to be called
+slurs in chat and stuff like that. But it’s also the fear of, well, my full name just got shared
+or my address just got shared. For me, it was like my Discord got hit, which is a whole
+other platform.” – TS04
+TS05 echoes these concerns, acknowledging that while hate raids originated with Twitch, “when
+someone makes it their mission to harm you, they’ll look for whatever they can to access you.” As
+a result, the high motivation involved in these attacks has raised questions and frustration within
+the community regarding platform accountability.
+In tandem, our quantitative and qualitative data on hate raids indicate that the experiences
+of the streamers from Black and LGBTQ+ communities align with the media’s portrayal of hate
+raids—that is, as highly-targeted and motivated attacks. However, through our quantitative analysis
+(Section 4.1.1), we also identified a variation of hate raids that deviated from this depiction, a
+form of hate raids akin to subcultural trolling that did not target specific streamers according to
+their identities, instead using “canned hate” to spread hate against Black and Jewish identities en
+masse in popular channels with high visibility. That is, these hate raids contained identity-based
+attacks, but were spread across the platform indiscriminately, indicating that an eagerness to cause
+widely-visible, attention-grabbing chaos may have also motivated the attackers.
+4.2
+Community response to hate raids
+As hate raids swept the platform, the community’s need and urgency for tools and resources
+to mitigate the threat grew. We performed a series of interviews with both streamers and bot
+developers involved with marginalized communities on Twitch to understand the following: (1)
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+17
+how streamers and their communities addressed the threat of hate raids in the short term, (2) what
+array of tools and resources were assembled to mitigate the impact of hate raids, (3) the efficacy of
+the grassroots organization for #TwitchDoBetter and #ADayOffTwitch, and (4) the longer-term
+effects of hate raids on streamers and their communities.
+4.2.1
+Short term responses by streamers. Four of the seven streamers we interviewed expressed
+that they employed both proactive and reactive mitigation techniques to protect themselves from
+hate raids in the short term. The kinds of techniques varied, often depending on the severity
+of the threat. On one end of the spectrum, one streamer explained that because their attackers
+had escalated to threatening violence against their children, they involved law enforcement and
+retained a lawyer. While these vectors of attack were impossible to address solely on-platform, the
+majority of streamers experienced attacks that manifested within the Twitch ecosystem of chat and
+engagement notifications (e.g., follows and raids). As such, these streamers were able to mitigate
+some of the impact of hate raids via modifications to their streams’ moderation protocols. One
+streamer added more users to their moderation teams, recruiting them from longtime members
+of their community who were “constantly hanging out inside of the chat” and “offering up their
+services... so that they can keep an eye on the chat,” a pattern previously identified in [49] and [47].
+Several streamers detailed variations of informational-support seeking, resource aggregation, and
+development of new tools in ways similar to those previously detailed in crisis informatics literature.
+For instance, one streamer described Stream Deck presets that were helpful for an emergency
+response; a Stream Deck is a physical control pad with preset studio settings (e.g., switching media
+scenes, camera angles, executing chat commands). They described commands that they added for
+moderation purposes:
+“We added more commands to like basically put it in follower mode and to turn off the
+chat to where it’s only emotes only so that they can’t put in any hateful words. Shutting
+things down for 10 minutes, but with a push of a button.” – TS02
+Similarly, another streamer outlined channel lockdown protocols they followed for hate raids,
+incorporating the idea of a “panic button” into a human moderator pipeline to handle incidents
+post-facto:
+“I had a panic button that turned off alerts, locked down chat, my mods would record
+times of incidents such as follow botting, we added different terms to the banned words
+list, had the highest auto mod settings available.” – TS05
+One variation of the Twitch Panic Button was developed and publicly advertised by nutty, a
+Twitch streamer, to be a rapid response mechanism integrated with a Stream Deck so that a single
+push of a button (or in customized cases, a voice-activated trigger phrase) enabled subscribers-only
+mode and cleared existing chat from both the chat client and the stream display [10]. Furthermore,
+after performing damage control, nutty’s tool attempted to reclaim the stream space; for instance,
+in nutty’s stream, the button triggered changing background lights and snarky automatically
+generated messages. An official tool with functionality similar to a panic button, named “Shield
+Mode,” was rolled out by Twitch in late November, 2022.
+In addition to the automated tools like the panic button, we found that streamers were aware of
+bot developers that developed bespoke features or new bots altogether to help handle the wave of
+hate raids. In our interviews, a streamer mentioned one bot in particular, Sery_Bot:
+“Also there’s an additional thing that has been added to a lot of... streamers chats called
+Sery_Bot. Someone who isn’t working for Twitch created a bot where it kind of shuts down
+all the other bots. Like it blocks them from being able to say anything. Or once they can
+come into your chat, it blocks them out. So a lot of us have added that.” – TS02
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
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+Catherine Han et al.
+Sery_Bot was developed by Sery, a developer who also sometimes streamed on Twitch. On
+August 14, 2021, Sery publicly solicited the Twitch community via Twitter for examples of hate
+raid messages and other relevant information to begin developing his bot. In the span of just a
+couple of weeks, Sery developed a variety of features—for instance, text-based commands in IRC
+like !hateraidon that performed a similar function to the panic button. In addition to providing
+utility already provided by other tools, Sery_Bot also integrated community-based block lists of
+account usernames to automatically check new chat messages against. Subsequent months entailed
+list updates, more feature development (e.g., checking account age of chatters and profile picture
+scanning for repeat offensive images, like swastikas). With the rollout of so many features so
+rapidly, Sery_Bot became viral, and in just two months, it amassed over 55,000 integrations over
+different Twitch channels.
+TS02 highlighted both the effectiveness and widespread adoption of such a third-party bot
+amongst streamers in the context of hate raids; however, they also indicated that discomfort with
+or distrust of technology—particularly third-party bots—may have inhibited the adoption of tools
+and resources meant to mitigate such threats within the community.
+4.2.2
+Resources from tool developers and other community members. The short-term responses
+from streamers alluded to the availability of community-sourced tools and streamers’ reliance on
+them to combat hate raids. Our interviews with both streamers and bot developers illuminated the
+various kinds of tools and resources the community created and what the development process was
+like in response to real-time threats. Streamers’ perspectives gave insights into what kinds of tools
+were visible and widespread throughout the community. Four streamers explicitly mentioned the
+use of third-party bots for hate raid mitigation or prevention. One streamer noted that in addition
+to guides for making the aforementioned panic buttons, they were well-informed of the various
+bots that were developed individually by different bot developers, all for the purpose of responding
+to hate raids:
+“There was Smash Bot that was created. Mix It Up Bot, Sery Bot, StopHateBot, WiseBot,
+time out bot. All of those things were kind of developed.” – TS03
+Another streamer contrasted the fast wave of tool development by the community members with
+the poor communication and delayed response from Twitch:
+“And yet, for some reason we have six queers in a trench coat who have somehow made
+all these tools in the span of three days for us to use that no, they don’t eradicate the issue,
+but they definitely helped kind of mitigate it immensely. We had [user] who was making
+full master lists along with [user] of all the bots that were being created which... Twitch I
+think should reach out to them and get that master list and pay them for their work and
+say, these are all bots that are out doing things that are worthwhile or valuable.” – TS01
+TS01 underscored that these tools were developed by members of the communities targeted by
+hate raids in a rapid-response fashion that Twitch as a platform simply could not; furthermore,
+TS01 emphasized that these quickly-developed tools were also effective in mitigating specifically
+the bot-mediated harassment even just with fairly naive methods.
+To supplement our understanding of moderation bots’ roles in the hate raid ecosystem, we
+interviewed two bot developers (referred to as BD in quote attributions) to understand (1) their
+perspectives and experiences with the community’s needs, (2) Twitch as a platform for development,
+and (3) technical challenges they encountered while developing features for hate raids. One bot
+developer noted a sort of cat-and-mouse game between the community members and attackers,
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+19
+resulting in fast-paced changes in the sophistication of hate raids and applicable mitigation tech-
+niques. This bot developer remarked on the primitive, manual nature of how hate raids started,
+only to quickly become more coordinated and varied:
+“So they weren’t that organized back then, started with a couple guys who just came into
+[a streamer]’s voice chat while he was streaming Phasmophobia, and they were shouting
+the N word, and then he gave them a really strong reaction by immediately ending the
+stream, deleting the VOD and so on. So they came back and spammed all nasty stuff in
+chat.” – BD02
+This bot developer also illuminated some of the motivation for hate raid participants: to elicit a
+strong, disruptive reaction from the streamer. Similarly, there were approaches that the larger
+community initially employed, such as joining the attackers’ Discord servers where hate raids are
+organized, that the attackers responded to:
+“And it’s also a little bit of a double-edged sword because we originally used to enter the
+offensive Discord servers where they would gather up and organize these hate raids with
+a second account, and then report the Discord server and the respective messages. And
+now of course, they learned that we do that, and they also set up a similar set of security
+measures.” – BD02
+As such, both the attackers and the defenders in the hate raid ecosystem were made aware of what
+strategies the other side was employing, and they adapted their methods in response. From one
+bot developer’s perspective, they analyzed the threat of hate raid messages and identified that
+attackers used “automated tools to just spam the chat,” and in response began developing a bot
+as a counter measure. This bot developer noted that the hate spam sent by an army of bots was
+difficult to mitigate with manual moderation, so identified a bot-mediated moderation approach as
+an effective way to respond to the attack.
+4.2.3
+Collective action for #TwitchDoBetter/#ADayOffTwitch. In addition to the different ways the
+community attempted to better protect themselves from hate raids, there were also attempts by
+the community to raise awareness through collective action. Two hashtags, #TwitchDoBetter and
+#ADayOffTwitch, rallied support from Twitch users via Twitter. #TwitchDoBetter was started in
+an attempt to raise awareness of the harassment of targeted creators on Twitch. Subsequently,
+#ADayOffTwitch was a boycott of Twitch that took place on September 1, 2021, meaning participants
+would not stream, watch streams, or participate in any chats. This day took place with hopes that
+reduced engagement on the platform would highlight the urgency of better safety for creators on
+Twitch. We found through our interviews with streamers that while the community was able to
+raise awareness through these movements, there was some disagreement about their long-term
+impact within the community. One streamer we interviewed who was a co-organizer of the walkout
+felt that the movements were successful in meeting what they perceived to be the goal, which was
+to raise awareness:
+“I think it worked in the way that I had hoped. We raised awareness. We actively called
+on a MAJOR streaming platform to make changes and we’re seeing the fruits of our labor.
+It’s not always about money like so many bigger streamers commented. Sometimes we
+have to understand that reputation is a currency.” – TS05
+However, setting an open-ended goal of raising awareness for these community-organized move-
+ments did not satisfy another participant. In contrast, TS01 felt that ultimately, these movements
+failed to narrow in on concrete demands of Twitch and therefore failed to be as effective and
+impactful as they could have been:
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+20
+Catherine Han et al.
+“I feel like they should have done a better job of sitting down and figuring out an actualized
+list of demands. Why are we taking a day off of Twitch? Because at face value, the reason
+we’re taking the day off of Twitch is because hate raids suck and that’s a true assessment.
+But what about after that? Why do those hate raids suck? What do we want to see to
+address those hate raids? How do we want Twitch to address it? How do we want Twitch
+to actually get engaged more about it? How do we want Twitch to respond to this? How
+does that carry over into future endeavors? What does that look like for a conversation
+around how they need to update their security? There was just little to no demand to be
+had whatsoever. And so, what could have been an actual movement or an actual kind of
+protest type of thing, just wound up being plainly speaking, a bunch of people just not
+logging in.” – TS01
+While these movements were organized within the community, perceptions of their goals and
+effectiveness varied throughout. Still, despite conflict around the goal and organization of the
+movement, #ADayOffTwitch did indeed significantly impact the number of viewers and streamers
+engaging with the platform; per one external estimate, this movement led to up to 15% less
+engagement on Twitch overall during the walkout [39].
+4.2.4
+Longer-term impacts of hate raids on streamers. Even with all of the mitigation attempts and
+movements to raise awareness, hate raids undoubtedly caused distress and skepticism throughout
+the community. Our interviews with streamers indicate that the visceral nature of these attacks
+paired with Twitch’s response has largely shaped their views of the platform as unprepared and
+detached from the community’s suffering. All seven of the participants expressed disappointment
+with Twitch’s failure to consider abuse protections proactively, the slow rollout of features and tools
+to mitigate the harm of hate raids, and poor communication with between Twitch and stakeholders.
+One streamer expressed resigned frustration that this experience had been consistent with Twitch’s
+attitudes toward protecting its at-risk communities in the past:
+“I think Twitch’s response has been absolutely abysmal. I think that very frankly speaking,
+it’s pretty pathetic. Twitch has a longstanding historical track record of not knowing how
+to communicate ever at all. So, while I do think that their communication for this was
+abysmal, I would be remiss to omit the part where it is exactly what I expected them to
+do. And Twitch is going to continue falling on their face over topics of this nature and
+conversations of this type every single time so long as they insist that silence is the best
+solution. And they need to do better than put out a simple tweet saying, ‘We hear you, we
+see you and we want you to know that we care, we promise.”’ – TS01
+Streamers also felt that poor communication even around existing mitigation tools led to un-
+necessary chaos during hate raids. One streamer noted that enabling two-factor authentication
+was a common suggestion by the community and Twitch for streamers to protect themselves.
+However, these suggestions conflate the verification of user identity with that of accounts chatting
+in that user’s channel. Therefore, even if there are tools that may better protect individuals, poor
+communication may lead to the misuse of the tool or misinterpretation of the protections it actually
+offers.
+In addition to disappointment with Twitch’s communication response, several streamers lamented
+the lack of tooling Twitch had prepared for such attacks, even for features that had been requested
+in the past or existed on other platforms:
+“The chat verification tools [released at the tail end of the hate raids] are really nice, and I
+think that that’s what a lot of people have wanted for so long. I’m not sure exactly why it
+took them that long to implement. I feel like it should have been implemented.” – TS03
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+21
+“I went to Twitch HQ for [a Black History summit in the past], and that was one of the
+things that all of us echoed and said and was like, ‘If I banned someone, they should not
+be able to continue consuming my content.’ It needs to be like some of these other sites.
+Twitter and Facebook are perfect examples. When I block somebody, it’s scorched earth.
+As far as they’re concerned, I no longer exist to them. That’s what it needs to be.” – TS01
+These embody some of the frustrations that streamers have had for baseline protection features
+that the community had been wanting for years. The overall emotional harm of hate raids was even
+enough to dissuade some members to leave Twitch or even streaming altogether; one streamer
+explains that the hate raids gave them a lot of anxiety, and that they know streamers who “walked
+away entirely because of that anxiety and distress.” Another streamer expressed concern that their
+protective measures to prevent anomalous viewership might even affect their stream’s long-term
+growth:
+“We have things that we’re trying to do at all times and if we blockade the people who
+want to watch us, they are going to inherently want to move on elsewhere.” – TS01
+More broadly, the threat of hate raids and their impact on streamers in the future still looms over
+several of the participants. One streamer noted that, while there may be a sense of fatigue among
+the community concerning hate raids, the lack of recent publicity over hate raids may not be an
+indication that the larger threat has passed:
+“I really think that it’s either happen[ing] less or because we’ve been dealing with it now
+for so long, people are just... There’s only so many times that you can post and be like,
+‘Yep, got hate raided again today. Yep, got hate raided again today.’ So that could also be a
+factor as to why I’m not seeing it as much on Twitter.” – TS03
+5
+DISCUSSION
+In this paper, we make three primary contributions: (1) the descriptive characterization of a novel
+form of long-term harassment campaigns on livestreaming platforms; (2) the definition of hate
+raids as a dually-motivated phenomenon: first as a hate-driven attack, and second as an act of
+seeking attention; (3) the observation that members of targeted communities rapidly responded to
+the threat of hate raids to address the shortcomings of protections provided by Twitch. In each of
+the following paragraphs, we elaborate on these contributions.
+5.1
+Characterization of Hate Raids
+Although hate raids on Twitch caused significant disruption and emotional harm to streamers,
+these attacks were relatively technically unsophisticated. Accounts were created en masse (likely
+in an automated fashion) to serve a single purpose, hateful comments were largely identical across
+channels, and user-specified identity tags were operationalized to attack marginalized groups.
+Many of these tactics might have been prevented if Twitch had followed established trust and
+safety practices like rate-limiting account creation [57], adding a delay between account creation
+and platform participation, deploying additional identity verification requirements (e.g., SMS or
+phone) [58],6 and protecting at-risk streamers by safeguarding automated access to sensitive data,
+such as identity-based channel tags.
+Although there are trade-offs between adding friction in joining communities and protecting
+users from abuse, the security practices employed by Twitch at the time of this wave of hate raids
+did not deter these relatively unsophisticated attacks. The broader history of Trust and Safety is
+often characterized by reactive feature development as attack vectors become apparent on each
+6Phone verification was added as a feature during the later phases of hate raids, indicating that it may have been under
+development but not yet released when this wave of hate raids began.
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+22
+Catherine Han et al.
+specific platform, but a common set of forms of attacks have appeared many times throughout the
+history of social platforms and, as in this case, they do not become substantially more sophisticated
+as they are ported from platform to platform [16, 29, 31]. The appearance of these attacks and
+the form that they take on any new platform is often predictable, and it is much easier to build
+safeguards during earlier development phases than to be forced to reactively add them under time
+pressure when crises arise. Future community-driven platforms should prioritize the allocation of
+resources to teams developing defensive tactics a necessary first step for curbing online abuse of
+this nature before it causes significant harm.
+The qualitative accounts of streamers’ experiences that we examine affirm that highly-targeted
+hate raids can lead to long-term emotional distress and can even threaten streamers’ physical
+safety. While Twitch has begun to take steps to combat hate raids via automated tooling (e.g.,
+AutoMod), optional account verification methods, and the aforementioned Shield Mode, the threat
+of highly-motivated hate raids coordinated off-platform continues to loom over its streamers. In
+March 2022, a wave of hate raids orchestrated by streamers on Cozy.tv, a livestreaming platform
+founded by far-right white nationalist Nick Fuentes, hit Twitch, this time targeting women and
+LGBTQ+ streamers with homophobic, transphobic, and misogynistic messages in their Twitch
+channels, direct messages, and Discord servers [43].7 As hate raids continue to threaten streamers
+with varying degrees of off-platform coordination, legitimate user participation, and bot account
+manipulation, the need for platforms to consider both increasingly sophisticated threat models and
+historically common patterns of attacks has only grown. Platforms must consider preemptively
+what their policies, protection, and communication processes will be, and by designing these
+mechanisms for the needs of their at-risk communities, they can better protect all of their users.
+The design of proactive prevention measures that do not disproportionately burden or disadvantage
+marginalized communities—with respect to their online engagement and technical overhead—
+remains an important question for future research and development.
+5.2
+Dual Motivation of Hate Raids
+We draw several primary characteristics from Marwick [30] and Phillips [41] as a baseline to com-
+pare hate raids with: first, per Phillips, subcultural trolling benefits from (and to some extent relies
+on) amplification [41, pp. 3–6, 56–61], and fits within existing media narratives, often referencing
+mainstream concepts and/or publicized events [41, pp. 115–118] in absurd or repurposed ways.
+Second, per Marwick, morally-motivated networked harassment also benefits from amplification,
+but it also relies heavily on identity and identity conflicts to justify harassment campaigns that
+have none of the underlying absurd logic that characterize subcultural trolling [30, pp. 5–8]. More-
+over, where subcultural trolling originates from specific communities, often in planned, targeted
+attacks, morally-motivated networked harassment often originates more organically and is partially
+self-amplifying through the properties of networks such as those on Twitter. As we discussed in
+Section 4.1, the hate raids on Twitch share variants of each of these characteristics, and we therefore
+argue that they lie in a space between subcultural trolling and morally-motivated networked
+harassment.
+5.3
+Stakeholder Rapid Response
+We observed many similar behaviors in Twitch hate raids that occur during natural disaster response
+as documented in crisis informatics literature — informational-support seeking, aggregation of
+7These hate raids were performed manually, and as such would likely not have been deterred by security measures
+designed to prevent automated attacks from bots; however, their occurrence represents a continued threat to streamers
+from marginalized groups on the platform.
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+23
+resources, and development of new tools and technologies to address specialized needs arising
+from the crisis. We also observed the use of social media for social support-seeking and solidarity,
+even leading to the organization of a significant protest.
+During the hate raids, there was no formal organization (e.g., a state or federal government)
+coordinating public response, as is often the case in the aftermath of natural disasters; while Twitch
+did respond to the hate raids in several ways, these did not involve coordinating with its users at any
+scale. As such, responses to hate raids more closely resembled those documented in literature on
+longer-term conflicts where public institutions play less of a role because they have been weakened
+as a result of the conflict [33, pp. 2–3].
+Users were able to respond to rapidly evolving situations during the hate raids in ways that
+brought relief to their communities far more quickly than Twitch was able to. They developed and
+rapidly iterated on tools to counter the attacks and improved those tools as attacks changed. The
+first of these tools appeared within days of when the hate raids started to gain public attention.
+Users also created guides on how to use Twitch’s moderation features and Discord’s moderation
+features (for streamers who had servers affiliated with their streams), and on how streamers could
+better protect their personal information. Guides for all of these already existed in forms created
+by the respective platforms, but the community-created guides gained significantly more traction
+in this case because of their applicability to the specific circumstances of hate raids and because of
+the shared trust between community members.
+With this work we do not mean to suggest that, because users were effective in rapidly responding
+to these issues, Twitch should cede their authority to users on Trusty & Safety issues. Instead, we
+note that Twitch and its users each have different strengths in how they are able to respond, and
+that Twitch and other platforms with similar moderation structures could gain much value from
+better communication and collaboration with users on moderation problems that arise. Volunteer
+moderators’ domain-specific knowledge and reputational trust paired with the findings from
+prior work showing that experienced moderators can successfully onboard volunteers into new
+moderation contexts [46] suggests that Twitch as a platform can gain insight and trust from their
+users by building connections with power users (e.g., prominent community tool developers like
+Sery). By consulting with such users, Twitch can also improve the dissemination of resource
+guides and the visibility of community-built tools. This access to information may be particularly
+effective in enhancing coordinated action because users are far more agile than the platform in
+organizing and producing tools to respond to imminent threats. As both Seering et al. and Roberts
+suggest [44, 46], the use of volunteer moderation for commercial platforms brings to question the
+ethics in the division of labor between volunteers and platforms. We argue that platforms should
+consult with power users to improve communication and tooling, and that these platforms should
+consider paying such power users for their valuable, contextual knowledge to compensate them
+for their large contributions to their communities.
+Finally, we reiterate the recommendations of prior work [1] rooted in intersectional feminist
+theory: that platforms must center the needs of their most marginalized, vulnerable users in their
+design. Platforms designed around existing structural inequalities recreate and further disseminate
+these systems of oppression [35]. We argue that addressing the needs of the oppressed more
+effectively encompasses the needs of all users, allowing platforms to be better prepared to mitigate
+inevitable attempts of abuse.
+5.4
+Limitations
+We acknowledge that our analysis is not based on a comprehensive view of the platform. Because
+smaller communities may have a tacit expectation of privacy, we intentionally did not collect chat
+data from channels with less than an average of 100 viewers. However, many communities targeted
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+24
+Catherine Han et al.
+by hate raids were not necessarily large, mainstream channels. According to Twitch, as of 2018,
+81.5% of its creators and viewers were male [61], and user surveys have shown that a majority are
+white. As such, we expect that some of the highly-targeted hate raiding behavior was not captured
+in our large-scale data collection methodology. Furthermore, our hate raid detection mechanism was
+based on community-aggregated lists of known malicious bots. Because of this, we may not have
+detected categories of hate raids that were not actively documented by community members. This
+likely narrows the variance in attack structure and message content flagged in our dataset. Even
+with these limitations, however, we argue that our quantitative perspective still provides insights
+into various technical characteristics and attacker motivations of hate raids. Particularly, when
+paired with our qualitative results that specifically seek the perspectives of targeted community
+members, we believe that we are able to capture multiple facets of a nuanced and dynamic threat
+model.
+6
+CONCLUSION
+Our large-scale quantitative measurement of hate raids across mainstream channels on Twitch
+and interviews with community members from targeted groups confirm that hate raids are indeed
+highly-targeted and hate-driven attacks. Our quantitative analysis reveals an additional mode of
+hate raid, however, that is similar to subcultural trolling and networked harassment. We find that the
+technical characteristics of these attacks mirror many of the naïve methods of other forms of online
+abuse, such as spam. The content of these hate raid messages are deeply entrenched in two main
+hateful ideologies: anti-Black racism and antisemitism. Our interviews demonstrate the various
+approaches—both proactive and reactive—to defense that the community took in response to hate
+raids. Our analysis furthers our understanding of the complexities in the ecosystem surrounding
+hate raids, highlights lessons to be learned in designing proactive harassment mitigation into a
+platform from the start, and brings attention to the interplay between platform and community
+governance in the face of a collective crisis.
+7
+ACKNOWLEDGEMENTS
+This work was supported in part by the National Science Foundation under grants #2030859 and
+#2127309 to the Computing Research Association for the CIFellows Project and NSF Graduate
+Research Fellowship #DGE-1656518. We would like to thank the participants in this study for
+their time and openness in discussing their experiences, as well as Sery and PleasantlyTwstd for
+expert feedback on the nature of hate raids during the study. We would also like to thank Michael
+Bernstein for feedback on study design and communication of findings.
+REFERENCES
+[1] Lindsay Blackwell, Jill Dimond, Sarita Schoenebeck, and Cliff Lampe. 2017. Classification and Its Consequences for
+Online Harassment: Design Insights from HeartMob. Proc. ACM Hum.-Comput. Interact. 1, CSCW, Article 24 (Dec.
+2017), 19 pages. https://doi.org/10.1145/3134659
+[2] Jie Cai and Donghee Yvette Wohn. 2022. Coordination and Collaboration: How do Volunteer Moderators Work as a
+Team in Live Streaming Communities? Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems
+(2022).
+[3] Carlos Castillo. 2016. Big crisis data: social media in disasters and time-critical situations. Cambridge University Press,
+Cambridge, UK.
+[4] Eshwar Chandrasekharan, Chaitrali Gandhi, Matthew Wortley Mustelier, and Eric Gilbert. 2019. Crossmod: A Cross-
+Community Learning-Based System to Assist Reddit Moderators. Proc. ACM Hum.-Comput. Interact. 3, CSCW, Article
+174 (Nov. 2019), 30 pages. https://doi.org/10.1145/3359276
+[5] Justin Cheng, Michael Bernstein, Cristian Danescu-Niculescu-Mizil, and Jure Leskovec. 2017. Anyone Can Become
+a Troll: Causes of Trolling Behavior in Online Discussions. In Proceedings of the 2017 ACM Conference on Computer
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+25
+Supported Cooperative Work and Social Computing (Portland, Oregon, USA) (CSCW ’17). ACM, New York, NY, USA,
+1217–1230. https://doi.org/10.1145/2998181.2998213
+[6] Marc Cheong and Vincent C S Lee. 2011. A microblogging-based approach to terrorism informatics: Exploration and
+chronicling civilian sentiment and response to terrorism events via Twitter. Information Systems Frontiers 13, 1 (2011),
+45–59. https://doi.org/10.1007/s10796-010-9273-x
+[7] Bill Cooney. [n.d.].
+New Twitch stats reveal how few viewers are needed to be a “top” streamer.
+Dexerto
+([n. d.]).
+https://www.dexerto.com/entertainment/new-twitch-stats-reveal-how-few-viewers-are-needed-to-be-
+a-top-streamer-1527638/
+[8] Amanda C Cote. 2017. “I Can Defend Myself”: Women’s Strategies for Coping With Harassment While Gaming Online.
+Games and Culture 12, 2 (2017), 136–155. https://doi.org/10.1177/1555412015587603
+[9] John W Creswell. 2013. Qualitative Inquiry and Research Design: Choosing Among Five Traditions. SAGE, Thousand
+Oaks, CA.
+[10] Ralston Dacanay. [n.d.]. Twitch Streamer Creates Third-Party ’Panic Button’ to Counter Hate Raids. DBLTAP
+([n. d.]). https://www.dbltap.com/posts/twitch-streamer-creates-third-party-panic-button-to-counter-hate-raids-
+01fekqmgacvw
+[11] Cecilia D’Anastasio. [n.d.]. Twitch Sues Users Over Alleged ‘Hate Raids’ Against Streamers. Wired ([n. d.]). https:
+//www.wired.com/story/twitch-sues-users-over-alleged-hate-raids/
+[12] Srayan Datta and Eytan Adar. 2019. Extracting inter-community conflicts in reddit. In Proceedings of the international
+AAAI conference on Web and Social Media.
+[13] Julian Dibbell. 1993. A Rape in Cyberspace: How an Evil Clown, a Haitian Trickster Spirit, Two Wizards, and a Cast of
+Dozens Turned a Database Into a Society. The Village Voice December 23 (1993), 36–42. https://www.villagevoice.com/
+2005/10/18/a-rape-in-cyberspace/
+[14] Tuğrulcan Elmas, Rebekah Overdorf, Ahmed Furkan Özkalay, and Karl Aberer. 2022. Ephemeral Astroturfing Attacks:
+The Case of Fake Twitter Trends. In EuroS&P ’22.
+[15] Jesse Fox and Wai Yen Tang. 2017. Women’s experiences with general and sexual harassment in online video games:
+Rumination, organizational responsiveness, withdrawal, and coping strategies. New Media & Society 19, 8 (2017),
+1290–1307. https://doi.org/10.1177/1461444816635778
+[16] Sara Gordon. 1994. IRC and Security — Can the two co-exist? (1994).
+[17] Kishonna L Gray. 2017. They’re just too urban”: Black gamers streaming on Twitch. In Digital Sociologies, Jessie Daniels,
+Karen Gregory, and Tressie McMillan Cottom (Eds.). Vol. 1. Policy Press, Bristol, England, Chapter 22, 355–368.
+[18] Nathan Grayson. [n.d.]. Marginalized streamers beg Twitch to ‘do better’ in wake of hate raids, poor pay. The
+Washington Post ([n. d.]). https://www.washingtonpost.com/video-games/2021/08/11/twitch-do-better-hate-raids/
+[19] Nathan Grayson. [n.d.]. Twitch hate raids are more than just a Twitch problem, and they’re only getting worse. The
+Washington Post ([n. d.]). https://www.washingtonpost.com/video-games/2021/08/25/twitch-hate-raids-streamers-
+discord-cybersecurity/
+[20] Susan Herring, Kirk Job-Sluder, Rebecca Scheckler, and Sasha Barab. 2002. Searching for Safety Online: Managing
+“Trolling” in a Feminist Forum. The Information Society 18, 5 (2002), 371–384. https://doi.org/10.1080/01972240290108186
+[21] Dylan Horetski. [n.d.]. Twitch hate raids return in massive wave of attacks on LGBTQIA+ streamers. Dexerto
+([n. d.]). https://www.dexerto.com/entertainment/twitch-hate-raids-return-in-massive-wave-of-attacks-on-lgbtqia-
+streamers-1781574/
+[22] Jialun Aaron Jiang, Charles Kiene, Skyler Middler, Jed R. Brubaker, and Casey Fiesler. 2019. Moderation Challenges
+in Voice-based Online Communities on Discord. Proc. ACM Hum.-Comput. Interact. 3, CSCW, Article 55 (Nov. 2019),
+23 pages. https://doi.org/10.1145/3359157
+[23] Chris Kanich, Christian Kreibich, Kirill Levchenko, Brandon Enright, Geoffrey M Voelker, Vern Paxson, and Stefan
+Savage. 2008. Spamalytics: An empirical analysis of spam marketing conversion. In 15th ACM conference on Computer
+and communications security.
+[24] Charles Kiene, Andrés Monroy-Hernández, and Benjamin Mako Hill. 2016. Surviving an “Eternal September”:
+How an Online Community Managed a Surge of Newcomers. In Proceedings of the 2016 CHI Conference on Human
+Factors in Computing Systems (San Jose, California, USA) (CHI ’16). ACM, New York, NY, USA, 1152–1156.
+https:
+//doi.org/10.1145/2858036.2858356
+[25] Srijan Kumar, Justin Cheng, Jure Leskovec, and V.S. Subrahmanian. 2017. An Army of Me: Sockpuppets in Online
+Discussion Communities. In WWW ’17.
+[26] Chen Ling, Utkucan Balci, Jeremy Blackburn, and Gianluca Stringhini. 2021. A First Look at Zoombombing. In IEEESP.
+[27] Richard MacKinnon. 1997. Virtual Rape. Journal of Computer-Mediated Communication 2, 4 (1997), 1–2.
+https:
+//doi.org/10.1111/j.1083-6101.1997.tb00200.x
+[28] Kaitlin Mahar, Amy X. Zhang, and David Karger. 2018. Squadbox: A Tool to Combat Email Harassment Using
+Friendsourced Moderation. In Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems (Montreal
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+26
+Catherine Han et al.
+QC, Canada) (CHI ’18). ACM, New York, NY, USA, Article 586, 13 pages. https://doi.org/10.1145/3173574.3174160
+[29] Enrico Mariconti, Guillermo Suarez-Tangil, Jeremy Blackburn, Emiliano De Cristofaro, Nicolas Kourtellis, Ilias Leon-
+tiadis, Jordi Luque Serrano, and Gianluca Stringhini. [n.d.]. "You Know What to Do" Proactive Detection of YouTube
+Videos Targeted by Coordinated Hate Attacks. Proceedings of the ACM on Human-Computer Interaction CSCW ([n. d.]).
+[30] Alice E Marwick. 2021. Morally Motivated Networked Harassment as Normative Reinforcement. Social Media + Society
+7, 2 (2021), 20563051211021378. https://doi.org/10.1177/20563051211021378
+[31] Adrienne Massanari. 2017. #Gamergate and The Fappening: How Reddit’s algorithm, governance, and culture support
+toxic technocultures. New Media & Society 19, 3 (2017), 329–346.
+[32] Danaë Metaxa-Kakavouli, Paige Maas, and Daniel P. Aldrich. 2018. How Social Ties Influence Hurricane Evacuation
+Behavior. Proc. ACM Hum.-Comput. Interact. 2, CSCW, Article 122 (nov 2018), 16 pages. https://doi.org/10.1145/3274391
+[33] Andrés Monroy-Hernández, danah boyd, Emre Kiciman, Munmun De Choudhury, and Scott Counts. 2013. The New
+War Correspondents: The Rise of Civic Media Curation in Urban Warfare. In Proceedings of the 2013 Conference on
+Computer Supported Cooperative Work (San Antonio, Texas, USA) (CSCW ’13). Association for Computing Machinery,
+New York, NY, USA, 1443–1452. https://doi.org/10.1145/2441776.2441938
+[34] David Moore, Colleen Shannon, Douglas J Brown, Geoffrey M Voelker, and Stefan Savage. 2006. Inferring internet
+denial-of-service activity. ACM Transactions on Computer Systems (TOCS) (2006).
+[35] Safiya Umoja Noble. 2018. Algorithms of Oppression. NYU Press, New York, NY, USA.
+https://doi.org/10.2307/j.
+ctt1pwt9w5
+[36] Leysia Palen and Kenneth M Anderson. 2016. Crisis informatics–New data for extraordinary times. Science 353, 6296
+(2016), 224–225. https://doi.org/10.1126/science.aag2579
+[37] Leysia Palen, Sarah Vieweg, Jeannette Sutton, Sophia B Liu, and Amanda Hughes. 2007. Crisis informatics: Studying
+crisis in a networked world. In Proceedings of the Third International Conference on E-Social Science. 7–9.
+[38] Manish Pandey. [n.d.]. Twitch announces new tools to fight hate raids. BBC ([n. d.]). https://www.bbc.com/news/
+newsbeat-58594732
+[39] Ash Parrish. [n.d.]. Twitch viewership noticeably dropped when streamers took a day off in protest. The Verge ([n. d.]).
+https://www.theverge.com/2021/9/2/22654534/streamers-twitch-walkout-viewership-drop
+[40] Whitney Phillips. 2011. LOLing at tragedy: Facebook trolls, memorial pages and resistance to grief online. First Monday
+16, 12 (2011), 12 pages. https://doi.org/10.5210/fm.v16i12.3168
+[41] Whitney Phillips. 2015. This is why we can’t have nice things: Mapping the relationship between online trolling and
+mainstream culture. MIT Press, Cambridge, MA, USA.
+[42] Whitney Phillips. 2019. It Wasn’t Just the Trolls: Early Internet Culture, “Fun,” and the Fires of Exclusionary Laughter.
+Social Media + Society 5, 3 (2019), 2056305119849493. https://doi.org/10.1177/2056305119849493
+[43] Blaine Polhamus. [n.d.]. Hate raids return to Twitch, another wave of attacks target LGBTQIA+ streamers. DOT
+ESPORTS ([n. d.]). https://dotesports.com/streaming/news/hate-raids-return-to-twitch-another-wave-of-attacks-
+target-lgbtqia-streamers
+[44] Sarah T. Roberts. 2016. Commercial Content Moderation: Digital Laborers’ Dirty Work. In The Intersectional Internet:
+Race, Sex, Class and Culture Online, Safiya Umoja Noble and Brendesha M. Tynes (Eds.). Peter Lang Digital Formations
+series, New York, NY, USA, 147–160.
+[45] Morgan Klaus Scheuerman, Stacy M. Branham, and Foad Hamidi. 2018. Safe Spaces and Safe Places: Unpacking
+Technology-Mediated Experiences of Safety and Harm with Transgender People. Proc. ACM Hum.-Comput. Interact. 2,
+CSCW, Article 155 (Nov. 2018), 27 pages. https://doi.org/10.1145/3274424
+[46] Joseph Seering, Brianna Dym, Geoff Kaufman, and Michael Bernstein. 2022. Pride and Professionalization in Volunteer
+Moderation: Lessons for Effective in Platform-User Collaboration. Journal of Online Trust and Safety (2022).
+[47] Joseph Seering and Sanjay R. Kairam. 2022. Who Moderates on Twitch and What Do They Do? Quantifying Practices
+in Community Moderation on Twitch. Proc. ACM Hum.-Comput. Interact. 7, GROUP, Article 18 (dec 2022), 18 pages.
+https://doi.org/10.1145/3567568
+[48] Joseph Seering, Robert Kraut, and Laura Dabbish. 2017. Shaping Pro and Anti-Social Behavior on Twitch Through
+Moderation and Example-Setting. In Proceedings of the 2017 ACM Conference on Computer Supported Cooperative Work
+and Social Computing (Portland, Oregon, USA) (CSCW ’17). ACM, New York, NY, USA, 111–125. https://doi.org/10.
+1145/2998181.2998277
+[49] Joseph Seering, Tony Wang, Jina Yoon, and Geoff Kaufman. 2019. Moderator engagement and community development
+in the age of algorithms. New Media & Society 21, 7 (2019), 1417–1443. https://doi.org/10.1177/1461444818821316
+[50] Bryan Semaan and Gloria Mark. 2011. Technology-Mediated Social Arrangements to Resolve Breakdowns in In-
+frastructure during Ongoing Disruption. ACM Trans. Comput.-Hum. Interact. 18, 4, Article 21 (12 2011), 21 pages.
+https://doi.org/10.1145/2063231.2063235
+[51] Anna DuVal Smith. 1999. Problems of Conflict Management in Virtual Communities. In Communities in Cyberspace
+(1st ed.), Marc A Smith and P Kollock (Eds.). Routledge, New York, NY, USA, 135–166.
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance
+27
+[52] Robert Soden and Leysia Palen. 2014. From Crowdsourced Mapping to Community Mapping: The Post-earthquake
+Work of OpenStreetMap Haiti. In COOP 2014 - Proceedings of the 11th International Conference on the Design of
+Cooperative Systems, 27-30 May 2014, Nice (France), Chiara Rossitto, Luigina Ciolfi, David Martin, and Bernard Conein
+(Eds.). Springer International Publishing, Cham, 311–326.
+[53] Robert Soden and Leysia Palen. 2016. Infrastructure in the Wild: What Mapping in Post-Earthquake Nepal Reveals
+about Infrastructural Emergence. In Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems
+(San Jose, California, USA) (CHI ’16). Association for Computing Machinery, New York, NY, USA, 2796–2807. https:
+//doi.org/10.1145/2858036.2858545
+[54] Bijan Stephen. [n.d.]. The lockdown live-streaming numbers are out, and they’re huge. The Verge ([n. d.]). https://www.
+theverge.com/2020/5/13/21257227/coronavirus-streamelements-arsenalgg-twitch-youtube-livestream-numbers
+[55] Hibby Thach, Samuel Mayworm, Daniel Delmonaco, and Oliver Haimson. 2022. (In)visible moderation: A digital
+ethnography of marginalized users and content moderation on Twitch and Reddit. New Media & Society (2022).
+[56] Kurt Thomas, Devdatta Akhawe, Michael Bailey, Dan Boneh, Sunny Consolvo, Nicola Dell, Zakir Durumeric,
+Patrick Gage Kelley, Deepak Kumar, Damon McCoy, Sarah Meiklejohn, Thomas Ristenpart, and Gianluca Stringhini.
+2021. SoK: Hate, Harassment, and the Changing Landscape of Online Abuse. In IEEESP.
+[57] Kurt Thomas, Chris Grier, Dawn Song, and Vern Paxson. 2011. Suspended accounts in retrospect: an analysis of twitter
+spam. In ACM SIGCOMM conference on Internet measurement conference.
+[58] Kurt Thomas, Dmytro Iatskiv, Elie Bursztein, Tadek Pietraszek, Chris Grier, and Damon McCoy. 2014. Dialing back
+abuse on phone verified accounts. In ACM SIGSAC Conference on Computer and Communications Security.
+[59] Inc. Twitch Interactive. [n.d.]. Celebrate Yourself and Your Community with 350+ New Tags. Twitch Blog ([n. d.]).
+https://blog.twitch.tv/en/2021/05/26/celebrate-yourself-and-your-community-with-350-new-tags/
+[60] Jessica Vitak, Kalyani Chadha, Linda Steiner, and Zahra Ashktorab. 2017. Identifying Women’s Experiences With
+and Strategies for Mitigating Negative Effects of Online Harassment. In Proceedings of the 2017 ACM Conference on
+Computer Supported Cooperative Work and Social Computing (Portland, Oregon, USA) (CSCW ’17). ACM, New York,
+NY, USA, 1231–1245. https://doi.org/10.1145/2998181.2998337
+[61] Adam Yosilewitz. [n.d.]. StreamElements Analysis on Twitch Bullying. StreamElements ([n. d.]).
+https://blog.
+streamelements.com/streamelements-analysis-on-twitch-bullying-c3f2b2240318
+[62] Himanshu Zade, Kushal Shah, Vaibhavi Rangarajan, Priyanka Kshirsagar, Muhammad Imran, and Kate Starbird. 2018.
+From Situational Awareness to Actionability: Towards Improving the Utility of Social Media Data for Crisis Response.
+Proc. ACM Hum.-Comput. Interact. 2, CSCW, Article 195 (nov 2018), 18 pages. https://doi.org/10.1145/3274464
+A
+PRIMARY INTERVIEW QUESTIONS
+(1) Over the course of the past few months, have you been impacted either directly or indirectly
+by hate raids?
+(a) If so, how?
+(b) (If they were hate raided or observed hate raids) Can you describe what the hate raid(s)
+were like?
+(2) What did you do to protect yourself from hate raids if anything?
+(a) (If not mentioned) Did you add any new moderation tools?
+(b) (If not mentioned) Did you add new moderators or request additional moderator support?
+(3) How effective were each of these strategies for protecting yourself?
+(4) How did you learn about new ways to protect yourself?
+(a) (If not mentioned) How did you learn about how to use new tools?
+(b) (If not mentioned) How did you learn about any new strategies for protecting your personal
+information?
+(c) (If not mentioned) Were you involved in any spaces were these topics were discussed?
+(5) Were you involved in any forms of collective action like #TwitchDoBetter or #ADayOffTwitch?
+(6) How do you feel about Twitch’s response to the Hate Raids?
+(a) How do you feel about the lawsuit that Twitch has announced against the perpetrators?
+(b) Do you think that the new moderation features Twitch released have helped?
+(c) How do you feel about the way Twitch communicated about the Hate Raids in August and
+September?
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
+28
+Catherine Han et al.
+(7) What do you think Twitch could do better in the future in handling cases like this one?
+B
+INTERVIEW CODEBOOKS
+Streamer Category Label
+Description
+Effectiveness of Twitch’s responses
+Chunks about specific aspects of Twitch’s responses,
+including communication, lawsuit, tools they added,
+etc.
+Instrumental community support
+Chunks about community resource sharing and in-
+strumental/informational support
+Social community support
+Chunks about social/interpersonal support they re-
+ceived
+Community organization
+Chunks about collective action or group-organized
+things, e.g., #TwitchDoBetter
+Degree of raid targeting
+Degree of attack personalization (how targeted?)
+Frequency of hate raids experienced
+Frequency (how often?)
+Raid vectors
+Different attack vectors (how many different ways)
+Raid responses (short-term)
+Things the streamer did in-the-moment or during
+the weeks while the hate raids were going on to
+protect themselves/others
+Raid impact (long-term)
+Longer-term impact on streamers’ careers, health,
+well-being
+Bot Developer Category Label
+Description
+Community need
+Chunks about how a need for specific third-
+party resources for the community revealed, if
+streamers ask specifically for features, develop-
+ers’ own observations/pro-social motivations, and
+gaps/shortcomings in Twitch-provided tools
+Developer dependence
+Chunks about the degree to which streamers (large
+vs. small might have different experiences) depend
+on third-party bot developers to better protect
+themselves from hate raids, how many channels
+(how was the adoption), how effective (numbers of
+raids/bots/messages intercepted or moderated)
+Hate raid arms race
+Chunks about the kind of arms race or “cat and
+mouse game” bot developers experienced while
+rolling out features to combat hate raids
+Effectiveness of Twitch tools
+Chunks about bot developers’ perspectives on the
+efficacy of Twitch’s technical tools before/after the
+hate raids
+Twitch development obstacles
+Chunks about Twitch obstacles/hurdles that made
+effective bot development difficult
+Twitch communication
+Chunks about Twitch communications with the
+community (and how it fueled their dissatisfaction
+with the platform)
+Developer coordination
+Chunks about how the community of developers
+organized
+, Vol. 1, No. 1, Article . Publication date: January 2023.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf,len=1346
+page_content='Hate Raids on Twitch: Echoes of the Past, New Modalities,  and Implications for Platform Governance  CATHERINE HAN, Computer Science Department, Stanford University, USA  JOSEPH SEERING, Computer Science Department, Stanford University, USA  DEEPAK KUMAR, Computer Science Department, Stanford University, USA  JEFFREY T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' HANCOCK, Communication Department, Stanford University, USA  ZAKIR DURUMERIC, Computer Science Department, Stanford University, USA  In the summer of 2021, users on the livestreaming platform Twitch were targeted by a wave of “hate raids,” a  form of attack that overwhelms a streamer’s chatroom with hateful messages, often through the use of bots  and automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Using a mixed-methods approach, we combine a quantitative measurement of attacks across  the platform with interviews of streamers and third-party bot developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We present evidence that confirms  that some hate raids were highly-targeted, hate-driven attacks, but we also observe another mode of hate  raid similar to networked harassment and specific forms of subcultural trolling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We show that the streamers  who self-identify as LGBTQ+ and/or Black were disproportionately targeted and that hate raid messages were  most commonly rooted in anti-Black racism and antisemitism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We also document how these attacks elicited  rapid community responses in both bolstering reactive moderation and developing proactive mitigations for  future attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We conclude by discussing how platforms can better prepare for attacks and protect at-risk  communities while considering the division of labor between community moderators, tool-builders, and  platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  CCS Concepts: • Human-centered computing → Human computer interaction (HCI);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Collaborative  and social computing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' • Security and privacy → Social aspects of security and privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Additional Key Words and Phrases: Online harassment, online communities, moderation, platform governance  ACM Reference Format:  Catherine Han, Joseph Seering, Deepak Kumar, Jeffrey T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Hancock, and Zakir Durumeric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Hate Raids on  Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, 1 (January 2023),  28 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org//  1  INTRODUCTION  Content Warning: This paper studies hateful online content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' When necessary for clarity, this  paper directly quotes user-generated content that contains offensive/hateful speech, profanity,  and other potentially triggering content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Livestreaming platforms have boomed in popularity in recent years and become a major part  of many users’ Internet experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The livestreaming industry saw a 45% uptick in viewership  Authors’ addresses: Catherine Han, cathan@stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='edu, Computer Science Department, Stanford University, Stanford,  USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Joseph Seering, jseering@stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='edu, Computer Science Department, Stanford University, Stanford, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Deepak  Kumar, kumarde@stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='edu, Computer Science Department, Stanford University, Stanford, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Jeffrey T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Hancock,  hancockj@stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='edu, Communication Department, Stanford University, Stanford, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Zakir Durumeric, zakird@  stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='edu, Computer Science Department, Stanford University, Stanford, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee  provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and  the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Copyrights for components of this work owned by others than ACM must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' To copy otherwise, or republish, to post on servers or to redistribute to lists, requires  prior specific permission and/or a fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  © 2023 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  XXXX-XXXX/2023/1-ART $15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='00  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org//  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='03946v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='CY]  10 Jan 2023  2  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  between March and April 2020 [54], likely in part due to the COVID-19 pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Twitch is a  popular livestreaming platform, and much like any other rapidly growing online platform, its  communities have suffered from hate and harassment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' July to October 2021 marked an intense  period of harassment on Twitch with many streamers experiencing a surge of “hate raids.” In the  most common form of hate raid, a streamer’s chatroom is overwhelmed by a rapid influx of Twitch  accounts posting hateful messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Because of their dissatisfaction with Twitch’s handling of hate  raids and poor treatment of marginalized-identity streamers, these streamers and their communities  came together, gathering resources, developing tools and strategies to protect themselves, and  organizing a major protest [18, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This series of events reflected frustration within the community—  particularly from minority streamers—toward Twitch and its perceived inaction on issues of trust,  security, and safety on the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In this paper, we investigate the nature of hate raids on Twitch, how they affected vulnerable  communities, and how stakeholders reacted to hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We combine an at-scale measurement  of the hate raid phenomenon across 9,664 popular channels’ chats on Twitch with interviews of  seven LGBTQ+ and/or Black Twitch streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In addition, we interview two Twitch users that  developed third-party moderation tools in response to hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In our analysis, we explore the  following three research questions:  RQ1: What are hate raids: how are they orchestrated and who do they target?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  We first  seek to detail the fundamental characteristics of hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1 Our measurement of hate raids across  9,664 popular channels on Twitch reveals that 98% of hate raid messages consisted of identity-based  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' However, while the content of these attacks was mostly anti-Black or antisemitic, the  raids themselves selected targets indiscriminately with respect to streamer identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These hate  raids blurred the line between what prior work called “trolling” or disruptive behavior [41] and  networked harassment [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' To better understand how attackers selected their targets, we examined  Twitch’s streamer tags—a feature streamers use to categorize themselves and their community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Among streams that use tags, we find evidence that attackers may have leveraged these tags to  discover and attack marginalized-identity streamers: particularly with Black, African American,  and LGBTQ+ tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  RQ2: How do hate raids affect members of targeted groups?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Because a quantitative per-  spective on hate raids cannot fully depict the lived experiences of targeted community members,  we interviewed seven Black and/or LGBTQ+ streamers on Twitch about the impact of these at-  tacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Through these interviews, we find that the perspectives of targeted streamers aligned with  mainstream media portrayals of these attacks: hate raids are seen as highly-targeted attacks often  persecuting Black and LGBTQ+ communities on Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While identity-based attacks have always  plagued these at-risk communities online, streamers found that this wave of hate raids was distinct  in its highly-targeted nature and the persistence of its perpetrators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Furthermore, we find that the  community saw hate raids as one piece of a larger campaign of harassment, often involving other  platforms and in some cases extending into more extreme offline experiences (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', involving law  enforcement, swatting2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  RQ3: How did different groups of stakeholders respond?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  To better understand the different  ways community members and Twitch responded to hate raids, we further draw upon data from  interviews with streamers and bot developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We observed that streamers largely turned to their  community and third-party bot developers for moderation, emotional, and technical support against  1Some news reports stated that these raids began as an abuse of a built-in “raiding” feature originally intended to help grow  a sense of community [38], but we did not find direct evidence of this in our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2A harassment tactic that involves calling emergency services or police to a target’s residence  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  3  hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Volunteer bot developers created tools adopted by tens of thousands of streamers who felt  that they might be targeted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These developers worked to constantly update their tools throughout  the hate raid period, as the sophistication of hate raids evolved in response to developers’ efforts to  combat these attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In addition to an influx of support via resource aggregation, tool development,  and volunteer moderation, the community rallied together for a social movement and virtual  walkout to raise awareness for their longstanding frustrations with Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While attitudes toward  the degree of success of these movements varied among our interviewees, these community-driven  movements gained attention and impacted overall platform engagement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Our mixed-methods approach to understanding hate raids provides the following three primary  research contributions:  (1) We characterize a novel form of long-term harassment campaigns on Twitch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' not only do we  observe that hate raids leverage the real-time nature of livestreaming platforms, but we also  find that they exploit automation to select targets and amplify their attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (2) We observe that the content and orchestration of hate raid messages indicate a dual motivation:  first, hate-driven and second, attention-seeking, consistent with prior research into networked  harassment and subcultural trolling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (3) We find that members of these targeted communities, unhindered by the frictions platforms  face when developing new features and policies, rapidly assembled high-quality resources  and produced technical tools to address their needs and the limitations of Twitch’s response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Grounded in our data, we conclude by discussing the implications of our findings for livestreaming  platform design and the broader community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We argue that platforms and researchers must proac-  tively consider the unique experiences of targeted communities online, the dependency on and  potential for community-based moderation and tool-building, and the range of motivations behind  the actors coordinating hate-based attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2  RELATED WORK  This paper builds on three key bodies of related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' First, we review literature on morally-  motivated networked harassment [30] and subcultural trolling [41], and we identify characteristics  of each that hate raids share.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Second, we review online hate-based attacks documented in the  literature, situating hate raids within taxonomies of their characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Finally, we discuss ties to  literature on volunteer moderation and coordinated action, identifying connections between hate  raids and crisis informatics literature and highlighting how users’ responses to hate raids parallel  responses to natural disasters and other crises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Harassment and “trolling” in online spaces  In this paper, we situate the Twitch hate raids within prior work that discusses online harassment  and “trolling.” Definitions for both of these terms have varied widely;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' for example, trolling has been  defined as broadly as “behavior that falls outside acceptable bounds defined by [.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='] communities”  [5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1] and as specifically as in Phillips’ description of “subcultural trolling” as a nuanced cultural  phenomenon with historical and moral roots [40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Similarly, Marwick identified more than ten  different types of behaviors listed under the umbrella term of “online harassment” in prior work  [30, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We operate under the definitions of the two terms provided by Marwick and Phillips,  and we focus on the form of harassment that Marwick terms “networked harassment,” where an  individual is harassed by many people connected by social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Note that, subsequent to her original publications on subcultural trolling, Phillips wrote about  the dangers of referring to something as “just” trolling [42, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While in this paper, we compare  aspects of hate raids to aspects of Phillips’ characterization of subcultural trolling, this should  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  not be construed to mean that hate raids are “just” trolling by any means;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' they cause real harm  to targets that should not be taken lightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Moreover, these attacks occurred in the context of a  long history of racist, sexist, and transphobic behaviors in online spaces that have been especially  prevalent in online gaming spaces [15, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These behaviors have forced targeted users to hide their  identities or even to withdraw from online spaces entirely [8, 15, 45, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Characterizing hate-based attacks  Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' [56] identify three axes on which hate-based attacks can be classified:  (1) The Audience exposed to the attack, which can include the target and/or a different audience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (2) The Medium through which the attacker reaches a target, which frequently includes media  such as text, images, or video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (3) The Capabilities that are required for the attack to succeed: whether the attack requires  deception of an audience and/or a third-party authority, whether it requires amplification,  and whether it requires privileged access to information, an account, or a device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In the context of online hate and harassment behaviors, the most similar to hate raids is “brigading,”  where a single target (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', a YouTube video or Twitter account) is simultaneously attacked by a semi-  coordinated set of antagonistic users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For example, 4chan users often coordinate to target YouTube  videos that they are ideologically or otherwise opposed to [29];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Reddit users have previously, in  large groups, entered other community spaces to harass and intimidate other subreddits [12];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Zoom  users have leveraged legitimate insider access to join online meetings to disrupt and harass the  other participants, otherwise known as “Zoombombing” [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Of the above criteria, the medium through which hate raids took place is primarily text, though  in some cases other media on external platforms were involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As we discuss later in this work,  they required an audience that included both the target and a wider array of viewers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In some  cases, the attacks included revealing personal information of targets (“doxxing”), and they benefited  greatly from amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  However, as we discuss in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1, these attacks had a number of other attributes worth  mentioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For example, the capabilities required for this attack included that they were heavily  automated and occurred over a significant period of time (several months), hearkening to more  traditional cybersecurity attacks, such as Distributed Denial-of-Service (DDoS) [34] and for-profit  spam and scam campaigns [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Though Zoombombing often operates under a notion of the  infiltration of a private meeting, public Twitch streams share the capability of seeing the reactions  and impact of the attack in Zoombombing attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Therefore, we draw upon prior work in the  cybersecurity space to structure our understanding of abuse executed en masse via illegitimate  accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Contextualizing the hate raids on Twitch through both a lens of subcultural trolling and  morally-motivated networked harassment and a traditional cybersecurity lens better frames the  underlying motivation and tactics of these activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3  Volunteer moderation, coordinated action, and crisis informatics  Prior work examining platform governance and volunteer labor in online social spaces has high-  lighted a variety of dynamics that inform our analysis of hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While Twitch is a multi-modal  platform incorporating text-based chat, video, and audio, the phenomenon of hate raids echoes  the moderation challenges discussed by Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' for voice-based communities [22], as both  Twitch and Discord share ephemeral and real-time components of user interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Additionally,  we discuss the experience of hate raids and the resulting mobilization of less visible streamers  on Twitch and members of marginalized communities on the platform more broadly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Prior work  details the obstacles that such communities in particular face with regards to platform visibility and  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  5  accountability [55], further contextualizing the friction we observe between Twitch and its users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Several examples [2, 46, 48] in the literature emphasize the importance of volunteer labor in these  communities, reporting that volunteer moderators on livestreaming platforms — both individually  and in collaboration — have the capacity to effectively and quickly address norm-violating behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2, we discuss the impact of community moderation and community-developed auto-  mated moderation tools, adding to conversation in prior work that has raised questions surrounding  platform governance and the distribution of labor in content moderation [4, 24, 44, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  As we detail below, one of the core characteristics of users’ responses was collective action to  create tools and aggregate informational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' A small number of examples of collective action  to counter harassment at this scale have been documented in social computing literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Blackwell  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' reported on “HeartMob,” a platform where users can submit reports of being harassed and  volunteers will provide support — supportive messages, help with reporting harassment, and/or  help documenting abuse [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' On a much smaller scale, Mahar, Zhang, and Karger’s “Squadbox”  allowed users to coordinate trusted friends to help shield them from harassment via email [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' A  small body of work from the early-mid 1990s [13, 27, 51] and early 2000s [20] also documented  individual cases of harassment and communities’ discussions about how to respond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  A broader related body of work, situated in part in CSCW literature, comes from the field of  crisis informatics [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Though this field has largely focused on responses to offline crises (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=',  natural disasters [32, 52, 53, 62], terrorist attacks and mass shootings [3, 6, 37], and in some cases  ongoing violent conflict [33, 50]), many of the core principles are also mirrored in responses to  hateful attacks based on social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As we discuss in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2, we observe many of the same  behaviors in our research on Twitch hate raids that occur during natural disaster response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Per this  literature, we have organized our results to address questions about crisis response that parallel  questions commonly asked in crisis informatics literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3  METHODS  We examine broad patterns in hate raids and common themes in individual messages, and we  complement this analysis with insights from interviews with impacted individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In this section,  we describe the methodologies of our (1) large-scale collection and analysis of Twitch chat messages,  moderation actions, and channel attributes collected from 9,664 channels from September 2 to  September 16, 2021, (2) interviews with seven Black and/or LGBTQ+ streamers, and (3) interviews  with developers of two third-party Twitch moderation bots that were widely deployed in response  to hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Twitch Chat Data Collection  To understand how hate raids impacted high-visibility streams on Twitch, we generated a corpus of  channels to gather messages from.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We used Twitch’s API to pull information about online streamers  ordered by their current number of viewers, from high to low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We pulled this data every hour for  a week from May 4 to May 11, 2021 to compute an average number of viewers per stream when  the channel was live.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For our corpus, we only considered channels that had an average of at least  100 viewers each time they streamed and that also streamed at least three times over the course of  a week.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  We continuously gathered data from the channels on this list for two weeks in September, from  September 2 to September 16, 2021, during which time many hate raid attacks occurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Each  channel on Twitch has an associated chatroom built on Internet Relay Chat (IRC) protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' When  connecting to each channel’s chat, we sent requests for information about the channel’s chatroom  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  6  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  modes—unique chat, subscribers-only mode, and slow mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3 We also sent requests for command  and membership capabilities, which allow us to identify the usage of certain moderation and room  state commands and to determine when users joined or left chat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' the CLEARCHAT command indicates  that all of a specific users’ messages were purged from the chat, often as a result of a moderation  action, like a timeout or a ban, while the membership capability reveals when specific users are  joining and leaving the chat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In total, we collected 244,738,672 messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For each message that was  sent, we collected various pieces of metadata to contextualize it: what channel it was sent in, the  account that sent the message, the text content of the message, the timestamp of when it was sent  to the chat, the status of the chatroom (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', if it was in “slow mode”), and basic, publicly-visible  information about the account that sent the message (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', if the account is a subscriber, follower,  or moderator of the channel it is participating in).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' All data that was collected for this portion of  this study was public to any user viewing the stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Detecting Hate Raids  We started with a collection of 1,319,890 likely malicious bot accounts curated by and shared  among the Twitch community so that streamers could proactively ban and block these accounts  from participating in their chats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We searched our Twitch chat dataset for messages sent by these  accounts, creating a seed set of messages from 516 of these likely bot accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We then used  approximate string matching computed using the Levenshtein distance with a threshold of 95%  similarity to find messages with the same content despite some evasion techniques used by hate raid  attackers, such as prepending randomness to the same message contents across different accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  We continue this process of finding approximate message content until no new messages were  discovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Through this method, we found matching message contents found by an additional  1,067 discovered bot accounts for a total of 1,583 bots participating in hate raids (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We then  determined hate raid events to be windows of time where bot accounts in our dataset were seen  sending messages within two minutes of prior messages sent by bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We restricted this window to  a short interval because raiding behavior (both benign and malicious) often involves an influx of  similar messages sent across different accounts within a short period of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3  Streamer and Third-Party Bot Developer Interviews  We conducted semi-structured interviews with seven Twitch streamers who identified as Black  and/or LGBTQ+ and with two Twitch users who created third-party moderation bots to combat  hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These interviews were conducted from early October through mid-November 2021,  shortly after the major spike in hate raids in late September.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interviews lasted between 20 minutes  and one hour, with length varying based on participants’ exposure to hate raids, their roles within  the community, and their knowledge of moderation tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We recruited participants from lists of  streamers who had previously participated in visible roles during LGBTQ+ focused events on Twitch,  including featured streamers during Pride Month, streamers who were reported in news articles  as having been heavily targeted by hate raids, and streamers who actively participated in hate  raid-focused conversations in both public and semi-private spaces dedicated to hate raid responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  We recruited specifically from Black and LGBTQ+ streamers because these were the groups at the  center of discourse surrounding hate raids and were the most visibly targeted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interview questions  focused on the same topics as the research questions, with a full list of primary questions presented  in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Due to the open-ended, semi-structured nature of these interviews, we asked  additional follow-up questions when relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3https://help.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='tv/s/article/chat-commands  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  7  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Compiling hate raid logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We collected the hate raid logs in a series of four steps: (1) we began with  a list of known malicious bot account names collected by moderators, streamers, and other community  members on Twitch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' (2) we used this to filter the chat logs for messages sent by malicious bots;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' (3) after  confirming the contents of these messages are hateful, we used this seed set of messages to spider for similar  content being sent by accounts not already in this list;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' (4) we iterated with this notion of message content  similarity until no new bot accounts were detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  We do not report identity characteristics for each streamer individually because doing so might  identify them, but the following are aggregated, self-reported demographic categories: four stream-  ers identified as Black, two as Hispanic, and one as white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Five identified as women, one identified  as nonbinary, two identified as transgender, two identified as queer, and one also identified as  aromantic and asexual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Some interviewees identified with more than one of these categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The  bot developer interviewees both identified as white, male, and heterosexual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Following interview completion and transcription, interview text was separated into chunks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Each chunk contained a single idea, which ranged in length from several words to several sentences  using a variant of the method described in Creswell [9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 86–89, 184–185].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These chunks were each  given category labels, which included categories such as “Frequency of hate raids experienced,”  “Streamers’ short-term responses to hate raids,” and “Social support received by streamers.” The full  codebook is included in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Initial category labels were defined by the research questions,  but labels were iteratively added to the codebook when a chunk did not fit any existing labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' A  Cohen’s Kappa statistic was calculated to determine inter-rater reliability, with the final round of  coding achieving a Cohen’s Kappa of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The results of this analysis are summarized by category  label in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  Ethical Considerations  We gathered data from 9,664 different Twitch channels, each with at least 100 viewers on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Even though chat data from all channels on Twitch is publicly viewable, we elected to restrict  the scope of our analysis to this set of larger channels to protect any assumption of privacy that  smaller channels and their communities might have;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' channels with regular audiences of 100 or  more viewers represent an exceedingly small proportion of Twitch channels overall—in May 2021,  nearly 99% of streams had fewer than 50 average concurrent viewers [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This restriction applies a  significant limitation to our quantitative analysis, as we cannot draw conclusions regarding hate  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Bots  Chat  logs  Spidertofindmessages  withthesamecontent  Messagessentbybots  Moderators  Hatefulmessagelogs  个  Streamers  Known  malicious  8  botlists  8  Othercommunitymembers  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=',bot developers)  Verified for hateful  Messagessentbybots  contentbyresearcher  (1)  (2)  (3)  (4)8  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  raid messages sent to smaller channels, but we believe that the ethical considerations in respecting  privacy justify this limitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The final list contains 9,664 active channels that match these criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In the chat data we collected, we took precautions to minimize the risk of inadvertently affecting  communities: our script did not send any messages or interact with the chat, and we did not attempt  to de-anonymize the involved accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Furthermore, to gather our qualitative data, we interviewed members of Black and/or LGBTQ+  communities concerning their experiences with hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Because of the sensitive nature of this  research, participants were notified of the full purpose of the interview in advance, as well as what  types of questions would be asked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Additionally, we reminded participants both on the consent form  and at the beginning of the interview that they could decline to answer any questions or stop at  any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interviews typically lasted between 20 to 60 minutes, and participants were compensated  with an Amazon gift code for $15 or local currency equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' To protect participants’ anonymity,  we have removed any potentially personally identifiable information from their quotes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This work  was approved by the Stanford University Institutional Review Board (IRB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4  RESULTS  We measure hate raids across the platform and present our findings of their quantitative characteris-  tics below (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We pair these measurements with a synthesis of the qualitative perspectives  of streamers from at-risk communities and community bot developers on the responses of different  stakeholders (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Characterizations of Hate Raids  Mainstream news outlets characterized the hate raids during late summer of 2021 as targeted,  bot-mediated abuse often aimed toward marginalized streamers [11, 19, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find two forms  hate raids: first, a broad, scattershot form of hate raids akin to classic subcultural trolling [41] that  incorporates racist and antisemitic elements, and second, hate raids that targeted specific streamers  based on their identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Quantitative Perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We first sought to understand what hate raids looked like quanti-  tatively across the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4 To achieve this, we characterized hate raids observed in a corpus of  244M messages across 9,664 channels collected during a 14-day period from September 2 to Septem-  ber 16, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Of these messages, 2,947 messages were identified as being part of hate raids through  the methods discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We observed 60 hate raid attacks in 57 unique channels—three of  these channels were hate raided twice on separate occasions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Technical Characteristics  We find that 50% of channels that were hate raided had at least  32 bot accounts involved in the attack (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Some channels, however, experienced attacks  with an acutely large number of bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For example, one channel received hate raid messages  from 222 unique bot accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We found that on average, there were 48 messages per raid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These  messages were typically sent in close succession to one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In the majority of raids, all of the  messages were sent in less than 16 seconds (Figure 4), though a smaller proportion of raids lasted  for minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Most messages were sent from unique bot accounts, with 302 bots (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1%) sending  more than one message in the same raid;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' even when these bots did send more than one message,  the median number of messages sent by a single bot was two (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Overall, bots appear to have been largely throwaway, single-use accounts often created for  the purpose of enacting these hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The usernames of the bots we observe in our dataset  4Note that, as discussed above, we focus here on within-chat hate raids rather than on forms of follow-botting that were  sometimes included under the umbrella term of hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  9  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' CDF of the number of unique bots that participated in an instance of a hate raid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find that the  median bot count was 32, demonstrating the typical scale of these attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' CDF of the number of different channels a bot account hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Almost 65% of the bot accounts we  identified were found in only one channel, implying that the majority of these bots were created for a single  use in our observation period, though it is possible that these bots were used additional times in channels  that were not in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  were predominantly (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6%) strings of letters and numbers that appear to have been automatically  generated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', y9y7n18r0g6raem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Of the bots we detected sending messages (𝑁 = 1, 583), many  (25%) of the bots were created within a two-day window of their first use in our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While  these bots appear to have been created for use in a single hate raid, we find that 3% were made  far in advance of their first use—these are accounts created at least several weeks before observed  chatting in our corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This trend toward many single-use accounts likely controlled and created by  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  CDFof numberof uniquemaliciousbotsperhateraidattack  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='8  CDF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  0  50  100  150  200  Number of botsCDFofnumberofdifferentchannelsraidedperbot  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='85  CDF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='65  1  2  3  4  5  6  Numberofchannels10  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' CDF of the duration of hate raid instances in seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The hate raids we observed were largely a short  burst of hateful messages sent in close succession, often within the span of seconds or minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' CDF of the number of messages sent per hate raid instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The median message count is 36, showing  the usual scale of the observed hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Note that this number reflects how many messages actually  appeared in the stream chat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' reactive moderation actions taken by the streamer and/or their volunteer  moderators may have prevented bots from sending additional messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  a single entity echoes the literature in “sockpuppetry,” where accounts are created and controlled by  a “puppetmaster” for engaging in deceptive behavior influencing the surrounding community [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Likewise, the small proportion of aged accounts may indicate what prior work defines as “zombie”  accounts, which are ones that are created ahead of time but are dormant for a long period or  indicate benign account compromise [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  CDF of duration of hate raid attacks  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  0  50  100  150  200  250  300  Time (s)CDFofnumberof messagesperhateraidattack  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='8  CDF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  0  50  100  150  200  Number of messagesHate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  11  We found limited evidence of bot account reuse;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' the majority of bots were only observed  participating in a single channel within our sample, and even then, most bots sent only one message  (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We also found that slightly more than 20% of the known bots sent hate raid messages in  at least two different channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As of the time of this analysis, there were two ways to sign up for a  Twitch account: (1) through e-mail and (2) through phone number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The cost of creating Twitch  accounts could thus be as low as the cost of creating e-mail accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' During this period, Twitch did  move quickly to disable accounts that participated in malicious activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' When querying Twitch’s  API to understand the ages of these accounts, we successfully fetched information for only 33 (4%)  of the bot accounts in our dataset because the malicious accounts had been disabled by the time we  queried the API for their information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Only three of the 57 targeted channels experienced a hate raid attack more than once, meaning  that our corpus contains 60 observed attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Two of these channels experienced two attacks in  close succession—within 30 minutes of the first attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Additionally, both channels experienced  a similar pattern where, between the two attacks, the shared text of the messages spammed by  different bot accounts in the same raid changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For instance, in one of the channels, the message  content spammed in the first attack was a violent, anti-Black racist statement mocking Twitch  community efforts to organize against hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Just 27 minutes later, a second attack began with  accounts spamming a different anti-Black racist message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We note that, while both raids were  anti-Black in nature, the target of this raid was white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Degree of Targeting  Because of the tendency toward identity-based attacks we observed in the  hate raid messages, we next more closely examined the contents of these messages for a semantic  understanding of hate raid targeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Although the bursty messaging pattern with identical message  content that we observed in hate raids may appear similar to other, more benign behaviors on  Twitch (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', chanting5 and pro-social raiding), the content of hate raid messages distinguishes  them as clearly malicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find that the hate raids in our dataset spanned several different  kinds of hate—most often identity-based—and weaponized these hateful ideologies via graphic and  threatening language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  To better characterize how hate was expressed in the raids, we categorized the content of  the hate raid messages in our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We evaluated each message along two axes: (1) what  identities were attacked in the message, and (2) in what method this identity-based hate was  operationalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Following best practices for grounded theory coding, two researchers agreed upon  a master codebook (Table 1) and independently coded 2,947 messages sent across 60 different attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  The Kupper-Hafner agreement was computed to determine inter-rater agreement because some  messages were assigned multiple labels, and the coding achieved an agreement of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Ultimately,  the researchers met to agree on the final codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We found that the most common category of hate  expressed was anti-Black racism, which was present in nearly all of the hate raids in our dataset  (59, 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We observed that anti-Black racism was most often operationalized through violent  threats (43 of 59, 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='9%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We also noted that the content in hate raid messages was frequently an  amalgam of hateful ideologies—for instance, while anti-Black racism is an explicit category of  identity-based hate, messaging with anti-Black attacks often co-occured with QAnon propaganda  (23 of 59, 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='0%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These ideologies often overlap with their hateful roots (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', white supremacy  underlies anti-Black racism, antisemitism, and aspects of QAnon), but the way that these themes  were presented together was typically disjointed, separated into different parts of a single message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  For instance, the following message both expresses anti-Black racism and supports QAnon:  5An experimental feature introduced by Twitch in May 2021 that allows streamers and their moderators to “suggest”  messages to be duplicated or “chanted” by other users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  12  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Hateful Ideology  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Meaning  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Antisemitic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Demonstrating prejudice toward Jewish people  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Anti-Black  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Demonstrating prejudice toward Black people  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Anti-Trans  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Demonstrating prejudice toward transgender peo-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='ple  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Individual streamer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Harassing a particular streamer or individual (not  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='necessarily the streamer whose channel the mes-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='sage is sent in)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Mode of Operation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Meaning  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Violent threat  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Threats of violence (describing explicit actions)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Known propaganda  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Using known hate symbols or references (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', most  commonly excerpts from the Great Replacement or  1488*)  Direct attack  Attacks that appear to directly address the streamer  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', attacks in the second person) or align with the  streamer’s identity  Fearmongering  Inspiring fear or resignation by emphasizing the  futility of counter-hate raid efforts  Weaponized emote  Coopting Twitch emotes for harassment purposes  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', TriHard**)  Dehumanization  Implications that a group of people is not human  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', comparisons with animals)  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Codebook for hate raid message content—Codebooks for hate raid message content separated  into two axes: (1) hateful ideology and (2) the mode in which they were operationalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  1488 is a pairing of two popular hate symbols, both regarding white supremacy and neo-Nazism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  ** TriHard is a global Twitch emote depicting the face of a Black streamer, TriHex, and it has been used in the  past to alienate Black streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Violent threat Known propaganda Direct attack Fearmongering Weaponized emote  Antisemitic  10  12  2  0  3  Anti-Black  43  11  4  7  3  Individual  6  0  0  3  0  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Number of raids containing categories of operationalized hate—Anti-Black racism was the  most common form of identity-based hate we identified, and it was most often operationalized through  violent threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We do not list anti-Trans attacks in this table because they were not present in our dataset of  messages, though they may have been present in hate raids we were not able to capture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  “7i9nnde4k WayneLambright Legion | kiII -> bIacks | behead -> bIacks| <readacted> is a  cloutchasing clown he isnt even hateraiding he is just following”  There are four clear parts to this message, each with a separate meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This message’s pattern  is a common one throughout our dataset;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' in this case, pipes (“|”) were used to delimit separate parts,  as attackers presented several pieces of unrelated hateful content in one message, but other symbols  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', brackets, braces, “==>”, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=') were also used to separate or relate concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In this example, the  first component promotes Wayne Lambright, who ran for president in the United States in 2020  on a campaign supporting QAnon, anti-Black racism, and pseudoscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The second and third  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  13  Stream Tags  LGBTQIA+  Black+AfAm  No Tag  Hate raided streams (N=57)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='5%  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6%  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2%  Not hate raided streams (N=9,664)  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4%  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2%  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='6%  p-value  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='11  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Streamer tags—The results of a two-sample proportion test of the self-assigned identity tags (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=',  LGBTQIA+, Black, African American) between the channels that were and were not hate raided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find that  both LGBTQIA+ and Black + African American tags were disproportionately represented among hate raided  streams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  parts both express violent anti-Black threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Finally, the last piece is an attack on an individual  streamer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We note that in the messages attacking this streamer, they are neither present as a user  in the chat nor are they the streamer of the channel itself;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' these attacks attempted to harass this  streamer through fabricating negative associations between them and hate raid orchestration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Streamer Tags  Because the contents of these hate raid messages were largely rooted in anti-  Black racism and antisemitism, we next investigated the use of Twitch tags as potential vectors  for targeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' When streaming on Twitch, streamers can choose to categorize their streams with  “tags,” which are ways to publicly describe the stream for viewers to better search for streams  of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These tags are maintained by Twitch, but the list of available tags are updated based  upon community feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In May 2021, Twitch introduced over 350 opt-in tags for streamers  to better categorize their channels into a particular community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These tags were largely identity-  based, including “gender, sexual orientation, race, nationality, ability, mental health, and more” [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  However, some streamers feared that the same tags that were meant to increase visibility within a  community could be abused to “single out minority streamers,” [38] and other members of these  communities discouraged use of these tags as a preventative measure [21] to hide themselves from  potential attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We observe 54 of 57 channels (94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='7%) tag themselves with at least one such  category;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' however, we focus our attention on the tags that give insight into streamer identities  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', LGBTQ+, Black, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=') because the messages consisted of identity-based attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  To better understand tags’ potential usage as a mechanism for targeting marginalized com-  munities, we performed two-sample proportion tests to compare the presence of these identity  tags between channels that were and were not hate raided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find quantitative evidence that  suggests that tags may indeed have been used to find targets for harassment at scale: both the  LGBTQ+ and Black/African American tags were disproportionately represented (𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='05) in  the hate-raided streams (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We do not find, however, any usage of the Jewish identity tag  despite the heavy usage of anti-Semitic language in hate raid messages, and we note that the  disproportionate representation of LGBTQ+ streamers deviates from the identities attacked in the  contents of the messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In order to more fully understand the disparity between the identities of the targeted streamers  and the identities attacked in the content of the message, we categorized the racial identities of  (1) the streamers who were raided and (2) a random sample (𝑁 = 370) of the broader corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Two  researchers independently categorized these streamers by their perceived racial category in broad  buckets: white, person of color (PoC), and unavailable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Two streamers in the hate-raided sample  were unable to be categorized due to the streamer either not including a video feed of their face  or using a racially ambiguous virtual avatar (“VTuber” model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We found that the majority of  streamers were white in both the hate raided sample and the random sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We found that the  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  14  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  mainstream sample consisted of 41% PoC streamers, which is higher than what we observed among  hate raid victims (35%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We note that there is a very large discrepancy between the proportion of  PoC streamers identified through manual coding versus the Black/African American tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This  may be because these tags are not assigned by default, and in order to apply them, streamers must  explicitly select them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We performed a two-sample proportion test to evaluate whether the racial  identities of the populations of (1) the victims of hate raids in our mainstream corpus and (2) our  mainstream corpus differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In this case, we failed to reject the null hypothesis (𝑝 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='05), meaning  that we do not have evidence to say that the set of hate raids we quantified, which often missed the  mark in the identities targeted in their content and the identities of the victim, disproportionately  targeted PoC streamers as coded in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' It is possible that this is in part due to an intersection  of race and gender/sexual identity where the proportions of LGBTQ+-identifying streamers were  unequal between racial groups, but we do not have the sample size to adequately test this within  our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' However, the above analysis does present evidence that hate raids occurred in different  proportions across different identity tags, suggesting that tags may have been used as a targeting  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Our sample size of 57 hate raided channels is inadequate to perform rigorous statistical testing  to determine whether the broader set of attacks disproportionately targeted Black streamers, but  we note that the proportion of anti-Black content in hate raid messages (98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3%) is far greater than  the proportion of Black streamers that we detected experiencing hate raids (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='5%);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' further, only 2  of these Black streamers received hate raid messages that specifically contained racist anti-Black  language, though implicitly racist and/or antisemitic undertones and references were still present  in some.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This disparity between the identities of the streamers and the kinds of hate spewed in  their chats indicates that many of these attacks were indiscriminate in their targets—in most but  not all cases, they were not tailored to the specific streamer, but rather contained a consistent  breadth of hate regardless of their target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Paired with our tag analysis, we find that the extent  of targeting in the observed hate raids may have relied on the usage of tags due to the ease of  automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Through this large-scale, quantitative perspective, we find evidence of another mode  of hate raids that included identity-based attacks but did not align the content of their messages  with the targeted streamers’ identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Rather, we see recurring themes and shared message text  across hate raids in different channels regardless of the streamers’ racial identities;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' we describe  such general, reused hateful content sent en masse as “canned hate.”  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Perspectives of Streamers from Targeted Communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While the content of the hate raid  messages primarily targeted Black and Jewish identities, analysis of tags revealed that streamers  who were attacked were disproportionately likely to be those using Black and/or LGBTQ+ tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' To  better understand these nuances, we consider the perspectives of streamers from these targeted  communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We conducted a series of interviews with seven Twitch streamers (labeled as TS  in quote attributions) that identified as Black and/or LGBTQ+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In this section, we discuss their  accounts of how members of these communities perceived the targeted nature of hate raids and  the different channels through which they were executed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Degree of Targeting  In our interviews with streamers, we found that streamers’ experiences  largely aligned with media descriptions of hate raids as a highly-targeted attack, often specifically  targeted toward Black and LGBTQ+ creators on Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Six of the seven streamers we interviewed  explicitly described the primary targets of hate raids as Black, BIPOC, transgender, or LGBTQ+  communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In addition to these commonly targeted demographics, two streamers noted that  visibility also played a role in attackers’ choice in targeted channels:  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' New Modalities,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' and Implications for Platform Governance  15  “Specifically like one of my friends who has a bigger viewership,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' they’ve been affected a  lot more.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS01  “[My experience] was very mild in comparison to other streamers’ who were either vocally  and proudly trans or Black or both,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' as those were absolutely the target demographics.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' –  TS06  From these streamers’ perspectives,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' viewership and reputation factored into which streamers were  more likely to be targeted,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' in addition to their race and gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Additionally, while interviewees acknowledged that Black and LGBTQ+ communities have  always been at-risk for hate and harassment on online platforms, three of seven participants stated  that this wave of hate raids was drastically more severe than the attacks they had experienced  before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For instance, one streamer described the hate raid they experienced in 2021 as “arguably  the worst raid” and “most egregious iteration” they have seen to date (TS01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Per these accounts,  we sought to examine what aspects of hate raids in 2021 distinguished them from previous attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Several streamers explained that this sharp peak in severity manifested in the persistence and scale  of the attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The reported frequency of hate raids varied across the streamers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' while one streamer  stated that they were hate raided only once, two others observed a drastic increase in the duration  and frequency of the hate raids they experienced firsthand and witnessed in other channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One  streamer recounted how they were hate raided for two weeks straight:  “The highlight was the first stream that they hit me in, I had a four and a half hour stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  They were in my stream for about three and a half of those hours,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' nonstop hate raiding  me.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS01  Another streamer (TS03) contrasted their experience with hate raids before and during this particu-  larly active period,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' where before,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' hate-driven attacks occurred as a single burst that “wasn’t an  all day,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' every day or an hours long thing” and would “die out for a while.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' in 2021,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' they  witnessed hate raids that were far worse:  “They were raided for three hours straight,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' just three hours of just following and trying to  put messages in chat,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' trying dox them,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' whether it was by putting an address in a message  or making a username with the address and just following incessantly.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS03  While we did not find raids of this type within our dataset,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' we did not capture data from every  targeted channel for reasons discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  TS05 notes that the degree of automation played a key role in the impact of the threat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' the usage  of bots grew over time and later reached unprecedented scale—they would use a tool to block  suspected bot accounts all night long, blocking 300,000 to 400,000 bots at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' They described the  churn of newly created and weaponized bot accounts as “incessant and overwhelming.” In addition,  TS05 commented on the sharp growth in attacks throughout the summer:  “It went from 0-100 in no time at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' But it got scary because they were finding personal  information about me and throwing it into however many public internet locations as  possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' I had 70+ people sending me screenshots of an address associated with me for  weeks.” – TS05  Both TS03 and TS05’s experiences of these raids raised another concern—the targeted nature of  the content of these messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The carefully-crafted contents of these messages, in addition to  expressing identity attacks against their targets, sought to threaten even the physical well-being of  their targets via doxxing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The impact of such targeted attacks and the violent threats underlying  doxxing even pushed one streamer to escalate their mitigation strategies beyond their stream:  “Law enforcement got involved, I had to find a lawyer, [the attackers] were threatening  violence against my children.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' It was a scary time for me.” – TS05  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  16  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  TS05’s experience was not unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' TS01 also expressed that others also experienced swatting as  a result of being doxxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' These experiences of online harassment have manifested in potential  psychological, physical, and even financial harm for already marginalized groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Through both the incessant and bespoke nature of these attacks, we found that these streamers’  perceptions and experiences of hate raids defined them as highly-motivated attacks on individuals  based on their identities, targeting Black and LGBTQ+ communities in particular;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' while attacks on  these marginalized communities have always existed in online spaces, the severity and persistence  of hate raids distinguishes them from what many members of these communities had experienced  before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Cross-Platform Attacks  As explained by several streamers, the targeted nature of these attacks  resulted in a varied set of vectors threatening their psychological and physical safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' To better  define the range of threats hate raids posed to streamers, we asked each participant to describe  their experiences with hate raids and what attack vectors were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find that four of the  seven streamers envisioned hate raids on Twitch as one piece of a larger campaign of harassment,  highlighting the multi-platform nature of these orchestrated attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For instance, TS01’s address  and phone number were released in public locations off Twitch, and attackers even made videos  on other platforms to help disseminate their personal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This was then leveraged to  flood their phone with calls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Similarly, TS02 and TS04 noted that Discord was another platform  of concern;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Discord servers of targeted streamers were attacked, and some of the hate raids were  organized in Discord servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' TS04 described the complexity of the multi-platform nature of these  attacks:  “Where I find that companies really fall flat is understanding the impact of things that  happen on their platform, the things that are planned on their platform and committed  on another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' I think this is part of the issue with some of these hate raids is that it is  personal info being hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' It’s people’s personal stuff outside of hate raids, outside of Twitch  being shared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' It is also being called slurs in chat, and that’s harmful absolutely to be called  slurs in chat and stuff like that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' But it’s also the fear of, well, my full name just got shared  or my address just got shared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' For me, it was like my Discord got hit, which is a whole  other platform.” – TS04  TS05 echoes these concerns, acknowledging that while hate raids originated with Twitch, “when  someone makes it their mission to harm you, they’ll look for whatever they can to access you.” As  a result, the high motivation involved in these attacks has raised questions and frustration within  the community regarding platform accountability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In tandem, our quantitative and qualitative data on hate raids indicate that the experiences  of the streamers from Black and LGBTQ+ communities align with the media’s portrayal of hate  raids—that is, as highly-targeted and motivated attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' However, through our quantitative analysis  (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1), we also identified a variation of hate raids that deviated from this depiction, a  form of hate raids akin to subcultural trolling that did not target specific streamers according to  their identities, instead using “canned hate” to spread hate against Black and Jewish identities en  masse in popular channels with high visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' That is, these hate raids contained identity-based  attacks, but were spread across the platform indiscriminately, indicating that an eagerness to cause  widely-visible, attention-grabbing chaos may have also motivated the attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Community response to hate raids  As hate raids swept the platform, the community’s need and urgency for tools and resources  to mitigate the threat grew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We performed a series of interviews with both streamers and bot  developers involved with marginalized communities on Twitch to understand the following: (1)  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  17  how streamers and their communities addressed the threat of hate raids in the short term, (2) what  array of tools and resources were assembled to mitigate the impact of hate raids, (3) the efficacy of  the grassroots organization for #TwitchDoBetter and #ADayOffTwitch, and (4) the longer-term  effects of hate raids on streamers and their communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Short term responses by streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Four of the seven streamers we interviewed expressed  that they employed both proactive and reactive mitigation techniques to protect themselves from  hate raids in the short term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The kinds of techniques varied, often depending on the severity  of the threat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' On one end of the spectrum, one streamer explained that because their attackers  had escalated to threatening violence against their children, they involved law enforcement and  retained a lawyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While these vectors of attack were impossible to address solely on-platform, the  majority of streamers experienced attacks that manifested within the Twitch ecosystem of chat and  engagement notifications (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', follows and raids).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As such, these streamers were able to mitigate  some of the impact of hate raids via modifications to their streams’ moderation protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One  streamer added more users to their moderation teams, recruiting them from longtime members  of their community who were “constantly hanging out inside of the chat” and “offering up their  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' so that they can keep an eye on the chat,” a pattern previously identified in [49] and [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Several streamers detailed variations of informational-support seeking, resource aggregation, and  development of new tools in ways similar to those previously detailed in crisis informatics literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  For instance, one streamer described Stream Deck presets that were helpful for an emergency  response;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' a Stream Deck is a physical control pad with preset studio settings (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', switching media  scenes, camera angles, executing chat commands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' They described commands that they added for  moderation purposes:  “We added more commands to like basically put it in follower mode and to turn off the  chat to where it’s only emotes only so that they can’t put in any hateful words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Shutting  things down for 10 minutes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' but with a push of a button.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS02  Similarly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' another streamer outlined channel lockdown protocols they followed for hate raids,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  incorporating the idea of a “panic button” into a human moderator pipeline to handle incidents  post-facto:  “I had a panic button that turned off alerts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' locked down chat,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' my mods would record  times of incidents such as follow botting,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' we added different terms to the banned words  list,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' had the highest auto mod settings available.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS05  One variation of the Twitch Panic Button was developed and publicly advertised by nutty,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' a  Twitch streamer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' to be a rapid response mechanism integrated with a Stream Deck so that a single  push of a button (or in customized cases,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' a voice-activated trigger phrase) enabled subscribers-only  mode and cleared existing chat from both the chat client and the stream display [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Furthermore,  after performing damage control, nutty’s tool attempted to reclaim the stream space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' for instance,  in nutty’s stream, the button triggered changing background lights and snarky automatically  generated messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' An official tool with functionality similar to a panic button, named “Shield  Mode,” was rolled out by Twitch in late November, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In addition to the automated tools like the panic button, we found that streamers were aware of  bot developers that developed bespoke features or new bots altogether to help handle the wave of  hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In our interviews, a streamer mentioned one bot in particular, Sery_Bot:  “Also there’s an additional thing that has been added to a lot of.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' streamers chats called  Sery_Bot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Someone who isn’t working for Twitch created a bot where it kind of shuts down  all the other bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Like it blocks them from being able to say anything.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Or once they can  come into your chat, it blocks them out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' So a lot of us have added that.” – TS02  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  18  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Sery_Bot was developed by Sery, a developer who also sometimes streamed on Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' On  August 14, 2021, Sery publicly solicited the Twitch community via Twitter for examples of hate  raid messages and other relevant information to begin developing his bot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In the span of just a  couple of weeks, Sery developed a variety of features—for instance, text-based commands in IRC  like !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='hateraidon that performed a similar function to the panic button.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In addition to providing  utility already provided by other tools, Sery_Bot also integrated community-based block lists of  account usernames to automatically check new chat messages against.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Subsequent months entailed  list updates, more feature development (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', checking account age of chatters and profile picture  scanning for repeat offensive images, like swastikas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' With the rollout of so many features so  rapidly, Sery_Bot became viral, and in just two months, it amassed over 55,000 integrations over  different Twitch channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  TS02 highlighted both the effectiveness and widespread adoption of such a third-party bot  amongst streamers in the context of hate raids;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' however, they also indicated that discomfort with  or distrust of technology—particularly third-party bots—may have inhibited the adoption of tools  and resources meant to mitigate such threats within the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Resources from tool developers and other community members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The short-term responses  from streamers alluded to the availability of community-sourced tools and streamers’ reliance on  them to combat hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Our interviews with both streamers and bot developers illuminated the  various kinds of tools and resources the community created and what the development process was  like in response to real-time threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Streamers’ perspectives gave insights into what kinds of tools  were visible and widespread throughout the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Four streamers explicitly mentioned the  use of third-party bots for hate raid mitigation or prevention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One streamer noted that in addition  to guides for making the aforementioned panic buttons, they were well-informed of the various  bots that were developed individually by different bot developers, all for the purpose of responding  to hate raids:  “There was Smash Bot that was created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Mix It Up Bot, Sery Bot, StopHateBot, WiseBot,  time out bot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' All of those things were kind of developed.” – TS03  Another streamer contrasted the fast wave of tool development by the community members with  the poor communication and delayed response from Twitch:  “And yet, for some reason we have six queers in a trench coat who have somehow made  all these tools in the span of three days for us to use that no, they don’t eradicate the issue,  but they definitely helped kind of mitigate it immensely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We had [user] who was making  full master lists along with [user] of all the bots that were being created which.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Twitch I  think should reach out to them and get that master list and pay them for their work and  say, these are all bots that are out doing things that are worthwhile or valuable.” – TS01  TS01 underscored that these tools were developed by members of the communities targeted by  hate raids in a rapid-response fashion that Twitch as a platform simply could not;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' furthermore,  TS01 emphasized that these quickly-developed tools were also effective in mitigating specifically  the bot-mediated harassment even just with fairly naive methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  To supplement our understanding of moderation bots’ roles in the hate raid ecosystem, we  interviewed two bot developers (referred to as BD in quote attributions) to understand (1) their  perspectives and experiences with the community’s needs, (2) Twitch as a platform for development,  and (3) technical challenges they encountered while developing features for hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One bot  developer noted a sort of cat-and-mouse game between the community members and attackers,  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  19  resulting in fast-paced changes in the sophistication of hate raids and applicable mitigation tech-  niques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This bot developer remarked on the primitive, manual nature of how hate raids started,  only to quickly become more coordinated and varied:  “So they weren’t that organized back then, started with a couple guys who just came into  [a streamer]’s voice chat while he was streaming Phasmophobia, and they were shouting  the N word, and then he gave them a really strong reaction by immediately ending the  stream, deleting the VOD and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' So they came back and spammed all nasty stuff in  chat.” – BD02  This bot developer also illuminated some of the motivation for hate raid participants: to elicit a  strong, disruptive reaction from the streamer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Similarly, there were approaches that the larger  community initially employed, such as joining the attackers’ Discord servers where hate raids are  organized, that the attackers responded to:  “And it’s also a little bit of a double-edged sword because we originally used to enter the  offensive Discord servers where they would gather up and organize these hate raids with  a second account, and then report the Discord server and the respective messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' And  now of course, they learned that we do that, and they also set up a similar set of security  measures.” – BD02  As such, both the attackers and the defenders in the hate raid ecosystem were made aware of what  strategies the other side was employing, and they adapted their methods in response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' From one  bot developer’s perspective, they analyzed the threat of hate raid messages and identified that  attackers used “automated tools to just spam the chat,” and in response began developing a bot  as a counter measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This bot developer noted that the hate spam sent by an army of bots was  difficult to mitigate with manual moderation, so identified a bot-mediated moderation approach as  an effective way to respond to the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3  Collective action for #TwitchDoBetter/#ADayOffTwitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In addition to the different ways the  community attempted to better protect themselves from hate raids, there were also attempts by  the community to raise awareness through collective action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Two hashtags, #TwitchDoBetter and  #ADayOffTwitch, rallied support from Twitch users via Twitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' #TwitchDoBetter was started in  an attempt to raise awareness of the harassment of targeted creators on Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Subsequently,  #ADayOffTwitch was a boycott of Twitch that took place on September 1, 2021, meaning participants  would not stream, watch streams, or participate in any chats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This day took place with hopes that  reduced engagement on the platform would highlight the urgency of better safety for creators on  Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We found through our interviews with streamers that while the community was able to  raise awareness through these movements, there was some disagreement about their long-term  impact within the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One streamer we interviewed who was a co-organizer of the walkout  felt that the movements were successful in meeting what they perceived to be the goal, which was  to raise awareness:  “I think it worked in the way that I had hoped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We raised awareness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We actively called  on a MAJOR streaming platform to make changes and we’re seeing the fruits of our labor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  It’s not always about money like so many bigger streamers commented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Sometimes we  have to understand that reputation is a currency.” – TS05  However, setting an open-ended goal of raising awareness for these community-organized move-  ments did not satisfy another participant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In contrast, TS01 felt that ultimately, these movements  failed to narrow in on concrete demands of Twitch and therefore failed to be as effective and  impactful as they could have been:  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  20  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  “I feel like they should have done a better job of sitting down and figuring out an actualized  list of demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Why are we taking a day off of Twitch?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Because at face value, the reason  we’re taking the day off of Twitch is because hate raids suck and that’s a true assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  But what about after that?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Why do those hate raids suck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' What do we want to see to  address those hate raids?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' How do we want Twitch to address it?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' How do we want Twitch  to actually get engaged more about it?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' How do we want Twitch to respond to this?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' How  does that carry over into future endeavors?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' What does that look like for a conversation  around how they need to update their security?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' There was just little to no demand to be  had whatsoever.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' And so, what could have been an actual movement or an actual kind of  protest type of thing, just wound up being plainly speaking, a bunch of people just not  logging in.” – TS01  While these movements were organized within the community, perceptions of their goals and  effectiveness varied throughout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Still, despite conflict around the goal and organization of the  movement, #ADayOffTwitch did indeed significantly impact the number of viewers and streamers  engaging with the platform;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' per one external estimate, this movement led to up to 15% less  engagement on Twitch overall during the walkout [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  Longer-term impacts of hate raids on streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Even with all of the mitigation attempts and  movements to raise awareness, hate raids undoubtedly caused distress and skepticism throughout  the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Our interviews with streamers indicate that the visceral nature of these attacks  paired with Twitch’s response has largely shaped their views of the platform as unprepared and  detached from the community’s suffering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' All seven of the participants expressed disappointment  with Twitch’s failure to consider abuse protections proactively, the slow rollout of features and tools  to mitigate the harm of hate raids, and poor communication with between Twitch and stakeholders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  One streamer expressed resigned frustration that this experience had been consistent with Twitch’s  attitudes toward protecting its at-risk communities in the past:  “I think Twitch’s response has been absolutely abysmal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' I think that very frankly speaking,  it’s pretty pathetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Twitch has a longstanding historical track record of not knowing how  to communicate ever at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' So, while I do think that their communication for this was  abysmal, I would be remiss to omit the part where it is exactly what I expected them to  do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' And Twitch is going to continue falling on their face over topics of this nature and  conversations of this type every single time so long as they insist that silence is the best  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' And they need to do better than put out a simple tweet saying, ‘We hear you, we  see you and we want you to know that we care, we promise.”’ – TS01  Streamers also felt that poor communication even around existing mitigation tools led to un-  necessary chaos during hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One streamer noted that enabling two-factor authentication  was a common suggestion by the community and Twitch for streamers to protect themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  However, these suggestions conflate the verification of user identity with that of accounts chatting  in that user’s channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Therefore, even if there are tools that may better protect individuals, poor  communication may lead to the misuse of the tool or misinterpretation of the protections it actually  offers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  In addition to disappointment with Twitch’s communication response, several streamers lamented  the lack of tooling Twitch had prepared for such attacks, even for features that had been requested  in the past or existed on other platforms:  “The chat verification tools [released at the tail end of the hate raids] are really nice, and I  think that that’s what a lot of people have wanted for so long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' I’m not sure exactly why it  took them that long to implement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' I feel like it should have been implemented.” – TS03  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  21  “I went to Twitch HQ for [a Black History summit in the past], and that was one of the  things that all of us echoed and said and was like, ‘If I banned someone, they should not  be able to continue consuming my content.’ It needs to be like some of these other sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Twitter and Facebook are perfect examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' When I block somebody, it’s scorched earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  As far as they’re concerned, I no longer exist to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' That’s what it needs to be.” – TS01  These embody some of the frustrations that streamers have had for baseline protection features  that the community had been wanting for years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The overall emotional harm of hate raids was even  enough to dissuade some members to leave Twitch or even streaming altogether;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' one streamer  explains that the hate raids gave them a lot of anxiety,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' and that they know streamers who “walked  away entirely because of that anxiety and distress.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Another streamer expressed concern that their  protective measures to prevent anomalous viewership might even affect their stream’s long-term  growth:  “We have things that we’re trying to do at all times and if we blockade the people who  want to watch us,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' they are going to inherently want to move on elsewhere.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' – TS01  More broadly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' the threat of hate raids and their impact on streamers in the future still looms over  several of the participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' One streamer noted that, while there may be a sense of fatigue among  the community concerning hate raids, the lack of recent publicity over hate raids may not be an  indication that the larger threat has passed:  “I really think that it’s either happen[ing] less or because we’ve been dealing with it now  for so long, people are just.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' There’s only so many times that you can post and be like,  ‘Yep, got hate raided again today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Yep, got hate raided again today.’ So that could also be a  factor as to why I’m not seeing it as much on Twitter.” – TS03  5  DISCUSSION  In this paper, we make three primary contributions: (1) the descriptive characterization of a novel  form of long-term harassment campaigns on livestreaming platforms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' (2) the definition of hate  raids as a dually-motivated phenomenon: first as a hate-driven attack, and second as an act of  seeking attention;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' (3) the observation that members of targeted communities rapidly responded to  the threat of hate raids to address the shortcomings of protections provided by Twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In each of  the following paragraphs, we elaborate on these contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1  Characterization of Hate Raids  Although hate raids on Twitch caused significant disruption and emotional harm to streamers,  these attacks were relatively technically unsophisticated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Accounts were created en masse (likely  in an automated fashion) to serve a single purpose, hateful comments were largely identical across  channels, and user-specified identity tags were operationalized to attack marginalized groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Many of these tactics might have been prevented if Twitch had followed established trust and  safety practices like rate-limiting account creation [57], adding a delay between account creation  and platform participation, deploying additional identity verification requirements (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', SMS or  phone) [58],6 and protecting at-risk streamers by safeguarding automated access to sensitive data,  such as identity-based channel tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Although there are trade-offs between adding friction in joining communities and protecting  users from abuse, the security practices employed by Twitch at the time of this wave of hate raids  did not deter these relatively unsophisticated attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The broader history of Trust and Safety is  often characterized by reactive feature development as attack vectors become apparent on each  6Phone verification was added as a feature during the later phases of hate raids, indicating that it may have been under  development but not yet released when this wave of hate raids began.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  22  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  specific platform, but a common set of forms of attacks have appeared many times throughout the  history of social platforms and, as in this case, they do not become substantially more sophisticated  as they are ported from platform to platform [16, 29, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The appearance of these attacks and  the form that they take on any new platform is often predictable, and it is much easier to build  safeguards during earlier development phases than to be forced to reactively add them under time  pressure when crises arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Future community-driven platforms should prioritize the allocation of  resources to teams developing defensive tactics a necessary first step for curbing online abuse of  this nature before it causes significant harm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  The qualitative accounts of streamers’ experiences that we examine affirm that highly-targeted  hate raids can lead to long-term emotional distress and can even threaten streamers’ physical  safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' While Twitch has begun to take steps to combat hate raids via automated tooling (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=',  AutoMod), optional account verification methods, and the aforementioned Shield Mode, the threat  of highly-motivated hate raids coordinated off-platform continues to loom over its streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In  March 2022, a wave of hate raids orchestrated by streamers on Cozy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='tv, a livestreaming platform  founded by far-right white nationalist Nick Fuentes, hit Twitch, this time targeting women and  LGBTQ+ streamers with homophobic, transphobic, and misogynistic messages in their Twitch  channels, direct messages, and Discord servers [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='7 As hate raids continue to threaten streamers  with varying degrees of off-platform coordination, legitimate user participation, and bot account  manipulation, the need for platforms to consider both increasingly sophisticated threat models and  historically common patterns of attacks has only grown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Platforms must consider preemptively  what their policies, protection, and communication processes will be, and by designing these  mechanisms for the needs of their at-risk communities, they can better protect all of their users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  The design of proactive prevention measures that do not disproportionately burden or disadvantage  marginalized communities—with respect to their online engagement and technical overhead—  remains an important question for future research and development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2  Dual Motivation of Hate Raids  We draw several primary characteristics from Marwick [30] and Phillips [41] as a baseline to com-  pare hate raids with: first, per Phillips, subcultural trolling benefits from (and to some extent relies  on) amplification [41, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 3–6, 56–61], and fits within existing media narratives, often referencing  mainstream concepts and/or publicized events [41, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 115–118] in absurd or repurposed ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Second, per Marwick, morally-motivated networked harassment also benefits from amplification,  but it also relies heavily on identity and identity conflicts to justify harassment campaigns that  have none of the underlying absurd logic that characterize subcultural trolling [30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 5–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' More-  over, where subcultural trolling originates from specific communities, often in planned, targeted  attacks, morally-motivated networked harassment often originates more organically and is partially  self-amplifying through the properties of networks such as those on Twitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As we discussed in  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1, the hate raids on Twitch share variants of each of these characteristics, and we therefore  argue that they lie in a space between subcultural trolling and morally-motivated networked  harassment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='3  Stakeholder Rapid Response  We observed many similar behaviors in Twitch hate raids that occur during natural disaster response  as documented in crisis informatics literature — informational-support seeking, aggregation of  7These hate raids were performed manually, and as such would likely not have been deterred by security measures  designed to prevent automated attacks from bots;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' however, their occurrence represents a continued threat to streamers  from marginalized groups on the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  23  resources, and development of new tools and technologies to address specialized needs arising  from the crisis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We also observed the use of social media for social support-seeking and solidarity,  even leading to the organization of a significant protest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  During the hate raids, there was no formal organization (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', a state or federal government)  coordinating public response, as is often the case in the aftermath of natural disasters;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' while Twitch  did respond to the hate raids in several ways, these did not involve coordinating with its users at any  scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As such, responses to hate raids more closely resembled those documented in literature on  longer-term conflicts where public institutions play less of a role because they have been weakened  as a result of the conflict [33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Users were able to respond to rapidly evolving situations during the hate raids in ways that  brought relief to their communities far more quickly than Twitch was able to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' They developed and  rapidly iterated on tools to counter the attacks and improved those tools as attacks changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The  first of these tools appeared within days of when the hate raids started to gain public attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Users also created guides on how to use Twitch’s moderation features and Discord’s moderation  features (for streamers who had servers affiliated with their streams), and on how streamers could  better protect their personal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Guides for all of these already existed in forms created  by the respective platforms, but the community-created guides gained significantly more traction  in this case because of their applicability to the specific circumstances of hate raids and because of  the shared trust between community members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  With this work we do not mean to suggest that, because users were effective in rapidly responding  to these issues, Twitch should cede their authority to users on Trusty & Safety issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Instead, we  note that Twitch and its users each have different strengths in how they are able to respond, and  that Twitch and other platforms with similar moderation structures could gain much value from  better communication and collaboration with users on moderation problems that arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Volunteer  moderators’ domain-specific knowledge and reputational trust paired with the findings from  prior work showing that experienced moderators can successfully onboard volunteers into new  moderation contexts [46] suggests that Twitch as a platform can gain insight and trust from their  users by building connections with power users (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', prominent community tool developers like  Sery).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' By consulting with such users, Twitch can also improve the dissemination of resource  guides and the visibility of community-built tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This access to information may be particularly  effective in enhancing coordinated action because users are far more agile than the platform in  organizing and producing tools to respond to imminent threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As both Seering et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' and Roberts  suggest [44, 46], the use of volunteer moderation for commercial platforms brings to question the  ethics in the division of labor between volunteers and platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We argue that platforms should  consult with power users to improve communication and tooling, and that these platforms should  consider paying such power users for their valuable, contextual knowledge to compensate them  for their large contributions to their communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Finally, we reiterate the recommendations of prior work [1] rooted in intersectional feminist  theory: that platforms must center the needs of their most marginalized, vulnerable users in their  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Platforms designed around existing structural inequalities recreate and further disseminate  these systems of oppression [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We argue that addressing the needs of the oppressed more  effectively encompasses the needs of all users, allowing platforms to be better prepared to mitigate  inevitable attempts of abuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='4  Limitations  We acknowledge that our analysis is not based on a comprehensive view of the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Because  smaller communities may have a tacit expectation of privacy, we intentionally did not collect chat  data from channels with less than an average of 100 viewers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' However, many communities targeted  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  24  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  by hate raids were not necessarily large, mainstream channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' According to Twitch, as of 2018,  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='5% of its creators and viewers were male [61], and user surveys have shown that a majority are  white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' As such, we expect that some of the highly-targeted hate raiding behavior was not captured  in our large-scale data collection methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Furthermore, our hate raid detection mechanism was  based on community-aggregated lists of known malicious bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Because of this, we may not have  detected categories of hate raids that were not actively documented by community members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' This  likely narrows the variance in attack structure and message content flagged in our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Even  with these limitations, however, we argue that our quantitative perspective still provides insights  into various technical characteristics and attacker motivations of hate raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Particularly, when  paired with our qualitative results that specifically seek the perspectives of targeted community  members, we believe that we are able to capture multiple facets of a nuanced and dynamic threat  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  6  CONCLUSION  Our large-scale quantitative measurement of hate raids across mainstream channels on Twitch  and interviews with community members from targeted groups confirm that hate raids are indeed  highly-targeted and hate-driven attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Our quantitative analysis reveals an additional mode of  hate raid, however, that is similar to subcultural trolling and networked harassment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We find that the  technical characteristics of these attacks mirror many of the naïve methods of other forms of online  abuse, such as spam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The content of these hate raid messages are deeply entrenched in two main  hateful ideologies: anti-Black racism and antisemitism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Our interviews demonstrate the various  approaches—both proactive and reactive—to defense that the community took in response to hate  raids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Our analysis furthers our understanding of the complexities in the ecosystem surrounding  hate raids, highlights lessons to be learned in designing proactive harassment mitigation into a  platform from the start, and brings attention to the interplay between platform and community  governance in the face of a collective crisis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  7  ACKNOWLEDGEMENTS  This work was supported in part by the National Science Foundation under grants #2030859 and  #2127309 to the Computing Research Association for the CIFellows Project and NSF Graduate  Research Fellowship #DGE-1656518.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We would like to thank the participants in this study for  their time and openness in discussing their experiences, as well as Sery and PleasantlyTwstd for  expert feedback on the nature of hate raids during the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' We would also like to thank Michael  Bernstein for feedback on study design and communication of findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  REFERENCES  [1] Lindsay Blackwell, Jill Dimond, Sarita Schoenebeck, and Cliff Lampe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Classification and Its Consequences for  Online Harassment: Design Insights from HeartMob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='-Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, CSCW, Article 24 (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  2017), 19 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/3134659  [2] Jie Cai and Donghee Yvette Wohn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Coordination and Collaboration: How do Volunteer Moderators Work as a  Team in Live Streaming Communities?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [3] Carlos Castillo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Big crisis data: social media in disasters and time-critical situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Cambridge University Press,  Cambridge, UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [4] Eshwar Chandrasekharan, Chaitrali Gandhi, Matthew Wortley Mustelier, and Eric Gilbert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Crossmod: A Cross-  Community Learning-Based System to Assist Reddit Moderators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='-Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 3, CSCW, Article  174 (Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2019), 30 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/3359276  [5] Justin Cheng, Michael Bernstein, Cristian Danescu-Niculescu-Mizil, and Jure Leskovec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Anyone Can Become  a Troll: Causes of Trolling Behavior in Online Discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In Proceedings of the 2017 ACM Conference on Computer  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  25  Supported Cooperative Work and Social Computing (Portland, Oregon, USA) (CSCW ’17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM, New York, NY, USA,  1217–1230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/2998181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2998213  [6] Marc Cheong and Vincent C S Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' A microblogging-based approach to terrorism informatics: Exploration and  chronicling civilian sentiment and response to terrorism events via Twitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Information Systems Frontiers 13, 1 (2011),  45–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1007/s10796-010-9273-x  [7] Bill Cooney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' A Rape in Cyberspace: How an Evil Clown, a Haitian Trickster Spirit, Two Wizards, and a Cast of  Dozens Turned a Database Into a Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Ephemeral Astroturfing Attacks:  The Case of Fake Twitter Trends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='  [15] Jesse Fox and Wai Yen Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' IRC and Security — Can the two co-exist?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='  [17] Kishonna L Gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Policy Press, Bristol, England, Chapter 22, 355–368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [18] Nathan Grayson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='com/video-games/2021/08/25/twitch-hate-raids-streamers-  discord-cybersecurity/  [20] Susan Herring, Kirk Job-Sluder, Rebecca Scheckler, and Sasha Barab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Searching for Safety Online: Managing  “Trolling” in a Feminist Forum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The Information Society 18, 5 (2002), 371–384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='com/entertainment/twitch-hate-raids-return-in-massive-wave-of-attacks-on-lgbtqia-  streamers-1781574/  [22] Jialun Aaron Jiang, Charles Kiene, Skyler Middler, Jed R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Moderation Challenges  in Voice-based Online Communities on Discord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='-Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='3174160  [29] Enrico Mariconti, Guillermo Suarez-Tangil, Jeremy Blackburn, Emiliano De Cristofaro, Nicolas Kourtellis, Ilias Leon-  tiadis, Jordi Luque Serrano, and Gianluca Stringhini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='  [30] Alice E Marwick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Morally Motivated Networked Harassment as Normative Reinforcement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1177/20563051211021378  [31] Adrienne Massanari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' #Gamergate and The Fappening: How Reddit’s algorithm, governance, and culture support  toxic technocultures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' New Media & Society 19, 3 (2017), 329–346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [32] Danaë Metaxa-Kakavouli, Paige Maas, and Daniel P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Aldrich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' How Social Ties Influence Hurricane Evacuation  Behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='-Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2, CSCW, Article 122 (nov 2018), 16 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/3274391  [33] Andrés Monroy-Hernández, danah boyd, Emre Kiciman, Munmun De Choudhury, and Scott Counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' The New  War Correspondents: The Rise of Civic Media Curation in Urban Warfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Association for Computing Machinery,  New York, NY, USA, 1443–1452.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/2441776.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2441938  [34] David Moore, Colleen Shannon, Douglas J Brown, Geoffrey M Voelker, and Stefan Savage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Inferring internet  denial-of-service activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Transactions on Computer Systems (TOCS) (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [35] Safiya Umoja Noble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Algorithms of Oppression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' NYU Press, New York, NY, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='  ctt1pwt9w5  [36] Leysia Palen and Kenneth M Anderson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Crisis informatics–New data for extraordinary times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Science 353, 6296  (2016), 224–225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='aag2579  [37] Leysia Palen, Sarah Vieweg, Jeannette Sutton, Sophia B Liu, and Amanda Hughes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Crisis informatics: Studying  crisis in a networked world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In Proceedings of the Third International Conference on E-Social Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 7–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [38] Manish Pandey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Hate Raids on Twitch: Echoes of the Past, New Modalities, and Implications for Platform Governance  27  [52] Robert Soden and Leysia Palen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' From Crowdsourced Mapping to Community Mapping: The Post-earthquake  Work of OpenStreetMap Haiti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In COOP 2014 - Proceedings of the 11th International Conference on the Design of  Cooperative Systems, 27-30 May 2014, Nice (France), Chiara Rossitto, Luigina Ciolfi, David Martin, and Bernard Conein  (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Springer International Publishing, Cham, 311–326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [53] Robert Soden and Leysia Palen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Infrastructure in the Wild: What Mapping in Post-Earthquake Nepal Reveals  about Infrastructural Emergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems  (San Jose, California, USA) (CHI ’16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Association for Computing Machinery, New York, NY, USA, 2796–2807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='2858545  [54] Bijan Stephen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='com/2020/5/13/21257227/coronavirus-streamelements-arsenalgg-twitch-youtube-livestream-numbers  [55] Hibby Thach, Samuel Mayworm, Daniel Delmonaco, and Oliver Haimson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' New Media & Society (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [56] Kurt Thomas, Devdatta Akhawe, Michael Bailey, Dan Boneh, Sunny Consolvo, Nicola Dell, Zakir Durumeric,  Patrick Gage Kelley, Deepak Kumar, Damon McCoy, Sarah Meiklejohn, Thomas Ristenpart, and Gianluca Stringhini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' In IEEESP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [57] Kurt Thomas, Chris Grier, Dawn Song, and Vern Paxson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Suspended accounts in retrospect: an analysis of twitter  spam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In ACM SIGCOMM conference on Internet measurement conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [58] Kurt Thomas, Dmytro Iatskiv, Elie Bursztein, Tadek Pietraszek, Chris Grier, and Damon McCoy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Dialing back  abuse on phone verified accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In ACM SIGSAC Conference on Computer and Communications Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  [59] Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Twitch Interactive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' Celebrate Yourself and Your Community with 350+ New Tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Twitch Blog ([n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content='  https://blog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='twitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='tv/en/2021/05/26/celebrate-yourself-and-your-community-with-350-new-tags/  [60] Jessica Vitak, Kalyani Chadha, Linda Steiner, and Zahra Ashktorab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Identifying Women’s Experiences With  and Strategies for Mitigating Negative Effects of Online Harassment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' In Proceedings of the 2017 ACM Conference on  Computer Supported Cooperative Work and Social Computing (Portland, Oregon, USA) (CSCW ’17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM, New York,  NY, USA, 1231–1245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/2998181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='2998337  [61] Adam Yosilewitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+page_content=' StreamElements Analysis on Twitch Bullying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' StreamElements ([n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=']).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  https://blog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  streamelements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='com/streamelements-analysis-on-twitch-bullying-c3f2b2240318  [62] Himanshu Zade, Kushal Shah, Vaibhavi Rangarajan, Priyanka Kshirsagar, Muhammad Imran, and Kate Starbird.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  From Situational Awareness to Actionability: Towards Improving the Utility of Social Media Data for Crisis Response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='-Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 2, CSCW, Article 195 (nov 2018), 18 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='1145/3274464  A  PRIMARY INTERVIEW QUESTIONS  (1) Over the course of the past few months, have you been impacted either directly or indirectly  by hate raids?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (a) If so, how?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (b) (If they were hate raided or observed hate raids) Can you describe what the hate raid(s)  were like?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (2) What did you do to protect yourself from hate raids if anything?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (a) (If not mentioned) Did you add any new moderation tools?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (b) (If not mentioned) Did you add new moderators or request additional moderator support?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (3) How effective were each of these strategies for protecting yourself?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (4) How did you learn about new ways to protect yourself?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (a) (If not mentioned) How did you learn about how to use new tools?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (b) (If not mentioned) How did you learn about any new strategies for protecting your personal  information?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (c) (If not mentioned) Were you involved in any spaces were these topics were discussed?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (5) Were you involved in any forms of collective action like #TwitchDoBetter or #ADayOffTwitch?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (6) How do you feel about Twitch’s response to the Hate Raids?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (a) How do you feel about the lawsuit that Twitch has announced against the perpetrators?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (b) Do you think that the new moderation features Twitch released have helped?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (c) How do you feel about the way Twitch communicated about the Hate Raids in August and  September?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  28  Catherine Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  (7) What do you think Twitch could do better in the future in handling cases like this one?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  B  INTERVIEW CODEBOOKS  Streamer Category Label  Description  Effectiveness of Twitch’s responses  Chunks about specific aspects of Twitch’s responses,  including communication, lawsuit, tools they added,  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  Instrumental community support  Chunks about community resource sharing and in-  strumental/informational support  Social community support  Chunks about social/interpersonal support they re-  ceived  Community organization  Chunks about collective action or group-organized  things, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=', #TwitchDoBetter  Degree of raid targeting  Degree of attack personalization (how targeted?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=')  Frequency of hate raids experienced  Frequency (how often?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=')  Raid vectors  Different attack vectors (how many different ways)  Raid responses (short-term)  Things the streamer did in-the-moment or during  the weeks while the hate raids were going on to  protect themselves/others  Raid impact (long-term)  Longer-term impact on streamers’ careers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' health,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='  well-being  Bot Developer Category Label  Description  Community need  Chunks about how a need for specific third-  party resources for the community revealed,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' if  streamers ask specifically for features,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' develop-  ers’ own observations/pro-social motivations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' and  gaps/shortcomings in Twitch-provided tools  Developer dependence  Chunks about the degree to which streamers (large  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' small might have different experiences) depend  on third-party bot developers to better protect  themselves from hate raids,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' how many channels  (how was the adoption),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' how effective (numbers of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='raids/bots/messages intercepted or moderated)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Hate raid arms race  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Chunks about the kind of arms race or “cat and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='mouse game” bot developers experienced while  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='rolling out features to combat hate raids  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Effectiveness of Twitch tools  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Chunks about bot developers’ perspectives on the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='efficacy of Twitch’s technical tools before/after the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='hate raids  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Twitch development obstacles  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Chunks about Twitch obstacles/hurdles that made  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='effective bot development difficult  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Twitch communication  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Chunks about Twitch communications with the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='community (and how it fueled their dissatisfaction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='with the platform)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Developer coordination  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='Chunks about how the community of developers  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content='organized  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' 1, Article .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
+page_content=' Publication date: January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/x9E2T4oBgHgl3EQfhQeR/content/2301.03946v1.pdf'}
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+Modeling virus transmission risks in commuting with emerging mobility
+services: A case study of COVID-19
+Baichuan Moa,∗, Peyman Noursalehib, Haris N. Koutsopoulosc, Jinhua Zhaob
+aDepartment of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
+bDepartment of Urban Studies and Planning, Massachusetts Institute of Technology, Cambridge, MA 20139
+cDepartment of Civil and Environmental Engineering, Northeastern University, Boston, MA 02115
+Abstract
+Commuting is an important part of daily life. With the gradual recovery from COVID-19 and more people
+returning to work from the office, the transmission of COVID-19 during commuting becomes a concern.
+Recent emerging mobility services (such as ride-hailing and bike-sharing) further deteriorate the infection
+risks due to shared vehicles or spaces during travel. Hence, it is important to quantify the infection risks
+in commuting. This paper proposes a probabilistic framework to estimate the risk of infection during an
+individual’s commute considering different travel modes, including public transit, ride-share, bike, and
+walking. The objective is to evaluate the probability of infection as well as the estimation errors (i.e.,
+uncertainty quantification) given the origin-destination (OD), departure time, and travel mode. We first
+define a general trip planning function to generate trip trajectories and probabilities of choosing different
+paths according to the OD, departure time, and travel mode. Then, we consider two channels of infections:
+1) infection by close contact and 2) infection by touching surfaces. The infection risks are calculated on a
+trip segment basis. Different sources of data (such as smart card data, travel surveys, and population data)
+are used to estimate the potential interactions between the individual and the infectious environment. A
+first-order approximation is used to simplify the computational complexity. We also derive the closed-form
+formulation for the estimation errors, enabling us to quantify the uncertainty of the estimation results. The
+model is implemented in the MIT community as a case study. We evaluate the commute infection risks for
+employees and students. Results show that most of the individuals have an infection probability close to zero.
+The maximum infection probability is around 0.8%, implying that the probability of getting infected during
+the commuting process is low. Individuals with larger travel distances, traveling in transit, and traveling
+during peak hours are more likely to get infected. Practical implementations of the model are also discussed.
+Keywords: COVID-19; Infection risk; Emerging mobility.
+1. Introduction
+COVID-19 has greatly affected people’s lives all over the world. Recently, with the vaccination and
+people’s prevention consciousness, we are stepping into a new era of living with the virus. With the gradual
+recovery from the pandemic, more and more people return to work from the office.
+Commuting is an important part of the daily lives of people working in an office.
+In light of the
+infectiousness of COVID-19, the infection risk during the commuting process is a concern, especially
+∗Corresponding author
+Preprint submitted to Elsevier
+January 9, 2023
+arXiv:2301.02594v1  [stat.AP]  6 Jan 2023
+
+for people using public transportation, as indicated by many previous studies (Mo et al., 2021; Zhou and
+Koutsopoulos, 2021). On the other hand, recent emerging mobility services (such as ride-hailing and bike-
+sharing) further deteriorate the infection risks due to shared vehicles or spaces during travel. Therefore, it
+is important to quantify the infection risks in commuting more broadly, where the results are helpful for
+people to evaluate their health risks and better inform their commuting route/travel mode choices, and for
+policymakers to reach informed decisions.
+Many previous studies have modeled the COVID-19 infection risks in public transit systems, an important
+travel mode of commuting. These studies can be categorized from the macro-level at the city scale (Mo
+et al., 2021) or the micro-scale at the vehicle scale (Shinohara et al., 2021; Zhou and Koutsopoulos, 2021).
+Researchers have also considered the impact of commuting on the broader spatial transmission of COVID-19
+and the related control strategies (Mitze and Kosfeld, 2022; Ando et al., 2021; Fajgelbaum et al., 2021;
+Kondo, 2021). There are also studies evaluating the impact of COVID-19 on the commuting process with
+empirical data (such as surveys), such as the impact of COVID-19 on ridership changes, travel mode choices
+(Tan and Ma, 2021; Medlock et al., 2021), and departure time change (Ecke et al., 2022).
+However, there are still two research gaps. First, none of the previous studies have considered the infection
+modeling for the commuting process as a whole with multiple travel modes and multi-modal trip itineraries.
+Second, most of the previous studies regarding infection risk modeling only output the probability of infection
+(or the R0 value indicating the spreading intensity). The estimation uncertainties (i.e., how accurate are the
+estimates) are not provided.
+In this study, we propose a probabilistic framework to estimate the risk of infection during an individual’s
+commute considering different travel modes, including public transit, ride-share, bike, and walking. The
+model enables evaluating both the probability of infection and the estimation errors (i.e., uncertainty quan-
+tification). We first define a general trip planning function to generate trip trajectories and probabilities of
+choosing different paths according to the origin, destination, departure time, and travel mode. Two channels
+of infection are considered: 1) infection by close contact and 2) infection by touching surfaces. The infection
+risks are calculated on a trip segment basis. Different sources of data (such as smart card data, travel surveys,
+and population data) are used to estimate the potential interactions between the individual and the infectious
+environment. A first-order approximation technique is used to simplify the computational complexity. We
+derive the closed-form formulations for the estimation errors, enabling us to quantify the uncertainties of
+the estimation results. The model is implemented in the MIT community as a case study. We evaluate
+the commute infection risks for employees and students. Results show that most of the individuals have an
+infection probability close to zero. The maximum infection probability is around 0.8%, implying that the
+probability of getting infected during the commuting process is low. Individuals with larger travel distances,
+traveling with transit, and traveling during peak hours are more likely to get infected.
+The main contribution of this paper is twofold:
+• This is the first study dedicated to virus transmission modeling during commuting with the consid-
+eration of various travel modes and multi-modal trip itineraries. Infections due to close contact and
+touching surfaces are both captured.
+• In addition to estimating infection probabilities, this paper also calculates the estimation errors (i.e.,
+the standard deviation of the estimated probabilities) for uncertainty quantification, which has not been
+done in the literature.
+The remainder of the paper is organized as follows. The literature review is shown in Section 2. In
+2
+
+Section 3, we describe the problem and discuss the solution methods. We apply the proposed framework to
+the MIT community as a case study in Section 4. Finally, we conclude our study and summarize the main
+findings in Section 5.
+2. Literature review
+2.1. Infection modeling in public transit
+Public transit is an important travel mode for commuting. Previous studies have explored epidemic
+spreading and infection risk modeling in transit networks. Mo et al. (2021) propose a time-varying weighted
+encounter network to model the spreading of infectious diseases through public transit systems. The model
+is implemented at the metropolitan level for population infection calculation. Zhou and Koutsopoulos (2021)
+propose a modified Wells-Riley model for infection probability calculation in public transportation systems
+at the vehicle level. The model captures the spatial and temporal passenger flow characteristics in terms of
+the number of boarding and alighting passengers and the number of infectors. Similarly, Ku et al. (2021)
+analyzed the degree of infection exposure in public transport by simulating how passengers encounter and
+infect each other during their journeys.
+Shinohara et al. (2021) adopted a two-zone-based exponential
+model to calculate the infection risks in commuter trains by collecting air exchange rate data under various
+conditions. Zhao et al. (2022) developed a Wells-Riley model-based method to quantitatively evaluate the
+infection risk of riding public transit. They compared the effectiveness of different countermeasures in
+managing the spread.
+2.2. Impact of COVID-19 on commuting
+COVID-19 may affect the commuting process in many aspects, such as ridership and service frequency
+decrease, changes in passengers’ travel mode choices, route choices, and departure times choices. Previous
+studies have evaluated these impacts using different sources of empirical data. For example, many studies
+have used the smart card data to analyze the impact of COVID-19 on transit ridership changes (Ahangari
+et al., 2020; Chang et al., 2021; Wilbur et al., 2020; Jenelius and Cebecauer, 2020). There are also studies
+on ridership changes in ride-hailing systems (Meredith-Karam et al., 2021) and bike-sharing systems (Wang
+and Noland, 2021). Tan and Ma (2021) conducted a survey to understand commuters’ mode choice changes
+during the COVID-19 pandemic. They used a logistic regression model with personal attributes, travel
+attributes, and perception of COVID-19 based on a sample of 559 responses to a survey. Ecke et al. (2022)
+examine how people’s commuting behavior changed before and after COVID-19. The results show that
+people did not significantly change their commuting behavior in terms of commuting time and commuting
+mode.
+2.3. Impact of commuting on COVID-19 spreading
+Commuting may contribute to the spreading of COVID-19 by transporting infectious passengers across
+different regions. For example, Mitze and Kosfeld (2022) proposed a spatial econometric model of the
+epidemic spread to identify the role played by commuting-to-work patterns for spatial disease transmission
+and explored if the imposed containment policies affected the strength of this transmission channel. Ando
+et al. (2021) investigated the relationship among commuting, the risk of COVID-19, and COVID-19-induced
+anxiety using internet-based survey data from 27,036 respondents.
+Fajgelbaum et al. (2021) designed
+an optimal dynamic lockdown strategy against COVID-19 within a commuting network. Kondo (2021)
+developed a spatial susceptible–exposed–infectious–recovered model to analyze the effects of restricting
+inter-regional commuting mobility on the spatial spread of the COVID-19 infection in Japan.
+3
+
+2.4. Research gaps
+To the best of the authors’ knowledge, no existing papers have considered dedicated infection modeling
+for the commuting process as a whole with multiple travel modes and multi-modal trip itineraries. Most
+of them focus on infection modeling for a single travel mode (e.g., public transit), or consider the general
+modeling of epidemic spreading at a city level, where the commuting process is just a part of the big
+framework without using travel mode or itinerary-specific modeling methodologies. On the other hand, most
+of the previous studies regarding infection risk modeling only output the probability of infection or the R0
+value indicating the spreading intensity. The estimation uncertainties (i.e., how accurate are the results) are
+not calculated.
+3. Methodology
+3.1. Problem definition
+Consider a set of individuals I. For each individual i ∈ I, suppose that we know their origin oi,
+destination di, departure time ti, and travel mode mi for their daily commuting. The objective of this study is
+to estimate the probability of individual i getting affected: P(i infected | oi, di, ti, mi). Besides, we also aim
+to quantify the estimation uncertainty. If we treat P(i infected | oi, di, ti, mi) as a random variable, another
+goal of the study is to obtain the standard error of the estimation:
+�
+Var[P(i infected | oi, di, ti, mi)].
+In the following sections, we first illustrate how P(i infected | oi, di, ti, mi) is estimated. The estimation
+of standard errors is illustrated in Section 3.5.
+3.2. Trip itinerary generation
+Given an individual i’s trip information (oi, di, ti, mi), there exists a trip planner function TP(·) that
+takes (oi, di, ti, mi) as input, and outputs a set of feasible paths for the individual Ri and the associated path
+choice probability PPath(r) for all paths r ∈ Ri, that is:
+Ri, PPath(r)r∈Ri = TP(oi, di, ti, mi)
+(1)
+For example, we can define TP(·) as a composed function of the Google Map API and a C-logit model:
+TP(oi, di, ti, mi) = C-Logit ◦ Google Map API(oi, di, ti, mi)
+(2)
+Specifically, the Google Map API returns the path set Ri and path attributes Xr for all r ∈ Ri (e.g., travel
+time, travel cost, etc.), that is:
+Ri, (Xr)r∈Ri = Google Map API(oi, di, ti, mi)
+(3)
+The C-Logit model outputs the path choice probability and the standard errors for each path. The c-Logit
+model is an extension of the multinomial logit (MNL) model to correct for the correlation among paths due
+to overlapping (Cascetta et al., 1996). The key idea is to define a term called the “commonality factor” of
+path r (i.e., CFr), which measures the degree of similarity of path r with the other paths of the same OD.
+Based on the C-logit model, the probability of choosing path r can be calculated as
+PPath(r) = C-Logit(Xr) =
+exp[βT · (Xr, CFr)]
+�
+r′∈Ri exp[βT · (Xr′, CFr′)]
+(4)
+4
+
+where β is the parameter vector to estimate. The formulation of CFr can be found in Cascetta et al. (1996).
+Note the TP(·) can be defined more broadly than google map API plus the C-logit model.
+Other
+examples include the k-shortest path in a multiple-modal network compounded with any behavioral model
+for path choices (Mo et al., 2022).
+3.3. Infection modeling for a trip segment
+3.3.1. Definition of a trip segment
+A path r ∈ Ri usually contains multiple trip segments, such as walking from home to a bus station,
+taking a bus, and walking from a bus station to the office. The infection may happen at every trip segment. In
+this study, we define a segment s of a path as continuous travel with the same travel mode along the path. Let
+the set of all segments for path r be Sr. It is worth noting that, if a transit trip has one or more transfers, we
+separate the transit trip into multiple segments based on transfers because the passenger needs to first alight
+and then board a new vehicle, which is equivalent to changing to a “new travel mode” in infection modeling.
+We also ignore short walking segments (less than 3 minutes or less than 1km, e.g., transfer walking) for
+modeling convenience.
+We provide three examples to illustrate the definition of segments (Figure 1). The first example shows
+three segments: walking from home to a subway station, taking the subway, and walking from a subway
+station to the office. The second example is a ride-hailing trip with only a single segment. The third example
+shows a transit trip with a transfer, which is separated into two segments by definition.
+Figure 1: Illustration of the segment definition
+3.3.2. Infection risk for each segment
+We consider two different channels for infection: 1) infected by close contact with infectious persons
+and 2) infected by touching infectious surfaces.
+Infection by close contact: Consider a trip segment s ∈ Sr. We define Ps as the set of persons that have
+been in the six feet infectious range of individual i. For a person p ∈ Ps, let the duration of the interaction
+5
+
+Example 1
+品
+Transit
+Walk
+Walk
+Segment 1
+Segment 2
+Segment 3
+Example 2
+Ride hailing
+Segment 1
+Example 3
+ Transit
+Segment 1
+Segment 2between i and p be di,p. If p is infectious, i would have a probability of getting infected. Depending on
+whether the interaction happens indoors (e.g., in a bus) or outdoors (e.g., walking by), there are two different
+physical models.
+In an indoor environment, the probability of i getting infected by p can be calculated by the well-known
+Wells-Riley model (Riley et al., 1978):
+PIndoor(p → i | p infectious) = 1 − exp
+�−b · q · di,p
+QIndoor
+�
+(5)
+where b is the breathing rate per person (m3 /hour); q is the quanta generation rate (/hour), Q is the room
+ventilation rate of clean air (m3 /hour).
+In an outdoor environment, Rowe et al. (2021) proposed an airshed model that derives a similar infection
+probability formulation:
+POutdoor(p → i | p infectious) = 1 − exp
+�−b · q · di,p
+QOutdoor
+�
+(6)
+where QOutdoor = L · H · V∞ is the outdoor ventilation rate of clean air. H and L are the height and length
+(perpendicular to the wind direction) for a hypothetical outdoor modeling space. V∞ is the wind velocity
+(m/h). The suggested values for H and L are around 5m and 50m, respectively.
+Hence, given the set of contact persons, the total infectious probability of i during the segment s due to
+close contact is
+P(s)
+Cont(i infected) = 1 −
+�
+p∈Ps
+��
+1 − PIn/Outdoor(p → i | p infectious)
+�
+· P(p infectious) + P(p not infectious)
+�
+(7)
+where Eq. 7 is due to the fact that the probability of getting infected by at least one of p ∈ Ps equals one
+minus the probability of not getting infected by anyone.
+Infection by touching surfaces: Wilson et al. (2021) estimate the infection probability of a single
+hand-to-fomite touch as a function of viral bioburden. Their estimation already accounts for uncertainties in
+transfer efficiency, fractions of the hand used for surface and face contact, and surface areas of the hand and of
+fomites available for contact. Define this probability as PTouch(i infected | V ), where V is the viral bioburden
+of this tough. For simplicity, let us assume the viral bioburden during a trip segment is a constant and the
+value is Vs. We also assume that the number of touches during segment s (defined as Ns) is proportional
+to the duration of travel in s (defined as Ts), and the factor is γ (i.e., Ns = γs · Ts). Therefore, the total
+infection probability for individual i due to surface touching is:
+P(s)
+Surf(i infected) = 1 −
+�
+1 − PTouch(i infected | Vs)
+�Ns
+(8)
+The empirical values of Vs can be obtained from Harvey et al. (2020) who collected viral bioburden data in
+daily activity environments. Since the infection risk for a single tough is small, Eq. 8 can be approximated
+by first-order Taylor series:
+P(s)
+Surf(i infected) ≈ γs · Ts · PTouch(i infected | Vs)
+(9)
+6
+
+where Eq. 9 is computationally more efficient than Eq. 8.
+3.3.3. Infection risk by different travel modes
+Each segment s ∈ Sr is associated with a specific travel mode. Though we provide a general infection
+risk calculation model in Section 3.3.2, it is important to specify the model parameters and variables for
+each travel mode. In this section, we assume that the infectious environment is the same during the travel in
+a segment s and the values are bs, qs, QIndoor
+s
+, and QOutdoor
+s
+.
+Infection risk of transit segment: A transit segment (either bus or rail) usually includes multiple stops.
+Let the set of stops for the transit segment s except for the last one be As. We exclude the last stop because
+individual i will alight when he/she arrives at the last stop. Let the set of passengers in a vehicle (exclude
+individual i) when the vehicle departs from station a ∈ As be Ps,a. Ps,a can be obtained by smart card data
+and Ps = ∪a∈AsPs,a. Let the vehicle travel time from station a to the next stop be TTa.
+Then the infection probability for individual i due to close contact in the vehicle when it travels from
+station a to the next stop is:
+P(s,a)
+Cont (i infected) = 1 −
+�
+p∈Ps,a
+�
+P(p infectious) · exp
+�−bs · qs · TTa
+QIndoor
+s
+�
++ (1 − P(p infectious))
+�
+(10)
+For any p ∈ Ps,a, we can use smart card data to obtain their origin stations. Hence, P(p infectious) and
+P(p not infectious) can be approximated by regional infection statistics based on their origin stations. The
+total infection probability in the transit segment is:
+P(s)
+Cont (i infected) = 1 −
+�
+a∈As
+�
+1 − P(s,a)
+Cont
+�
+when s is a transit segment
+(11)
+Eqs. 10 and 11 may be computationally inefficient. When P(p infectious) is small, we can use the
+following approximation by ignoring all second-order multiplication terms with
+�
+P(p infectious)
+�2:
+�
+p∈Ps,a
+�
+P(p infectious) · exp
+�−bs · qs · TTa
+QIndoor
+s
+�
++ (1 − P(p infectious))
+�
+=
+�
+p∈Ps,a
+�
+1 − P(p infectious) ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+� ��
+≈ 1 −
+�
+p∈Ps,a
+P(p infectious) ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+��
+(12)
+Then we have
+P(s,a)
+Cont (i infected) ≈
+�
+p∈Ps,a
+P(p infectious) ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+��
+(13)
+which is simply the summation of probabilities of getting infected by anyone in Ps,a. Similarly, if P(s,a)
+Cont is
+7
+
+small, we can approximate P(s)
+Cont as:
+P(s)
+Cont(i infected) ≈
+�
+a∈As
+�
+p∈Ps,a
+P(p infectious) ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+��
+when s is a transit segment
+(14)
+where Eqs. 13 and 14 are computationally more efficient because we replace the production with a summation.
+In terms of the surface-touching infection, we only need to specify Vs (viral bioburden), γs (touching
+rate), and Ts (travel time) to use Eq. 9. It is worth noting that Vs can vary across different times of the day
+and transit routes according to the demand level. In general, times and routes with higher demand should
+have higher Vs.
+Infection risk of walk/bike segment: For a walk or bike segment, we assume there is no surface touching
+infection risk because the commuter does not need to tough public surfaces during commuting:
+P(s)
+Surf(i infected) = 0
+when s is a bike/walk segment
+(15)
+For the close-contact infection, we can approximate Ps from the pedestrian density data set. Denote the
+average contact time for an encounter as dW/B. With the same approximation techniques, we can calculate
+the infection probability as
+P(s)
+Cont(i infected) ≈ |Ps| · P(p infectious) ·
+�
+1 − exp
+�−bs · qs · dW/B
+QOutdoor
+s
+��
+when s is a bike/walk segment
+(16)
+where P(p infectious) can be obtained from the regional infectious statistics based on the walk/bike routes;
+|Ps| is the average number of encounters during the segment.
+Infection risk of ride-hailing segment: When commuting with ride-hailing, Ps includes the driver and
+potential shared riders. Ps can be obtained from ride-hailing open source data to approximate the average
+number of persons in a vehicle. The contact time di,p for the driver and individual i is Ts (total segment
+travel time). While di,p for individual i and shared riders will be approximated by shared rides data. With
+the same first-order approximation, we can calculate the infection probability due to close contact as
+P(s)
+Cont(i infected) ≈
+�
+s∈Ps
+P(p infectious) ·
+�
+1 − exp
+�−bs · qs · di,p
+QIndoor
+s
+��
+when s is a ride-hailing segment
+(17)
+In terms of surface-touching risks, it is possible that the previous riders are infectious and thus the seats
+are contaminated. We can also specify Vs and γs then use Eq. 9 for the infection risk calculation. However,
+it is worth noting that Vs for ride-hailing should be much smaller than that of transit.
+Infection risk of driving segment: Driving is a private commute mode and there is generally no close
+contact or infectious surface touching during the travel.
+Hence, we simply assume P(s)
+Surf(i infected) =
+P(s)
+Cont (i infected) = 0 when s is a driving segment.
+8
+
+3.4. Infection risk integration
+Section 3.3 provides the formulations for the calculation of infection risks for a specific segment. Since
+a commuting path r consists of multiple segments, the total infection probability if using path r ∈ Ri is:
+P(i infected | r) = 1 −
+�
+s∈Sr
+P(i not infected in segment s)
+= 1 −
+�
+s∈Sr
+�
+1 − P(s)
+Surf(i infected)
+�
+·
+�
+1 − P(s)
+Cont(i infected)
+�
+(18)
+Similarly, if the infectious probability is small in each segment, we have:
+P(i infected | r) ≈
+�
+s∈Sr
+�
+P(s)
+Cont(i infected) + P(s)
+Surf(i infected)
+�
+(19)
+Combining with the path choice probabilities from Section 3.2, we get the total infectious probability of
+individual i during commuting:
+P(i infected | oi, di, ti, mi) =
+�
+r∈Ri
+PPath(r) · P(i infected | r)
+(20)
+3.5. Uncertainty quantification
+Though Eq. 20 provides the final infection probability for a given trip, the estimation may suffer from
+errors due to uncertainties in parameters. In this section, we treat P(i infected | oi, di, ti, mi) as a random
+variable and aim to calculate its standard errors:
+�
+Var[P(i infected | oi, di, ti, mi)].
+In this study, we focus on the uncertainty due to the infection calculations. Hence, let us assume PPath(r)
+is fixed. Then:
+Var[P(i infected | oi, di, ti, mi)] =
+�
+r∈Ri
+�
+PPath(r)
+�2 · Var[P(i infected | r)]
+(21)
+From Eq. 19, we can further decompose the variance to different segments due to the independence
+across segments:
+Var[P(i infected | r)] =
+�
+s∈Sr
+�
+Var
+�
+P(s)
+Cont(i infected)
+�
++ Var
+�
+P(s)
+Surf(i infected)
+��
+(22)
+Therefore, we only need to specify Var
+�
+P(s)
+Cont(i infected)
+�
+and Var
+�
+P(s)
+Surf(i infected)
+�
+for different types
+(i.e., travel modes) of segments.
+Transit segment: According to Eq. 14, the infection probability due to close contact in public transit is
+simply the probability summation over different stations and encounters. In the real world, Ps,a is uncertain
+due to demand variations in public transit systems. However, it is generally hard to model the uncertainty of
+a set. Therefore, let us define the average probability that a passenger in Ps,a is infectious as ¯µs,a. Then Eq.
+14 can be rewrite as:
+P(s)
+Cont(i infected) ≈
+�
+a∈As
+|Ps,a| · ¯µs,a ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+��
+when s is a transit segment
+(23)
+9
+
+where |Ps,a| is the number of passengers in the vehicle (excluding i) when the vehicle departs from station
+a. The variance can be formulated as:
+Var[P(s)
+Cont(i infected)] =
+�
+a∈As
+Var
+�
+|Ps,a| · ¯µs,a ·
+�
+1 − exp
+�−bs · qs · TTa
+QIndoor
+s
+���
+when s is a transit segment
+(24)
+Deriving the closed-form formulation for the variance of the product of several random variables (or the
+exponential of several variables) is difficult. In some simple cases, one may use Jensen’s inequality to get
+the variance lower (or upper) bound. However, consider a general function f(Z) (may not be convex or
+concave), where Z is a vector of random variables. Obtaining the analytical form of Var[f(Z)] is generally
+hard. Therefore, we propose a bootstrapping-based algorithm to estimate the empirical variance (Algorithm
+1). The inputs of the algorithm are f(Z), the distribution of Z (i.e., P(Z)), and maximum sample times M.
+The idea is to sample Z ∼ P(Z) and use samples to estimate the variance.
+Algorithm 1 Bootstrapping-based empirical variance estimation algorithm
+1: function Bootstrapping-Variance(f(Z), P(Z), M)
+2:
+for m = 1, 2, ..., M do
+3:
+Sample Z(m) ∼ P(Z)
+4:
+¯f(Z) =
+1
+M
+�M
+m=1 f(Z(m))
+▷ Estimate empirical mean
+5:
+Var[f(Z)] =
+1
+M
+�M
+m=1
+�
+f(Z(m)) − ¯f(Z)
+�2
+▷ Estimate empirical variance
+6:
+return Var[f(Z)]
+It is worth noting that, the sampling process in Algorithm 1 (Line 3) can be done independently, jointly,
+or sequentially, depending on whether the elements in Z are independent, dependent, or conditionally
+independent.
+Given Algorithm 1, we can estimate Var
+�
+|Ps,a| · ¯µs,a ·
+�
+1 − exp
+�
+−bs·qs·TTa
+QIndoor
+s
+���
+through the distribution
+of |Ps,a|, ¯µs,a, bs, qs, TTa, and Qs. In this study, we assume that |Ps,a| (vehicle load) and TTa (travel
+time) are normally distributed based on the observations in the empirical data. Their distribution parameters
+can be estimated from the smart card and automated vehicle location data. bs, qs, and Qs are uniformly
+distributed and their distributions are shown in Table 1 based on the literature. For ¯µs,a, the distribution is
+hard to parameterize because it is generated by sampling different Ps,a. We, therefore, keep all samples for
+¯µs,a as an empirical distribution. Then every sample of ¯µs,a ∼ P(¯µs,a) is essentially a bootstrap from its
+sample pool.
+In terms of surface touching infection, from Eq. 9, we use Algorithm 1 to estimate the variance by
+setting f(Z) = γs · Ts · PTouch(i infected | Vs) and Z = (γs, Ts, Vs, PTouch(i infected | Vs). The distribution
+of PTouch(i infected | Vs) can be obtained from the data in Wilson et al. (2021). The distribution of Vs can
+be obtained from the results in Harvey et al. (2020). The distribution of Ts can be obtained from the AVL
+data. γs is assumed to be uniformly distributed and its distribution is given in Table 1.
+Walk/Bike segment: The variance of contact-based infection risks in the walk and bike segments,
+10
+
+according to Eq. 16, can be expressed as:
+Var[P(s)
+Cont(i infected)] = Var
+�
+|Ps| · ¯µs ·
+�
+1 − exp
+�−bs · qs · dW/B
+QOutdoor
+s
+� ��
+when s is a bike/walk segment
+(25)
+where ¯µs is the average infectious probability of encounters in Ps. It has a similar formulation as Eq. 24,
+thus can be calculated using Algorithm 1. The distribution of |Ps| can be obtained from pedestrian flow data.
+The distribution of ¯µs can be obtained from regional statistics. All infection-related parameters (including
+dW/B) are assumed to be uniformly distributed and their distributions are shown in Table 1. Since we assume
+there are no infection risks related to surface touching for the walk and bike segments, we do not need to
+consider their variances.
+Ride hailing segment: For the ride-hailing segment, since Ps is relatively small (maximum three
+riders in a vehicle), we assume |Ps| follows a multinomial distribution across {0, 1, 2, 3} (i.e., maximum 2
+other passengers plus 1 driver). The specific distribution can be obtained from ride-sharing data. To get
+Var[P(s)
+Cont(i infected)] for ride-hailing segments, the sampling process is as follows (slightly different from
+Algorithm 1):
+• Step 1: Sample |Ps| from the multinomial distribution.
+• Step 2: Based on the value of |Ps|, sample the same number of passengers and drivers to generate the
+|Ps, for each passenger p ∈ Ps, we also sample di,p (shared trip time).
+• Step 3: Sample other infection-related parameters from the distribution defined in Table 1. Calculate
+the infection probability close contact based on Eq. 17.
+After M samples, we can estimate the sample variance as an approximation of Var[P(s)
+Cont(i infected)] similar
+to Algorithm 1. The variance of surface touching-based infection probability is calculated in the same way
+as a transit segment except for replacing the distributions of Ts, Vs, and γs.
+For the driving segment, since we assume there is no infection risk, the variances are not calculated.
+4. Case study
+The case study is based on available data from MIT. The model is implemented for the commuting of all
+MIT students and staff in the greater Boston area.
+4.1. Data sources and parameter settings
+We use data from various sources in this study to estimate the infection risk and set up parameters. The
+first data set is the MIT staff commuting survey. The survey collects (oi, di, ti, mi) of every individual
+i ∈ I. Given this information, for every individual i, we generate the set of paths Ri and the associated path
+attributes (i.e., walking time, waiting time, in-vehicle time, travel cost) based on the Google map API. For
+simplicity, we only consider the first path associated with the travel mode mi recommended by google map
+API (i.e., ignoring the path choice estimation). This assumption is reasonable because in most cases there
+is only one transit route available if mi = Transit. For driving, biking, or ride-hailing, individuals usually
+follow the navigation system and thus choose the first option provided by the google map API.
+11
+
+Another data source we use for infection risk calculation in the transit segment is the smart card data
+from the Massachusetts Bay Transportation Authority (MBTA). We use the historical smart card data at the
+same time of the day (one-hour interval) in the last 2 weeks to calculate the mean and variance of the number
+of passengers in Ps,a. Specifically, the smart card data provides the tap-in time and locations. We adopted
+the destination estimation model proposed by Sánchez-Martínez (2017) to obtain the destination of each trip.
+Then, a network loading model (Mo et al., 2020) is used to obtain the vehicle load at each time interval. The
+mean infectious probability ¯µs,a for passengers in the vehicle is calculated based on regional statistics and
+their origins. The travel time between stops (i.e., TTa) is obtained from automated vehicle location (AVL)
+data.
+In terms of the bike and walk segments, there is no open-source pedestrian and cyclist density data
+available for this study. Therefore, we generate the synthetic pedestrian and cyclists density data by combining
+population data in Boston (Massachusetts Demographics by Cubit, 2020), Massachusetts Travel Survey
+(MTS) (Boston Region Metropolitan Planning Organization, 2011), and national household travel survey
+(NHTS) data (Federal Highway Administration, 2017). The synthetic pedestrian density data include the
+mean and variance of the number of cyclists and pedestrians at a specific street for each time interval (in
+this study, every 1 minute). The detailed data generation process is shown in Appendix A. The basic idea is
+to generate many bike and walk trajectory samples using the available dataset and aggregate these samples
+at the street-minute level. Therefore, given a bike/walk segment s of individual i, based on its trajectory,
+we can sample the number of bike/walk encounters using the generated cyclists and pedestrians density data
+above. This process is replicated multiple times to get the distribution of |Ps|. The distribution of ¯µs is
+calculated based on neighborhood infection rates (Fisher, 2020). The contact time (dW/B) is assumed to be
+uniformly distributed with U(4, 6) seconds for a walking trip and U(2, 4) seconds for a biking trip.
+For the ride-hailing segment, we only need the distribution of |Ps| (number of passengers), di,p (shared
+trip duration). However, there is no public ride-hailing data for Boston. In this study, we use the open-source
+Transportation Network Company (TNC) data in Chicago (Chicago Data Portal, 2018) to calculate the
+distribution of |Ps| and di,p as an approximation for those of Boston.
+Through the Google Map API, we can obtain the value of Ts. However, the distribution of Ts is unknown.
+Ideally, the distribution of Ts can be obtained from GPS data. Given the data limitations, we assume Ts is
+normally distributed and the value obtained from the Google Map API is the mean. The standard deviation
+is assumed to be Ts × 30% based on the empirical study (Li et al., 2013). It is worth noting that, for the
+transit segment, instead of using Google Map data, we obtain the stop-to-stop travel time using AVL data.
+Hence, we calculate the segment travel time as Ts = �
+a∈As TTa. The mean and variance of Ts are just the
+summations of the mean and variance of TTa, respectively, by assuming independence across segments.
+The infection-related parameters are summarized in Table 1:
+4.2. Data description and statistics
+The MIT staff commuting survey consists of 974 individual responses with information on (oi, di, ti, mi).
+Note that only commuting trips toward MIT are considered. The distributions of their departure times, travel
+modes, and job categories are shown in Figure 2.
+Since only trips toward MIT are considered, most of their departure times are in the morning hours
+(Figure 2a). There are also some people going to campus in the evening, which may be students living close
+by or staff on night shifts. In terms of travel modes (Figure 2b), more than 40% of the MIT staff and students
+choose transit as their commuting mode. Driving is the second most popular mode. Of all individuals filling
+12
+
+Table 1: Infection-related parameters
+Mode
+Parameters and distribution
+bs (m3/h)
+qs (/h)
+V∞ (m/s)
+L (m)
+H (m)
+QIndoor
+s
+(m3/h)
+γs (/h)
+Vs (gc/cm2)
+Transit (Train)
+U(0.65, 0.79)
+U(1, 31)
+N.A.
+N.A.
+N.A.
+U(800, 1100)
+U(3, 5)
+U(30, 100)
+Transit (Bus)
+U(0.65, 0.79)
+U(1, 31)
+N.A.
+N.A.
+N.A.
+U(300, 500)
+U(3, 5)
+U(30, 100)
+Bike
+U(1.4, 1.8)
+U(2, 100)
+U(2, 4)
+U(30, 60)
+U(2.5, 5)
+N.A.
+N.A.
+N.A.
+Walk
+U(1.2, 1.6)
+U(2, 100)
+U(1, 2)
+U(30, 60)
+U(2.5, 5)
+N.A.
+N.A.
+N.A.
+Ride-hailing
+U(0.65, 0.79)
+U(1, 31)
+N.A.
+N.A.
+N.A.
+U(90, 120)
+U(1, 3)
+U(2, 50)
+N.A.: Not applicable
+The parameters for transit infections are obtained from Zhou and Koutsopoulos (2021).
+The parameters for quanta generation rates are obtained from Buonanno et al. (2020b) and Buonanno et al. (2020a).
+The parameters for outdoor infection models are obtained from Rowe et al. (2021).
+The ride-hailing ventilation rate is based on Ott et al. (2008).
+The viral bioburden data is adapted from Harvey et al. (2020) (assuming 10% viruses are infectious).
+out the survey, around 30% are graduate students. Respondents also include faculty and staff (e.g., admin,
+service, support, research).
+(a) Departure time distribution
+(b) Travel mode distribution
+(c) Person type distribution
+Figure 2: Descriptive statistics of MIT staff commuting survey (RH indicates Ride-hailing)
+Figure 3 shows the distribution of travel information collected by the Google Map API. Most of the
+commuting trips have only one segment (Figure 3a). The maximum number of segments is five. The travel
+times of all trips are approximately log-normal distributed with a long tail (Figure 3b). The travel times for
+most of the trips are within 1 hour.
+For transit trips, Figure 4 shows the box plots of travel times between two consecutive stations and the
+associated passenger load for Bus Route 1 in Boston. Route 1 is a popular bus service along Massachusetts
+Avenue. The travel time to the first stop is relatively large as vehicles usually depart from garages (Figure
+4a). In terms of passenger load (Figure 4b), the middle stops in the route have a relatively larger number
+of passengers onboard. The graphs show that both travel time and passenger loads are uncertain and the
+uncertainties should be captured in the virus transmission modeling.
+Figure 5 shows the spatial distribution for the inferred number of walk and bike trips at 8:00 AM (details
+in Appendix A). Their spatial distributions are similar. More trips happen at places with higher population
+densities. The number of walking trips is larger than that of bike trips.
+13
+
+0.14
+0.12
+0.10
+Density
+0.08
+0.06
+0.04
+0.02
+0.00
+5
+7
+9
+1113
+15
+1719
+ 21
+Departure time (hour of the day)0.40
+0.35
+0.30
+Density
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+Walk
+Bike
+Transit
+RH
+Drive Other0.30
+0.25
+0.20
+Density
+0.15
+0.10
+0.05
+0.00
+Admin
+Faculty
+Service
+Graduate
+Support
+Undergrad
+Research(a) Number of segments distribution
+(b) Travel mode distribution
+Figure 3: Distribution of the number of segments and travel times
+(a) Travel time to next stop
+(b) Passenger load
+Figure 4: Box plots of travel time and passenger load for Bus Route 1 (Stop ID represents the stop sequences from north to south)
+4.3. Results
+4.3.1. Infection risk for individuals
+After excluding individuals with “other” travel modes. We have 943 remaining individuals. We calculate
+their infection probabilities and standard deviations using the proposed method. Results are shown in Figure
+6. Most of the individuals have an infection probability close to zero. The maximum infection probability is
+around 0.8%. This implies that the probability of getting infected during commuting to MIT is quite low. The
+results are consistent with the previous studies modeling infection risks in transit (Zhou and Koutsopoulos,
+2021). In terms of the estimation errors, the standard deviations are approximately 50% of the estimated
+probability.
+Since individuals with different travel modes, departure times, and travel distances may have different
+infection probabilities.
+We run a linear regression model to analyze the impact of different factors on
+infection risks. The dependent variable is the inferred infection probability and the independent variables
+are as follows:
+• If faculty: Whether the individual is a faculty at MIT (Yes = 1).
+14
+
+0.7
+0.6
+0.5
+0.4
+Densi
+0.3
+0.2
+0.1
+0.0
+1
+2
+3
+4
+5
+Number of segments0.0200
+0.0175
+0.0150
+0.0125
+Density
+0.0100
+0.0075
+0.0050
+0.0025
+0.0000
+0
+25
+50 75 100 125 150 175 200
+Total travel time (min)Travel time to next stop (min)
+20
+15
+10
+5
+0
+3
+5
+1
+9
+11 13 15 17 19 21 23 25 27
+Stop ID80
+60
+40
+20
+0
+1
+3
+5
+7
+9
+ 11 13 15 17 19 21 23 25 27
+Stop ID(a) Number of bike trips
+(b) Number of walk trips
+Figure 5: Spatial distribution for the number of walk and bike trips at 8:00 AM
+• Distance (km): Euclidean distance from the individual’s home to MIT.
+• If transit: Whether the individual’s commuting mode is transit (Yes = 1).
+• If morning peak: Whether the individual’s departure time is between 6:00 AM and 9:00 AM (Yes =
+1).
+The results of the linear regression are shown in Table 2. “Distance×If transit” is added to differentiate
+the distance impact for transit and non-transit users. We find that the faculty is less likely to get infected.
+The reason may be that they usually drive to school and driving is the safest travel mode in terms of infection
+protection. Individuals who live further from the school and commute by transit have a higher infection risk.
+This may be due to the fact that they have a longer travel time and more close contacts, thus are more likely
+to be exposed to viruses. We also observe people with a departure time in the morning peak have a higher
+probability of being infected, which may be due to the larger amount of encounters in the morning peak
+hours. It is worth noting that “Distance” and “If transit” are not significant unless combining them together
+(i.e., “Distance×If transit”). This implies that the impact of distance on infection risks mainly applies to
+transit users.
+Table 2: Factors on infection probability (%)
+Variable
+Coefficient (p-value)
+Variable
+Coefficients (p-value)
+Intercept
+-0.015 (0.997)
+Distance
+0.048 (0.834)
+If transit
+4.409 (0.545)
+If morning peak
+16.658∗∗ (0.005)
+If faculty
+-16.881∗ (0.095)
+Distance×If transit
+3.404∗∗ (0.000)
+Number of samples: 943; R2: 0.313;
+∗∗: p-value < 0.05; ∗: p-value < 0.1;
+All coefficients are scaled by 1000.
+To better visualize the impact of distance, Figure 7 shows the predicted infection probability as a function
+of distance for both transit and non-transit users. In general, transit users are more likely to get infected, and
+15
+
+# Walk trips
+42.5
+42.45
+150
+42.4
+Latitude
+42.35
+100
+42.3
+Natic
+50
+42.25
+42.2
+-71.4
+-71.3
+-71.2
+-71.1
+-71
+-70.9
+Longitude# Bike trips
+16
+42.5+
+IOBURI
+14
+42.45
+12
+42.4
+10
+Latitude
+42.35
+8
+42.3
+6
+Natic
+4
+42.25
+2
+42.2
+-71.4
+-71.3
+-71.2
+-71.1
+-71
+-70.9
+LongitudeFigure 6: Inferred individual infection probabilities (sorted by values in descending order)
+the infection risk increases dramatically with the increase in commute distance. However, the infection risk
+of non-transit users is not significantly affected by distance.
+Figure 7: Predicted infection probability as a function of distance
+4.3.2. Spatiotemporal distribution of infection risk
+In addition to the infection risk calculation for actual survey respondents, the proposed method can also
+be used to evaluate the spatiotemporal distribution of infection risks by generating synthetic observations.
+For the spatial distribution, we generate synthetic observations with home addresses in different neigh-
+borhoods. We consider two travel modes: transit and walking. Note that for dummy samples with walking
+travel modes, we also consider home addresses within 10km of MIT. All dummy samples’ departure times
+are set at 8:00 AM.
+Figure 8a shows the infection probability of transit trips with home addresses in different neighborhoods.
+In general, people with residences further from MIT have higher infection risks. But the risk is also affected
+by specific transit routes (i.e., not perfectly proportional to distances). The spatial distribution for walking
+(Figure 8b) is similar. But the infection risk is much smaller than that of transit trips.
+16
+
+12
+Std. Dev.
+600-
+10
+500
+Icy
+8
+400
+Frequenc
+300
+6
+200
+100
+4
+0
+0
+1
+2
+3
+4
+5
+6
+7
+8
+2
+Probability of infection (×10-3)
+0
+0
+200
+400
+600
+800
+Sample IDInfection probability #(×10-3)
+1.75
+Transit user
+Non-transit user
+1.50
+1.25
+1.00
+0.75
+0.50
+0.25
+0.00
+0
+10
+20
+30
+40
+50
+Distance (km)(a) Transit trips
+(b) Walk trips
+Figure 8: Spatial distribution of infection probability
+In terms of the temporal distribution, we generate synthetic observations with departure times from 0:00
+to 24:00. Their home locations are assumed to be uniformly distributed across all neighborhoods. Figure
+9a shows the infection risk as a function of departure time for transit trips. The shaded areas are
+1
+10 of the
+estimation errors. The infection probabilities are higher when people depart during the morning and evening
+peak hours, which is reasonable because there is usually a higher passenger load (i.e., more close contacts)
+during rush hours. The infection probabilities for walking trips show a similar pattern (Figure 9b). The
+highest infection risks happen in the daytime (from 8:00 to 18:00), most likely due to the larger number of
+pedestrians.
+(a) Transit trips
+(b) Walk trips
+Figure 9: Temporal distribution of infection probability
+17
+
+ Infection probability
+0.2
+42.5
+42.45
+0.15
+42.4
+Latitude
+42.35
+0.1
+42.3
+Naticl
+0.05
+42.25
+42.2
+0
+itributors.@
+artoDB
+-71.4
+-71.3
+-71.2
+-71.1
+-71
+-70.9
+Longitude0.01
+ Infection probability
+42.5-
+Burlington
+WOBURN
+LYNN
+42.45
+0.008
+Lexington
+42.4
+0.006
+WALTHA
+inthrop
+Latitude
+42.35
+NEV
+0.004
+42.3
+Natick
+Needham
+42.25
+Dedham
+Milton (QUINCY
+0.002
+-Weymouth
+42.2
+@ OpenStreetMap
+ contributors,@ CartoDB
+-71.4
+-71.3
+-71.2
+-71.1
+-71
+-70.9
+Longitude3.2
+Infection probability×10-4)
+3.1
+3.0
+2.9
+2.8
+2.7
+2.6
+2.5
+2.4
+0:00
+4:00
+8:00
+12:00 16:00 20:00 24:00
+Departure time1.75
+Infection probability (×10-7)
+1.50
+1.25
+1.00
+0.75
+0.50
+0.25
+0.00
+0:00
+4:00
+8:00
+12:00 16:00 20:00 24:00
+Departure time5. Conclusion
+The paper proposes a probabilistic framework to estimate the risk of infection during commuting con-
+sidering different travel modes, including public transit, ride-share, bike, and walking. The model enables
+evaluating both the probability of infection and the estimation errors (i.e., uncertainty quantification). Dif-
+ferent sources of data (such as smart card data, travel surveys, and population data) are used to estimate
+commuting individual’s interaction with infectious environments. The model is applied using data related
+to the MIT community as a case study. We evaluate the commute infection risks for employees and students.
+Results show that most of the individuals have very low infection probability. The maximum infection
+probability is around 0.8%. Individuals with larger travel distances, traveling with transit, and traveling at
+peak hours are more likely to get infected.
+The model has several practical applications. 1) The model can be used to support decision-making
+for companies, schools, or communities during or post the pandemic regarding return to offices. They
+can collect their employees’ commuting information and use the model to evaluate the commuting risk for
+better planning. For example, employees with high infection risk may have separate seats from the low-risk
+employees. 2) Another implementation of the model is to add individual-level infection risk to their trip
+planning tool (such as Google Map). For example, in Figure 10, the trip planning tool not only shows the
+recommended routes based on travel time, but also the infection risks. Individuals can make better path
+choice decisions with this additional information.
+Figure 10: Example of implementing the model to trip planning
+6. Acknowledgement
+The authors would like to thank the MIT Quest for Intelligence for their support and data availability for
+this research.
+7. Author contribution statement
+Baichuan Mo: Conceptualization, Methodology, Software, Formal analysis, Data Curation, Writing -
+Original Draft, Writing - Review & Editing, Visualization. Peyman Noursalehi: Conceptualization, Soft-
+ware, Data Curation. Haris N. Koutsopoulos: Conceptualization, Writing - Review & Editing, Supervision.
+Jinhua Zhao: Conceptualization, Supervision, Project administration, Funding acquisition.
+18
+
+Origin
+Destination
+Division /Ashland
+Clark /Division
+天
+70
+C
+ORL
+ETA10:20AM
+Division/Ashland
+Ashland
+L
+会GLPL
+ETA10:23AM
+AAAAppendices
+Appendix A. Pedestrian and cyclist density calculation
+For the infection risk calculation of walking and bike trips, an important input is the number of close-
+contact encounters during the trip (i.e., the distribution of |Ps|). The distribution can be obtained from the
+mean and variance of the number of cyclists (denoted as Cb,τ) and pedestrians (denoted as Wb,τ) at specific
+street b for each time interval τ. Since there are no GPS or trajectory data available for this study, we generate
+the distribution of Cb,τ and Wb,τ using the following method.
+First, we collect population data (Massachusetts Demographics by Cubit, 2020) for each neighborhood
+(zip-code level) in the Boston metropolitan area. We use the Massachusetts Travel Survey (MTS) (Boston
+Region Metropolitan Planning Organization, 2011) to calculate the trip generation rates given the population.
+As MTS does not include bike and walk mode share, the national household travel survey (NHTS) data
+(Federal Highway Administration, 2017) is used to get the proportion of bike and walk trips as well as their
+temporal distributions using samples in Massachusetts. Combined with the trip generation rate, we simulate
+the number of bikes and walk trips for each neighborhood at different time intervals. Given limited actual
+bike and walk trips in NHTS data in Boston, it is hard to obtain the origin-destination (OD) distribution. But
+the distribution of travel distances and departure times can be obtained. For each bike walk trip, we generate
+the “hypothetical” trajectory as follows: 1) We first randomly sample an origin within the neighborhood. 2)
+Then, we sample the travel distance and departure time from the pre-defined distribution, as well as a specific
+direction (uniformly 0 ∼ 2π). The travel distance and direction yield the destination. 3) We generate the
+trajectory (i.e., a sequence of streets) of the trip. From these trajectories, we obtain the number of pedestrians
+and cyclists in the street for each street b and time interval τ (i.e., a sample of Cb,τ and Wb,τ). This process
+is repeated multiple times to get E[Cb,τ], E[Wb,τ] and Var[Cb,τ], Var[Wb,τ].
+The generated walking and bike trip distributions are shown in Figure 5 (the figure is aggregated at the
+zip code level).
+References
+Ahangari, S., Chavis, C., Jeihani, M., 2020. Public transit ridership analysis during the covid-19 pandemic.
+Medrxiv .
+Ando, H., Ikegami, K., Nagata, T., Tateishi, S., Eguchi, H., Tsuji, M., Matsuda, S., Fujino, Y., Ogami, A.,
+2021. Effect of commuting on the risk of covid-19 and covid-19-induced anxiety in japan, december 2020.
+Archives of Public Health 79, 1–10.
+Boston Region Metropolitan Planning Organization, 2011. Exploring the 2011 massachusetts travel survey:
+Mpo travel profiles. https://www.ctps.org/travel-profiles, Last accessed on 2022-11-04.
+Buonanno, G., Morawska, L., Stabile, L., 2020a. Quantitative assessment of the risk of airborne transmis-
+sion of sars-cov-2 infection: prospective and retrospective applications. Environment international 145,
+106112.
+Buonanno, G., Stabile, L., Morawska, L., 2020b. Estimation of airborne viral emission: Quanta emission
+rate of sars-cov-2 for infection risk assessment. Environment international 141, 105794.
+Cascetta, E., Nuzzolo, A., Russo, F., Vitetta, A., 1996. A modified logit route choice model overcoming
+path overlapping problems. specification and some calibration results for interurban networks, in: Trans-
+19
+
+portation and Traffic Theory. Proceedings of The 13th International Symposium On Transportation And
+Traffic Theory, Lyon, France, 24-26 July 1996.
+Chang, H.H., Lee, B., Yang, F.A., Liou, Y.Y., 2021. Does covid-19 affect metro use in taipei? Journal of
+transport geography 91, 102954.
+Chicago Data Portal, 2018. Transportation network providers - trips. https://data.cityofchicago.
+org/Transportation/Transportation-Network-Providers-Trips/m6dm-c72p, Last accessed
+on 2022-11-04.
+Ecke, L., Magdolen, M., Chlond, B., Vortisch, P., 2022.
+How the covid-19 pandemic changes daily
+commuting routines–insights from the german mobility panel. Case Studies on Transport Policy .
+Fajgelbaum, P.D., Khandelwal, A., Kim, W., Mantovani, C., Schaal, E., 2021. Optimal lockdown in a
+commuting network. American Economic Review: Insights 3, 503–22.
+Federal Highway Administration, 2017. National household travel survey. https://nhts.ornl.gov/,
+Last accessed on 2022-11-04.
+Fisher, A.R., 2020.
+Estimated COVID 19 by US Zip Code.
+https://github.com/adamrfisher/
+Estimated_COVID19_by_US_Zip_Code, Last accessed on 2022-11-04.
+Harvey, A.P., Fuhrmeister, E.R., Cantrell, M.E., Pitol, A.K., Swarthout, J.M., Powers, J.E., Nadimpalli, M.L.,
+Julian, T.R., Pickering, A.J., 2020. Longitudinal monitoring of sars-cov-2 rna on high-touch surfaces in a
+community setting. Environmental science & technology letters 8, 168–175.
+Jenelius, E., Cebecauer, M., 2020. Impacts of covid-19 on public transport ridership in sweden: Analysis of
+ticket validations, sales and passenger counts. Transportation Research Interdisciplinary Perspectives 8,
+100242.
+Kondo, K., 2021. Simulating the impacts of interregional mobility restriction on the spatial spread of
+covid-19 in japan. Scientific reports 11, 1–15.
+Ku, D., Yeon, C., Lee, S., Lee, K., Hwang, K., Li, Y.C., Wong, S.C., 2021. Safe traveling in public transport
+amid covid-19. Science advances 7, eabg3691.
+Li, R., Chai, H., Tang, J., 2013. Empirical study of travel time estimation and reliability. Mathematical
+Problems in Engineering 2013.
+Massachusetts Demographics by Cubit, 2020. Massachusetts zip codes by population. https://www.
+massachusetts-demographics.com/zip_codes_by_population, Last accessed on 2022-11-04.
+Medlock, K.B., Temzelides, T., Hung, S.Y.E., 2021. Covid-19 and the value of safe transport in the united
+states. Scientific reports 11, 1–12.
+Meredith-Karam, P., Kong, H., Wang, S., Zhao, J., 2021. The relationship between ridehailing and public
+transit in chicago: A comparison before and after covid-19. Journal of Transport Geography 97, 103219.
+Mitze, T., Kosfeld, R., 2022. The propagation effect of commuting to work in the spatial transmission of
+covid-19. Journal of Geographical Systems 24, 5–31.
+Mo, B., Feng, K., Shen, Y., Tam, C., Li, D., Yin, Y., Zhao, J., 2021. Modeling epidemic spreading
+through public transit using time-varying encounter network. Transportation Research Part C: Emerging
+Technologies 122, 102893.
+Mo, B., Ma, Z., Koutsopoulos, H.N., Zhao, J., 2020. Capacity-constrained network performance model for
+urban rail systems. Transportation Research Record 2674, 59–69.
+Mo, B., Von Franque, M.Y., Koutsopoulos, H.N., Attanucci, J.P., Zhao, J., 2022. Impact of unplanned long-
+term service disruptions on urban public transit systems. IEEE Open Journal of Intelligent Transportation
+Systems 3, 551–569.
+20
+
+Ott, W., Klepeis, N., Switzer, P., 2008. Air change rates of motor vehicles and in-vehicle pollutant con-
+centrations from secondhand smoke. Journal of exposure science & environmental epidemiology 18,
+312–325.
+Riley, E., Murphy, G., Riley, R., 1978. Airborne spread of measles in a suburban elementary school.
+American journal of epidemiology 107, 421–432.
+Rowe, B.R., Canosa, A., Drouffe, J.M., Mitchell, J., 2021. Simple quantitative assessment of the outdoor
+versus indoor airborne transmission of viruses and covid-19. Environmental research 198, 111189.
+Sánchez-Martínez, G.E., 2017. Inference of public transportation trip destinations by using fare transaction
+and vehicle location data: Dynamic programming approach. Transportation Research Record 2652, 1–7.
+Shinohara, N., Sakaguchi, J., Kim, H., Kagi, N., Tatsu, K., Mano, H., Iwasaki, Y., Naito, W., 2021. Survey of
+air exchange rates and evaluation of airborne infection risk of covid-19 on commuter trains. Environment
+international 157, 106774.
+Tan, L., Ma, C., 2021. Choice behavior of commuters’ rail transit mode during the covid-19 pandemic based
+on logistic model. Journal of Traffic and Transportation Engineering (English Edition) 8, 186–195.
+Wang, H., Noland, R.B., 2021. Bikeshare and subway ridership changes during the covid-19 pandemic in
+new york city. Transport policy 106, 262–270.
+Wilbur, M., Ayman, A., Ouyang, A., Poon, V., Kabir, R., Vadali, A., Pugliese, P., Freudberg, D., Laszka,
+A., Dubey, A., 2020. Impact of covid-19 on public transit accessibility and ridership. arXiv preprint
+arXiv:2008.02413 .
+Wilson, A.M., Weir, M.H., Bloomfield, S.F., Scott, E.A., Reynolds, K.A., 2021. Modeling covid-19 infection
+risks for a single hand-to-fomite scenario and potential risk reductions offered by surface disinfection.
+American journal of infection control 49, 846–848.
+Zhao, Q., Qi, Y., Wali, M.M., 2022. A method for assessing the covid-19 infection risk of riding public
+transit. International Journal of Transportation Science and Technology .
+Zhou, J., Koutsopoulos, H.N., 2021. Virus transmission risk in urban rail systems: Microscopic simulation-
+based analysis of spatio-temporal characteristics. Transportation Research Record 2675, 120–132.
+21
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf,len=1017
+page_content='Modeling virus transmission risks in commuting with emerging mobility  services: A case study of COVID-19  Baichuan Moa,∗, Peyman Noursalehib, Haris N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Koutsopoulosc, Jinhua Zhaob  aDepartment of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139  bDepartment of Urban Studies and Planning, Massachusetts Institute of Technology, Cambridge, MA 20139  cDepartment of Civil and Environmental Engineering, Northeastern University, Boston, MA 02115  Abstract  Commuting is an important part of daily life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' With the gradual recovery from COVID-19 and more people  returning to work from the office, the transmission of COVID-19 during commuting becomes a concern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Recent emerging mobility services (such as ride-hailing and bike-sharing) further deteriorate the infection  risks due to shared vehicles or spaces during travel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Hence, it is important to quantify the infection risks  in commuting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This paper proposes a probabilistic framework to estimate the risk of infection during an  individual’s commute considering different travel modes, including public transit, ride-share, bike, and  walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The objective is to evaluate the probability of infection as well as the estimation errors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=',  uncertainty quantification) given the origin-destination (OD), departure time, and travel mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We first  define a general trip planning function to generate trip trajectories and probabilities of choosing different  paths according to the OD, departure time, and travel mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Then, we consider two channels of infections:  1) infection by close contact and 2) infection by touching surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The infection risks are calculated on a  trip segment basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Different sources of data (such as smart card data, travel surveys, and population data)  are used to estimate the potential interactions between the individual and the infectious environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' A  first-order approximation is used to simplify the computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We also derive the closed-form  formulation for the estimation errors, enabling us to quantify the uncertainty of the estimation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  model is implemented in the MIT community as a case study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We evaluate the commute infection risks for  employees and students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Results show that most of the individuals have an infection probability close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The maximum infection probability is around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8%, implying that the probability of getting infected during  the commuting process is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Individuals with larger travel distances, traveling in transit, and traveling  during peak hours are more likely to get infected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Practical implementations of the model are also discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Keywords: COVID-19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection risk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Emerging mobility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Introduction  COVID-19 has greatly affected people’s lives all over the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Recently, with the vaccination and  people’s prevention consciousness, we are stepping into a new era of living with the virus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' With the gradual  recovery from the pandemic, more and more people return to work from the office.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Commuting is an important part of the daily lives of people working in an office.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In light of the  infectiousness of COVID-19, the infection risk during the commuting process is a concern, especially  ∗Corresponding author  Preprint submitted to Elsevier  January 9, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='02594v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='AP]  6 Jan 2023  for people using public transportation, as indicated by many previous studies (Mo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Zhou and  Koutsopoulos, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' On the other hand, recent emerging mobility services (such as ride-hailing and bike-  sharing) further deteriorate the infection risks due to shared vehicles or spaces during travel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, it  is important to quantify the infection risks in commuting more broadly, where the results are helpful for  people to evaluate their health risks and better inform their commuting route/travel mode choices, and for  policymakers to reach informed decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Many previous studies have modeled the COVID-19 infection risks in public transit systems, an important  travel mode of commuting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' These studies can be categorized from the macro-level at the city scale (Mo  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021) or the micro-scale at the vehicle scale (Shinohara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Zhou and Koutsopoulos, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Researchers have also considered the impact of commuting on the broader spatial transmission of COVID-19  and the related control strategies (Mitze and Kosfeld, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Ando et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Fajgelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Kondo, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' There are also studies evaluating the impact of COVID-19 on the commuting process with  empirical data (such as surveys), such as the impact of COVID-19 on ridership changes, travel mode choices  (Tan and Ma, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Medlock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021), and departure time change (Ecke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  However, there are still two research gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' First, none of the previous studies have considered the infection  modeling for the commuting process as a whole with multiple travel modes and multi-modal trip itineraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Second, most of the previous studies regarding infection risk modeling only output the probability of infection  (or the R0 value indicating the spreading intensity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The estimation uncertainties (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', how accurate are the  estimates) are not provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In this study, we propose a probabilistic framework to estimate the risk of infection during an individual’s  commute considering different travel modes, including public transit, ride-share, bike, and walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  model enables evaluating both the probability of infection and the estimation errors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', uncertainty quan-  tification).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We first define a general trip planning function to generate trip trajectories and probabilities of  choosing different paths according to the origin, destination, departure time, and travel mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Two channels  of infection are considered: 1) infection by close contact and 2) infection by touching surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The infection  risks are calculated on a trip segment basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Different sources of data (such as smart card data, travel surveys,  and population data) are used to estimate the potential interactions between the individual and the infectious  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' A first-order approximation technique is used to simplify the computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We  derive the closed-form formulations for the estimation errors, enabling us to quantify the uncertainties of  the estimation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model is implemented in the MIT community as a case study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We evaluate  the commute infection risks for employees and students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Results show that most of the individuals have an  infection probability close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The maximum infection probability is around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8%, implying that the  probability of getting infected during the commuting process is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Individuals with larger travel distances,  traveling with transit, and traveling during peak hours are more likely to get infected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The main contribution of this paper is twofold:  This is the first study dedicated to virus transmission modeling during commuting with the consid-  eration of various travel modes and multi-modal trip itineraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infections due to close contact and  touching surfaces are both captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In addition to estimating infection probabilities, this paper also calculates the estimation errors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=',  the standard deviation of the estimated probabilities) for uncertainty quantification, which has not been  done in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The remainder of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The literature review is shown in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In  2  Section 3, we describe the problem and discuss the solution methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We apply the proposed framework to  the MIT community as a case study in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Finally, we conclude our study and summarize the main  findings in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Literature review  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection modeling in public transit  Public transit is an important travel mode for commuting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Previous studies have explored epidemic  spreading and infection risk modeling in transit networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Mo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) propose a time-varying weighted  encounter network to model the spreading of infectious diseases through public transit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model  is implemented at the metropolitan level for population infection calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Zhou and Koutsopoulos (2021)  propose a modified Wells-Riley model for infection probability calculation in public transportation systems  at the vehicle level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model captures the spatial and temporal passenger flow characteristics in terms of  the number of boarding and alighting passengers and the number of infectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Similarly, Ku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021)  analyzed the degree of infection exposure in public transport by simulating how passengers encounter and  infect each other during their journeys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Shinohara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) adopted a two-zone-based exponential  model to calculate the infection risks in commuter trains by collecting air exchange rate data under various  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2022) developed a Wells-Riley model-based method to quantitatively evaluate the  infection risk of riding public transit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' They compared the effectiveness of different countermeasures in  managing the spread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Impact of COVID-19 on commuting  COVID-19 may affect the commuting process in many aspects, such as ridership and service frequency  decrease, changes in passengers’ travel mode choices, route choices, and departure times choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Previous  studies have evaluated these impacts using different sources of empirical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For example, many studies  have used the smart card data to analyze the impact of COVID-19 on transit ridership changes (Ahangari  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Wilbur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Jenelius and Cebecauer, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' There are also studies  on ridership changes in ride-hailing systems (Meredith-Karam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021) and bike-sharing systems (Wang  and Noland, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Tan and Ma (2021) conducted a survey to understand commuters’ mode choice changes  during the COVID-19 pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' They used a logistic regression model with personal attributes, travel  attributes, and perception of COVID-19 based on a sample of 559 responses to a survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Ecke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2022)  examine how people’s commuting behavior changed before and after COVID-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The results show that  people did not significantly change their commuting behavior in terms of commuting time and commuting  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Impact of commuting on COVID-19 spreading  Commuting may contribute to the spreading of COVID-19 by transporting infectious passengers across  different regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For example, Mitze and Kosfeld (2022) proposed a spatial econometric model of the  epidemic spread to identify the role played by commuting-to-work patterns for spatial disease transmission  and explored if the imposed containment policies affected the strength of this transmission channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Ando  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) investigated the relationship among commuting, the risk of COVID-19, and COVID-19-induced  anxiety using internet-based survey data from 27,036 respondents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Fajgelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) designed  an optimal dynamic lockdown strategy against COVID-19 within a commuting network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Kondo (2021)  developed a spatial susceptible–exposed–infectious–recovered model to analyze the effects of restricting  inter-regional commuting mobility on the spatial spread of the COVID-19 infection in Japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Research gaps  To the best of the authors’ knowledge, no existing papers have considered dedicated infection modeling  for the commuting process as a whole with multiple travel modes and multi-modal trip itineraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Most  of them focus on infection modeling for a single travel mode (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', public transit), or consider the general  modeling of epidemic spreading at a city level, where the commuting process is just a part of the big  framework without using travel mode or itinerary-specific modeling methodologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' On the other hand, most  of the previous studies regarding infection risk modeling only output the probability of infection or the R0  value indicating the spreading intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The estimation uncertainties (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', how accurate are the results) are  not calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Methodology  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Problem definition  Consider a set of individuals I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For each individual i ∈ I, suppose that we know their origin oi,  destination di, departure time ti, and travel mode mi for their daily commuting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The objective of this study is  to estimate the probability of individual i getting affected: P(i infected | oi, di, ti, mi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Besides, we also aim  to quantify the estimation uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' If we treat P(i infected | oi, di, ti, mi) as a random variable, another  goal of the study is to obtain the standard error of the estimation:  �  Var[P(i infected | oi, di, ti, mi)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In the following sections, we first illustrate how P(i infected | oi, di, ti, mi) is estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The estimation  of standard errors is illustrated in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Trip itinerary generation  Given an individual i’s trip information (oi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' mi),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' there exists a trip planner function TP(·) that  takes (oi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' mi) as input,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' and outputs a set of feasible paths for the individual Ri and the associated path  choice probability PPath(r) for all paths r ∈ Ri,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' that is:  Ri,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' PPath(r)r∈Ri = TP(oi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' mi)  (1)  For example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' we can define TP(·) as a composed function of the Google Map API and a C-logit model:  TP(oi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' mi) = C-Logit ◦ Google Map API(oi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' mi)  (2)  Specifically,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' the Google Map API returns the path set Ri and path attributes Xr for all r ∈ Ri (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', travel  time, travel cost, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ), that is:  Ri, (Xr)r∈Ri = Google Map API(oi, di, ti, mi)  (3)  The C-Logit model outputs the path choice probability and the standard errors for each path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The c-Logit  model is an extension of the multinomial logit (MNL) model to correct for the correlation among paths due  to overlapping (Cascetta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The key idea is to define a term called the “commonality factor” of  path r (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', CFr), which measures the degree of similarity of path r with the other paths of the same OD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Based on the C-logit model, the probability of choosing path r can be calculated as  PPath(r) = C-Logit(Xr) =  exp[βT · (Xr, CFr)]  �  r′∈Ri exp[βT · (Xr′, CFr′)]  (4)  4  where β is the parameter vector to estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The formulation of CFr can be found in Cascetta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Note the TP(·) can be defined more broadly than google map API plus the C-logit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Other  examples include the k-shortest path in a multiple-modal network compounded with any behavioral model  for path choices (Mo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection modeling for a trip segment  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Definition of a trip segment  A path r ∈ Ri usually contains multiple trip segments, such as walking from home to a bus station,  taking a bus, and walking from a bus station to the office.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The infection may happen at every trip segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In  this study, we define a segment s of a path as continuous travel with the same travel mode along the path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Let  the set of all segments for path r be Sr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' It is worth noting that, if a transit trip has one or more transfers, we  separate the transit trip into multiple segments based on transfers because the passenger needs to first alight  and then board a new vehicle, which is equivalent to changing to a “new travel mode” in infection modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  We also ignore short walking segments (less than 3 minutes or less than 1km, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', transfer walking) for  modeling convenience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  We provide three examples to illustrate the definition of segments (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The first example shows  three segments: walking from home to a subway station, taking the subway, and walking from a subway  station to the office.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The second example is a ride-hailing trip with only a single segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The third example  shows a transit trip with a transfer, which is separated into two segments by definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Figure 1: Illustration of the segment definition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection risk for each segment  We consider two different channels for infection: 1) infected by close contact with infectious persons  and 2) infected by touching infectious surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection by close contact: Consider a trip segment s ∈ Sr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We define Ps as the set of persons that have  been in the six feet infectious range of individual i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For a person p ∈ Ps, let the duration of the interaction  5  Example 1  品  Transit  Walk  Walk  Segment 1  Segment 2  Segment 3  Example 2  Ride hailing  Segment 1  Example 3  Transit  Segment 1  Segment 2between i and p be di,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' If p is infectious, i would have a probability of getting infected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Depending on  whether the interaction happens indoors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', in a bus) or outdoors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', walking by), there are two different  physical models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In an indoor environment, the probability of i getting infected by p can be calculated by the well-known  Wells-Riley model (Riley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 1978):  PIndoor(p → i | p infectious) = 1 − exp  �−b · q · di,p  QIndoor  �  (5)  where b is the breathing rate per person (m3 /hour);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' q is the quanta generation rate (/hour), Q is the room  ventilation rate of clean air (m3 /hour).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In an outdoor environment, Rowe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) proposed an airshed model that derives a similar infection  probability formulation:  POutdoor(p → i | p infectious) = 1 − exp  �−b · q · di,p  QOutdoor  �  (6)  where QOutdoor = L · H · V∞ is the outdoor ventilation rate of clean air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' H and L are the height and length  (perpendicular to the wind direction) for a hypothetical outdoor modeling space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' V∞ is the wind velocity  (m/h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The suggested values for H and L are around 5m and 50m, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Hence, given the set of contact persons, the total infectious probability of i during the segment s due to  close contact is  P(s)  Cont(i infected) = 1 −  �  p∈Ps  ��  1 − PIn/Outdoor(p → i | p infectious)  �  P(p infectious) + P(p not infectious)  �  (7)  where Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 7 is due to the fact that the probability of getting infected by at least one of p ∈ Ps equals one  minus the probability of not getting infected by anyone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection by touching surfaces: Wilson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021) estimate the infection probability of a single  hand-to-fomite touch as a function of viral bioburden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Their estimation already accounts for uncertainties in  transfer efficiency, fractions of the hand used for surface and face contact, and surface areas of the hand and of  fomites available for contact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Define this probability as PTouch(i infected | V ), where V is the viral bioburden  of this tough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For simplicity, let us assume the viral bioburden during a trip segment is a constant and the  value is Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We also assume that the number of touches during segment s (defined as Ns) is proportional  to the duration of travel in s (defined as Ts), and the factor is γ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ns = γs · Ts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, the total  infection probability for individual i due to surface touching is:  P(s)  Surf(i infected) = 1 −  �  1 − PTouch(i infected | Vs)  �Ns  (8)  The empirical values of Vs can be obtained from Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2020) who collected viral bioburden data in  daily activity environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Since the infection risk for a single tough is small, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 8 can be approximated  by first-order Taylor series:  P(s)  Surf(i infected) ≈ γs · Ts · PTouch(i infected | Vs)  (9)  6  where Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 9 is computationally more efficient than Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection risk by different travel modes  Each segment s ∈ Sr is associated with a specific travel mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Though we provide a general infection  risk calculation model in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2, it is important to specify the model parameters and variables for  each travel mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In this section, we assume that the infectious environment is the same during the travel in  a segment s and the values are bs, qs, QIndoor  s  , and QOutdoor  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection risk of transit segment: A transit segment (either bus or rail) usually includes multiple stops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Let the set of stops for the transit segment s except for the last one be As.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We exclude the last stop because  individual i will alight when he/she arrives at the last stop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Let the set of passengers in a vehicle (exclude  individual i) when the vehicle departs from station a ∈ As be Ps,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Ps,a can be obtained by smart card data  and Ps = ∪a∈AsPs,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Let the vehicle travel time from station a to the next stop be TTa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Then the infection probability for individual i due to close contact in the vehicle when it travels from  station a to the next stop is:  P(s,a)  Cont (i infected) = 1 −  �  p∈Ps,a  �  P(p infectious) · exp  �−bs · qs · TTa  QIndoor  s  �  + (1 − P(p infectious))  �  (10)  For any p ∈ Ps,a, we can use smart card data to obtain their origin stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Hence, P(p infectious) and  P(p not infectious) can be approximated by regional infection statistics based on their origin stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  total infection probability in the transit segment is:  P(s)  Cont (i infected) = 1 −  �  a∈As  �  1 − P(s,a)  Cont  �  when s is a transit segment  (11)  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 10 and 11 may be computationally inefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' When P(p infectious) is small,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' we can use the  following approximation by ignoring all second-order multiplication terms with  �  P(p infectious)  �2:  �  p∈Ps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a  �  P(p infectious) · exp  �−bs · qs · TTa  QIndoor  s  �  + (1 − P(p infectious))  �  =  �  p∈Ps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a  �  1 − P(p infectious) ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  � ��  ≈ 1 −  �  p∈Ps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a  P(p infectious) ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  ��  (12)  Then we have  P(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a)  Cont (i infected) ≈  �  p∈Ps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a  P(p infectious) ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  ��  (13)  which is simply the summation of probabilities of getting infected by anyone in Ps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Similarly, if P(s,a)  Cont is  7  small, we can approximate P(s)  Cont as:  P(s)  Cont(i infected) ≈  �  a∈As  �  p∈Ps,a  P(p infectious) ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  ��  when s is a transit segment  (14)  where Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 13 and 14 are computationally more efficient because we replace the production with a summation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In terms of the surface-touching infection, we only need to specify Vs (viral bioburden), γs (touching  rate), and Ts (travel time) to use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' It is worth noting that Vs can vary across different times of the day  and transit routes according to the demand level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In general, times and routes with higher demand should  have higher Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection risk of walk/bike segment: For a walk or bike segment, we assume there is no surface touching  infection risk because the commuter does not need to tough public surfaces during commuting:  P(s)  Surf(i infected) = 0  when s is a bike/walk segment  (15)  For the close-contact infection, we can approximate Ps from the pedestrian density data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Denote the  average contact time for an encounter as dW/B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' With the same approximation techniques, we can calculate  the infection probability as  P(s)  Cont(i infected) ≈ |Ps| · P(p infectious) ·  �  1 − exp  �−bs · qs · dW/B  QOutdoor  s  ��  when s is a bike/walk segment  (16)  where P(p infectious) can be obtained from the regional infectious statistics based on the walk/bike routes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  |Ps| is the average number of encounters during the segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection risk of ride-hailing segment: When commuting with ride-hailing, Ps includes the driver and  potential shared riders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Ps can be obtained from ride-hailing open source data to approximate the average  number of persons in a vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The contact time di,p for the driver and individual i is Ts (total segment  travel time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' While di,p for individual i and shared riders will be approximated by shared rides data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' With  the same first-order approximation, we can calculate the infection probability due to close contact as  P(s)  Cont(i infected) ≈  �  s∈Ps  P(p infectious) ·  �  1 − exp  �−bs · qs · di,p  QIndoor  s  ��  when s is a ride-hailing segment  (17)  In terms of surface-touching risks, it is possible that the previous riders are infectious and thus the seats  are contaminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We can also specify Vs and γs then use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 9 for the infection risk calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However,  it is worth noting that Vs for ride-hailing should be much smaller than that of transit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Infection risk of driving segment: Driving is a private commute mode and there is generally no close  contact or infectious surface touching during the travel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Hence, we simply assume P(s)  Surf(i infected) =  P(s)  Cont (i infected) = 0 when s is a driving segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection risk integration  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3 provides the formulations for the calculation of infection risks for a specific segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Since  a commuting path r consists of multiple segments, the total infection probability if using path r ∈ Ri is:  P(i infected | r) = 1 −  �  s∈Sr  P(i not infected in segment s)  = 1 −  �  s∈Sr  �  1 − P(s)  Surf(i infected)  � �  1 − P(s)  Cont(i infected)  �  (18)  Similarly, if the infectious probability is small in each segment, we have:  P(i infected | r) ≈  �  s∈Sr  �  P(s)  Cont(i infected) + P(s)  Surf(i infected)  �  (19)  Combining with the path choice probabilities from Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2, we get the total infectious probability of  individual i during commuting:  P(i infected | oi, di, ti, mi) =  �  r∈Ri  PPath(r) · P(i infected | r)  (20)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Uncertainty quantification  Though Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 20 provides the final infection probability for a given trip, the estimation may suffer from  errors due to uncertainties in parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In this section, we treat P(i infected | oi, di, ti, mi) as a random  variable and aim to calculate its standard errors:  �  Var[P(i infected | oi, di, ti, mi)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In this study, we focus on the uncertainty due to the infection calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Hence, let us assume PPath(r)  is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Then:  Var[P(i infected | oi, di, ti, mi)] =  �  r∈Ri  �  PPath(r)  �2 · Var[P(i infected | r)]  (21)  From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 19, we can further decompose the variance to different segments due to the independence  across segments:  Var[P(i infected | r)] =  �  s∈Sr  �  Var  �  P(s)  Cont(i infected)  �  + Var  �  P(s)  Surf(i infected)  ��  (22)  Therefore, we only need to specify Var  �  P(s)  Cont(i infected)  �  and Var  �  P(s)  Surf(i infected)  �  for different types  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', travel modes) of segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Transit segment: According to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 14, the infection probability due to close contact in public transit is  simply the probability summation over different stations and encounters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In the real world, Ps,a is uncertain  due to demand variations in public transit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However, it is generally hard to model the uncertainty of  a set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, let us define the average probability that a passenger in Ps,a is infectious as ¯µs,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Then Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  14 can be rewrite as:  P(s)  Cont(i infected) ≈  �  a∈As  |Ps,a| · ¯µs,a ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  ��  when s is a transit segment  (23)  9  where |Ps,a| is the number of passengers in the vehicle (excluding i) when the vehicle departs from station  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The variance can be formulated as:  Var[P(s)  Cont(i infected)] =  �  a∈As  Var  �  |Ps,a| · ¯µs,a ·  �  1 − exp  �−bs · qs · TTa  QIndoor  s  ���  when s is a transit segment  (24)  Deriving the closed-form formulation for the variance of the product of several random variables (or the  exponential of several variables) is difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In some simple cases, one may use Jensen’s inequality to get  the variance lower (or upper) bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However, consider a general function f(Z) (may not be convex or  concave), where Z is a vector of random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Obtaining the analytical form of Var[f(Z)] is generally  hard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, we propose a bootstrapping-based algorithm to estimate the empirical variance (Algorithm  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The inputs of the algorithm are f(Z), the distribution of Z (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', P(Z)), and maximum sample times M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The idea is to sample Z ∼ P(Z) and use samples to estimate the variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Algorithm 1 Bootstrapping-based empirical variance estimation algorithm  1: function Bootstrapping-Variance(f(Z), P(Z), M)  2:  for m = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', M do  3:  Sample Z(m) ∼ P(Z)  4:  ¯f(Z) =  1  M  �M  m=1 f(Z(m))  ▷ Estimate empirical mean  5:  Var[f(Z)] =  1  M  �M  m=1  �  f(Z(m)) − ¯f(Z)  �2  ▷ Estimate empirical variance  6:  return Var[f(Z)]  It is worth noting that, the sampling process in Algorithm 1 (Line 3) can be done independently, jointly,  or sequentially, depending on whether the elements in Z are independent, dependent, or conditionally  independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Given Algorithm 1, we can estimate Var  �  |Ps,a| · ¯µs,a ·  �  1 − exp  �  −bs·qs·TTa  QIndoor  s  ���  through the distribution  of |Ps,a|, ¯µs,a, bs, qs, TTa, and Qs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In this study, we assume that |Ps,a| (vehicle load) and TTa (travel  time) are normally distributed based on the observations in the empirical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Their distribution parameters  can be estimated from the smart card and automated vehicle location data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' bs, qs, and Qs are uniformly  distributed and their distributions are shown in Table 1 based on the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For ¯µs,a, the distribution is  hard to parameterize because it is generated by sampling different Ps,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We, therefore, keep all samples for  ¯µs,a as an empirical distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Then every sample of ¯µs,a ∼ P(¯µs,a) is essentially a bootstrap from its  sample pool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In terms of surface touching infection, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 9, we use Algorithm 1 to estimate the variance by  setting f(Z) = γs · Ts · PTouch(i infected | Vs) and Z = (γs, Ts, Vs, PTouch(i infected | Vs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution  of PTouch(i infected | Vs) can be obtained from the data in Wilson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution of Vs can  be obtained from the results in Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution of Ts can be obtained from the AVL  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' γs is assumed to be uniformly distributed and its distribution is given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Walk/Bike segment: The variance of contact-based infection risks in the walk and bike segments,  10  according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 16, can be expressed as:  Var[P(s)  Cont(i infected)] = Var  �  |Ps| · ¯µs ·  �  1 − exp  �−bs · qs · dW/B  QOutdoor  s  � ��  when s is a bike/walk segment  (25)  where ¯µs is the average infectious probability of encounters in Ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' It has a similar formulation as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 24,  thus can be calculated using Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution of |Ps| can be obtained from pedestrian flow data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The distribution of ¯µs can be obtained from regional statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' All infection-related parameters (including  dW/B) are assumed to be uniformly distributed and their distributions are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Since we assume  there are no infection risks related to surface touching for the walk and bike segments, we do not need to  consider their variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ride hailing segment: For the ride-hailing segment, since Ps is relatively small (maximum three  riders in a vehicle), we assume |Ps| follows a multinomial distribution across {0, 1, 2, 3} (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', maximum 2  other passengers plus 1 driver).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The specific distribution can be obtained from ride-sharing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' To get  Var[P(s)  Cont(i infected)] for ride-hailing segments, the sampling process is as follows (slightly different from  Algorithm 1):  Step 1: Sample |Ps| from the multinomial distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Step 2: Based on the value of |Ps|, sample the same number of passengers and drivers to generate the  |Ps, for each passenger p ∈ Ps, we also sample di,p (shared trip time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Step 3: Sample other infection-related parameters from the distribution defined in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Calculate  the infection probability close contact based on Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  After M samples, we can estimate the sample variance as an approximation of Var[P(s)  Cont(i infected)] similar  to Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The variance of surface touching-based infection probability is calculated in the same way  as a transit segment except for replacing the distributions of Ts, Vs, and γs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  For the driving segment, since we assume there is no infection risk, the variances are not calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Case study  The case study is based on available data from MIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model is implemented for the commuting of all  MIT students and staff in the greater Boston area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Data sources and parameter settings  We use data from various sources in this study to estimate the infection risk and set up parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  first data set is the MIT staff commuting survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The survey collects (oi, di, ti, mi) of every individual  i ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Given this information, for every individual i, we generate the set of paths Ri and the associated path  attributes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', walking time, waiting time, in-vehicle time, travel cost) based on the Google map API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For  simplicity, we only consider the first path associated with the travel mode mi recommended by google map  API (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', ignoring the path choice estimation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This assumption is reasonable because in most cases there  is only one transit route available if mi = Transit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For driving, biking, or ride-hailing, individuals usually  follow the navigation system and thus choose the first option provided by the google map API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  11  Another data source we use for infection risk calculation in the transit segment is the smart card data  from the Massachusetts Bay Transportation Authority (MBTA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We use the historical smart card data at the  same time of the day (one-hour interval) in the last 2 weeks to calculate the mean and variance of the number  of passengers in Ps,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Specifically, the smart card data provides the tap-in time and locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We adopted  the destination estimation model proposed by Sánchez-Martínez (2017) to obtain the destination of each trip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Then, a network loading model (Mo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020) is used to obtain the vehicle load at each time interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  mean infectious probability ¯µs,a for passengers in the vehicle is calculated based on regional statistics and  their origins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The travel time between stops (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', TTa) is obtained from automated vehicle location (AVL)  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In terms of the bike and walk segments, there is no open-source pedestrian and cyclist density data  available for this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, we generate the synthetic pedestrian and cyclists density data by combining  population data in Boston (Massachusetts Demographics by Cubit, 2020), Massachusetts Travel Survey  (MTS) (Boston Region Metropolitan Planning Organization, 2011), and national household travel survey  (NHTS) data (Federal Highway Administration, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The synthetic pedestrian density data include the  mean and variance of the number of cyclists and pedestrians at a specific street for each time interval (in  this study, every 1 minute).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The detailed data generation process is shown in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The basic idea is  to generate many bike and walk trajectory samples using the available dataset and aggregate these samples  at the street-minute level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Therefore, given a bike/walk segment s of individual i, based on its trajectory,  we can sample the number of bike/walk encounters using the generated cyclists and pedestrians density data  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This process is replicated multiple times to get the distribution of |Ps|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution of ¯µs is  calculated based on neighborhood infection rates (Fisher, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The contact time (dW/B) is assumed to be  uniformly distributed with U(4, 6) seconds for a walking trip and U(2, 4) seconds for a biking trip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  For the ride-hailing segment, we only need the distribution of |Ps| (number of passengers), di,p (shared  trip duration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However, there is no public ride-hailing data for Boston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In this study, we use the open-source  Transportation Network Company (TNC) data in Chicago (Chicago Data Portal, 2018) to calculate the  distribution of |Ps| and di,p as an approximation for those of Boston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Through the Google Map API, we can obtain the value of Ts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However, the distribution of Ts is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ideally, the distribution of Ts can be obtained from GPS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Given the data limitations, we assume Ts is  normally distributed and the value obtained from the Google Map API is the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The standard deviation  is assumed to be Ts × 30% based on the empirical study (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' It is worth noting that, for the  transit segment, instead of using Google Map data, we obtain the stop-to-stop travel time using AVL data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Hence, we calculate the segment travel time as Ts = �  a∈As TTa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The mean and variance of Ts are just the  summations of the mean and variance of TTa, respectively, by assuming independence across segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The infection-related parameters are summarized in Table 1:  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Data description and statistics  The MIT staff commuting survey consists of 974 individual responses with information on (oi, di, ti, mi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Note that only commuting trips toward MIT are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distributions of their departure times, travel  modes, and job categories are shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Since only trips toward MIT are considered, most of their departure times are in the morning hours  (Figure 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' There are also some people going to campus in the evening, which may be students living close  by or staff on night shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In terms of travel modes (Figure 2b), more than 40% of the MIT staff and students  choose transit as their commuting mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Driving is the second most popular mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Of all individuals filling  12  Table 1: Infection-related parameters  Mode  Parameters and distribution  bs (m3/h)  qs (/h)  V∞ (m/s)  L (m)  H (m)  QIndoor  s  (m3/h)  γs (/h)  Vs (gc/cm2)  Transit (Train)  U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='65, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='79)  U(1, 31)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  U(800, 1100)  U(3, 5)  U(30, 100)  Transit (Bus)  U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='65, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='79)  U(1, 31)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  U(300, 500)  U(3, 5)  U(30, 100)  Bike  U(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8)  U(2, 100)  U(2, 4)  U(30, 60)  U(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5, 5)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Walk  U(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='6)  U(2, 100)  U(1, 2)  U(30, 60)  U(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5, 5)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ride-hailing  U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='65, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='79)  U(1, 31)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  U(90, 120)  U(1, 3)  U(2, 50)  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' : Not applicable  The parameters for transit infections are obtained from Zhou and Koutsopoulos (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The parameters for quanta generation rates are obtained from Buonanno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2020b) and Buonanno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The parameters for outdoor infection models are obtained from Rowe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The ride-hailing ventilation rate is based on Ott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The viral bioburden data is adapted from Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' (2020) (assuming 10% viruses are infectious).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  out the survey, around 30% are graduate students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Respondents also include faculty and staff (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', admin,  service, support, research).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  (a) Departure time distribution  (b) Travel mode distribution  (c) Person type distribution  Figure 2: Descriptive statistics of MIT staff commuting survey (RH indicates Ride-hailing)  Figure 3 shows the distribution of travel information collected by the Google Map API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Most of the  commuting trips have only one segment (Figure 3a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The maximum number of segments is five.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The travel  times of all trips are approximately log-normal distributed with a long tail (Figure 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The travel times for  most of the trips are within 1 hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  For transit trips, Figure 4 shows the box plots of travel times between two consecutive stations and the  associated passenger load for Bus Route 1 in Boston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Route 1 is a popular bus service along Massachusetts  Avenue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The travel time to the first stop is relatively large as vehicles usually depart from garages (Figure  4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In terms of passenger load (Figure 4b), the middle stops in the route have a relatively larger number  of passengers onboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The graphs show that both travel time and passenger loads are uncertain and the  uncertainties should be captured in the virus transmission modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Figure 5 shows the spatial distribution for the inferred number of walk and bike trips at 8:00 AM (details  in Appendix A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Their spatial distributions are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' More trips happen at places with higher population  densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The number of walking trips is larger than that of bike trips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='10  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  5  7  9  1113  15  1719  21  Departure time (hour of the day)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='30  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  Walk  Bike  Transit  RH  Drive Other0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='20  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  Admin  Faculty  Service  Graduate  Support  Undergrad  Research(a) Number of segments distribution  (b) Travel mode distribution  Figure 3: Distribution of the number of segments and travel times  (a) Travel time to next stop  (b) Passenger load  Figure 4: Box plots of travel time and passenger load for Bus Route 1 (Stop ID represents the stop sequences from north to south)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Results  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Infection risk for individuals  After excluding individuals with “other” travel modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We have 943 remaining individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We calculate  their infection probabilities and standard deviations using the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Results are shown in Figure  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Most of the individuals have an infection probability close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The maximum infection probability is  around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This implies that the probability of getting infected during commuting to MIT is quite low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  results are consistent with the previous studies modeling infection risks in transit (Zhou and Koutsopoulos,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In terms of the estimation errors, the standard deviations are approximately 50% of the estimated  probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Since individuals with different travel modes, departure times, and travel distances may have different  infection probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  We run a linear regression model to analyze the impact of different factors on  infection risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The dependent variable is the inferred infection probability and the independent variables  are as follows:  If faculty: Whether the individual is a faculty at MIT (Yes = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  Densi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0  1  2  3  4  5  Number of segments0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0175  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0150  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0125  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0000  0  25  50 75 100 125 150 175 200  Total travel time (min)Travel time to next stop (min)  20  15  10  5  0  3  5  1  9  11 13 15 17 19 21 23 25 27  Stop ID80  60  40  20  0  1  3  5  7  9  11 13 15 17 19 21 23 25 27  Stop ID(a) Number of bike trips  (b) Number of walk trips  Figure 5: Spatial distribution for the number of walk and bike trips at 8:00 AM  Distance (km): Euclidean distance from the individual’s home to MIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  If transit: Whether the individual’s commuting mode is transit (Yes = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  If morning peak: Whether the individual’s departure time is between 6:00 AM and 9:00 AM (Yes =  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The results of the linear regression are shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' “Distance×If transit” is added to differentiate  the distance impact for transit and non-transit users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We find that the faculty is less likely to get infected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The reason may be that they usually drive to school and driving is the safest travel mode in terms of infection  protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Individuals who live further from the school and commute by transit have a higher infection risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  This may be due to the fact that they have a longer travel time and more close contacts, thus are more likely  to be exposed to viruses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We also observe people with a departure time in the morning peak have a higher  probability of being infected, which may be due to the larger amount of encounters in the morning peak  hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' It is worth noting that “Distance” and “If transit” are not significant unless combining them together  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', “Distance×If transit”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This implies that the impact of distance on infection risks mainly applies to  transit users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Table 2: Factors on infection probability (%)  Variable  Coefficient (p-value)  Variable  Coefficients (p-value)  Intercept  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='015 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='997)  Distance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='048 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='834)  If transit  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='409 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='545)  If morning peak  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='658∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='005)  If faculty  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='881∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='095)  Distance×If transit  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='404∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='000)  Number of samples: 943;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' R2: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='313;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  ∗∗: p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='05;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' ∗: p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  All coefficients are scaled by 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  To better visualize the impact of distance, Figure 7 shows the predicted infection probability as a function  of distance for both transit and non-transit users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' In general, transit users are more likely to get infected, and  15  # Walk trips  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='45  150  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  Latitude  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='35  100  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  Natic  50  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  71  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='9  Longitude# Bike trips  16  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5+  IOBURI  14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='45  12  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  10  Latitude  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='35  8  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  6  Natic  4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  2  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  71  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='9  LongitudeFigure 6: Inferred individual infection probabilities (sorted by values in descending order)  the infection risk increases dramatically with the increase in commute distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' However, the infection risk  of non-transit users is not significantly affected by distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Figure 7: Predicted infection probability as a function of distance  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Spatiotemporal distribution of infection risk  In addition to the infection risk calculation for actual survey respondents, the proposed method can also  be used to evaluate the spatiotemporal distribution of infection risks by generating synthetic observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  For the spatial distribution, we generate synthetic observations with home addresses in different neigh-  borhoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We consider two travel modes: transit and walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Note that for dummy samples with walking  travel modes, we also consider home addresses within 10km of MIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' All dummy samples’ departure times  are set at 8:00 AM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Figure 8a shows the infection probability of transit trips with home addresses in different neighborhoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  In general, people with residences further from MIT have higher infection risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' But the risk is also affected  by specific transit routes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', not perfectly proportional to distances).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The spatial distribution for walking  (Figure 8b) is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' But the infection risk is much smaller than that of transit trips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  16  12  Std.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  600-  10  500  Icy  8  400  Frequenc  300  6  200  100  4  0  0  1  2  3  4  5  6  7  8  2  Probability of infection (×10-3)  0  0  200  400  600  800  Sample IDInfection probability #(×10-3)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='75  Transit user  Non-transit user  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  0  10  20  30  40  50  Distance (km)(a) Transit trips  (b) Walk trips  Figure 8: Spatial distribution of infection probability  In terms of the temporal distribution, we generate synthetic observations with departure times from 0:00  to 24:00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Their home locations are assumed to be uniformly distributed across all neighborhoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Figure  9a shows the infection risk as a function of departure time for transit trips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The shaded areas are  1  10 of the  estimation errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The infection probabilities are higher when people depart during the morning and evening  peak hours, which is reasonable because there is usually a higher passenger load (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', more close contacts)  during rush hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The infection probabilities for walking trips show a similar pattern (Figure 9b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The  highest infection risks happen in the daytime (from 8:00 to 18:00), most likely due to the larger number of  pedestrians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  (a) Transit trips  (b) Walk trips  Figure 9: Temporal distribution of infection probability  17  Infection probability  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='15  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  Latitude  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  Naticl  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='05  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  0  itributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' @  artoDB  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  71  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='9  Longitude0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='01  Infection probability  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5-  Burlington  WOBURN  LYNN  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='008  Lexington  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='006  WALTHA  inthrop  Latitude  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='35  NEV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='004  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  Natick  Needham  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  Dedham  Milton (QUINCY  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='002  Weymouth  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  @ OpenStreetMap  contributors,@ CartoDB  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  71  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='9  Longitude3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='2  Infection probability×10-4)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='4  0:00  4:00  8:00  12:00 16:00 20:00 24:00  Departure time1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='75  Infection probability (×10-7)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='00  0:00  4:00  8:00  12:00 16:00 20:00 24:00  Departure time5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Conclusion  The paper proposes a probabilistic framework to estimate the risk of infection during commuting con-  sidering different travel modes, including public transit, ride-share, bike, and walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model enables  evaluating both the probability of infection and the estimation errors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', uncertainty quantification).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Dif-  ferent sources of data (such as smart card data, travel surveys, and population data) are used to estimate  commuting individual’s interaction with infectious environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The model is applied using data related  to the MIT community as a case study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We evaluate the commute infection risks for employees and students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Results show that most of the individuals have very low infection probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The maximum infection  probability is around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Individuals with larger travel distances, traveling with transit, and traveling at  peak hours are more likely to get infected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The model has several practical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 1) The model can be used to support decision-making  for companies, schools, or communities during or post the pandemic regarding return to offices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' They  can collect their employees’ commuting information and use the model to evaluate the commuting risk for  better planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For example, employees with high infection risk may have separate seats from the low-risk  employees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 2) Another implementation of the model is to add individual-level infection risk to their trip  planning tool (such as Google Map).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For example, in Figure 10, the trip planning tool not only shows the  recommended routes based on travel time, but also the infection risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Individuals can make better path  choice decisions with this additional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Figure 10: Example of implementing the model to trip planning  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Acknowledgement  The authors would like to thank the MIT Quest for Intelligence for their support and data availability for  this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Author contribution statement  Baichuan Mo: Conceptualization, Methodology, Software, Formal analysis, Data Curation, Writing -  Original Draft, Writing - Review & Editing, Visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Peyman Noursalehi: Conceptualization, Soft-  ware, Data Curation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Haris N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Koutsopoulos: Conceptualization, Writing - Review & Editing, Supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Jinhua Zhao: Conceptualization, Supervision, Project administration, Funding acquisition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  18  Origin  Destination  Division /Ashland  Clark /Division  天  70  C  ORL  ETA10:20AM  Division/Ashland  Ashland  L  会GLPL  ETA10:23AM  AAAAppendices  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Pedestrian and cyclist density calculation  For the infection risk calculation of walking and bike trips, an important input is the number of close-  contact encounters during the trip (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', the distribution of |Ps|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The distribution can be obtained from the  mean and variance of the number of cyclists (denoted as Cb,τ) and pedestrians (denoted as Wb,τ) at specific  street b for each time interval τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Since there are no GPS or trajectory data available for this study, we generate  the distribution of Cb,τ and Wb,τ using the following method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  First, we collect population data (Massachusetts Demographics by Cubit, 2020) for each neighborhood  (zip-code level) in the Boston metropolitan area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' We use the Massachusetts Travel Survey (MTS) (Boston  Region Metropolitan Planning Organization, 2011) to calculate the trip generation rates given the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  As MTS does not include bike and walk mode share, the national household travel survey (NHTS) data  (Federal Highway Administration, 2017) is used to get the proportion of bike and walk trips as well as their  temporal distributions using samples in Massachusetts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Combined with the trip generation rate, we simulate  the number of bikes and walk trips for each neighborhood at different time intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Given limited actual  bike and walk trips in NHTS data in Boston, it is hard to obtain the origin-destination (OD) distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' But  the distribution of travel distances and departure times can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' For each bike walk trip, we generate  the “hypothetical” trajectory as follows: 1) We first randomly sample an origin within the neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 2)  Then, we sample the travel distance and departure time from the pre-defined distribution, as well as a specific  direction (uniformly 0 ∼ 2π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The travel distance and direction yield the destination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' 3) We generate the  trajectory (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', a sequence of streets) of the trip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' From these trajectories, we obtain the number of pedestrians  and cyclists in the street for each street b and time interval τ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', a sample of Cb,τ and Wb,τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' This process  is repeated multiple times to get E[Cb,τ], E[Wb,τ] and Var[Cb,τ], Var[Wb,τ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  The generated walking and bike trip distributions are shown in Figure 5 (the figure is aggregated at the  zip code level).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  References  Ahangari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Chavis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Jeihani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Public transit ridership analysis during the covid-19 pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Medrxiv .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ando, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ikegami, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Nagata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Tateishi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Eguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Tsuji, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Matsuda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Fujino, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ogami, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=',  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Effect of commuting on the risk of covid-19 and covid-19-induced anxiety in japan, december 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Archives of Public Health 79, 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Boston Region Metropolitan Planning Organization, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Exploring the 2011 massachusetts travel survey:  Mpo travel profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='ctps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='org/travel-profiles, Last accessed on 2022-11-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Buonanno, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Morawska, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Stabile, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Quantitative assessment of the risk of airborne transmis-  sion of sars-cov-2 infection: prospective and retrospective applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Environment international 145,  106112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Buonanno, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Stabile, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Morawska, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Estimation of airborne viral emission: Quanta emission  rate of sars-cov-2 for infection risk assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Environment international 141, 105794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Cascetta, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Nuzzolo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Russo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Vitetta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' A modified logit route choice model overcoming  path overlapping problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' specification and some calibration results for interurban networks, in: Trans-  19  portation and Traffic Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Proceedings of The 13th International Symposium On Transportation And  Traffic Theory, Lyon, France, 24-26 July 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Chang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Lee, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Yang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Liou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Does covid-19 affect metro use in taipei?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Journal of  transport geography 91, 102954.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Chicago Data Portal, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Transportation network providers - trips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' https://data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='cityofchicago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  org/Transportation/Transportation-Network-Providers-Trips/m6dm-c72p, Last accessed  on 2022-11-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ecke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Magdolen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Chlond, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Vortisch, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  How the covid-19 pandemic changes daily  commuting routines–insights from the german mobility panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Case Studies on Transport Policy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Fajgelbaum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Khandelwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kim, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Mantovani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Schaal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Optimal lockdown in a  commuting network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' American Economic Review: Insights 3, 503–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Federal Highway Administration, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' National household travel survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' https://nhts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='ornl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='gov/,  Last accessed on 2022-11-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Fisher, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Estimated COVID 19 by US Zip Code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='com/adamrfisher/  Estimated_COVID19_by_US_Zip_Code, Last accessed on 2022-11-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Harvey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Fuhrmeister, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Cantrell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Pitol, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Swarthout, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Powers, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Nadimpalli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=',  Julian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Pickering, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Longitudinal monitoring of sars-cov-2 rna on high-touch surfaces in a  community setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Environmental science & technology letters 8, 168–175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Jenelius, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Cebecauer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Impacts of covid-19 on public transport ridership in sweden: Analysis of  ticket validations, sales and passenger counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Transportation Research Interdisciplinary Perspectives 8,  100242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Kondo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Simulating the impacts of interregional mobility restriction on the spatial spread of  covid-19 in japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Scientific reports 11, 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Ku, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Yeon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Hwang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Wong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Safe traveling in public transport  amid covid-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Science advances 7, eabg3691.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Chai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Empirical study of travel time estimation and reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Mathematical  Problems in Engineering 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Massachusetts Demographics by Cubit, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Massachusetts zip codes by population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  massachusetts-demographics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='com/zip_codes_by_population, Last accessed on 2022-11-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Medlock, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Temzelides, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Hung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Covid-19 and the value of safe transport in the united  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Scientific reports 11, 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Meredith-Karam, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' The relationship between ridehailing and public  transit in chicago: A comparison before and after covid-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Journal of Transport Geography 97, 103219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Mitze, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kosfeld, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content=' Journal of Geographical Systems 24, 5–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Mo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Feng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Shen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Tam, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content=' Transportation Research Part C: Emerging  Technologies 122, 102893.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Mo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ma, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Koutsopoulos, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content=' Transportation Research Record 2674, 59–69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Mo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Von Franque, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Koutsopoulos, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Attanucci, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Impact of unplanned long-  term service disruptions on urban public transit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' IEEE Open Journal of Intelligent Transportation  Systems 3, 551–569.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  20  Ott, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Klepeis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Switzer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Air change rates of motor vehicles and in-vehicle pollutant con-  centrations from secondhand smoke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Journal of exposure science & environmental epidemiology 18,  312–325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Riley, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Murphy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Riley, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Airborne spread of measles in a suburban elementary school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  American journal of epidemiology 107, 421–432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Rowe, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Canosa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Drouffe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Mitchell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Simple quantitative assessment of the outdoor  versus indoor airborne transmission of viruses and covid-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Environmental research 198, 111189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Sánchez-Martínez, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Inference of public transportation trip destinations by using fare transaction  and vehicle location data: Dynamic programming approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Transportation Research Record 2652, 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Shinohara, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Sakaguchi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kagi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Tatsu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Mano, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Iwasaki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Naito, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
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+page_content=' Environment  international 157, 106774.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Tan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Choice behavior of commuters’ rail transit mode during the covid-19 pandemic based  on logistic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Journal of Traffic and Transportation Engineering (English Edition) 8, 186–195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Noland, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Bikeshare and subway ridership changes during the covid-19 pandemic in  new york city.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Transport policy 106, 262–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Wilbur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ayman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Ouyang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Poon, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Kabir, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Vadali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Pugliese, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Freudberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Laszka,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Dubey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Impact of covid-19 on public transit accessibility and ridership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' arXiv preprint  arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='02413 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Wilson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Weir, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Bloomfield, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Scott, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Reynolds, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Modeling covid-19 infection  risks for a single hand-to-fomite scenario and potential risk reductions offered by surface disinfection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  American journal of infection control 49, 846–848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Zhao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Wali, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' A method for assessing the covid-19 infection risk of riding public  transit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' International Journal of Transportation Science and Technology .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', Koutsopoulos, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Virus transmission risk in urban rail systems: Microscopic simulation-  based analysis of spatio-temporal characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content=' Transportation Research Record 2675, 120–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}
+page_content='  21' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/zNE0T4oBgHgl3EQftgHb/content/2301.02594v1.pdf'}